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
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...
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.
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 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
Fractional Heat Conduction Models and Thermal Diffusivity Determination
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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.
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.
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.
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.
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)
Lim, S C; Teo, L P
2009-01-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion
Fractional diffusion equations and anomalous diffusion
Evangelista, Luiz Roberto
2018-01-01
Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.
López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin
2017-09-01
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
Hopf bifurcations in a fractional reaction–diffusion model for the ...
African Journals Online (AJOL)
The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...
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.
Fractional single-phase-lagging heat conduction model for describing anomalous diffusion
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T.N. Mishra
2016-03-01
Full Text Available The fractional single-phase-lagging (FSPL heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging (SPL heat conduction model. Based on the FSPL heat conduction model, anomalous diffusion within a finite thin film is investigated. The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model. The analytical solution is obtained using Laplace transform method. The whole analysis is presented in dimensionless form. Numerical examples of particular interest have been studied and discussed in details.
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.
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
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.
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.
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)
Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform
Directory of Open Access Journals (Sweden)
Devendra Kumar
2015-01-01
Full Text Available In this paper, we propose a simple numerical algorithm for solving multi-dimensional diffusion equations of fractional order which describes density dynamics in a material undergoing diffusion by using homotopy analysis transform method. The fractional derivative is described in the Caputo sense. This homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The technique is not limited to the small parameter, such as in the classical perturbation method. The scheme gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.
Directory of Open Access Journals (Sweden)
Koca Ilknur
2017-01-01
Full Text Available Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.
Diffusion with space memory modelled with distributed order space fractional differential equations
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M. Caputo
2003-06-01
Full Text Available Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik, 2000a,b were fi rst used in the time domain; they are here considered in the space domain and introduced in the constitutive equation of diffusion. The solution of the classic problems are obtained, with closed form formulae. In general, the Green functions act as low pass fi lters in the frequency domain. The major difference with the case when a single space fractional derivative is present in the constitutive equations of diffusion (Caputo and Plastino, 2002 is that the solutions found here are potentially more fl exible to represent more complex media (Caputo, 2001a. The difference between the space memory medium and that with the time memory is that the former is more fl exible to represent local phenomena while the latter is more fl exible to represent variations in space. Concerning the boundary value problem, the difference with the solution of the classic diffusion medium, in the case when a constant boundary pressure is assigned and in the medium the pressure is initially nil, is that one also needs to assign the fi rst order space derivative at the boundary.
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Meng Zhi-Jun
2016-01-01
Full Text Available This paper addresses a new application of the local fractional variational iteration algorithm III to solve the local fractional diffusion equation defined on Cantor sets associated with non-differentiable heat transfer.
Fractional diffusion equation for heterogeneous medium
International Nuclear Information System (INIS)
Polo L, M. A.; Espinosa M, E. G.; Espinosa P, G.; Del Valle G, E.
2011-11-01
The asymptotic diffusion approximation for the Boltzmann (transport) equation was developed in 1950 decade in order to describe the diffusion of a particle in an isotropic medium, considers that the particles have a diffusion infinite velocity. In this work is developed a new approximation where is considered that the particles have a finite velocity, with this model is possible to describe the behavior in an anomalous medium. According with these ideas the model was obtained from the Fick law, where is considered that the temporal term of the current vector is not negligible. As a result the diffusion equation of fractional order which describes the dispersion of particles in a highly heterogeneous or disturbed medium is obtained, i.e., in a general medium. (Author)
Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport
Gherardi, Marco; Calabrese, Ludovico; Tamm, Mikhail; Cosentino Lagomarsino, Marco
2017-10-01
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.
Fractional Number Operator and Associated Fractional Diffusion Equations
Rguigui, Hafedh
2018-03-01
In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.
International Nuclear Information System (INIS)
Bortolini, Marco; Gamberi, Mauro; Graziani, Alessandro; Manzini, Riccardo; Mora, Cristina
2013-01-01
Highlights: ► A multi-location model to estimate solar radiation components is proposed. ► Proposed model joins solar radiation data from several weather stations. ► Clearness index is correlated to the diffuse component through analytic functions. ► Third degree polynomial function best fits data for annual and seasonal scenarios. ► A quality control procedure and independent datasets strength model performances. - Abstract: Hourly and daily solar radiation data are crucial for the design of energy systems based on the solar source. Global irradiance, measured on the horizontal plane, is, generally, available from weather station databases. The direct and diffuse fractions are measured rarely and should be analytically calculated for many geographical locations. Aim of this paper is to present a multi-location model to estimate the expected profiles of the horizontal daily diffuse component of solar radiation. It focuses on the European (EU) geographical area joining data from 44 weather stations located in 11 countries. Data are collected by the World Radiation Data Centre (WRDC) between 2004 and 2007. Different analytic functions, correlating the daily diffuse fraction of solar radiation to the clearness index, are calculated and compared to outline the analytic expressions of the best fitting curves. The effect of seasonality on solar irradiance is considered developing summer and winter scenarios together with annual models. Similarities among the trends for the 4 years are, further, discussed. The most adopted statistical indices are used as key performance factors. Finally, data from three locations not included in the dataset considered for model development allow to test the proposed approach against an independent dataset. Obtained results show the effectiveness of adopting a multi-location approach to estimate solar radiation components on the horizontal surface instead of developing several single location models. This is due to the increase
Distributed-order fractional diffusions on bounded domains
Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P.
2011-01-01
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed over the unit interval, to model a mixture of delay sources. In this paper, we provide explicit strong solutions and stochastic analogues for distributed-order fractional Cauchy problems on bounded domains with Dirichlet boundary conditions. Stochastic solutio...
Particle Simulation of Fractional Diffusion Equations
Allouch, Samer
2017-07-12
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green\\'s function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.
Particle Simulation of Fractional Diffusion Equations
Allouch, Samer; Lucchesi, Marco; Maî tre, O. P. Le; Mustapha, K. A.; Knio, Omar
2017-01-01
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green's function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.
Grain boundary diffusion in terms of the tempered fractional calculus
Energy Technology Data Exchange (ETDEWEB)
Sibatov, R.T., E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432017, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation); Svetukhin, V.V. [Ulyanovsk State University, 432017, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation); Institute of Nanotechnology and Microelectronics of the Russian Academy of Sciences, 115487, 18 Nagatinskaya str., Moscow (Russian Federation)
2017-06-28
Mathematical treatment of grain-boundary diffusion based on the model first proposed by Fisher is usually formulated in terms of normal diffusion equations in a two-component nonhomogeneous medium. On the other hand, fractional equations of anomalous diffusion proved themselves to be useful in description of grain-boundary diffusion phenomena. Moreover, the most important propagation regime predicted by Fisher's model demonstrates subdiffusive behavior. However, the direct link between fractional approach and the Fisher model and its modifications has not found yet. Here, we fill this gap and show that solution of fractional subdiffusion equation offers general properties of classical solutions obtained by Whipple and Suzuoka. The tempered fractional approach is a convenient tool for studying precipitation in granular materials as the tempered subdiffusion limited process. - Highlights: • The link connected fractional diffusion approach and Fisher's model of grain-boundary diffusion is derived. • The subdiffusion exponent of grain-boundary diffusion can differ from 1/2. • Nucleation in granular materials is modeled by the process limited by tempered subdiffusion.
Grain boundary diffusion in terms of the tempered fractional calculus
International Nuclear Information System (INIS)
Sibatov, R.T.; Svetukhin, V.V.
2017-01-01
Mathematical treatment of grain-boundary diffusion based on the model first proposed by Fisher is usually formulated in terms of normal diffusion equations in a two-component nonhomogeneous medium. On the other hand, fractional equations of anomalous diffusion proved themselves to be useful in description of grain-boundary diffusion phenomena. Moreover, the most important propagation regime predicted by Fisher's model demonstrates subdiffusive behavior. However, the direct link between fractional approach and the Fisher model and its modifications has not found yet. Here, we fill this gap and show that solution of fractional subdiffusion equation offers general properties of classical solutions obtained by Whipple and Suzuoka. The tempered fractional approach is a convenient tool for studying precipitation in granular materials as the tempered subdiffusion limited process. - Highlights: • The link connected fractional diffusion approach and Fisher's model of grain-boundary diffusion is derived. • The subdiffusion exponent of grain-boundary diffusion can differ from 1/2. • Nucleation in granular materials is modeled by the process limited by tempered subdiffusion.
On the numerical solution of the neutron fractional diffusion equation
International Nuclear Information System (INIS)
Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto
2014-01-01
Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative
Fractional Diffusion Limit for Collisional Kinetic Equations
Mellet, Antoine
2010-08-20
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.
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...
Symmetry properties of fractional diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Gazizov, R K; Kasatkin, A A; Lukashchuk, S Yu [Ufa State Aviation Technical University, Karl Marx strausse 12, Ufa (Russian Federation)], E-mail: gazizov@mail.rb.ru, E-mail: alexei_kasatkin@mail.ru, E-mail: lsu@mail.rb.ru
2009-10-15
In this paper, nonlinear anomalous diffusion equations with time fractional derivatives (Riemann-Liouville and Caputo) of the order of 0-2 are considered. Lie point symmetries of these equations are investigated and compared. Examples of using the obtained symmetries for constructing exact solutions of the equations under consideration are presented.
Yan, Hao; Wang, Shao-Qiang; Yu, Kai-Liang; Wang, Bin; Yu, Qin; Bohrer, Gil; Billesbach, Dave; Bracho, Rosvel; Rahman, Faiz; Shugart, Herman H.
2017-10-01
Diffuse radiation can increase canopy light use efficiency (LUE). This creates the need to differentiate the effects of direct and diffuse radiation when simulating terrestrial gross primary production (GPP). Here, we present a novel GPP model, the diffuse-fraction-based two-leaf model (DTEC), which includes the leaf response to direct and diffuse radiation, and treats maximum LUE for shaded leaves (ɛmsh defined as a power function of the diffuse fraction (Df)) and sunlit leaves (ɛmsu defined as a constant) separately. An Amazonian rainforest site (KM67) was used to calibrate the model by simulating the linear relationship between monthly canopy LUE and Df. This showed a positive response of forest GPP to atmospheric diffuse radiation, and suggested that diffuse radiation was more limiting than global radiation and water availability for Amazon rainforest GPP on a monthly scale. Further evaluation at 20 independent AmeriFlux sites showed that the DTEC model, when driven by monthly meteorological data and MODIS leaf area index (LAI) products, explained 70% of the variability observed in monthly flux tower GPP. This exceeded the 51% accounted for by the MODIS 17A2 big-leaf GPP product. The DTEC model's explicit accounting for the impacts of diffuse radiation and soil water stress along with its parameterization for C4 and C3 plants was responsible for this difference. The evaluation of DTEC at Amazon rainforest sites demonstrated its potential to capture the unique seasonality of higher GPP during the diffuse radiation-dominated wet season. Our results highlight the importance of diffuse radiation in seasonal GPP simulation.Plain Language SummaryAs diffuse radiation can increase canopy light use efficiency (LUE), there is a need to differentiate the effects of direct and diffuse radiation in simulating terrestrial gross primary production (GPP). A novel diffuse-fraction (Df)-based two leaf GPP model (DTEC) developed by this study considers these effects. Evaluation
Fractional Diffusion in Gaussian Noisy Environment
Directory of Open Access Journals (Sweden)
Guannan Hu
2015-03-01
Full Text Available We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: \\(D_t^{(\\alpha} u(t, x=\\textit{B}u+u\\cdot \\dot W^H\\, where \\(D_t^{(\\alpha}\\ is the Caputo fractional derivative of order \\(\\alpha\\in (0,1\\ with respect to the time variable \\(t\\, \\(\\textit{B}\\ is a second order elliptic operator with respect to the space variable \\(x\\in\\mathbb{R}^d\\ and \\(\\dot W^H\\ a time homogeneous fractional Gaussian noise of Hurst parameter \\(H=(H_1, \\cdots, H_d\\. We obtain conditions satisfied by \\(\\alpha\\ and \\(H\\, so that the square integrable solution \\(u\\ exists uniquely.
Diffusive Fractionation of Lithium Isotopes in Olivine Grain Boundaries
Homolova, V.; Watson, E. B.
2012-12-01
Diffusive fractionation of isotopes has been documented in silicate melts, aqueous fluids, and single crystals. In polycrystalline rocks, the meeting place of two grains, or grain boundaries, may also be a site of diffusive fractionation of isotopes. We have undertaken an experimental and modeling approach to investigate diffusive fractionation of lithium (Li) isotopes by grain boundary diffusion. The experimental procedure consists of packing a Ni metal capsule with predominantly ground San Carlos olivine and subjecting the capsule to 1100C and 1GPa for two days in a piston cylinder apparatus to create a nominally dry, 'dunite rock'. After this synthesis step, the capsule is sectioned and polished. One of the polished faces of the 'dunite rock' is then juxtaposed to a source material of spodumene and this diffusion couple is subject to the same experimental conditions as the synthesis step. Li abundances and isotopic profiles (ratios of count rates) were analyzed using LA-ICP-MS. Li concentrations linearly decrease away from the source from 550ppm to the average concentration of the starting olivine (2.5ppm). As a function of distance from the source, the 7Li/6Li ratio decreases to a minimum before increasing to the background ratio of the 'dunite rock'. The 7Li/6Li ratio minimum coincides with the lowest Li concentrations above average 'dunite rock' abundances. The initial decrease in the 7Li/6Li ratio is similar to that seen in other studies of diffusive fractionation of isotopes and is thought to be caused by the higher diffusivity (D) of the lighter isotope relative to the heavier isotope. The relationship between D and mass (m) is given by (D1/D2) =(m2/m1)^β, where β is an empirical fractionation factor; 1 and 2 denote the lighter and heavier isotope, respectively. A fit to the Li isotopic data reveals an effective DLi of ~1.2x10^-12 m/s^2 and a β of 0.1. Numerical modelling was utilized to elucidate the relationship between diffusive fractionation
Bounded fractional diffusion in geological media: Definition and Lagrangian approximation
Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang
2016-01-01
Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.
The distribution and seasonal variations of diffuse fraction
International Nuclear Information System (INIS)
Anane-Fenin, K.
1989-06-01
A moving average approach is used to develop linear and polynomial regression models for the diffuse fraction averaged over 10, 15, 20 and 30 days. The correlations do not appear to be influenced by climate conditions or altitude. It is noted that the correlations vary with season. The time-dependent variations of the diffuse fraction correlations are examined by studying the residual differences between the measured diffuse fraction and those calculated from the over-all best-fit correlation. The residuals exhibit no pronounced pattern leading to the conclusion that the observed seasonal variation is caused by air mass and water vapour and that atmospheric turbidity plays little or no part. (author). 14 refs, 9 figs, 8 tabs
Yan, Hao; Wang, Shao-Qiang; da Rocha, Humberto R.; Rap, Alexandru; Bonal, Damien; Butt, Nathalie; Coupe, Natalia Restrepo; Shugart, Herman H.
2017-11-01
Understanding the mechanism of photosynthetic seasonality in Amazonian evergreen forests is critical for its formulation in global climate and carbon cycle models. However, the control of the unexpected photosynthetic seasonality is highly uncertain. Here we use eddy-covariance data across a network of Amazonian research sites and a novel evapotranspiration (E) and two-leaf-photosynthesis-coupled model to investigate links between photosynthetic seasonality and climate factors on monthly scales. It reproduces the GPP seasonality (R2 = 0.45-0.69) with a root-mean-square error (RMSE) of 0.67-1.25 g C m-2 d-1 and a Bias of -0.03-1.04 g C m-2 d-1 for four evergreen forest sites. We find that the proportion of diffuse and direct sunlight governs the photosynthetic seasonality via their interaction with sunlit and shaded leaves, supported by a proof that canopy light use efficiency (LUE) has a strong linear relationship with the fraction of diffuse sunlight for Amazonian evergreen forests. In the transition from dry season to rainy season, incident total radiation (Q) decreased while LUE and diffuse fraction increased, which produced the large seasonal increase ( 34%) in GPP of evergreen forests. We conclude that diffuse radiation is an important environmental driver of the photosynthetic seasonality in tropical Amazon forests yet depending on light utilization by sunlit and shaded leaves. Besides, the GPP model simulates the precipitation-dominated GPP seasonality (R2 = 0.40-0.69) at pasture and savanna sites. These findings present an improved physiological method to relate light components with GPP in tropical Amazon.
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Burrage, Kevin; Hale, Nicholas; Kay, David
2012-01-01
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time
Weiss, C. J.; Beskardes, G. D.; Everett, M. E.
2016-12-01
In this presentation we review the observational evidence for anomalous electromagnetic diffusion in near-surface geophysical exploration and how such evidence is consistent with a detailed, spatially-correlated geologic medium. To date, the inference of multi-scale geologic correlation is drawn from two independent methods of data analysis. The first of which is analogous to seismic move-out, where the arrival time of an electromagnetic pulse is plotted as a function of transmitter/receiver separation. The "anomalous" diffusion is evident by the fractional-order power law behavior of these arrival times, with an exponent value between unity (pure diffusion) and 2 (lossless wave propagation). The second line of evidence comes from spectral analysis of small-scale fluctuations in electromagnetic profile data which cannot be explained in terms of instrument, user or random error. Rather, the power-law behavior of the spectral content of these signals (i.e., power versus wavenumber) and their increments reveals them to lie in a class of signals with correlations over multiple length scales, a class of signals known formally as fractional Brownian motion. Numerical results over simulated geology with correlated electrical texture - representative of, for example, fractures, sedimentary bedding or metamorphic lineation - are consistent with the (albeit limited, but growing) observational data, suggesting a possible mechanism and modeling approach for a more realistic geology. Furthermore, we show how similar simulated results can arise from a modeling approach where geologic texture is economically captured by a modified diffusion equation containing exotic, but manageable, fractional derivatives. These derivatives arise physically from the generalized convolutional form for the electromagnetic constitutive laws and thus have merit beyond mere mathematical convenience. In short, we are zeroing in on the anomalous, fractional diffusion limit from two converging
International Nuclear Information System (INIS)
Fang Chao; Cao Jianzhu; Sun Lifeng
2011-01-01
The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide (UO 2 ) particle is built. The adsorption effect of the fission product on the surface of the UO 2 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor. (nuclear physics)
Semianalytic Solution of Space-Time Fractional Diffusion Equation
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A. Elsaid
2016-01-01
Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.
Kinetic isotopic fractionation during diffusion of ionic species in water
Richter, Frank M.; Mendybaev, Ruslan A.; Christensen, John N.; Hutcheon, Ian D.; Williams, Ross W.; Sturchio, Neil C.; Beloso, Abelardo D.
2006-01-01
Experiments specifically designed to measure the ratio of the diffusivities of ions dissolved in water were used to determine DLi/DK,D/D,D/D,D/D,andD/D. The measured ratio of the diffusion coefficients for Li and K in water (D Li/D K = 0.6) is in good agreement with published data, providing evidence that the experimental design being used resolves the relative mobility of ions with adequate precision to also be used for determining the fractionation of isotopes by diffusion in water. In the case of Li, we found measurable isotopic fractionation associated with the diffusion of dissolved LiCl (D/D=0.99772±0.00026). This difference in the diffusion coefficient of 7Li compared to 6Li is significantly less than that reported in an earlier study, a difference we attribute to the fact that in the earlier study Li diffused through a membrane separating the water reservoirs. Our experiments involving Mg diffusing in water found no measurable isotopic fractionation (D/D=1.00003±0.00006). Cl isotopes were fractionated during diffusion in water (D/D=0.99857±0.00080) whether or not the co-diffuser (Li or Mg) was isotopically fractionated. The isotopic fractionation associated with the diffusion of ions in water is much smaller than values we found previously for the isotopic fractionation of Li and Ca isotopes by diffusion in molten silicate liquids. A major distinction between water and silicate liquids is that water surrounds dissolved ions with hydration shells, which very likely play an important but still poorly understood role in limiting the isotopic fractionation associated with diffusion.
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Burrage, Kevin
2012-01-01
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.
A fractional reaction-diffusion description of supply and demand
Benzaquen, Michael; Bouchaud, Jean-Philippe
2018-02-01
We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Jain, Sonal
2018-01-01
In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.
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)
Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
Elsaid, A.; Abdel Latif, M. S.; Maneea, M.
2016-01-01
Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on ...
Fractional Diffusion Limit for Collisional Kinetic Equations
Mellet, Antoine; Mischler, Sté phane; Mouhot, Clé ment
2010-01-01
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a
Modelling of Innovation Diffusion
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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
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q
2013-03-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
Linear fractional diffusion-wave equation for scientists and engineers
Povstenko, Yuriy
2015-01-01
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...
Higher Order and Fractional Diffusive Equations
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D. Assante
2015-07-01
Full Text Available We discuss the solution of various generalized forms of the Heat Equation, by means of different tools ranging from the use of Hermite-Kampé de Fériet polynomials of higher and fractional order to operational techniques. We show that these methods are useful to obtain either numerical or analytical solutions.
Zhokh, Alexey A.; Strizhak, Peter E.
2018-04-01
The solutions of the time-fractional diffusion equation for the short and long times are obtained via an application of the asymptotic Green's functions. The derived solutions are applied to analysis of the methanol mass transfer through H-ZSM-5/alumina catalyst grain. It is demonstrated that the methanol transport in the catalysts pores may be described by the obtained solutions in a fairly good manner. The measured fractional exponent is equal to 1.20 ± 0.02 and reveals the super-diffusive regime of the methanol mass transfer. The presence of the anomalous transport may be caused by geometrical restrictions and the adsorption process on the internal surface of the catalyst grain's pores.
Carson, James K.
2018-06-01
Glass spheres are often used as filler materials for composites. Comparatively few articles in the literature have been devoted to the measurement or modelling of thermal properties of composites containing glass spheres, and there does not appear to be any reported data on the measurement of thermal diffusivities over a range of filler volume fractions. In this study, the thermal diffusivities of guar-gel/glass sphere composites were measured using a transient comparative method. The addition of the glass beads to the gel increased the thermal diffusivity of the composite, more than doubling the thermal diffusivity of the composite relative to the diffusivity of the gel at the maximum glass volume fraction of approximately 0.57. Thermal conductivities of the composites were derived from the thermal diffusivity measurements, measured densities and estimated specific heat capacities of the composites. Two approaches to modelling the effective thermal diffusivity were considered.
Lutz, S. R.; van Meerveld, H. J.; Waterloo, M. J.; Broers, H. P.; van Breukelen, B. M.
2012-04-01
Concentration measurements are indispensable for the assessment of subsurface and surface water pollution by agrochemicals such as pesticides. However, monitoring data is often ambiguous and easily misinterpreted as a decrease in concentration could be caused by transformation, dilution or changes in the application of the pesticide. In this context, compound specific isotope analysis (CSIA) has recently emerged as a complementary monitoring technique. It is based on the measurement of the isotopic composition (e.g. δ13C and δ2H) of the contaminant. Since transformation processes are likely accompanied by isotope fractionation, thus a change in this composition, CSIA offers the opportunity to gain additional knowledge about transport and degradation processes as well as to track pollutants back to their sources. Isotopic techniques have not yet been applied in a comprehensive way in the analysis of catchment-wide organic pollution. We therefore incorporated fractionation processes associated with the fate of pesticides into the numerical flow and solute transport model HydroGeoSphere in order to assess the feasibility of CSIA within the context of catchment monitoring. The model was set up for a hypothetical hillslope transect which drains into a river. Reactive solute transport was driven by two pesticides applications within one year and actual data for rainfall and potential evapotranspiration from a meteorological station in the Netherlands. Degradation of the pesticide was assumed to take place at a higher rate under the prevailing oxic conditions in the topsoil than in deeper, anoxic subsurface layers. In terms of CSIA, these two degradation pathways were associated with different strengths of isotope fractionation for both hydrogen and carbon atoms. By simulating changes in δ13C and δ2H, the share of the oxic and the anoxic reaction on the overall degradation could be assessed. Model results suggest that CSIA is suitable for assessing degradation of
Similarity Solutions for Multiterm Time-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
A. Elsaid
2016-01-01
Full Text Available Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.
Isotope Fractionation by Diffusion in Liquids (Final Technical Report)
Energy Technology Data Exchange (ETDEWEB)
Richter, Frank [Univ. of Chicago, IL (United States)
2016-11-09
The overall objective of the DOE-funded research by grant DE-FG02-01ER15254 was document and quantify kinetic isotope fractionations during chemical and thermal (i.e., Soret) diffusion in liquids (silicate melts and water) and in the later years to include alloys and major minerals such as olivine and pyroxene. The research involved both laboratory experiments and applications to natural settings. The key idea is that major element zoning on natural geologic materials is common and can arise for either changes in melt composition during cooling and crystallization or from diffusion. The isotope effects associated with diffusion that we have documented are the key for determining whether or not the zoning observed in a natural system was the result of diffusion. Only in those cases were the zoning is demonstrably due to diffusion can use independently measured rates of diffusion to constrain the thermal evolution of the system.
New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.
Ingo, Carson; Magin, Richard L; Parrish, Todd B
2014-11-01
Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.
New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis
Directory of Open Access Journals (Sweden)
Carson Ingo
2014-11-01
Full Text Available Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag–Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.
Modelling altered fractionation schedules
International Nuclear Information System (INIS)
Fowler, J.F.
1993-01-01
The author discusses the conflicting requirements of hyperfractionation and accelerated fractionation used in radiotherapy, and the development of computer modelling to predict how to obtain an optimum of tumour cell kill without exceeding normal-tissue tolerance. The present trend is to shorten hyperfractionated schedules from 6 or 7 weeks to give overall times of 4 or 5 weeks as in new schedules by Herskovic et al (1992) and Harari (1992). Very high doses are given, much higher than can be given when ultrashort schedules such as CHART (12 days) are used. Computer modelling has suggested that optimum overall times, to yield maximum cell kill in tumours ((α/β = 10 Gy) for a constant level of late complications (α/β = 3 Gy) would be X or X-1 weeks, where X is the doubling time of the tumour cells in days (Fowler 1990). For median doubling times of about 5 days, overall times of 4 or 5 weeks should be ideal. (U.K.)
On the solutions of fractional reaction-diffusion equations
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Jagdev Singh
2013-05-01
Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.
Directory of Open Access Journals (Sweden)
Zhaoqiang Yang
2017-01-01
Full Text Available A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.
A fractional spline collocation-Galerkin method for the time-fractional diffusion equation
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Pezza L.
2018-03-01
Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.
Mustapha, K.
2017-06-03
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le
2017-01-01
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.
Magin, Richard L.; Akpa, Belinda S.; Neuberger, Thomas; Webb, Andrew G.
2011-12-01
We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-( bD) α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm -2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.
An analytic algorithm for the space-time fractional reaction-diffusion equation
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M. G. Brikaa
2015-11-01
Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.
International Nuclear Information System (INIS)
Li, Gongsheng; Zhang, Dali; Jia, Xianzheng; Yamamoto, Masahiro
2013-01-01
This paper deals with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the fractional order in the 1D time-fractional diffusion equation with smooth initial functions by using boundary measurements. The uniqueness results for the inverse problem are proved on the basis of the inverse eigenvalue problem, and the Lipschitz continuity of the solution operator is established. A modified optimal perturbation algorithm with a regularization parameter chosen by a sigmoid-type function is put forward for the discretization of the minimization problem. Numerical inversions are performed for the diffusion coefficient taking on different functional forms and the additional data having random noise. Several factors which have important influences on the realization of the algorithm are discussed, including the approximate space of the diffusion coefficient, the regularization parameter and the initial iteration. The inversion solutions are good approximations to the exact solutions with stability and adaptivity demonstrating that the optimal perturbation algorithm with the sigmoid-type regularization parameter is efficient for the simultaneous inversion. (paper)
Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations
International Nuclear Information System (INIS)
Chakraverty, S.; Tapaswini, Smita
2014-01-01
The fractional diffusion equation is one of the most important partial differential equations (PDEs) to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 < α ≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases. (general)
Fractional anisotropy and diffusivity changes in thyroid-associated orbitopathy
Energy Technology Data Exchange (ETDEWEB)
Han, Ji Sung; Seo, Hyung Suk; Lee, Young Hen [Korea University Ansan Hospital, Department of Radiology, Ansan, Gyeonggido (Korea, Republic of); Lee, Hwa [Korea University Ansan Hospital, Department of Ophthalmology, Ansan (Korea, Republic of); Suh, Sang-il [Korea University Guro Hospital, Department of Radiology, Seoul (Korea, Republic of); Jeong, Eun-Kee; Sapkota, Nabraj [University of Utah, Utah Center for Advanced Imaging Research, Salt Lake City, UT (United States); Kim, Ki Joon [Nanoori Hospital, Department of Neurosurgery, Seoul (Korea, Republic of)
2016-12-15
To investigate the extraocular muscle (EOM) changes in thyroid-associated orbitopathy (TAO) on DTI and the correlations between DTI parameters and clinical features. Twenty TAO patients and 20 age- and sex-matched controls provided informed consent and were enrolled. Ten-directional DTI was acquired in orbit. Fractional anisotropy (FA), mean, axial, and radial diffusivities were obtained at medial and lateral EOMs in both orbits. EOM thickness was measured in patients using axial CT images. FA and diffusivities were compared between patients and controls. The relationships between DTI values and muscle thickness and exophthalmos were evaluated. DTI values compared between patients in active and inactive phases by clinical activity score of TAO. DTI values were also compared between acute and chronic stages by the duration of disease. In medial EOM, FA was significantly lower in patients (p < 0.001) and negatively correlated with muscle thickness (r = -0.604, p < 0.001). Radial diffusivity was significantly higher in patients (p = 0.010) and correlated with muscle thickness (r = 0.349, p = 0.027). In lateral EOM, DTI values did not differ between patients and controls. In the acute stage, the diffusivities of the medial rectus EOM were increased compared with the chronic stage. DTI values of the medial and lateral rectus EOM did not differ significantly between active and inactive phases. DTI can be used to diagnose TAO with FA and radial diffusivity change in EOM. Diffusivities can be used to differentiate acute and chronic stage of TAO. However, DTI values showed limitation in reflecting TAO activity according to the CAS. (orig.)
International Nuclear Information System (INIS)
Owolabi, Kolade M.
2016-01-01
The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions.
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.
International Nuclear Information System (INIS)
Charkes, N.D.
1984-01-01
Using compartmental analysis methods, a mathematical basis is given for the measurement of absolute and fractional cardiac output with diffusible tracers. Cardiac output is shown to be the product of the blood volume and the sum of the rate constants of tracer egress from blood, modified by a factor reflecting transcapillary diffusibility, the transfer fraction. The return of tracer to the blood and distant (intracellular) events are shown to play no role in the solution. Fractional cardiac output is the ratio of the rate constant of tracer egress from blood to an organ, divided by the sum of the egress constants from blood. Predominantly extracellular ions such as sodium or bromide are best suited for this technique, although theoretically any diffusible tracer whose compartmental model can be solved may be used. It is shown that fractional cardiac output is independent of the transfer fraction, and therefore can be measured accurately by tracers which are not freely diffusible
On Solution of a Fractional Diffusion Equation by Homotopy Transform Method
International Nuclear Information System (INIS)
Salah, A.; Hassan, S.S.A.
2012-01-01
The homotopy analysis transform method (HATM) is applied in this work in order to find the analytical solution of fractional diffusion equations (FDE). These equations are obtained from standard diffusion equations by replacing a second-order space derivative by a fractional derivative of order α and a first order time derivative by a fractional derivative. Furthermore, some examples are given. Numerical results show that the homotopy analysis transform method is easy to implement and accurate when applied to a fractional diffusion equations.
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)
Diffusion-driven magnesium and iron isotope fractionation in Hawaiian olivine
Teng, F.-Z.; Dauphas, N.; Helz, R.T.; Gao, S.; Huang, S.
2011-01-01
Diffusion plays an important role in Earth sciences to estimate the timescales of geological processes such as erosion, sediment burial, and magma cooling. In igneous systems, these diffusive processes are recorded in the form of crystal zoning. However, meaningful interpretation of these signatures is often hampered by the fact that they cannot be unambiguously ascribed to a single process (e.g., magmatic fractionation, diffusion limited transport in the crystal or in the liquid). Here we show that Mg and Fe isotope fractionations in olivine crystals can be used to trace diffusive processes in magmatic systems. Over sixty olivine fragments from Hawaiian basalts show isotopically fractionated Mg and Fe relative to basalts worldwide, with up to 0.4??? variation in 26Mg/24Mg ratios and 1.6??? variation in 56Fe/54Fe ratios. The linearly and negatively correlated Mg and Fe isotopic compositions [i.e., ??56Fe=(??3.3??0.3)????26Mg], co-variations of Mg and Fe isotopic compositions with Fe/Mg ratios of olivine fragments, and modeling results based on Mg and Fe elemental profiles demonstrate the coupled Mg and Fe isotope fractionation to be a manifestation of Mg-Fe inter-diffusion in zoned olivines during magmatic differentiation. This characteristic can be used to constrain the nature of mineral zoning in igneous and metamorphic rocks, and hence determine the residence times of crystals in magmas, the composition of primary melts, and the duration of metamorphic events. With improvements in methodology, in situ isotope mapping will become an essential tool of petrology to identify diffusion in crystals. ?? 2011 Elsevier B.V.
Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan
2018-01-01
In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.
Enriched reproducing kernel particle method for fractional advection-diffusion equation
Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam
2018-06-01
The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.
A new fractional operator of variable order: Application in the description of anomalous diffusion
Yang, Xiao-Jun; Machado, J. A. Tenreiro
2017-09-01
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
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)
Singh, Brajesh K; Srivastava, Vineet K
2015-04-01
The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.
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.
A fractional model for dye removal
Directory of Open Access Journals (Sweden)
Ji-Huan He
2016-01-01
Full Text Available The adsorption process has a fractional property, and a fractional model is suggested to study a transport model of direct textile industry wastewater. An approximate solution of the concentration is obtained by the variational iteration method.
Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport
International Nuclear Information System (INIS)
Litvinenko, Yuri E.; Effenberger, Frederic
2014-01-01
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
Modelling nematode movement using time-fractional dynamics.
Hapca, Simona; Crawford, John W; MacMillan, Keith; Wilson, Mike J; Young, Iain M
2007-09-07
We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.
Fractional calculus phenomenology in two-dimensional plasma models
Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill
2006-10-01
Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).
Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials
Directory of Open Access Journals (Sweden)
Wu Guo-Cheng
2017-01-01
Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
Directory of Open Access Journals (Sweden)
Xuehui Yin
2015-01-01
Full Text Available The traditional integer-order partial differential equations and gradient regularization based image denoising techniques often suffer from staircase effect, speckle artifacts, and the loss of image contrast and texture details. To address these issues, in this paper, a difference curvature driven fractional anisotropic diffusion for image noise removal is presented, which uses two new techniques, fractional calculus and difference curvature, to describe the intensity variations in images. The fractional-order derivatives information of an image can deal well with the textures of the image and achieve a good tradeoff between eliminating speckle artifacts and restraining staircase effect. The difference curvature constructed by the second order derivatives along the direction of gradient of an image and perpendicular to the gradient can effectively distinguish between ramps and edges. Fourier transform technique is also proposed to compute the fractional-order derivative. Experimental results demonstrate that the proposed denoising model can avoid speckle artifacts and staircase effect and preserve important features such as curvy edges, straight edges, ramps, corners, and textures. They are obviously superior to those of traditional integral based methods. The experimental results also reveal that our proposed model yields a good visual effect and better values of MSSIM and PSNR.
International Nuclear Information System (INIS)
Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh
2016-01-01
A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.
Negligible fractionation of Kr and Xe isotopes by molecular diffusion in water
Tyroller, Lina; Brennwald, Matthias S.; Busemann, Henner; Maden, Colin; Baur, Heinrich; Kipfer, Rolf
2018-06-01
Molecular diffusion is a key transport process for noble gases in water. Such diffusive transport is often thought to cause a mass-dependent fractionation of noble gas isotopes that is inversely proportional to the square root of the ratio of their atomic mass, referred to as the square root relation. Previous studies, challenged the commonly held assumption that the square root relation adequately describes the behaviour of noble gas isotopes diffusing through water. However, the effect of diffusion on noble gas isotopes has only been determined experimentally for He, Ne and Ar to date, whereas the extent of fractionation of Kr and Xe has not been measured. In the present study the fractionation of Kr and Xe isotopes diffusing through water immobilised by adding agar was quantified through measuring the respective isotope ratio after diffusing through the immobilised water. No fractionation of Kr and Xe isotopes was observed, even using high-precision noble gas analytics. These results complement our current understanding on isotopic fractionation of noble gases diffusing through water. Therefore this complete data set builds a robust basis to describe molecular diffusion of noble gases in water in a physical sound manner which is fundamental to assess the physical aspects of gas dynamics in aquatic systems.
Energy Technology Data Exchange (ETDEWEB)
Klauser, A.S.; Kremser, C. [Medical University of Innsbruck, Department of Radiology, Innsbruck (Austria); Abd Ellah, M. [Medical University of Innsbruck, Department of Radiology, Innsbruck (Austria); Assiut University, Department of Diagnostic Radiology, South Egypt Cancer Institute, Assiut (Egypt); Taljanovic, M. [University of Arizona, College of Medicine, Banner- University Medical Center, Department of Medical Imaging, Tucson (United States); Schmidle, G.; Gabl, M. [Medical University of Innsbruck, Department for Trauma Surgery, Innsbruck (Austria); Cartes-Zumelzu, F.; Steiger, R.; Gizewski, E.R. [Medical University of Innsbruck, Department of Neuroradiology, Neuroimaging core facility, Innsbruck (Austria)
2018-03-15
To quantitatively assess carpal tunnel syndrome (CTS) with DTI by evaluating two approaches to determine cut-off values. In forty patients with CTS diagnosis confirmed by nerve conduction studies (NCs) and 14 healthy subjects (mean age 58.54 and 57.8 years), cross-sectional area (CSA), apparent diffusion coefficient (ADC) and fractional anisotropy (FA) at single and multiple levels with intraobserver agreement were evaluated. Maximum and mean CSA and FA showed significant differences between healthy subjects and patients (12.85 mm{sup 2} vs. 28.18 mm{sup 2}, p < 0.001, and 0.613 vs. 0.524, p=0.007, respectively) (10.12 mm{sup 2} vs. 19.9 mm{sup 2}, p<0.001 and 0.617 vs. 0.54, p=0.003, respectively), but not maximum and mean ADC (p > 0.05). For cut-off values, mean and maximum CSA showed the same sensitivity and specificity (93.3 %). However, mean FA showed better sensitivity than maximum FA (82.6 % vs. 73.9 %), but lower specificity (66.7 % vs. 80 %), and significant correlation for maximum CSA, 97 % (p < 0.01), with good correlation for maximum ADC and FA, 84.5 % (p < 0.01) and 62 % (p=0.056), respectively. CSA and FA showed significant differences between healthy subjects and patients. Single measurement at maximum CSA is suitable for FA determination. (orig.)
Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion
Chen, Yao; Wang, Xudong; Deng, Weihua
2017-10-01
This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.
Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon
2017-09-01
Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.
DEFF Research Database (Denmark)
Rolle, Massimo; Jin, Biao
2017-01-01
Diffusive isotope fractionation of organic contaminants in aqueous solution is difficult to quantify, and only a few experimental data sets are available for compounds of environmental interest. In this study, we investigate diffusive fractionation of perdeuterated and nondeuterated benzene...... and toluene. Multitracer experiments were carried out in 1-D gel dissection tubes and in a quasi-2-D flow-through porous medium. The experiments allowed us to simultaneously and directly compare the diffusive and dispersive behavior of benzene and toluene. We observed an unexpected, opposite behavior...... of the two monoaromatic hydrocarbons. Toluene showed a normal diffusive isotope effect (DC7D8/DC7H8 = 0.96) with enrichment of the nondeuterated isotopologue in the direction of the diffusive and transverse dispersive fluxes. Conversely, the measured trends for benzene indicate inverse diffusive...
Directory of Open Access Journals (Sweden)
Lihong Zhang
2017-11-01
Full Text Available In this article, a family of nonlinear diffusion equations involving multi-term Caputo-Fabrizio time fractional derivative is investigated. Some maximum principles are obtained. We also demonstrate the application of the obtained results by deriving some estimation for solution to reaction-diffusion equations.
A variable-order fractal derivative model for anomalous diffusion
Directory of Open Access Journals (Sweden)
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.
On the Fractional Nagumo Equation with Nonlinear Diffusion and Convection
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available We presented the Nagumo equation using the concept of fractional calculus. With the help of two analytical techniques including the homotopy decomposition method (HDM and the new development of variational iteration method (NDVIM, we derived an approximate solution. Both methods use a basic idea of integral transform and are very simple to be used.
Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets
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Ai-Min Yang
2013-01-01
Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.
Fractional Order Models of Industrial Pneumatic Controllers
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Abolhassan Razminia
2014-01-01
Full Text Available This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD controller and integral-derivative (FrID are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.
Gao, Qing; Srinivasan, Girish; Magin, Richard L; Zhou, Xiaohong Joe
2011-05-01
To theoretically develop and experimentally validate a formulism based on a fractional order calculus (FC) diffusion model to characterize anomalous diffusion in brain tissues measured with a twice-refocused spin-echo (TRSE) pulse sequence. The FC diffusion model is the fractional order generalization of the Bloch-Torrey equation. Using this model, an analytical expression was derived to describe the diffusion-induced signal attenuation in a TRSE pulse sequence. To experimentally validate this expression, a set of diffusion-weighted (DW) images was acquired at 3 Tesla from healthy human brains using a TRSE sequence with twelve b-values ranging from 0 to 2600 s/mm(2). For comparison, DW images were also acquired using a Stejskal-Tanner diffusion gradient in a single-shot spin-echo echo planar sequence. For both datasets, a Levenberg-Marquardt fitting algorithm was used to extract three parameters: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). Using adjusted R-squared values and standard deviations, D, β, and μ values and the goodness-of-fit in three specific regions of interest (ROIs) in white matter, gray matter, and cerebrospinal fluid, respectively, were evaluated for each of the two datasets. In addition, spatially resolved parametric maps were assessed qualitatively. The analytical expression for the TRSE sequence, derived from the FC diffusion model, accurately characterized the diffusion-induced signal loss in brain tissues at high b-values. In the selected ROIs, the goodness-of-fit and standard deviations for the TRSE dataset were comparable with the results obtained from the Stejskal-Tanner dataset, demonstrating the robustness of the FC model across multiple data acquisition strategies. Qualitatively, the D, β, and μ maps from the TRSE dataset exhibited fewer artifacts, reflecting the improved immunity to eddy currents. The diffusion-induced signal attenuation in a TRSE pulse sequence
Moving-boundary problems for the time-fractional diffusion equation
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Sabrina D. Roscani
2017-02-01
Full Text Available We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation. The time-fractional derivative of order $\\alpha\\in (0,1$ is taken in the sense of Caputo. We study the asymptotic behaivor, as t tends to infinity, of a general solution by using a fractional weak maximum principle. Also, we give some particular exact solutions in terms of Wright functions.
Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation
Abuasad, Salah; Hashim, Ishak
2018-04-01
In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.
2013-01-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
Martelloni, Gianluca; Bagnoli, Franco
2016-04-01
Richardson's treatise on turbulent diffusion in 1926 [24] and today, the list of system displaying anomalous dynamical behavior is quite extensive. We only report some examples: charge carrier transport in amorphous semiconductors [25], porous systems [26], reptation dynamics in polymeric systems [27, 28], transport on fractal geometries [29], the long-time dynamics of DNA sequences [30]. In this scenario, the fractional calculus is used to generalized the Fokker-Planck linear equation -∂P (x,t)=D ∇2P (x,t), ∂t (3) where P (x,t) is the density of probability in the space x=[x1, x2, x3] and time t, while D >0 is the diffusion coefficient. Such processes are characterized by Eq. (1). An example of Eq. (3) generalization is ∂∂tP (x,t)=D∇ αP β(x,t) - ∞ - 1 , (4) where the fractional based-derivatives Laplacian Σ(∂α/∂xα)i, (i = 1, 2, 3), of non-linear term Pβ(x,t) is taken into account [31]. Another generalized form is represented by equation ∂∂tδδP(x,t)=D ∇ αP(x,t) δ > 0 α ≤ 2 , (5) that considers also the fractional time-derivative [32]. These fractional-described processes exhibit a power law patters as expressed by Eq. (2). This general introduction introduces the presented work, whose aim is to develop a theoretical model in order to forecast the triggering and propagation of landslides, using the techniques of fractional calculus. The latter is suitable for modeling the water infiltration (i.e., the pore water pressure diffusion in the soil) and the dynamical processes in the fractal media [33]. Alternatively the fractal representation of temporal and spatial derivative (the fractal order only appears in the denominator of the derivative) is considered and the results are compared to the fractional one. The prediction of landslides and the discovering of the triggering mechanism, is one of the challenging problems in earth science. Landslides can be triggered by different factors but in most cases the trigger is an intense or long rain
Luchko, Yuri
2013-05-30
In this paper, we consider a reaction-diffusion problem with an unknown nonlinear source function that has to be determined from overposed data. The underlying model is in the form of a time-fractional reaction-diffusion equation and the work generalizes some known results for the inverse problems posed for PDEs of parabolic type. For the inverse problem under consideration, a uniqueness result is proved and a numerical algorithm with some theoretical qualification is presented in the one-dimensional case. The key both to the uniqueness result and to the numerical algorithm relies on the maximum principle which has recently been shown to hold for the fractional diffusion equation. In order to show the effectiveness of the proposed method, results of numerical simulations are presented. © 2013 IOP Publishing Ltd.
Fractional calculus with applications in mechanics vibrations and diffusion processes
Atanackovic, T; Stankovic, Bogoljub; Zorica , Dusan
2014-01-01
This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton-type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are then analyzed num
A Computational Model of Fraction Arithmetic
Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.
2017-01-01
Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…
Fractional diffusion equation with distributed-order material derivative. Stochastic foundations
International Nuclear Information System (INIS)
Magdziarz, M; Teuerle, M
2017-01-01
In this paper, we present the stochastic foundations of fractional dynamics driven by the fractional material derivative of distributed-order type. Before stating our main result, we present the stochastic scenario which underlies the dynamics given by the fractional material derivative. Then we introduce the Lévy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with the material derivative of distributed-order type. (paper)
International Nuclear Information System (INIS)
Sandev, D. Trivche
2010-01-01
The fractional calculus basis, Mittag-Leffler functions, various relaxation-oscillation and diffusion-wave fractional order equation and systems of fractional order equations are considered in this thesis. To solve these fractional order equations analytical methods, such as the Laplace transform method and method of separation of variables are employed. Some applications of the fractional calculus are considered, particularly physical system with anomalous diffusive behavior. (Author)
International Nuclear Information System (INIS)
Furuta, Hiroshi; Yamamoto, Ichiro
1996-01-01
Diffusion coefficients in 4-component mixture D ij (4) were expressed explicitly in terms of binary diffusion coefficients and mole fractions by solving a ratio of determinants defined by Hirschfelder et al. The explicit expressions of D ij (4) were divided into two terms, a term due to the i-j pairs of attention and a term common to all the pairs out of the 4 components. The two terms of D ij (4) had extended structures similar to corresponding those of D ij (3) respectively. (author)
DEFF Research Database (Denmark)
Buizert, C.; Sowers, T.; Blunier, T.
2013-01-01
During rapid variations of the atmospheric mixing ratio of a trace gas, diffusive transport in the porous firn layer atop ice sheets and glaciers alters the isotopic composition of that gas relative to the overlying atmosphere. Records of past atmospheric trace gas isotopic composition from ice...... cores and firn need to be corrected for this diffusive fractionation artifact. We present a novel, semi-empirical method to accurately estimate the magnitude of the diffusive fractionation in the ice core record. Our method (1) consists of a relatively simple analytical calculation; (2) requires only...... commonly available ice core data; (3) is not subject to the uncertainties inherent to estimating the accumulation rate, temperature, close-off depth and depth-diffusivity relationship back in time; (4) does not require knowledge of the true atmospheric variations, but uses the smoothed records obtained...
FEM for time-fractional diffusion equations, novel optimal error analyses
Mustapha, Kassem
2016-01-01
A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with respect to both the convergence order of the approximate solution and the regularity of the initial data. By using novel energy arguments, for each fixed time $t$, optimal error bounds in the spatial $L^2$- and $H^1$-norms are derived for both cases: smooth...
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
Transient heat conduction in a pebble fuel applying fractional model
International Nuclear Information System (INIS)
Gomez A, R.; Espinosa P, G.
2009-10-01
In this paper we presents the equation of thermal diffusion of temporary-fractional order in the one-dimensional space in spherical coordinates, with the objective to analyze the heat transference between the fuel and coolant in a fuel element of a Pebble Bed Modular Reactor. The pebble fuel is the heterogeneous system made by microsphere constitutes by U O, pyrolytic carbon and silicon carbide mixed with graphite. To describe the heat transfer phenomena in the pebble fuel we applied a constitutive law fractional (Non-Fourier) in order to analyze the behaviour transient of the temperature distribution in the pebble fuel with anomalous thermal diffusion effects a numerical model is developed. (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.
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)
Comparative study of void fraction models
International Nuclear Information System (INIS)
Borges, R.C.; Freitas, R.L.
1985-01-01
Some models for the calculation of void fraction in water in sub-cooled boiling and saturated vertical upward flow with forced convection have been selected and compared with experimental results in the pressure range of 1 to 150 bar. In order to know the void fraction axial distribution it is necessary to determine the net generation of vapour and the fluid temperature distribution in the slightly sub-cooled boiling region. It was verified that the net generation of vapour was well represented by the Saha-Zuber model. The selected models for the void fraction calculation present adequate results but with a tendency to super-estimate the experimental results, in particular the homogeneous models. The drift flux model is recommended, followed by the Armand and Smith models. (F.E.) [pt
Application of the Fractional Diffusion Equation for Predicting Market Behaviour
Jonathan M. Blackledge
2010-01-01
Most Financial modelling system rely on an underlying hypothesis known as the Eficient Market Hypothesi (EMH) including the famous BlackScholes formula for placing an option. However, the EMH has a fundamental flaw: it is based on the assumption that economic processes are normally distributed and it has long been known that this is not the case. This fundamental assumption leads to a number of shortcomings associated with using the EMH to analyse financial data which includes failure to pred...
Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results
Directory of Open Access Journals (Sweden)
V. Ilyin
2010-01-01
Full Text Available We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the probability distribution function obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial.
International Nuclear Information System (INIS)
Jolapara, Milan; Kesavadas, Chandrasekharan; Saini, Jitender; Patro, Satya Narayan; Gupta, Arun Kumar; Kapilamoorthy, Tirur Raman; Bodhey, Narendra; Radhakrishnan, V.V.
2009-01-01
The signal characteristics of an epidermoid on T2-weighted imaging have been attributed to the presence of increased water content within the tumor. In this study, we explore the utility of diffusion tensor imaging (DTI) and diffusion tensor metrics (DTM) in knowing the microstructural anatomy of epidermoid cysts. DTI was performed in ten patients with epidermoid cysts. Directionally averaged mean diffusivity (D av ), exponential diffusion, and DTM-like fractional anisotropy (FA), diffusion tensor mode (mode), linear (CL), planar (CP), and spherical (CS) anisotropy were measured from the tumor as well as from the normal-looking white matter. Epidermoid cysts showed high FA. However, D av and exponential diffusion values did not show any restriction of diffusion. Diffusion tensor mode values were near -1, and CP values were high within the tumor. This suggested preferential diffusion of water molecules along a two-dimensional geometry (plane) in epidermoid cysts, which could be attributed to the parallel-layered arrangement of keratin filaments and flakes within these tumors. Thus, advanced imaging modalities like DTI with DTM can provide information regarding the microstructural anatomy of the epidermoid cysts. (orig.)
International Nuclear Information System (INIS)
Chang, Yong Min; Kim, Yong Sun; Kang, Duk Sik; Lee, Young Joo; Sohn, Chul Ho; Woo, Seung Koo; Suh, Kyung Jin
2005-01-01
We wished to analyze, qualitatively and quantitatively, the noise performance of fractional anisotropy brain images along with the different diffusion gradient numbers by using the histogram method. Diffusion tensor images were acquired using a 3.0 T MR scanner from ten normal volunteers who had no neurological symptoms. The single-shot spin-echo EPI with a Stejskal-Tanner type diffusion gradient scheme was employed for the diffusion tensor measurement. With a b-valuee of 1000 s/mm 2 , the diffusion tensor images were obtained for 6, 11, 23, 35 and 47 diffusion gradient directions. FA images were generated for each DTI scheme. The histograms were then obtained at selected ROIs for the anatomical structures on the FA image. At the same ROI location, the mean FA value and the standard deviation of the mean FA value were calculated. The quality of the FA image was improved as the number of diffusion gradient directions increased by showing better contrast between the WM and GM. The histogram showed that the variance of FA values was reduced as the number of diffusion gradient directions increased. This histogram analysis was in good agreement with the result obtained using quantitative analysis. The image quality of the FA map was significantly improved as the number of diffusion gradient directions increased. The histogram analysis well demonstrated that the improvement in the FA images resulted from the reduction in the variance of the FA values included in the ROI
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
An inverse problem for a one-dimensional time-fractional diffusion problem
Jin, Bangti; Rundell, William
2012-01-01
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique
International Nuclear Information System (INIS)
Pierantozzi, T.; Vazquez, L.
2005-01-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case
Theory and simulation of time-fractional fluid diffusion in porous media
International Nuclear Information System (INIS)
Carcione, José M; Sanchez-Sesma, Francisco J; Gavilán, Juan J Perez; Luzón, Francisco
2013-01-01
We simulate a fluid flow in inhomogeneous anisotropic porous media using a time-fractional diffusion equation and the staggered Fourier pseudospectral method to compute the spatial derivatives. A fractional derivative of the order of 0 < ν < 2 replaces the first-order time derivative in the classical diffusion equation. It implies a time-dependent permeability tensor having a power-law time dependence, which describes memory effects and accounts for anomalous diffusion. We provide a complete analysis of the physics based on plane waves. The concepts of phase, group and energy velocities are analyzed to describe the location of the diffusion front, and the attenuation and quality factors are obtained to quantify the amplitude decay. We also obtain the frequency-domain Green function. The time derivative is computed with the Grünwald–Letnikov summation, which is a finite-difference generalization of the standard finite-difference operator to derivatives of fractional order. The results match the analytical solution obtained from the Green function. An example of the pressure field generated by a fluid injection in a heterogeneous sandstone illustrates the performance of the algorithm for different values of ν. The calculation requires storing the whole pressure field in the computer memory since anomalous diffusion ‘recalls the past’. (paper)
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
Fractional virus epidemic model on financial networks
Directory of Open Access Journals (Sweden)
Balci Mehmet Ali
2016-01-01
Full Text Available In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.
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
Park, Moongyu; Cushman, John Howard; O'Malley, Dan
2014-09-30
The collective molecular reorientations within a nematic liquid crystal fluid bathing a spherical colloid cause the colloid to diffuse anomalously on a short time scale (i.e., as a non-Brownian particle). The deformations and fluctuations of long-range orientational order in the liquid crystal profoundly influence the transient diffusive regimes. Here we show that an anisotropic fractional Brownian process run with a nonlinear multiscaling clock effectively mimics this collective and transient phenomenon. This novel process has memory, Gaussian increments, and a multiscale mean square displacement that can be chosen independently from the fractal dimension of a particle trajectory. The process is capable of modeling multiscale sub-, super-, or classical diffusion. The finite-size Lyapunov exponents for this multiscaling process are defined for future analysis of related mixing processes.
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.
International Nuclear Information System (INIS)
Ribeiro, Haroldo V; Alves, Luiz G A; Zola, Rafael S; Lenzi, Ervin K; Tateishi, Angel A
2014-01-01
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of the particle is zero. Here, we propose an extension for the comb model via Langevin-like equations driven by fractional Gaussian noises (long-range correlated). By carrying out computer simulations, we show that the correlations in the y-direction affect the diffusive behavior in the x-direction in a non-trivial fashion, resulting in a quite rich diffusive scenario characterized by usual, superdiffusive or subdiffusive scaling of second moment in the x-direction. We further show that the long-range correlations affect the probability distribution of the particle positions in the x-direction, making their tails longer when noise in the y-direction is persistent and shorter for anti-persistent noise. Our model thus combines and allows the study/analysis of the interplay between different mechanisms of anomalous diffusion (geometric constraints and long-range correlations) and may find direct applications for describing diffusion in complex systems such as living cells. (paper)
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)
Liu, Lin; Zheng, Liancun; Liu, Fawang; Zhang, Xinxin
2016-09-01
An improved Cattaneo-Christov flux model is proposed which can be used to capture the effects of the time and spatial relaxations, the time and spatial inhomogeneous diffusion and the spatial transition probability of cell transport in a highly non-homogeneous medium. Solutions are obtained by numerical discretization method where the time and spatial fractional derivative are discretized by the L1-approximation and shifted Grünwald definition, respectively. The solvability, stability and convergence of the numerical method for the special case of the Cattaneo-Christov equation are proved. Results indicate that the fractional convection diffusion-wave equation is an evolution equation which displays the coexisting characteristics of parabolicity and hyperbolicity. In other words, for α in (0, 1), the cells transport occupies the characteristics of coupling convection diffusion and wave spreading. Moreover, the effects of pertinent time parameter, time and spatial fractional derivative parameters, relaxation parameter, weight coefficient and the convection velocity on the anomalous transport of cells are shown graphically and analyzed in detail.
Mass fractionation of noble gases in diffusion-limited hydrodynamic hydrogen escape
International Nuclear Information System (INIS)
Zahnle, K.; Pollack, J.B.; Kasting, J.F.
1990-01-01
The theory of mass fractionation by hydrogen is presently extended to atmospheres in which hydrogen is not the major constituent. This theoretical framework is applied to three different cases. In the first, it is shown that the fractionation of terrestrial atmospheric neon with respect to mantle neon is explainable as a consequence of diffusion-limited hydrogen escape from a steam atmosphere toward the end of the accretion process. In the second, the anomalously high Ar-38/Ar-36 ratio of Mars is shown to be due to hydrodynamic fractionation by a vigorously escaping and very pure hydrogen wind. In the last case, it is speculated that the currently high Martian D/H ratio emerged during the hydrodynamic escape phase which fractionated Ar. 35 refs
A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games
Institute of Scientific and Technical Information of China (English)
Kecai Cao; Yang Quan Chen; Daniel Stuart
2016-01-01
Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end.Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model,respectively.
Liang, Yingjie; Chen, Wen; Magin, Richard L.
2016-07-01
Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (α and β) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing α and β, and that the normal or Gaussian case with α = 1 and β = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.
Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative
Directory of Open Access Journals (Sweden)
José Francisco Gómez Aguilar
2014-01-01
Full Text Available An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as 0<β, γ≤1 for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters σx and σt are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.
The Galerkin finite element method for a multi-term time-fractional diffusion equation
Jin, Bangti
2015-01-01
© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Directory of Open Access Journals (Sweden)
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
Agarwal, P.; El-Sayed, A. A.
2018-06-01
In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor
2014-08-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity of the involved phenomena. Many studies have reported a time delay between the neural activity and the cerebral blood flow, which has been described by adding a delay parameter in some of the existing models. An alternative approach is proposed in this paper, where a fractional system is used to model the neurovascular coupling. Thanks to its nonlocal property, a fractional derivative is suitable for modeling the phenomena with delay. The proposed model is coupled with the first version of the well-known balloon model, which relates the cerebral blood flow to the Blood Oxygen Level Dependent (BOLD) signal measured using functional Magnetic Resonance Imaging (fMRI). Through some numerical simulations, the properties of the fractional model are explained and some preliminary comparisons to a real BOLD data set are provided. © 2014 IEEE.
Revised models of interstellar nitrogen isotopic fractionation
Wirström, E. S.; Charnley, S. B.
2018-03-01
Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.
Dynamical models of happiness with fractional order
Song, Lei; Xu, Shiyun; Yang, Jianying
2010-03-01
This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.
Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates
Directory of Open Access Journals (Sweden)
Povstenko YZ
2011-01-01
Full Text Available Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time , the Hankel transform with respect to the radial coordinate , the finite Fourier transform with respect to the angular coordinate , and the exponential Fourier transform with respect to the spatial coordinate . Numerical results are illustrated graphically.
A numerical solution for a class of time fractional diffusion equations with delay
Directory of Open Access Journals (Sweden)
Pimenov Vladimir G.
2017-09-01
Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation
Jin, Bangti; Lazarov, Raytcho; Liu, Yikan; Zhou, Zhi
2014-01-01
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite...
GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD
2016-01-01
This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...
Chen, Hao; Lv, Wen; Zhang, Tongtong
2018-05-01
We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.
Magnetic diffusion and ionization fractions in dense molecular clouds: The role of charged grains
International Nuclear Information System (INIS)
Elmegreen, B.G.
1979-01-01
The ionization fraction is determined for dense molecular clouds by considering charge exchange, dissociative recombination, radiative recombination, and collisions between grains and charged species. The inclusion of grains tends to lower the ionization fraction for a given cosmic-ray ionization rate zeta and metal depletion delta. The observed values of the ionization fractions in dense cloud cores (i.e., -8 ) are obtained for reasonable values of zeta=10 -17 s -1 and delta=0.1.For temperatures less than 30 K, each grain alternates in charge between -e and 0. The resulting motion of the grains in a self-graviting cloud that contains a magnetic field will be periodic; their response to electromagnetic forces will depend on their instantaneous charge. This complex motion is calculated in order to determine the average viscous force between the grains and the neutral molecules in the cloud. The grain-neutral viscous force combines with the ion-neutral viscous force to regulate the motion of the neutral molecules relative to the magnetic field. The resultant The result neutral drift leads to a diffusion of the magnetic field out of the cloud. The time scale for this diffusion is calculated. Grain-related viscous forces dominate ion-related forces for ionization fractions less than 5 x 10 -8 . The magnetic diffusion time in a self-gravitating cloud that is supported by an internal magnetic field is shown to be at least 10 times larger thanthe free-fall time even when the ionization fraction is much less than 10 -8
Kim, Jinna
2010-01-01
Purpose Diffusion tensor imaging provides better understanding of pathophysiology of congenital anomalies, involving central nervous system. This study was aimed to specify the pathogenetic mechanism of heterotopia, proved by diffusion tensor imaging, and establish new findings of heterotopia on fractional anisotropy maps. Materials and Methods Diffusion-weighted imaging data from 11 patients (M : F = 7 : 4, aged from 1 to 22 years, mean = 12.3 years) who visited the epilepsy clinic and received a routine seizure protocol MRI exam were retrospectively analyzed. Fractional anisotropy (FA) maps were generated from diffusion tensor imaging of 11 patients with heterotopia. Regions of interests (ROI) were placed in cerebral cortex, heterotopic gray matter and deep gray matter, including putamen. ANOVA analysis was performed for comparison of different gray matter tissues. Results Heterotopic gray matter showed signal intensities similar to normal gray matter on T1 and T2 weighted MRI. The measured FA of heterotopic gray matter was higher than that of cortical gray matter (0.236 ± 0.011 vs. 0.169 ± 0.015, p < 0.01, one way ANOVA), and slightly lower than that of deep gray matter (0.236 ± 0.011 vs. 0.259 ± 0.016, p < 0.01). Conclusion Increased FA of heterotopic gray matter suggests arrested neuron during radial migration and provides better understanding of neurodevelopment. PMID:20499428
Yin, Deshun; Qu, Pengfei
2018-02-01
Protein lateral diffusion is considered anomalous in the plasma membrane. And this diffusion is related to membrane microstructure. In order to better describe the property of protein lateral diffusion and find out the inner relationship between protein lateral diffusion and membrane microstructure, this article applies variable-order fractional mean square displacement (f-MSD) function for characterizing the anomalous diffusion. It is found that the variable order can reflect the evolution of diffusion ability. The results of numerical simulation demonstrate variable-order f-MSD function can predict the tendency of anomalous diffusion during the process of confined diffusion. It is also noted that protein lateral diffusion ability during the processes of confined and hop diffusion can be split into three parts. In addition, the comparative analyses reveal that the variable order is related to the confinement-domain size and microstructure of compartment boundary too.
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.
Modeling electron fractionalization with unconventional Fock spaces.
Cobanera, Emilio
2017-08-02
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Stamova, Ivanka; Stamov, Gani
2017-12-01
In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.
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.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
2014-01-01
approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction
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
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.
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
Kailasanathan, Ranjith Kumar Abhinavam; Zhang, Ji; Fang, Tiegang; Roberts, William L.
2014-01-01
Soot surface temperature and volume fraction are measured in ethylene/air coflowing laminar diffusion flames at high pressures, diluted with one of four diluents (argon, helium, nitrogen, and carbon dioxide) using a two-color technique. Both
On conservation laws for models in discrete, noncommutative and fractional differential calculus
International Nuclear Information System (INIS)
Klimek, M.
2001-01-01
We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied
Koyama, Tetsuo; Marumoto, Kohei; Uchiyama, Yuki; Miyake, Hiroji; Domen, Kazuhisa
2015-04-01
This study aimed to evaluate the prognostic efficacy of magnetic resonance diffusion tensor fractional anisotropy (FA) for patients with hemiparesis due to intracerebral hemorrhage. Diffusion tensor FA brain images were acquired 14-21 days after putaminal and/or thalamic hemorrhage. The ratio of FA values within the cerebral peduncles of the affected and unaffected hemispheres (rFA) was calculated for each patient (n = 40) and assessed for correlation with Brunnstrom stage (BRS, 1-6), motor component of the functional independence measure (FIM-motor, 13-91), and the total length of stay (LOS) until discharge from rehabilitation (P hemiparesis due to putaminal and/or thalamic hemorrhage, particularly hand function recovery. Copyright © 2015 National Stroke Association. Published by Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Ya-Juan Hao
2013-01-01
Full Text Available The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.
Liu, Yikan
2015-01-01
In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and the involved multinomial Mittag-Leffler functions, we improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart as expected. As a direct application, w...
Fractional-moment Capital Asset Pricing model
International Nuclear Information System (INIS)
Li Hui; Wu Min; Wang Xiaotian
2009-01-01
In this paper, we introduce the definition of the 'α-covariance' and present the fractional-moment versions of Capital Asset Pricing Model,which can be used to price assets when asset return distributions are likely to be stable Levy (or Student-t) distribution during panics and stampedes in worldwide security markets in 2008. Furthermore, if asset returns are truly governed by the infinite-variance stable Levy distributions, life is fundamentally riskier than in a purely Gaussian world. Sudden price movements like the worldwide security market crash in 2008 turn into real-world possibilities.
Applications of fractional calculus to diffusion transport in clay-water system
International Nuclear Information System (INIS)
Korosak, D.; Cvikl, B.; Kramer, J.; Jecl, R.; Praprotnik, A.; Veselic, M.
2005-01-01
The analysis of the low-frequency conductivity spectra of the clay-water mixtures is presented. The conductivity spectra for samples at different water content values are shown to collapse to a single master curve when appropriately rescaled. The frequency dependence of the conductivity is shown to follow the power-law with the exponent η=0,67 before reaching the frequency-independent part. It is argued that the observed conductivity dispersion is a consequence of the anomalously diffusing ions in the clay-water system. The fractional Langevin equation is then used to describe the stochastic dynamics of the single ion. (author)
The determination of an unknown boundary condition in a fractional diffusion equation
Rundell, William
2013-07-01
In this article we consider an inverse boundary problem, in which the unknown boundary function ∂u/∂v = f(u) is to be determined from overposed data in a time-fractional diffusion equation. Based upon the free space fundamental solution, we derive a representation for the solution f as a nonlinear Volterra integral equation of second kind with a weakly singular kernel. Uniqueness and reconstructibility by iteration is an immediate result of a priori assumption on f and applying the fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. © 2013 Copyright Taylor and Francis Group, LLC.
Preconditioned iterative methods for space-time fractional advection-diffusion equations
Zhao, Zhi; Jin, Xiao-Qing; Lin, Matthew M.
2016-08-01
In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.
Modeling of heat conduction via fractional derivatives
Fabrizio, Mauro; Giorgi, Claudio; Morro, Angelo
2017-09-01
The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not.
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.
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.
Owolabi, Kolade M.
2018-03-01
In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.
Li, Zhiyuan; Yamamoto, Masahiro
2014-01-01
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof.
State-Space Modelling of Loudspeakers using Fractional Derivatives
DEFF Research Database (Denmark)
King, Alexander Weider; Agerkvist, Finn T.
2015-01-01
This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...
Fractional Calculus in Hydrologic Modeling: A Numerical Perspective
Energy Technology Data Exchange (ETDEWEB)
David A. Benson; Mark M. Meerschaert; Jordan Revielle
2012-01-01
Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.
International Nuclear Information System (INIS)
Iyiola, O.S.; Tasbozan, O.; Kurt, A.; Çenesiz, Y.
2017-01-01
In this paper, we consider the system of conformable time-fractional Robertson equations with one-dimensional diffusion having widely varying diffusion coefficients. Due to the mismatched nature of the initial and boundary conditions associated with Robertson equation, there are spurious oscillations appearing in many computational algorithms. Our goal is to obtain an approximate solutions of this system of equations using the q-homotopy analysis method (q-HAM) and examine the widely varying diffusion coefficients and the fractional order of the derivative.
Hourly distributions of the diffuse fraction of global solar irradiation in Cordoba (Spain)
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)
2009-02-15
Hourly global irradiations on tilted planes are required for dimensioning PV systems. However, for most sites, only global irradiations on a horizontal plane are available, and, given that to calculate the global irradiation on inclined planes the first step is to determine the diffuse component and this is not collected, we have studied the behaviour of the diffuse component on an hourly basis. Most parametrization models for the derivation of hourly diffuse irradiance from hourly global irradiance involve the clearness index, a parameter that implicitly includes solar altitude. The present paper has focused on the possibility of also including ''mean solar altitude anti {alpha}'' explicitly as a parameter in addition to the clearness index. Several analytical models are proposed, validated and compared here, using solar data collected on our station located in Cordoba (Spain). (author)
Hourly distributions of the diffuse fraction of global solar irradiation in Cordoba (Spain)
International Nuclear Information System (INIS)
Posadillo, R.; Lopez Luque, R.
2009-01-01
Hourly global irradiations on tilted planes are required for dimensioning PV systems. However, for most sites, only global irradiations on a horizontal plane are available, and, given that to calculate the global irradiation on inclined planes the first step is to determine the diffuse component and this is not collected, we have studied the behaviour of the diffuse component on an hourly basis. Most parametrization models for the derivation of hourly diffuse irradiance from hourly global irradiance involve the clearness index, a parameter that implicitly includes solar altitude. The present paper has focused on the possibility of also including 'mean solar altitude α-bar' explicitly as a parameter in addition to the clearness index. Several analytical models are proposed, validated and compared here, using solar data collected on our station located in Cordoba (Spain)
Langlands, T A M; Henry, B I; Wearne, S L
2009-12-01
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.
Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa
2017-12-01
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.
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.
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.
New method dynamically models hydrocarbon fractionation
Energy Technology Data Exchange (ETDEWEB)
Kesler, M.G.; Weissbrod, J.M.; Sheth, B.V. [Kesler Engineering, East Brunswick, NJ (United States)
1995-10-01
A new method for calculating distillation column dynamics can be used to model time-dependent effects of independent disturbances for a range of hydrocarbon fractionation. It can model crude atmospheric and vacuum columns, with relatively few equilibrium stages and a large number of components, to C{sub 3} splitters, with few components and up to 300 equilibrium stages. Simulation results are useful for operations analysis, process-control applications and closed-loop control in petroleum, petrochemical and gas processing plants. The method is based on an implicit approach, where the time-dependent variations of inventory, temperatures, liquid and vapor flows and compositions are superimposed at each time step on the steady-state solution. Newton-Raphson (N-R) techniques are then used to simultaneously solve the resulting finite-difference equations of material, equilibrium and enthalpy balances that characterize distillation dynamics. The important innovation is component-aggregation and tray-aggregation to contract the equations without compromising accuracy. This contraction increases the N-R calculations` stability. It also significantly increases calculational speed, which is particularly important in dynamic simulations. This method provides a sound basis for closed-loop, supervisory control of distillation--directly or via multivariable controllers--based on a rigorous, phenomenological column model.
Analysis of Drude model using fractional derivatives without singular kernels
Directory of Open Access Journals (Sweden)
Jiménez Leonardo Martínez
2017-11-01
Full Text Available We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF, and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.
An inverse problem for a one-dimensional time-fractional diffusion problem
Jin, Bangti
2012-06-26
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L 2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented. © 2012 IOP Publishing Ltd.
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
Jin, B.; Lazarov, R.; Pasciak, J.; Zhou, Z.
2014-01-01
© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
International Nuclear Information System (INIS)
Wang, Wenyan; Han, Bo; Yamamoto, Masahiro
2013-01-01
We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)
Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn
Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han
2018-06-01
We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
Jin, B.
2014-05-30
© 2014 Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. We consider the initial-boundary value problem for an inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data and a nonsmooth right-hand side in a bounded convex polyhedral domain. We analyse two semidiscrete schemes based on the standard Galerkin and lumped mass finite element methods. Almost optimal error estimates are obtained for right-hand side data f (x, t) ε L∞ (0, T; Hq(ω)), ≤1≥ 1, for both semidiscrete schemes. For the lumped mass method, the optimal L2(ω)-norm error estimate requires symmetric meshes. Finally, twodimensional numerical experiments are presented to verify our theoretical results.
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
Total variation regularization for a backward time-fractional diffusion problem
International Nuclear Information System (INIS)
Wang, Liyan; Liu, Jijun
2013-01-01
Consider a two-dimensional backward problem for a time-fractional diffusion process, which can be considered as image de-blurring where the blurring process is assumed to be slow diffusion. In order to avoid the over-smoothing effect for object image with edges and to construct a fast reconstruction scheme, the total variation regularizing term and the data residual error in the frequency domain are coupled to construct the cost functional. The well posedness of this optimization problem is studied. The minimizer is sought approximately using the iteration process for a series of optimization problems with Bregman distance as a penalty term. This iteration reconstruction scheme is essentially a new regularizing scheme with coupling parameter in the cost functional and the iteration stopping times as two regularizing parameters. We give the choice strategy for the regularizing parameters in terms of the noise level of measurement data, which yields the optimal error estimate on the iterative solution. The series optimization problems are solved by alternative iteration with explicit exact solution and therefore the amount of computation is much weakened. Numerical implementations are given to support our theoretical analysis on the convergence rate and to show the significant reconstruction improvements. (paper)
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.
International Nuclear Information System (INIS)
Kunimatsu, Akira; Aoki, Shigeki; Masutani, Yoshitaka; Abe, Osamu; Hayashi, Naoto; Mori, Harushi; Masumoto, Tomohiko; Ohtomo, Kuni
2004-01-01
In order to ensure that three-dimensional diffusion tensor tractography (3D-DTT) of the corticospinal tract (CST), is performed accurately and efficiently, we set out to find the optimal lower threshold of fractional anisotropy (FA) below which tract elongation is terminated (trackability threshold). Thirteen patients with acute or early subacute ischemic stroke causing motor deficits were enrolled in this study. We performed 3D-DTT of the CST with diffusion tensor MR (magnetic resonance) imaging. We segmented the CST and established a cross-section of the CST in a transaxial plane as a region of interest. Thus, we selectively measured the FA values of the right and left corticospinal tracts at the level of the cerebral peduncle, the posterior limb of the internal capsule, and the centrum semiovale. The FA values of the CST were also measured on the affected side at the level where the clinically relevant infarction was present in isotropic diffusion-weighted imaging. 3D-DTT allowed us to selectively measure the FA values of the CST. Among the 267 regions of interest we measured, the minimum FA value was 0.22. The FA values of the CST were smaller and more variable in the centrum semiovale than in the other regions. The mean minus twice the standard deviation of the FA values of the CST in the centrum semiovale was calculated at 0.22 on the normal unaffected side and 0.16 on the affected side. An FA value of about 0.20 was found to be the optimal trackability threshold. (author)
Cusimano, N.; Gerardo-Giorda, L.
2018-06-01
Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain model obtained by replacing the diffusive term of the classical formulation with a fractional power of the operator, defined in the spectral sense. The resulting nonlocal model describes different levels of tissue heterogeneity as the fractional exponent is varied. The numerical method for the solution of the fractional Monodomain relies on an integral representation of the nonlocal operator combined with a finite element discretisation in space, allowing to handle in a natural way bounded domains in more than one spatial dimension. Numerical tests in two spatial dimensions illustrate the features of the model. Activation times, action potential duration and its dispersion throughout the domain are studied as a function of the fractional parameter: the expected peculiar behaviour driven by tissue heterogeneities is recovered.
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
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
International Nuclear Information System (INIS)
Yin Chen; Xu Mingyu
2009-01-01
We set up a one-dimensional mathematical model with a Caputo fractional operator of a drug released from a polymeric matrix that can be dissolved into a solvent. A two moving boundaries problem in fractional anomalous diffusion (in time) with order α element of (0, 1] under the assumption that the dissolving boundary can be dissolved slowly is presented in this paper. The two-parameter regular perturbation technique and Fourier and Laplace transform methods are used. A dimensionless asymptotic analytical solution is given in terms of the Wright function
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
Energy Technology Data Exchange (ETDEWEB)
Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)
2015-07-15
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-07-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
International Nuclear Information System (INIS)
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-01-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series
Table-sized matrix model in fractional learning
Soebagyo, J.; Wahyudin; Mulyaning, E. C.
2018-05-01
This article provides an explanation of the fractional learning model i.e. a Table-Sized Matrix model in which fractional representation and its operations are symbolized by the matrix. The Table-Sized Matrix are employed to develop problem solving capabilities as well as the area model. The Table-Sized Matrix model referred to in this article is used to develop an understanding of the fractional concept to elementary school students which can then be generalized into procedural fluency (algorithm) in solving the fractional problem and its operation.
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.
Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases
Directory of Open Access Journals (Sweden)
Fazal Haq
2017-01-01
Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.
Spiking and bursting patterns of fractional-order Izhikevich model
Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha
2018-03-01
Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.
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.
International Nuclear Information System (INIS)
Koyama, Tetsuo; Ohmura, Takehisa; Miyake, Hiroji; Marumoto, Kohei; Domen, Kazuhisa
2012-01-01
Diffusion tensor imaging (DTI) using a 3.0 tesla magnetic resonance scanner was used to investigate white matter changes caused by idiopathic normal pressure hydrocephalus (INPH) in 10 patients diagnosed by clinical symptoms (gait disturbance, dementia, and/or urinary incontinence) and Evans index >0.3, and compared with findings for 10 age-matched controls (≥60 years). Then, using a computer-automated method, fractional anisotropy (FA) brain maps were generated and finally transformed into the standard space. Voxel-based FA values within two regions of interests (ROIs), the forceps minor and corticospinal tracts, were then separately evaluated. Within each ROI, statistical comparisons of results from the INPH and control groups were performed. In addition, for INPH patients, grading scores for clinical symptoms and FA values were correlated. The forceps minor mean FA value was much smaller for the INPH group (0.504) than for the control group (0.631). The corticospinal tract mean FA value was slightly smaller for the INPH group (0.588) than for the control group (0.632). Additional analyses indicated that lower FA values within the forceps minor tended to be associated with clinical symptoms such as urinary incontinence and gait disturbance. Our findings indicate FA values decreased in the forceps minor of INPH patients. We also found that lower values were associated with severer clinical symptoms, implying that DTI techniques may be developed for more accurate diagnosis. (author)
Directory of Open Access Journals (Sweden)
Inci Cilingir Sungu
2015-01-01
Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.
McCommis, Kyle S.; Koktzoglou, Ioannis; Zhang, Haosen; Goldstein, Thomas A.; Northrup, Benjamin E.; Li, Debiao; Gropler, Robert J.; Zheng, Jie
2010-01-01
Myocardial oxygen extraction fraction (OEF) during hyperemia can be estimated using a double-inversion-recovery (DIR) prepared T2-weighted black-blood sequence. Severe irregular ECG-triggering due to elevated heart rate and/or arrhythmias may render it difficult to adequately suppress the flowing left ventricle blood signal and thus potentially cause errors in the estimates of myocardial OEF. Thus, the goal of this study was to evaluate another black-blood technique, a diffusion-weighted (DW)-prepared TSE sequence for its ability to determine regional myocardial OEF during hyperemia. Control dogs and dogs with acute coronary artery stenosis were imaged with both the DIR- and DW-prepared TSE sequences at rest and during either dipyridamole or dobutamine hyperemia. Validation of MRI OEF estimates was performed using blood sampling from the artery and coronary sinus in control dogs. The two methods showed comparable correlations with blood sampling results (R2 = 0.9). Similar OEF estimations for all dogs were observed except for the group of dogs with severe coronary stenosis during dobutamine stress. In these dogs, the DW method provided more physiologically reasonable OEF (hyperemic OEF = 0.75 ± 0.08 vs resting OEF of 0.6) than the DIR method (hyperemic OEF = 0.56 ± 0.10). DW-preparation may be a valuable alternative for more accurate oxygenation measurements during irregular ECG-triggering. PMID:20512871
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.
Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie
2014-01-01
It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
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
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.
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.)
A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics
Lei, Dong; Liang, Yingjie; Xiao, Rui
2018-01-01
We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.
Inference on the hurst parameter and the variance of diffusions driven by fractional Brownian motion
Berzin, Corinne; León, José R
2014-01-01
This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered. It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools, and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations. Concerning the proofs of the limit theorems, the “Fourth Moment Theorem” is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proof...
Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong
2018-05-01
This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.
The fractional volatility model: An agent-based interpretation
Vilela Mendes, R.
2008-06-01
Based on the criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are reviewed and extended to account for leverage effects. Using agent-based models, one tries to find which agent strategies and (or) properties of the financial institutions might be responsible for the features of the fractional volatility model.
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ-stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α. We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ-stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
Nezhadhaghighi, Mohsen Ghasemi
2017-08-01
Here, we present results of numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy-tailed probability distribution functions. Assuming that the distribution function of the random fluctuations obeys Lévy statistics with a power-law scaling exponent, we investigate the fractional diffusion equation in the presence of μ -stable Lévy noise. We study the scaling properties of the global width and two-point correlation functions and then compare the analytical and numerical results for the growth exponent β and the roughness exponent α . We also investigate the fractional Fokker-Planck equation for heavy-tailed random fluctuations. We show that the fractional diffusion processes in the presence of μ -stable Lévy noise display special scaling properties in the probability distribution function (PDF). Finally, we numerically study the scaling properties of the heavy-tailed random fluctuations by using the diffusion entropy analysis. This method is based on the evaluation of the Shannon entropy of the PDF generated by the random fluctuations, rather than on the measurement of the global width of the process. We apply the diffusion entropy analysis to extract the growth exponent β and to confirm the validity of our numerical analysis.
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
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
Yang, Xu; Cao, Ding; Liang, Xiumei; Zhao, Jiannong
2017-07-01
Several studies have examined the relationships between diffusion tensor imaging (DTI)-measured fractional anisotropy (FA) and the symptoms of schizophrenia, but results vary across the studies. The aim of this study was to carry out a meta-analysis of correlation coefficients reported by relevant studies to evaluate the correlative relationships between FA of various parts of the brain and schizophrenia symptomatic assessments. Literature was searched in several electronic databases, and study selection was based on précised eligibility criteria. Correlation coefficients between FA of a part of the brain and schizophrenia symptom were first converted into Fisher's z-scores for meta-analyses, and then overall effect sizes were back transformed to correlation coefficients. Thirty-three studies (1121 schizophrenia patients; age 32.66 years [95% confidence interval (CI) 30.19, 35.13]; 65.95 % [57.63, 74.28] males) were included in this meta-analysis. Age was inversely associated with brain FA (z-scores [95% CI] -0.23 [-0.14, -0.32]; p ˂ 0.00001). Brain FA of various areas was inversely associated with negative symptoms of schizophrenia (z-score -0.30 [-0.23, -0.36]; p ˂ 0.00001) but was positively associated with positive symptoms of schizophrenia (z-score 0.16 [0.04, 0.27]; p = 0.007) and general psychopathology of schizophrenia (z-score 0.26 [0.15, 0.37]; p = 0.00001). Although, DTI-measured brain FA is found to be inversely associated with negative symptoms and positively associated with positive symptoms and general psychopathology of schizophrenia, the effect sizes of these correlations are low and may not be clinically significant. Moreover, brain FA was also negatively associated with age of patients.
International Nuclear Information System (INIS)
Yang, Xu; Cao, Ding; Liang, Xiumei; Zhao, Jiannong
2017-01-01
Several studies have examined the relationships between diffusion tensor imaging (DTI)-measured fractional anisotropy (FA) and the symptoms of schizophrenia, but results vary across the studies. The aim of this study was to carry out a meta-analysis of correlation coefficients reported by relevant studies to evaluate the correlative relationships between FA of various parts of the brain and schizophrenia symptomatic assessments. Literature was searched in several electronic databases, and study selection was based on precised eligibility criteria. Correlation coefficients between FA of a part of the brain and schizophrenia symptom were first converted into Fisher's z-scores for meta-analyses, and then overall effect sizes were back transformed to correlation coefficients. Thirty-three studies (1121 schizophrenia patients; age 32.66 years [95% confidence interval (CI) 30.19, 35.13]; 65.95 % [57.63, 74.28] males) were included in this meta-analysis. Age was inversely associated with brain FA (z-scores [95% CI] -0.23 [-0.14, -0.32]; p %<0.00001). Brain FA of various areas was inversely associated with negative symptoms of schizophrenia (z-score -0.30 [-0.23, -0.36]; p %<0.00001) but was positively associated with positive symptoms of schizophrenia (z-score 0.16 [0.04, 0.27]; p = 0.007) and general psychopathology of schizophrenia (z-score 0.26 [0.15, 0.37]; p = 0.00001). Although, DTI-measured brain FA is found to be inversely associated with negative symptoms and positively associated with positive symptoms and general psychopathology of schizophrenia, the effect sizes of these correlations are low and may not be clinically significant. Moreover, brain FA was also negatively associated with age of patients. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Yang, Xu [Chongqing Medical University, Department of Medical Imaging, Second Affiliated Hospital, Chongqing (China); Fifth People' s Hospital of Chongqing, Department of Medical Imaging, Chongqing (China); Cao, Ding [Chongqing Medical University, Department of Hepatobiliary Surgery, Second Affiliated Hospital, Chongqing (China); Liang, Xiumei [Fifth People' s Hospital of Chongqing, Department of Medical Imaging, Chongqing (China); Zhao, Jiannong [Chongqing Medical University, Department of Medical Imaging, Second Affiliated Hospital, Chongqing (China)
2017-07-15
Several studies have examined the relationships between diffusion tensor imaging (DTI)-measured fractional anisotropy (FA) and the symptoms of schizophrenia, but results vary across the studies. The aim of this study was to carry out a meta-analysis of correlation coefficients reported by relevant studies to evaluate the correlative relationships between FA of various parts of the brain and schizophrenia symptomatic assessments. Literature was searched in several electronic databases, and study selection was based on precised eligibility criteria. Correlation coefficients between FA of a part of the brain and schizophrenia symptom were first converted into Fisher's z-scores for meta-analyses, and then overall effect sizes were back transformed to correlation coefficients. Thirty-three studies (1121 schizophrenia patients; age 32.66 years [95% confidence interval (CI) 30.19, 35.13]; 65.95 % [57.63, 74.28] males) were included in this meta-analysis. Age was inversely associated with brain FA (z-scores [95% CI] -0.23 [-0.14, -0.32]; p %<0.00001). Brain FA of various areas was inversely associated with negative symptoms of schizophrenia (z-score -0.30 [-0.23, -0.36]; p %<0.00001) but was positively associated with positive symptoms of schizophrenia (z-score 0.16 [0.04, 0.27]; p = 0.007) and general psychopathology of schizophrenia (z-score 0.26 [0.15, 0.37]; p = 0.00001). Although, DTI-measured brain FA is found to be inversely associated with negative symptoms and positively associated with positive symptoms and general psychopathology of schizophrenia, the effect sizes of these correlations are low and may not be clinically significant. Moreover, brain FA was also negatively associated with age of patients. (orig.)
Large deflection of viscoelastic beams using fractional derivative model
International Nuclear Information System (INIS)
Bahranini, Seyed Masoud Sotoodeh; Eghtesad, Mohammad; Ghavanloo, Esmaeal; Farid, Mehrdad
2013-01-01
This paper deals with large deflection of viscoelastic beams using a fractional derivative model. For this purpose, a nonlinear finite element formulation of viscoelastic beams in conjunction with the fractional derivative constitutive equations has been developed. The four-parameter fractional derivative model has been used to describe the constitutive equations. The deflected configuration for a uniform beam with different boundary conditions and loads is presented. The effect of the order of fractional derivative on the large deflection of the cantilever viscoelastic beam, is investigated after 10, 100, and 1000 hours. The main contribution of this paper is finite element implementation for nonlinear analysis of viscoelastic fractional model using the storage of both strain and stress histories. The validity of the present analysis is confirmed by comparing the results with those found in the literature.
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...
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....
Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro
2018-01-01
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion L...
A void fraction model for annular two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Tandon, T.N.; Gupta, C.P.; Varma, H.K.
1985-01-01
An analytical model has been developed for predicting void fraction in two-phase annular flow. In the analysis, the Lockhart-Martinelli method has been used to calculate two-phase frictional pressure drop and von Karman's universal velocity profile is used to represent the velocity distribution in the annular liquid film. Void fractions predicted by the proposed model are generally in good agreement with a available experimental data. This model appears to be as good as Smith's correlation and better than the Wallis and Zivi correlations for computing void fraction.
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
Fractional-order in a macroeconomic dynamic model
David, S. A.; Quintino, D. D.; Soliani, J.
2013-10-01
In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.
DEFF Research Database (Denmark)
Rolle, Massimo; Jin, Biao
2017-01-01
and toluene. Multitracer experiments were carried out in 1-D gel dissection tubes and in a quasi-2-D flow-through porous medium. The experiments allowed us to simultaneously and directly compare the diffusive and dispersive behavior of benzene and toluene. We observed an unexpected, opposite behavior...... of the two monoaromatic hydrocarbons. Toluene showed a normal diffusive isotope effect (DC7D8/DC7H8 = 0.96) with enrichment of the nondeuterated isotopologue in the direction of the diffusive and transverse dispersive fluxes. Conversely, the measured trends for benzene indicate inverse diffusive...
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
Tempered fractional time series model for turbulence in geophysical flows
Meerschaert, Mark M.; Sabzikar, Farzad; Phanikumar, Mantha S.; Zeleke, Aklilu
2014-09-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model.
Tempered fractional time series model for turbulence in geophysical flows
International Nuclear Information System (INIS)
Meerschaert, Mark M; Sabzikar, Farzad; Phanikumar, Mantha S; Zeleke, Aklilu
2014-01-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model. (paper)
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.
Application of Integer and Fractional Models in Electrochemical Systems
Directory of Open Access Journals (Sweden)
Isabel S. Jesus
2012-01-01
Full Text Available This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.
Genetic Analysis of Cortical Thickness and Fractional Anisotropy of Water Diffusion in the Brain
Directory of Open Access Journals (Sweden)
Peter eKochunov
2011-10-01
Full Text Available ObjectivesThe thickness of the brain’s cortical gray matter (GM and the fractional anisotropy (FA of the cerebral white matter (WM each follow an inverted U-shape trajectory with age. Both measures are positively correlated, suggesting a common biological mechanism. We employed bivariate genetic analyses to localize quantitative trait loci (QTLs and individual genes acting pleiotropically upon these phenotypes.MethodsWhole-brain and regional GM thickness and FA values were measured from high-resolution anatomical (0.8mm isotropic and diffusion tensor MR images (1.7x1.7x3.0mm, 55 directions collected for 712 active participants (274/438 male/females, age=47.9±13.2years in the Genetics of Brain Structure study.ResultsBivariate, whole-genome quantitative trait loci (QTL analyses of the whole brain measures localized significant (LOD≥3.0 QTLs within chromosome region 15q22-23. More detailed localization was achieved using single nuclear polymorphism (SNP association and gene expression analyses. No significant association (p<510-5 was observed for 1565 SNPs located within the QTLs. However, post-hoc analysis indicated that 40% of the potentially significant (p≤10-3 polymorphisms were localized to the RORA and NARG2 genes. A potentially significant association (p=310-4 was also observed for the rs2456930 polymorphism that was previously reported as a significant GWAS finding in ADNI subjects. Lymphocyte expression measurements for two genes, located under QTL, RORA and ADAM10 were significantly (p<0.05 correlated with both FA and GM thickness values. Expression measurements for NARG2 was significantly correlated with GM thickness (p<0.05 but failed to show a significant correlation (p=0.09 with FA.Discussion This study identified a novel, significant QTL at 15q22-23. SNP association and correlation with gene-expression analyses indicated that RORA, NARG2 and ADAM10 jointly influence GM thickness and cerebral WM integrity.
Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling
International Nuclear Information System (INIS)
Burnecki, Krzysztof; Weron, Aleksander
2014-01-01
In this survey paper we present a systematic methodology which demonstrates how to identify the origins of fractional dynamics. We consider three mechanisms which lead to it, namely fractional Brownian motion, fractional Lévy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices A–F. Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data. (paper)
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem
2014-01-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity
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.
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.
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...
Fractional and multivariable calculus model building and optimization problems
Mathai, A M
2017-01-01
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...
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
On an Estimation Method for an Alternative Fractionally Cointegrated Model
DEFF Research Database (Denmark)
Carlini, Federico; Łasak, Katarzyna
In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following th...
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.)
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)
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
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
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1......,...,X_{T} given the initial values X_{-n}, n=0,1,..., as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to all previous work where it is assumed that initial values are zero. For the statistical analysis we assume...... the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including...
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...
Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.
Chen, Duan
2017-11-01
In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.
Moyes, Andrew B; Gaines, Sarah J; Siegwolf, Rolf T W; Bowling, David R
2010-11-01
Carbon isotope ratios (δ¹³C) of heterotrophic and rhizospheric sources of soil respiration under deciduous trees were evaluated over two growing seasons. Fluxes and δ¹³C of soil respiratory CO₂ on trenched and untrenched plots were calculated from closed chambers, profiles of soil CO₂ mole fraction and δ¹³C and continuous open chambers. δ¹³C of respired CO₂ and bulk carbon were measured from excised leaves and roots and sieved soil cores. Large diel variations (>5‰) in δ¹³C of soil respiration were observed when diel flux variability was large relative to average daily fluxes, independent of trenching. Soil gas transport modelling supported the conclusion that diel surface flux δ¹³C variation was driven by non-steady state gas transport effects. Active roots were associated with high summertime soil respiration rates and around 1‰ enrichment in the daily average δ¹³C of the soil surface CO₂ flux. Seasonal δ¹³C variability of about 4‰ (most enriched in summer) was observed on all plots and attributed to the heterotrophic CO₂ source. © 2010 Blackwell Publishing Ltd.
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
Kailasanathan, Ranjith Kumar Abhinavam
2014-05-20
Soot surface temperature and volume fraction are measured in ethylene/air coflowing laminar diffusion flames at high pressures, diluted with one of four diluents (argon, helium, nitrogen, and carbon dioxide) using a two-color technique. Both temperature and soot measurements presented are line-of-sight averages. The results aid in understanding the kinetic and thermodynamic behavior of the soot formation and oxidation chemistry with changes in diluents, ultimately leading to possible methods of reducing soot emission from practical combustion hardware. The diluted fuel and coflow exit velocities (top-hat profiles) were matched at all pressures to minimize shear effects. In addition to the velocity-matched flow rates, the mass fluxes were held constant for all pressures. Addition of a diluent has a pronounced effect on both the soot surface temperature and volume fraction, with the helium diluted flame yielding the maximum and carbon dioxide diluted flame yielding minimum soot surface temperature and volume fraction. At low pressures, peak soot volume fraction exists at the tip of the flame, and with an increase in pressure, the location shifts lower to the wings of the flame. Due to the very high diffusivity of helium, significantly higher temperature and volume fraction are measured and explained. Carbon dioxide has the most dramatic soot suppression effect. By comparing the soot yield with previously measured soot precursor concentrations in the same flame, it is clear that the lower soot yield is a result of enhanced oxidation rates rather than a reduction in precursor formation. Copyright © 2014 Taylor & Francis Group, LLC.
Tayebi, A.; Shekari, Y.; Heydari, M. H.
2017-07-01
Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.
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)
An approximate fractional Gaussian noise model with computational cost
Sø rbye, Sigrunn H.; Myrvoll-Nilsen, Eirik; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood
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)
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
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.
Energy Technology Data Exchange (ETDEWEB)
Surova, Yulia; Widner, Haakan [Lund University, Department of Clinical Sciences, Lund (Sweden); Skaane University Hospital, Department of Neurology, Lund (Sweden); Nilsson, Markus [Skaane University Hospital, Center for Medical Imaging and Physiology, Lund (Sweden); Lampinen, Bjoern [Lund University, Lund University Bioimaging Center, Lund (Sweden); Laett, Jimmy [Lund University, Department of Medical Radiation Physics, Lund (Sweden); Hall, Sara; Hansson, Oskar [Lund University, Department of Clinical Sciences, Malmoe (Sweden); Skaane University Hospital, Memory Clinic, Lund (Sweden); Westen, Danielle van [Lund University, Department of Clinical Sciences, Lund (Sweden); Lund University, Lund University Bioimaging Center, Lund (Sweden)
2018-03-15
In Parkinson's disease (PD), pathological microstructural changes occur that may be detected using diffusion magnetic resonance imaging (dMRI). However, there are few longitudinal studies that explore the effect of disease progression on diffusion indices. We prospectively included 76 patients with PD and 38 healthy controls (HC), all of whom underwent diffusion kurtosis imaging (DKI) as part of the prospective Swedish BioFINDER study at baseline and 2 years later. Annualized rates of change in DKI parameters, including fractional anisotropy (FA), mean diffusivity (MD), and mean kurtosis (MK), were estimated in the gray matter (GM) by placing regions of interest (ROIs) in the basal ganglia and the thalamus, and in the white matter (WM) by tract-based spatial statistics (TBSS) analysis. When adjusting for potential confounding factors (age, gender, baseline-follow-up interval, and software upgrade of MRI scanner), only a decrease in FA in the putamen of PD patients (β = - 0.248, P <.01) over 2 years was significantly different from the changes observed in HC over the same time period. This 2-year decrease in FA in the putamen in PD correlated with higher l-dopa equivalent dose at baseline (Spearman's rho =.399, P <.0001). The study indicates that in PD microstructural changes in the putamen occur selectively over a 2-year period and can be detected with DKI. (orig.)
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.
Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro
2017-05-01
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.
Directory of Open Access Journals (Sweden)
Treena Basu
2015-10-01
Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.
Energy Technology Data Exchange (ETDEWEB)
Katsuya, Tomoo; Inoue, Tomio; Ishizaka, Hiroshi; Aoki, Jun; Endo, Keigo [Gunma Univ., Maebashi (Japan). School of Medicine
2000-10-01
To clarify the contrast-enhancement pattern of the normal hematopoietic element by isolating the signal of the water fraction in vertebral bone marrow and to investigate whether this approach can be used to characterize bone marrow pathology in several diffuse bone marrow diseases. Two groups were examined: 30 normal healthy volunteers and 19 patients with primary diffuse bone marrow disease (aplastic anemia [n=8], myelodysplastic syndrome (MDS) [n=5], chronic myelogenic leukemia (CML) [n=4], polycythemia vera [n=2]). Isolation of the signal of hematopoietic tissue was done by the chemical-shift misregistration effect. Twenty consecutive T1-weighted midsagittal lumber vertebral images were obtained immediately after the intravenous administration of Gd-DTPA of 0.1 mmol/kg body weight, and the pattern of the time-intensity curve, the peak contrast-enhancement (CE) ratio, and the washout rate (%/min) of bone marrow in normal volunteers were compared with those in patients suffering from primary diffuse bone marrow disease. The pattern of the time-intensity curve of patients with aplastic anemia showed a low peak value followed by a slow washout. However, the pattern of time-intensity curves in patients with MDS, CML, and polycythemia vera was similar to that of normal volunteers. The peak CE ratio of the water fraction in normal marrow ranged from 0.45 to 1.26 (mean {+-}S.D.: 0.87{+-}0.18). Patients with aplastic anemia showed an abnormally lower peak CE ratio of the water fraction (mean {+-}S.D.: 0.34{+-}0.19, p<0.0001). On the other hand, the peak CE ratio of the water fraction in patients with MDS was significantly higher than that of normal volunteers (mean {+-}S.D. 1.35{+-}0.39, p<0.05). In contrast, the peak CE ratio of patients with CML or polycythemia vera did not differ significantly from that of normal volunteers. The mean washout rate of patients with aplastic anemia was significantly lower than that of normal volunteers (mean {+-}S.D.: 3.50{+-}2.51 %/min
International Nuclear Information System (INIS)
Katsuya, Tomoo; Inoue, Tomio; Ishizaka, Hiroshi; Aoki, Jun; Endo, Keigo
2000-01-01
To clarify the contrast-enhancement pattern of the normal hematopoietic element by isolating the signal of the water fraction in vertebral bone marrow and to investigate whether this approach can be used to characterize bone marrow pathology in several diffuse bone marrow diseases. Two groups were examined: 30 normal healthy volunteers and 19 patients with primary diffuse bone marrow disease (aplastic anemia [n=8], myelodysplastic syndrome (MDS) [n=5], chronic myelogenic leukemia (CML) [n=4], polycythemia vera [n=2]). Isolation of the signal of hematopoietic tissue was done by the chemical-shift misregistration effect. Twenty consecutive T1-weighted midsagittal lumber vertebral images were obtained immediately after the intravenous administration of Gd-DTPA of 0.1 mmol/kg body weight, and the pattern of the time-intensity curve, the peak contrast-enhancement (CE) ratio, and the washout rate (%/min) of bone marrow in normal volunteers were compared with those in patients suffering from primary diffuse bone marrow disease. The pattern of the time-intensity curve of patients with aplastic anemia showed a low peak value followed by a slow washout. However, the pattern of time-intensity curves in patients with MDS, CML, and polycythemia vera was similar to that of normal volunteers. The peak CE ratio of the water fraction in normal marrow ranged from 0.45 to 1.26 (mean ±S.D.: 0.87±0.18). Patients with aplastic anemia showed an abnormally lower peak CE ratio of the water fraction (mean ±S.D.: 0.34±0.19, p<0.0001). On the other hand, the peak CE ratio of the water fraction in patients with MDS was significantly higher than that of normal volunteers (mean ±S.D. 1.35±0.39, p<0.05). In contrast, the peak CE ratio of patients with CML or polycythemia vera did not differ significantly from that of normal volunteers. The mean washout rate of patients with aplastic anemia was significantly lower than that of normal volunteers (mean ±S.D.: 3.50±2.51 %/min vs. 7.13±1
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
Asymptotic solutions of diffusion models for risk reserves
Directory of Open Access Journals (Sweden)
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.
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.
Model for radial gas fraction profiles in vertical pipe flow
International Nuclear Information System (INIS)
Lucas, D.; Krepper, E.; Prasser, H.M.
2001-01-01
A one-dimensional model is presented, which predicts the radial volume fraction profiles from a given bubble size distribution. It bases on the assumption of an equilibrium of the forces acting on a bubble perpendicularly to the flow path (non drag forces). For the prediction of the flow pattern this model could be used within an procedure together with appropriate models for local bubble coalescence and break-up. (orig.)
Likelihood inference for a fractionally cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2012-01-01
such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order is possible. We define the statistical model by 0inference when the true values satisfy b0¿1/2 and d0-b0......We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters...... process in the parameters when errors are i.i.d. with suitable moment conditions and initial values are bounded. When the limit is deterministic this implies uniform convergence in probability of the conditional likelihood function. If the true value b0>1/2, we prove that the limit distribution of (ß...
Inter-fraction variations in respiratory motion models
Energy Technology Data Exchange (ETDEWEB)
McClelland, J R; Modat, M; Ourselin, S; Hawkes, D J [Centre for Medical Image Computing, University College London (United Kingdom); Hughes, S; Qureshi, A; Ahmad, S; Landau, D B, E-mail: j.mcclelland@cs.ucl.ac.uk [Department of Oncology, Guy' s and St Thomas' s Hospitals NHS Trust, London (United Kingdom)
2011-01-07
Respiratory motion can vary dramatically between the planning stage and the different fractions of radiotherapy treatment. Motion predictions used when constructing the radiotherapy plan may be unsuitable for later fractions of treatment. This paper presents a methodology for constructing patient-specific respiratory motion models and uses these models to evaluate and analyse the inter-fraction variations in the respiratory motion. The internal respiratory motion is determined from the deformable registration of Cine CT data and related to a respiratory surrogate signal derived from 3D skin surface data. Three different models for relating the internal motion to the surrogate signal have been investigated in this work. Data were acquired from six lung cancer patients. Two full datasets were acquired for each patient, one before the course of radiotherapy treatment and one at the end (approximately 6 weeks later). Separate models were built for each dataset. All models could accurately predict the respiratory motion in the same dataset, but had large errors when predicting the motion in the other dataset. Analysis of the inter-fraction variations revealed that most variations were spatially varying base-line shifts, but changes to the anatomy and the motion trajectories were also observed.
Towards a deterministic KPZ equation with fractional diffusion: the stationary problem
Abdellaoui, Boumediene; Peral, Ireneo
2018-04-01
In this work, we investigate by analysis the possibility of a solution to the fractional quasilinear problem: where is a bounded regular domain ( is sufficient), , 1 2s. The authors were partially supported by Ministerio de Economia y Competitividad under grants MTM2013-40846-P and MTM2016-80474-P (Spain).
Fractional calculus model of electrical impedance applied to human skin.
Vosika, Zoran B; Lazovic, Goran M; Misevic, Gradimir N; Simic-Krstic, Jovana B
2013-01-01
Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1) Weyl fractional derivative operator, 2) Cole equation, and 3) Constant Phase Element (CPE). These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Fractional calculus model of electrical impedance applied to human skin.
Directory of Open Access Journals (Sweden)
Zoran B Vosika
Full Text Available Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1 Weyl fractional derivative operator, 2 Cole equation, and 3 Constant Phase Element (CPE. These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
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.
Carasso, Alfred S; Vladár, András E
2012-01-01
Helium ion microscopes (HIM) are capable of acquiring images with better than 1 nm resolution, and HIM images are particularly rich in morphological surface details. However, such images are generally quite noisy. A major challenge is to denoise these images while preserving delicate surface information. This paper presents a powerful slow motion denoising technique, based on solving linear fractional diffusion equations forward in time. The method is easily implemented computationally, using fast Fourier transform (FFT) algorithms. When applied to actual HIM images, the method is found to reproduce the essential surface morphology of the sample with high fidelity. In contrast, such highly sophisticated methodologies as Curvelet Transform denoising, and Total Variation denoising using split Bregman iterations, are found to eliminate vital fine scale information, along with the noise. Image Lipschitz exponents are a useful image metrology tool for quantifying the fine structure content in an image. In this paper, this tool is applied to rank order the above three distinct denoising approaches, in terms of their texture preserving properties. In several denoising experiments on actual HIM images, it was found that fractional diffusion smoothing performed noticeably better than split Bregman TV, which in turn, performed slightly better than Curvelet denoising.
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
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.
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...
Fiege, A.; Ruprecht, P.; Simon, A. C.; Holtz, F.
2017-12-01
Mafic magma recharge is a common process that triggers physical and chemical mixing in magmatic systems and drives their evolution, resulting in, e.g., hybridization and volcanic eruptions. Once magma-magma contact is initiated, rapid heat-flux commonly leads to the formation of a cooling-induced crystal mush on the mafic side of the interface. Here, on a local scale (µm to cm), at the magma-magma interface, melt-melt diffusive exchange is required to approach equilibrium. Significant chemical potential gradients drive a complex, multi-element mass flux between the two systems (Liang, 2010). This diffusive-equilibration often controls crystal dissolution rates within the boundary layers and, thus, the formation of interconnected melt or fluid networks. Such networks provide important pathways for the transport of volatiles and trace metals from the mafic recharge magma to the felsic host magma, where the latter may feed volcanic activities and ore deposits. While major element diffusion in silicate melts is mostly well understood, even in complex systems, the available data for many trace element metals are limited (Liang, 2010; Zhang et al., 2010). Differences in diffusivity in a dynamic, mixing environment can cause trace element fractionation, in particular during crystallization and volatile exsolution and separation. This may affect trace element signatures in phenocrysts and magmatic volatile phases that can form near a magma-magma boundary. As a result, the chemistry of volcanic gases and magmatic-hydrothermal ore deposits may be partially controlled by such mixing phenomena. We performed melt-melt diffusion-couple experiments at 150 MPa, 1100°C, FMQ, FMQ+1 and FMQ+3 (FMQ: fayalite-magnetite-quartz oxygen fugacity buffer). Hydrated, sulfur-bearing cylinders of dacite and basaltic andesite were equilibrated for up to 20 h. Major and trace element gradients were measured by using laser-ablation ICP-MS and electron microprobe analyses. The results we will
International Nuclear Information System (INIS)
Huisman, Thierry A.G.M.; Loenneker, Thomas; Barta, Gerd; Bellemann, Matthias E.; Hennig, Juergen; Fischer, Joachim E.; Il'yasov, Kamil A.
2006-01-01
The objectives were to study the ''impact'' of the magnetic field strength on diffusion tensor imaging (DTI) metrics and also to determine whether magnetic-field-related differences in T2-relaxation times of brain tissue influence DTI measurements. DTI was performed on 12 healthy volunteers at 1.5 and 3.0 Tesla (within 2 h) using identical DTI scan parameters. Apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values were measured at multiple gray and white matter locations. ADC and FA values were compared and analyzed for statistically significant differences. In addition, DTI measurements were performed at different echo times (TE) for both field strengths. ADC values for gray and white matter were statistically significantly lower at 3.0 Tesla compared with 1.5 Tesla (% change between -1.94% and -9.79%). FA values were statistically significantly higher at 3.0 Tesla compared with 1.5 Tesla (% change between +4.04 and 11.15%). ADC and FA values are not significantly different for TE=91 ms and TE=125 ms. Thus, ADC and FA values vary with the used field strength. Comparative clinical studies using ADC or FA values should consequently compare ADC or FA results with normative ADC or FA values that have been determined for the field strength used. (orig.)
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
Zimmer, L.; Pereira, F.M.; van Oijen, J.A.; de Goey, L.P.H.
2017-01-01
A numerical model is developed aiming at investigating soot formation in ethylene counterflow diffusion flames. The mass and energy coupling between soot solid particles and gas-phase species is investigated in detail. A semi-empirical two-equation model is chosen for predicting soot mass fraction
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
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.
Modeling and analysis of fractional order DC-DC converter.
Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher
2017-07-11
Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
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)
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
Mathematical modeling of fish burger baking using fractional calculus
Directory of Open Access Journals (Sweden)
Bainy Eduarda M.
2017-01-01
Full Text Available Tilapia (Oreochromis sp. is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electrical oven with forced heat convection at 150ºC. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a nonlinear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91±0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control and economic optimization studies of the baking process can be conducted.
Experimental studies and model analysis of noble gas fractionation in porous media
Ding, Xin; Kennedy, B. Mack.; Evans, William C.; Stonestrom, David A.
2016-01-01
The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO2 was injected at the base of the column, providing a series of constant CO2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth-dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 ´ 10−11 m2), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO2 and atmospheric noble gases across a range of CO2 flux from ?700 to 10,000 g m−2 d−1. The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi-component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non-conserved (CO2) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.
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...
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
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.
Non-exponential extinction of radiation by fractional calculus modelling
International Nuclear Information System (INIS)
Casasanta, G.; Ciani, D.; Garra, R.
2012-01-01
Possible deviations from exponential attenuation of radiation in a random medium have been recently studied in several works. These deviations from the classical Beer-Lambert law were justified from a stochastic point of view by Kostinski (2001) . In his model he introduced the spatial correlation among the random variables, i.e. a space memory. In this note we introduce a different approach, including a memory formalism in the classical Beer-Lambert law through fractional calculus modelling. We find a generalized Beer-Lambert law in which the exponential memoryless extinction is only a special case of non-exponential extinction solutions described by Mittag-Leffler functions. We also justify this result from a stochastic point of view, using the space fractional Poisson process. Moreover, we discuss some concrete advantages of this approach from an experimental point of view, giving an estimate of the deviation from exponential extinction law, varying the optical depth. This is also an interesting model to understand the meaning of fractional derivative as an instrument to transmit randomness of microscopic dynamics to the macroscopic scale.
Seo, Nieun; Chung, Yong Eun; Park, Yung Nyun; Kim, Eunju; Hwang, Jinwoo; Kim, Myeong-Jin
2018-07-01
To compare the ability of diffusion-weighted imaging (DWI) parameters acquired from three different models for the diagnosis of hepatic fibrosis (HF). Ninety-five patients underwent DWI using nine b values at 3 T magnetic resonance. The hepatic apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ) and perfusion fraction (f) from a biexponential model, and the distributed diffusion coefficient (DDC) and intravoxel heterogeneity index (α) from a stretched exponential model were compared with the pathological HF stage. For the stretched exponential model, parameters were also obtained using a dataset of six b values (DDC # , α # ). The diagnostic performances of the parameters for HF staging were evaluated with Obuchowski measures and receiver operating characteristics (ROC) analysis. The measurement variability of DWI parameters was evaluated using the coefficient of variation (CoV). Diagnostic accuracy for HF staging was highest for DDC # (Obuchowski measures, 0.770 ± 0.03), and it was significantly higher than that of ADC (0.597 ± 0.05, p bi-exponential DWI model • Acquisition of six b values is sufficient to obtain accurate DDC and α.
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...
Li, Gui Dian; Liang, Ying Yin; Xu, Ping; Ling, Jian; Chen, Ying Ming
2016-04-01
The purpose of this study is to investigate the correlation of apparent diffusion coefficient (ADC) and fractional anisotropy (FA) values with fatty infiltration in the thigh muscles of patients with Duchenne muscular dystrophy (DMD) using diffusion-tensor imaging (DTI). Twenty-one boys with DMD were recruited. The grade of fatty infiltration and the ADC and FA values of four thigh muscles (rectus femoris, semitendinosus, sartorius, and gracilis) were measured, and the FA and ADC values were compared with the grade of fatty infiltration. Twenty age-matched healthy boys were enrolled as the control group. The differences in the ADC and FA values of the thigh muscles between patients with DMD and the control group were compared. The patients with DMD showed lower FA values and higher ADC values in all measured muscles when compared with the control group. The FA and ADC values were correlated with the grade of fatty infiltration. For the rectus femoris muscle, r = -0.753 and p = 0.007 for FA, and r = 0.685 and p = 0.001 for ADC. For the semitendinosus muscle, r = -0.621 and p = 0.041 for FA, and r = 0.705 and p = 0.021 for ADC. For the sartorius muscle, r = -0.662 and p = 0.027 for FA, and r = 0.701 and p = 0.017 for ADC. For the gracilis muscle, r = -0.618 and p = 0.043 for FA, and r = 0.695 and p = 0.022 for ADC. Damage to the thigh muscles in patients with DMD can be detected by ADC and FA values using DTI. DTI can be used to assess the severity of the disease.
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
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
Directory of Open Access Journals (Sweden)
Tobias Engelhorn
2012-01-01
Full Text Available Purpose of this study was to evaluate with diffusion-tensor imaging (DTI changes of radial diffusivity (RD and fractional anisotropy (FA in the optic nerve (ON and optic radiation (OR in glaucoma and to determine whether changes in RD and FA correlate with disease severity. Therefore, glaucoma patients and controls were examined using 3T. Regions of interest were positioned on RD and FA maps, and mean values were calculated for ON and OR and correlated with optic nerve atrophy and reduced spatial-temporal contrast sensitivity (STCS of the retina. We found, that RD in glaucoma patients was significantly higher in the ON (0.74 ± 0.21 versus 0.58 ± 0.17⋅10−3 mm2 s−1; P0.77. In conclusion, DTI at 3 Tesla allows robust RD and FA measurements in the ON and OR. Hereby, the extent of RD increase and FA decrease in glaucoma correlate with established ophthalmological examinations.
Moore, Emma; Schaefer, Rebecca S; Bastin, Mark E; Roberts, Neil; Overy, Katie
2017-08-01
Auditory cues are frequently used to support movement learning and rehabilitation, but the neural basis of this behavioural effect is not yet clear. We investigated the microstructural neuroplasticity effects of adding musical cues to a motor learning task. We hypothesised that music-cued, left-handed motor training would increase fractional anisotropy (FA) in the contralateral arcuate fasciculus, a fibre tract connecting auditory, pre-motor and motor regions. Thirty right-handed participants were assigned to a motor learning condition either with (Music Group) or without (Control Group) musical cues. Participants completed 20minutes of training three times per week over four weeks. Diffusion tensor MRI and probabilistic neighbourhood tractography identified FA, axial (AD) and radial (RD) diffusivity before and after training. Results revealed that FA increased significantly in the right arcuate fasciculus of the Music group only, as hypothesised, with trends for AD to increase and RD to decrease, a pattern of results consistent with activity-dependent increases in myelination. No significant changes were found in the left ipsilateral arcuate fasciculus of either group. This is the first evidence that adding musical cues to movement learning can induce rapid microstructural change in white matter pathways in adults, with potential implications for therapeutic clinical practice. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
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
A holographic model for the fractional quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Lippert, Matthew [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, 1090GL Amsterdam (Netherlands); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo,Kashiwa, Chiba 277-8568 (Japan); Taliotis, Anastasios [Theoretische Natuurkunde, Vrije Universiteit Brussel andThe International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-01-08
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ{sub 0}(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2,ℤ)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2,ℤ) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
A holographic model for the fractional quantum Hall effect
Lippert, Matthew; Meyer, René; Taliotis, Anastasios
2015-01-01
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ0(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an -invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
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)
Phase Diagram of a Simple Model for Fractional Topological Insulator
Chen, Hua; Yang, Kun
2012-02-01
We study a simple model of two species of (or spin-1/2) fermions with short-range intra-species repulsion in the presence of opposite (effetive) magnetic field, each at filling factor 1/3. In the absence of inter-species interaction, the ground state is simply two copies of the 1/3 Laughlin state, with opposite chirality. Due to the overall time-reversal symmetry, this is a fractional topological insulator. We show this phase is stable against moderate inter-species interactions. However strong enough inter-species repulsion leads to phase separation, while strong enough inter-species attraction drives the system into a superfluid phase. We obtain the phase diagram through exact diagonalization caluclations. Nature of the fractional topological insluator-superfluid phase transition is discussed using an appropriate Chern-Simons-Ginsburg-Landau effective field theory.
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
Deformed Calogero-Sutherland model and fractional quantum Hall effect
Atai, Farrokh; Langmann, Edwin
2017-01-01
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
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.
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.
Influence of the void fraction in the linear reactivity model
International Nuclear Information System (INIS)
Castillo, J.A.; Ramirez, J.R.; Alonso, G.
2003-01-01
The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)
Modeling discrete and continuous entities with fractions and decimals.
Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J
2015-03-01
When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.
International Nuclear Information System (INIS)
Savoye, S.; Beaucaire, C.; Grenut, B.; Fayette, A.
2015-01-01
.5 times in the cell with the highest ionic strength. The evolution of the Sr diffusive flux with the ionic strength was qualitatively reproduced by a surface diffusion model, based on the concept of relative diffusive mobility or mobile fraction
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.
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).
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
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
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)
Nonlocal relativistic diffusion (NoRD) model of cosmic ray propagation
International Nuclear Information System (INIS)
Uchaikin, V V; Sibatov, R T
2017-01-01
The problem of physical interpretation of the nonlocal relativistic diffusion (NoRD model) for cosmic ray transport in the Galaxy is discussed. The model accounts for the turbulent character of the interstellar medium and the relativistic principle of the speed limitation. Involving fractional calculus and non-Gaussian Lévy statistics yields numerical results compatible with observation data. A special attention is paid to the knee problem. The relativistic speed limit requirement steepens theoretical background spectrum at certain energies, and the position of the break, its sharpness and slopes of asymptotes depend on D α ( E ) and α . (paper)
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
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
Murine Models of Heart Failure With Preserved Ejection Fraction
Directory of Open Access Journals (Sweden)
Maria Valero-Muñoz, PhD
2017-12-01
Full Text Available Heart failure with preserved ejection fraction (HFpEF is characterized by signs and symptoms of heart failure in the presence of a normal left ventricular ejection fraction. Despite accounting for up to 50% of all clinical presentations of heart failure, the mechanisms implicated in HFpEF are poorly understood, thus precluding effective therapy. The pathophysiological heterogeneity in the HFpEF phenotype also contributes to this disease and likely to the absence of evidence-based therapies. Limited access to human samples and imperfect animal models that completely recapitulate the human HFpEF phenotype have impeded our understanding of the mechanistic underpinnings that exist in this disease. Aging and comorbidities such as atrial fibrillation, hypertension, diabetes and obesity, pulmonary hypertension, and renal dysfunction are highly associated with HFpEF, yet the relationship and contribution between them remains ill-defined. This review discusses some of the distinctive clinical features of HFpEF in association with these comorbidities and highlights the advantages and disadvantage of commonly used murine models used to study the HFpEF phenotype.
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
Modelling Ni diffusion in bentonite using different sorption models
International Nuclear Information System (INIS)
Pfingsten, W.; Baeyens, B.; Bradbury, M.
2010-01-01
Document available in extended abstract form only. An important component of the multi barrier disposal concept for a radioactive waste repository is the bentonite backfill surrounding the canisters containing vitrified high-level waste and spent fuel located in the tunnels deep within the chosen host rock. The effectiveness of the compacted bentonite barrier is such that calculations have indicated that many radionuclides have decayed to insignificant levels before having diffused through the thickness of bentonite. These calculations are performed using the simple Kd sorption concept in which the values are taken from batch type experiments performed on dispersed systems performed for a single metal at a time, usually at trace concentrations. However, in such complex systems many radionuclides, inactive metal contaminants/ground water components may be simultaneously present in the aqueous phase at a range of concentrations varying with time during the temporal evolution of the repository system. An important aspect influencing the sorption of any radioactive metal under a set of given geochemical conditions is its competition with other metals present, and how this may vary as a function of concentration. Competitive sorption effects are not currently included in safety assessments and are thus an issue which needs to be addressed. Here we provide some first estimates of the potential influence of competitive sorption effects on the migration of radioactive metals through compacted bentonite as a function of their concentration and the concentration of competing metals. Ni(II) and Fe(II) were chosen as possible competing cations since their concentration levels are expected to have values greater than trace levels and effects might be maximal and canister corrosion represents a permanent Fe source at the bentonite interface which could influence bivalent radionuclide diffusion. The modelling of the Ni(II) diffusion/sorption has been carried out using three
Particle Based Modeling of Electrical Field Flow Fractionation Systems
Directory of Open Access Journals (Sweden)
Tonguc O. Tasci
2015-10-01
Full Text Available Electrical Field Flow Fractionation (ElFFF is a sub method in the field flow fractionation (FFF family that relies on an applied voltage on the channel walls to effect a separation. ElFFF has fallen behind some of the other FFF methods because of the optimization complexity of its experimental parameters. To enable better optimization, a particle based model of the ElFFF systems has been developed and is presented in this work that allows the optimization of the main separation parameters, such as electric field magnitude, frequency, duty cycle, offset, flow rate and channel dimensions. The developed code allows visualization of individual particles inside the separation channel, generation of realistic fractograms, and observation of the effects of the various parameters on the behavior of the particle cloud. ElFFF fractograms have been generated via simulations and compared with experiments for both normal and cyclical ElFFF. The particle visualizations have been used to verify that high duty cycle voltages are essential to achieve long retention times and high resolution separations. Furthermore, by simulating the particle motions at the channel outlet, it has been demonstrated that the top channel wall should be selected as the accumulation wall for cyclical ElFFF to reduce band broadening and achieve high efficiency separations. While the generated particle based model is a powerful tool to estimate the outcomes of the ElFFF experiments and visualize particle motions, it can also be used to design systems with new geometries which may lead to the design of higher efficiency ElFFF systems. Furthermore, this model can be extended to other FFF techniques by replacing the electrical field component of the model with the fields used in the other FFF techniques.
Fractional Gaussian noise: Prior specification and model comparison
Sø rbye, Sigrunn Holbek; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Fractional Gaussian noise: Prior specification and model comparison
Sørbye, Sigrunn Holbek
2017-07-07
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Oliphant, Andrew J.; Stoy, Paul C.
2018-03-01
Photosynthesis is more efficient under diffuse than direct beam photosynthetically active radiation (PAR) per unit PAR, but diffuse PAR is infrequently measured at research sites. We examine four commonly used semiempirical models (Erbs et al., 1982, https://doi.org/10.1016/0038-092X(82)90302-4; Gu et al., 1999, https://doi.org/10.1029/1999JD901068; Roderick, 1999, https://doi.org/10.1016/S0168-1923(99)00028-3; Weiss & Norman, 1985, https://doi.org/10.1016/0168-1923(85)90020-6) that partition PAR into diffuse and direct beam components based on the negative relationship between atmospheric transparency and scattering of PAR. Radiation observations at 58 sites (140 site years) from the La Thuille FLUXNET data set were used for model validation and coefficient testing. All four models did a reasonable job of predicting the diffuse fraction of PAR (ϕ) at the 30 min timescale, with site median r2 values ranging between 0.85 and 0.87, model efficiency coefficients (MECs) between 0.62 and 0.69, and regression slopes within 10% of unity. Model residuals were not strongly correlated with astronomical or standard meteorological variables. We conclude that the Roderick (1999, https://doi.org/10.1016/S0168-1923(99)00028-3) and Gu et al. (1999, https://doi.org/10.1029/1999JD901068) models performed better overall than the two older models. Using the basic form of these models, the data set was used to find both individual site and universal model coefficients that optimized predictive accuracy. A new universal form of the model is presented in section 5 that increased site median MEC to 0.73. Site-specific model coefficients increased median MEC further to 0.78, indicating usefulness of local/regional training of coefficients to capture the local distributions of aerosols and cloud types.
NMR signals within the generalized Langevin model for fractional Brownian motion
Lisý, Vladimír; Tóthová, Jana
2018-03-01
The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.
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
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.
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.
International Nuclear Information System (INIS)
Svoboda, J.; Fischer, F.D.
2011-01-01
Diffusion in solids is a well-known phenomenon that has many consequences in technology and material science. Modelling of diffusion-controlled processes requires both a reliable theory of diffusion and reliable kinetic coefficients, as well as other thermodynamic data. Often the classical Darken theory, valid for stress-free systems with ideal vacancy source and sink activity, is generalized to multicomponent systems with ideal vacancy source and sink activity. Nazarov and Gurov presented a theory for stress-free systems with no vacancy source and sink activity. Recently we published a general theory of diffusion that accounted for the role of non-ideal vacancy source and sink activity, as well as the stress state. Since diffusion theories are tested and diffusion coefficients measured usually on diffusion couples, this paper presents evolution equations based on that general theory for a diffusion couple. In the limit, the equations of the Darken theory and the Nazarov and Gurov theory are valid for ideal vacancy source and sink activity and no vacancy source and sink activity, respectively. Simulations for binary and ternary diffusion couples demonstrate the influence of the vacancy source and sink activity and the stress state on evolution of site fraction profiles of components and vacancies, and on the Kirkendall effect.
An approximate fractional Gaussian noise model with computational cost
Sørbye, Sigrunn H.
2017-09-18
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
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.
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 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
Molina-Romero, Miguel; Gómez, Pedro A; Sperl, Jonathan I; Czisch, Michael; Sämann, Philipp G; Jones, Derek K; Menzel, Marion I; Menze, Bjoern H
2018-03-23
The compartmental nature of brain tissue microstructure is typically studied by diffusion MRI, MR relaxometry or their correlation. Diffusion MRI relies on signal representations or biophysical models, while MR relaxometry and correlation studies are based on regularized inverse Laplace transforms (ILTs). Here we introduce a general framework for characterizing microstructure that does not depend on diffusion modeling and replaces ill-posed ILTs with blind source separation (BSS). This framework yields proton density, relaxation times, volume fractions, and signal disentanglement, allowing for separation of the free-water component. Diffusion experiments repeated for several different echo times, contain entangled diffusion and relaxation compartmental information. These can be disentangled by BSS using a physically constrained nonnegative matrix factorization. Computer simulations, phantom studies, together with repeatability and reproducibility experiments demonstrated that BSS is capable of estimating proton density, compartmental volume fractions and transversal relaxations. In vivo results proved its potential to correct for free-water contamination and to estimate tissue parameters. Formulation of the diffusion-relaxation dependence as a BSS problem introduces a new framework for studying microstructure compartmentalization, and a novel tool for free-water elimination. © 2018 International Society for Magnetic Resonance in Medicine.
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....
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.
Space-fractional model for the spreading of matter in heterogeneous porous media
International Nuclear Information System (INIS)
Krepysheva, N.; Neel, M.Ch.
2005-01-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
Space-fractional model for the spreading of matter in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Krepysheva, N. [Institut National de Recherches Agronomiques (INRA), UMRA Climat-Sol-Environnement, 84 - Avignon (France); Neel, M.Ch. [Universite d' Avignon, Faculte des Sciences, UMRA Climat-Sol-Environnement, 84 - Avignon (France)
2005-07-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
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.
Lee, Hwang; Byun, Da-Eun; Kim, Ju Min; Kwon, Jung-Hwan
2018-01-01
To evaluate rate of migration from plastic debris, desorption of model hydrophobic organic chemicals (HOCs) from polyethylene (PE)/polypropylene (PP) films to water was measured using PE/PP films homogeneously loaded with the HOCs. The HOCs fractions remaining in the PE/PP films were compared with those predicted using a model characterized by the mass transfer Biot number. The experimental data agreed with the model simulation, indicating that HOCs desorption from plastic particles can generally be described by the model. For hexachlorocyclohexanes with lower plastic-water partition coefficients, desorption was dominated by diffusion in the plastic film, whereas desorption of chlorinated benzenes with higher partition coefficients was determined by diffusion in the aqueous boundary layer. Evaluation of the fraction of HOCs remaining in plastic films with respect to film thickness and desorption time showed that the partition coefficient between plastic and water is the most important parameter influencing the desorption half-life. Copyright © 2017 Elsevier Ltd. All rights reserved.
Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
Sun, Chunlong; Li, Gongsheng; Jia, Xianzheng
2017-01-01
The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short) from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data...
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.
Directory of Open Access Journals (Sweden)
Lavinia Laiti
2018-03-01
Full Text Available Accurate solar radiation estimates in Alpine areas represent a challenging task, because of the strong variability arising from orographic effects and mountain weather phenomena. These factors, together with the scarcity of observations in elevated areas, often cause large modelling uncertainties. In the present paper, estimates of hourly mean diffuse fraction values from global radiation data, provided by a number (13 of decomposition models (chosen among the most widely tested in the literature, are evaluated and compared with observations collected near the city of Bolzano, in the Adige Valley (Italian Alps. In addition, the physical factors influencing diffuse fraction values in such a complex orographic context are explored. The average accuracy of the models were found to be around 27% and 14% for diffuse and beam radiation respectively, the largest errors being observed under clear sky and partly cloudy conditions, respectively. The best performances were provided by the more complex models, i.e., those including a predictor specifically explaining the radiation components’ variability associated with scattered clouds. Yet, these models return non-negligible biases. In contrast, the local calibration of a single-equation logistical model with five predictors allows perfectly unbiased estimates, as accurate as those of the best-performing models (20% and 12% for diffuse and beam radiation, respectively, but at much smaller computational costs.
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.)
International Nuclear Information System (INIS)
Abdul-Sater, Hassan; Krishnamoorthy, Gautham
2013-01-01
Twenty four, laboratory scale, laminar to transitional, diffusion oxy-methane flames were simulated employing different radiation modeling options and their predictions compared against experimental measurements of: temperature, flame length and radiant fraction. The models employed were: gray and non-gray formulations of a recently proposed weighted-sum-of-gray gas model, non-adiabatic extension of the equilibrium based mixture fraction model and investigations into the effects of: the thermal boundary conditions, soot and turbulence radiation interactions (TRI). Predictions of gas, wall temperatures and flame lengths were in good agreement with experimental measurements. Flame lengths determined through the axial profiles of OH confirmed with the experimental trends by increasing with increase in fuel-inlet Reynolds numbers and decreasing with the increase in O 2 composition in oxidizer. The temperature and flame length predictions were not sensitive to the radiative property model employed. There were significant variations between the gray and non-gray model radiant fraction predictions with the variations in general increasing with decrease in Reynolds numbers possibly attributed to shorter flames and steeper temperature gradients. The inclusion of soot model and TRI model did not affect our predictions as a result of low soot volume fractions and the radiation emission enhancement to the temperature fluctuations being localized to the flame sheet. -- Highlights: • Twenty four, lab scale, laminar to transitional, diffusion, oxy-methane flames were simulated. • Equilibrium model adequately predicted the temperature and flame lengths. • The experimental trends in radiant fractions were replicated. • Gray and non-gray model differences in radiant fractions were amplified at low Re. • Inclusion of soot and TRI models did not affect our predictions
Koyama, Tetsuo; Marumoto, Kohei; Miyake, Hiroji; Domen, Kazuhisa
2013-11-01
This study examined the relationship between fractional anisotropy (FA) values of magnetic resonance-diffusion tensor imaging (DTI) and motor outcome (1 month after onset) in 15 patients with hemiparesis after ischemic stroke of corona radiata lesions. DTI data were obtained on days 14-18. FA values within the cerebral peduncle were analyzed using a computer-automated method. Motor outcome of hemiparesis was evaluated according to Brunnstrom stage (BRS; 6-point scale: severe to normal) for separate shoulder/elbow/forearm, wrist/hand, and lower extremity functions. The ratio of FA values in the affected hemisphere to those in the unaffected hemisphere (rFA) was assessed in relation to the BRS data (Spearman rank correlation test, P<.05). rFA values ranged from .715 to 1.002 (median=.924). BRS ranged from 1 to 6 (median=4) for shoulder/elbow/forearm, from 1 to 6 (median=5) for wrist/hand, and from 2 to 6 (median=4) for the lower extremities. Analysis revealed statistically significant relationships between rFA and upper extremity functions (correlation coefficient=.679 for shoulder/elbow/forearm and .706 for wrist/hand). Although slightly less evident, the relationship between rFA and lower extremity function was also statistically significant (correlation coefficient=.641). FA values within the cerebral peduncle are moderately associated with the outcome of both upper and lower extremity functions, suggesting that DTI may be applicable for outcome prediction in stroke patients with corona radiata infarct. Copyright © 2013 National Stroke Association. Published by Elsevier Inc. All rights reserved.
Wang, Xiandi; Wang, Hongli; Sun, Chi; Zhou, Shuyi; Meng, Tao; Lv, Feizhou; Ma, Xiaosheng; Xia, Xinlei; Jiang, Jianyuan
2018-04-26
Previous studies have indicated that decreased fractional anisotropy (FA) values on diffusion tensor imaging (DTI) are well correlated with the symptoms of nerve root compression. The aim of our study is to determine primary radiological parameters associated with decreased FA values in patients with lumbar spinal stenosis involving single L5 nerve root. Patients confirmed with single L5 nerve root compression by transforaminal nerve root blocks were included in this study. FA values of L5 nerve roots on both symptomatic and asymptomatic side were obtained. Conventional radiological parameters, such as disc height, degenerative scoliosis, dural sac cross-sectional area (DSCSA), foraminal height (FH), hypertrophic facet joint degeneration (HFJD), sagittal rotation (SR), sedimentation sign, sagittal translation and traction spur were measured. Correlation and regression analyses were performed between the radiological parameters and FA values of the symptomatic L5 nerve roots. A predictive regression equation was established. Twenty-one patients were included in this study. FA values were significantly lower at the symptomatic side comparing to the asymptomatic side (0.263 ± 0.069 vs. 0.334 ± 0.080, P = 0.038). DSCSA, FH, HFJD, and SR were significantly correlated with the decreased FA values, with r = 0.518, 0.443, 0.472 and - 0.910, respectively (P values, and the regression equation is FA = - 0.012 × SR + 0.002 × DSCSA. DSCSA and SR were primary contributors to decreased FA values in LSS patients involving single L5 nerve root, indicating that central canal decompression and segmental stability should be the first considerations in preoperative planning of these patients. These slides can be retrieved under Electronic Supplementary Material.
International Nuclear Information System (INIS)
Kim, Eung Yeop; Park, Hae Jeong; Kim, Dong Hyun; Lee, Seung Koo; Kim, Jin Na
2008-01-01
Many diffusion tensor imaging (DTI) studies of the corpus callosum (CC) have been performed with a relatively thick slice thickness in the axial plane, which may result in underestimating the fractional anisotropy (FA) of the CC due to a partial volume effect. We hypothesized that the FA of the CC can be more accurately measured by using mid-sagittal DTI. We compared the FA values of the CC between the axial and mid-sagittal DTI. Fourteen healthy volunteers underwent MRI at 3.0 T. DTI was performed in both the mid-sagittal and axial planes. One 5-mm mid-sagittal image and twenty-five 2-mm axial images were obtained for the CC. The five regions of interest (ROIs) that included the prefrontal (I), premotor and supplementary motor (II), motor (III), sensory (IV) and parietal, temporal and occipital regions (V) were drawn along the border of the CC on each sagittal FA map. The FA values obtained from each region were compared between the two sagittal maps. The FA values of all the regions, except for region V, were significantly increased on the mid-sagittal imaging. The FA values in region IV were significantly underestimated on the mid-sagittal image from the axial imaging, compared with those in the regions I and V (p = 0.037 and p = 0.001, respectively). The FA values of the CC were significantly higher on the midsagittal DTI than those on the axial DTI in regions I-IV, and particularly in the region IV. Mid-sagittal DTI may provide more accurate FA values of the CC than can the axial DTI, and mid-sagittal DTI may be more desirable for studies that compare between patients and healthy subjects
Tunable polymeric sorbent materials for fractionation of model naphthenates.
Mohamed, Mohamed H; Wilson, Lee D; Headley, John V
2013-04-04
The sorption properties are reported for several examples of single-component carboxylic acids representing naphthenic acids (NAs) with β-cyclodextrin (β-CD) based polyurethane sorbents. Seven single-component examples of NAs were chosen with variable z values, carbon number, and chemical structure as follows: 2-hexyldecanoic acid (z = 0 and C = 16; S1), n-caprylic acid (z = 0 and C = 8; S2), trans-4-pentylcyclohexanecarboxylic acid (z = -2 and C = 12; S3), 4-methylcyclohexanecarboxylic acid (z = -2 and C = 8; S4), dicyclohexylacetic acid (z = -4; C = 14; S5), 4-pentylbicyclo[2.2.2]octane-1-carboxylic acid (z = -4; C = 14; S6), and lithocholic acid (z = -6; C = 24; S7). The copolymer sorbents were synthesized at three relative β-CD:diisocyanate mole ratios (i.e., 1:1, 1:2, and 1:3) using 4,4'-dicyclohexylmethane diisocyanate (CDI) and 4,4'-diphenylmethane diisocyanate (MDI). The sorption properties of the copolymer sorbents were characterized using equilibrium sorption isotherms in aqueous solution at pH 9.00 with electrospray ionization mass spectrometry. The equilibrium fraction of the unbound carboxylate anions was monitored in the aqueous phase. The sorption properties of the copolymer sorbents (i.e., Qm) were obtained from the Sips isotherm model. The Qm values generally decrease as the number of accessible β-CD inclusion sites in the copolymer framework decreases. The chemical structure of the adsorbates played an important role in their relative uptake, as evidenced by the adsorbate lipophilic surface area (LSA) and the involvement of hydrophobic effects. The copolymers exhibit molecular selective sorption of the single-component carboxylates in mixtures which suggests their application as sorbents for fractionation of mixtures of NAs. By comparison, granular activated carbon (GAC) and chitosan sorbents did not exhibit any significant molecular selective sorption relative to the copolymer materials; however, evidence of variable sorption capacity was
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.)
Fractional model for heat conduction in polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2012-01-01
Full Text Available Time-fractional differential equations can accurately describe heat conduction in fractal media, such as wool fibers, goose down and polar bear hair. The fractional complex transform is used to convert time-fractional heat conduction equations with the modified Riemann-Liouville derivative into ordinary differential equations, and exact solutions can be easily obtained. The solution process is straightforward and concise.
Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions
Shahbari, Juhaina Awawdeh; Peled, Irit
2017-01-01
This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…
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
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.
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.
LENUS (Irish Health Repository)
Murphy, Melissa L
2011-09-27
Abstract Fractional anisotropy anomalies occurring in the white matter tracts in the brains of depressed patients may reflect microstructural changes underlying the pathophysiology of this disorder. We conducted a meta-analysis of fractional anisotropy abnormalities occurring in major depressive disorder using voxel-based diffusion tensor imaging studies. Using the Embase, PubMed and Google Scholar databases, 89 relevant data sets were identified, of which 7 (including 188 patients with major depressive disorder and 221 healthy controls) met our inclusion criteria. Authors were contacted to retrieve any additional data required. Coordinates were extracted from clusters of significant white matter fractional anisotropy differences between patients and controls. Relevant demographic, clinical and methodological variables were extracted from each study or obtained directly from authors. The meta-analysis was carried out using Signed Differential Mapping. Patients with depression showed decreased white matter fractional anisotropy values in the superior longitudinal fasciculus and increased fractional anisotropy values in the fronto-occipital fasciculus compared to controls. Using quartile and jackknife sensitivity analysis, we found that reduced fractional anisotropy in the left superior longitudinal fasciculus was very stable, with increases in the right fronto-occipital fasciculus driven by just one study. In conclusion, our meta-analysis revealed a significant reduction in fractional anisotropy values in the left superior longitudinal fasciculus, which may ultimately play an important role in the pathology of depression.
LENUS (Irish Health Repository)
Murphy, Melissa L
2011-09-01
Fractional anisotropy anomalies occurring in the white matter tracts in the brains of depressed patients may reflect microstructural changes underlying the pathophysiology of this disorder. We conducted a meta-analysis of fractional anisotropy abnormalities occurring in major depressive disorder using voxel-based diffusion tensor imaging studies. Using the Embase, PubMed and Google Scholar databases, 89 relevant data sets were identified, of which 7 (including 188 patients with major depressive disorder and 221 healthy controls) met our inclusion criteria. Authors were contacted to retrieve any additional data required. Coordinates were extracted from clusters of significant white matter fractional anisotropy differences between patients and controls. Relevant demographic, clinical and methodological variables were extracted from each study or obtained directly from authors. The meta-analysis was carried out using Signed Differential Mapping. Patients with depression showed decreased white matter fractional anisotropy values in the superior longitudinal fasciculus and increased fractional anisotropy values in the fronto-occipital fasciculus compared to controls. Using quartile and jackknife sensitivity analysis, we found that reduced fractional anisotropy in the left superior longitudinal fasciculus was very stable, with increases in the right fronto-occipital fasciculus driven by just one study. In conclusion, our meta-analysis revealed a significant reduction in fractional anisotropy values in the left superior longitudinal fasciculus, which may ultimately play an important role in the pathology of depression.
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.
Energy Technology Data Exchange (ETDEWEB)
Pernaton, E
1998-09-09
Two experimental devices have been elaborated in the purpose of simulating in laboratory the solubilization of methane in water and the migration by solubilization/diffusion of some gas species (methane, ethane, propane and nitrogen) through porous media saturated with water. Significant shifts in isotopic ratios of diffused methane (carbon and hydrogen) have been observed. Those fractionations for carbon isotopes, which in most cases are characterised by a {sup 12}C-enriched diffused methane, have fundamental consequences about the interpretation of the origin of methane in sedimentary basins and, in a more general way, about the genetic characterisation of hydrocarbon gases in reservoirs. Indeed, this gives an ambiguous origin for any gas having {sup 12}C-enriched methane, two different interpretations are possible: mixing between thermogenic and bacterial hydrocarbon gases and a diffusive trend during migration. Using a diagram C2/C1 versus {delta}{sup 13}C1, we have shown that in some geological cases, these two processes, mixing and diffusion, exist and that it is possible to discern them.The chemical and isotopic compositions of natural gases do not only reflect genetic processes but are also an indication of their migration. Moreover, the experiments have shown that the gas transport by solubilization/diffusion is a potential operator of gas leakage from natural accumulations. In consequence, a numerical model of gas migration through cap rocks of reservoirs has been elaborated and will be integrated into sedimentary basin models. (author)
Directory of Open Access Journals (Sweden)
Yuri Luchko
2017-12-01
Full Text Available In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to obtain two new representations of the fundamental solution in the form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed-form formulas for particular cases of the fundamental solution are derived. In particular, we solve the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.
Thin stillage fractionation using ultrafiltration: resistance in series model.
Arora, Amit; Dien, Bruce S; Belyea, Ronald L; Wang, Ping; Singh, Vijay; Tumbleson, M E; Rausch, Kent D
2009-02-01
The corn based dry grind process is the most widely used method in the US for fuel ethanol production. Fermentation of corn to ethanol produces whole stillage after ethanol is removed by distillation. It is centrifuged to separate thin stillage from wet grains. Thin stillage contains 5-10% solids. To concentrate solids of thin stillage, it requires evaporation of large amounts of water and maintenance of evaporators. Evaporator maintenance requires excess evaporator capacity at the facility, increasing capital expenses, requiring plant slowdowns or shut downs and results in revenue losses. Membrane filtration is one method that could lead to improved value of thin stillage and may offer an alternative to evaporation. Fractionation of thin stillage using ultrafiltration was conducted to evaluate membranes as an alternative to evaporators in the ethanol industry. Two regenerated cellulose membranes with molecular weight cut offs of 10 and 100 kDa were evaluated. Total solids (suspended and soluble) contents recovered through membrane separation process were similar to those from commercial evaporators. Permeate flux decline of thin stillage using a resistance in series model was determined. Each of the four components of total resistance was evaluated experimentally. Effects of operating variables such as transmembrane pressure and temperature on permeate flux rate and resistances were determined and optimum conditions for maximum flux rates were evaluated. Model equations were developed to evaluate the resistance components that are responsible for fouling and to predict total flux decline with respect to time. Modeling results were in agreement with experimental results (R(2) > 0.98).
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.
Pinto de Magalhães, Halua; Brennwald, Matthias S; Kipfer, Rolf
2017-03-22
Atmospheric noble gases are routinely used as natural tracers to analyze gas transfer processes in aquatic systems. Their isotopic ratios can be employed to discriminate between different physical transport mechanisms by comparison to the unfractionated atmospheric isotope composition. In many applications of aquatic systems molecular diffusion was thought to cause a mass dependent fractionation of noble gases and their isotopes according to the square root ratio of their masses. However, recent experiments focusing on isotopic fractionation within a single element challenged this broadly accepted assumption. The determined fractionation factors of Ne, Ar, Kr and Xe isotopes revealed that only Ar follows the prediction of the so-called square root relation, whereas within the Ne, Kr and Xe elements no mass-dependence was found. The reason for this unexpected divergence of Ar is not yet understood. The aim of our computational exercise is to establish the molecular-resolved mechanisms behind molecular diffusion of noble gases in water. We make the hypothesis that weak intermolecular interactions are relevant for the dynamical properties of noble gases dissolved in water. Therefore, we used ab initio molecular dynamics to explicitly account for the electronic degrees of freedom. Depending on the size and polarizability of the hydrophobic particles such as noble gases, their motion in dense and polar liquids like water is subject to different diffusive regimes: the inter-cavity hopping mechanism of small particles (He, Ne) breaks down if a critical particle size achieved. For the case of large particles (Kr, Xe), the motion through the water solvent is governed by mass-independent viscous friction leading to hydrodynamical diffusion. Finally, Ar falls in between the two diffusive regimes, where particle dispersion is propagated at the molecular collision time scale of the surrounding water molecules.
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.
Energy Technology Data Exchange (ETDEWEB)
Indriolo, Nick; Neufeld, D. A. [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218 (United States); Gerin, M. [LERMA, CNRS, Observatoire de Paris and ENS, F-75231 Paris Cedex 05 (France); Geballe, T. R. [Gemini Observatory, Hilo, HI 96720 (United States); Black, J. H. [Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory, SE-43992 Onsala (Sweden); Menten, K. M. [MPI fuer Radioastronomie, D-53121 Bonn (Germany); Goicoechea, J. R. [Departamento de Astrofisica, Centro de Astrobiologia (CSIC-INTA), E-28850 Madrid (Spain)
2012-10-20
Absorption lines from the molecules OH{sup +}, H{sub 2}O{sup +}, and H{sup +} {sub 3} have been observed in a diffuse molecular cloud along a line of sight near W51 IRS2. We present the first chemical analysis that combines the information provided by all three of these species. Together, OH{sup +} and H{sub 2}O{sup +} are used to determine the molecular hydrogen fraction in the outskirts of the observed cloud, as well as the cosmic-ray ionization rate of atomic hydrogen. H{sup +} {sub 3} is used to infer the cosmic-ray ionization rate of H{sub 2} in the molecular interior of the cloud, which we find to be {zeta}{sub 2} = (4.8 {+-} 3.4) Multiplication-Sign 10{sup -16} s{sup -1}. Combining the results from all three species we find an efficiency factor-defined as the ratio of the formation rate of OH{sup +} to the cosmic-ray ionization rate of H-of {epsilon} = 0.07 {+-} 0.04, much lower than predicted by chemical models. This is an important step in the future use of OH{sup +} and H{sub 2}O{sup +} on their own as tracers of the cosmic-ray ionization rate.
Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord
International Nuclear Information System (INIS)
Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University
1993-01-01
The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab
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.
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Astudillo V, A.; Paredes G, L. [ININ, Carretera Mexico-Toluca s/n, Ocoyoacac 52750, Estado de Mexico (Mexico); Resendiz G, G.; Posadas V, A. [Hospital Angeles Lomas, Av. Vialidad de la Barranca s/n, Col. Valle de las Palmas, 52763 Huixquilucan de Degallado, Estado de Mexico (Mexico); Mitsoura, E. [Universidad Autonoma del Estado de Mexico, Facultad de Medicina, Paseo Tollocan, Esq. Jesus Carranza s/n, Col. Moderna de la Cruz, 50180 Toluca, Estado de Mexico (Mexico); Rodriguez L, A.; Flores C, J. M., E-mail: armando.astudillo@inin.gob.mx [Hospital Medica Sur, Puente de Piedra 150, Col. Toriello Guerra, 14050 Tlalpan, Mexico D. F. (Mexico)
2015-10-15
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
International Nuclear Information System (INIS)
Astudillo V, A.; Paredes G, L.; Resendiz G, G.; Posadas V, A.; Mitsoura, E.; Rodriguez L, A.; Flores C, J. M.
2015-10-01
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
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
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.
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 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, ...
Stefferson, Michael W.; Norris, Samantha L.; Vernerey, Franck J.; Betterton, Meredith D.; E Hough, Loren
2017-08-01
Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.
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
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.
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.
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
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 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.)
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.
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
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.
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
Optimal distributed control of a diffuse interface model of tumor growth
Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Sprekels, Jürgen
2017-06-01
In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by Hawkins-Daruud et al in Hawkins-Daruud et al (2011 Int. J. Numer. Math. Biomed. Eng. 28 3-24). The model consists of a Cahn-Hilliard equation for the tumor cell fraction φ coupled to a reaction-diffusion equation for a function σ representing the nutrient-rich extracellular water volume fraction. The distributed control u monitors as a right-hand side of the equation for σ and can be interpreted as a nutrient supply or a medication, while the cost function, which is of standard tracking type, is meant to keep the tumor cell fraction under control during the evolution. We show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive the first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. The financial support of the FP7-IDEAS-ERC-StG #256872 (EntroPhase) and of the project Fondazione Cariplo-Regione Lombardia MEGAsTAR ‘Matematica d’Eccellenza in biologia ed ingegneria come accelleratore di una nuona strateGia per l’ATtRattività dell’ateneo pavese’ is gratefully acknowledged. The paper also benefited from the support of the MIUR-PRIN Grant 2015PA5MP7 ‘Calculus of Variations’ for PC and GG, and the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica) for PC, GG and ER.
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.
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.
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.
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.
International Nuclear Information System (INIS)
Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto
2015-01-01
Highlights: • The new version of neutron diffusion equation for simulating anomalous diffusion is presented. • Application of fractional calculus in the nuclear reactor is revealed. • A 3D-Multigroup program is developed based on the fractional operators. • The super-diffusion and sub-diffusion phenomena are modeled in the nuclear reactors core. - Abstract: The diffusion process is categorized in three parts, normal diffusion, super-diffusion and sub-diffusion. The classical neutron diffusion equation is used to model normal diffusion. A new scheme of derivatives is required to model anomalous diffusion phenomena. The fractional space derivatives are employed to model anomalous diffusion processes where a plume of particles spreads at an inconsistent rate with the classical Brownian motion model. In the fractional diffusion equation, the fractional Laplacians are used; therefore the statistical jump length of neutrons is unrestricted. It is clear that the fractional Laplacians are capable to model the anomalous phenomena in nuclear reactors. We have developed a NFDE-3D (neutron fractional diffusion equation) as a core calculation code to model normal and anomalous diffusion phenomena. The NFDE-3D is validated against the LMW-LWR reactor. The results demonstrate that reactors exhibit complex behavior versus order of the fractional derivatives which depends on the competition between neutron absorption and super-diffusion phenomenon
Mittag-Leffler function for discrete fractional modelling
Directory of Open Access Journals (Sweden)
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
Beam shaping for conformal fractionated stereotactic radiotherapy: a modeling study
International Nuclear Information System (INIS)
Hacker, Fred L.; Kooy, Hanne M.; Bellerive, Marc R.; Killoran, Joseph H.; Leber, Zachary H.; Shrieve, Dennis C.; Tarbell, Nancy J.; Loeffler, Jay S.
1997-01-01
Purpose: The patient population treated with fractionated stereotactic radiotherapy (SRT) is significantly different than that treated with stereotactic radiosurgery (SRS). Generally, lesions treated with SRT are larger, less spherical, and located within critical regions of the central nervous system; hence, they offer new challenges to the treatment planner. Here a simple, cost effective, beam shaping system has been evaluated relative to both circular collimators and an ideal dynamically conforming system for effectiveness in providing conformal therapy for these lesions. Methods and Materials: We have modeled a simple system for conformal arc therapy using four independent jaws. The jaw positions and collimator angle are changed between arcs but held fixed for the duration of each arc. Eleven previously treated SRT cases have been replanned using this system. The rectangular jaw plans were then compared to the original treatment plans which used circular collimators. The plans were evaluated with respect to tissue sparing at 100%, 80%, 50%, and 20% of the prescription dose. A plan was also done for each tumor in which the beam aperture was continuously conformed to the beams eye view projection of the tumor. This was used as an ideal standard for conformal therapy in the absence of fluence modulation. Results: For tumors with a maximum extent of over 3.5 cm the rectangular jaw plans reduced the mean volume of healthy tissue involved at the prescription dose by 57% relative to the circular collimator plans. The ideal conformal plans offered no significant further improvement at the prescription dose. The relative advantage of the rectangular jaw plans decreased at lower isodoses so that at 20% of the prescription dose tissue involvement for the rectangular jaw plans was equivalent to that for the circular collimator plans. At these isodoses the ideal conformal plans gave substantially better tissue sparing. Conclusion: A simple and economical field shaping
Effective-field-theory model for the fractional quantum Hall effect
International Nuclear Information System (INIS)
Zhang, S.C.; Hansson, T.H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive
A representation theory for a class of vector autoregressive models for fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a un...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...
Ziegler, C.; Gerteisen, D.
A dynamic two-phase model of a proton exchange membrane fuel cell with respect to the gas diffusion layer (GDL) is presented and compared with chronoamperometric experiments. Very good agreement between experiment and simulation is achieved for potential step voltammetry (PSV) and sine wave testing (SWT). Homogenized two-phase models can be categorized in unsaturated flow theory (UFT) and multiphase mixture (M 2) models. Both model approaches use the continuum hypothesis as fundamental assumption. Cyclic voltammetry experiments show that there is a deterministic and a stochastic liquid transport mode depending on the fraction of hydrophilic pores of the GDL. ESEM imaging is used to investigate the morphology of the liquid water accumulation in the pores of two different media (unteflonated Toray-TGP-H-090 and hydrophobic Freudenberg H2315 I3). The morphology of the liquid water accumulation are related with the cell behavior. The results show that UFT and M 2 two-phase models are a valid approach for diffusion media with large fraction of hydrophilic pores such as unteflonated Toray-TGP-H paper. However, the use of the homgenized UFT and M 2 models appears to be invalid for GDLs with large fraction of hydrophobic pores that corresponds to a high average contact angle of the GDL.
LPV model for PV cell and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for V-I characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Reviewed
LPV model for PV cells and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for VI characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Rev...
Sánchez, R.; van Milligen, B. Ph.; Carreras, B. A.
2005-05-01
It is argued that the modeling of plasma transport in tokamaks may benefit greatly from extending the usual local paradigm to accommodate scale-free transport mechanisms. This can be done by combining Lévy distributions and a nonlinear threshold condition within the continuous time random walk concept. The advantages of this nonlocal, nonlinear extension are illustrated by constructing a simple particle density transport model that, as a result of these ideas, spontaneously exhibits much of nondiffusive phenomenology routinely observed in tokamaks. The fluid limit of the system shows that the kind of equations that are appropriate to capture these dynamics are based on fractional differential operators. In them, effective diffusivities and pinch velocities are found that are dynamically set by the system in response to the specific characteristics of the fueling source and external perturbations. This fact suggests some dramatic consequences for the extrapolation of these transport properties to larger size systems.
International Nuclear Information System (INIS)
Sanchez, R.; Milligen, B.Ph. van; Carreras, B.A.
2005-01-01
It is argued that the modeling of plasma transport in tokamaks may benefit greatly from extending the usual local paradigm to accommodate scale-free transport mechanisms. This can be done by combining Levy distributions and a nonlinear threshold condition within the continuous time random walk concept. The advantages of this nonlocal, nonlinear extension are illustrated by constructing a simple particle density transport model that, as a result of these ideas, spontaneously exhibits much of nondiffusive phenomenology routinely observed in tokamaks. The fluid limit of the system shows that the kind of equations that are appropriate to capture these dynamics are based on fractional differential operators. In them, effective diffusivities and pinch velocities are found that are dynamically set by the system in response to the specific characteristics of the fueling source and external perturbations. This fact suggests some dramatic consequences for the extrapolation of these transport properties to larger size systems
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)
Strahm, Ivo; Munz, Nicole; Braun, Christian; Gälli, René; Leu, Christian; Stamm, Christian
2014-05-01
Water quality in the Swiss river network is affected by many micropollutants from a variety of diffuse sources. This study compares, for the first time, in a comprehensive manner the diffuse sources and the substance groups that contribute the most to water contamination in Swiss streams and highlights the major regions for water pollution. For this a simple but comprehensive model was developed to estimate emission from diffuse sources for the entire Swiss river network of 65 000 km. Based on emission factors the model calculates catchment specific losses to streams for more than 15 diffuse sources (such as crop lands, grassland, vineyards, fruit orchards, roads, railways, facades, roofs, green space in urban areas, landfills, etc.) and more than 130 different substances from 5 different substance groups (pesticides, biocides, heavy metals, human drugs, animal drugs). For more than 180 000 stream sections estimates of mean annual pollutant loads and mean annual concentration levels were modeled. This data was validated with a set of monitoring data and evaluated based on annual average environmental quality standards (AA-EQS). Model validation showed that the estimated mean annual concentration levels are within the range of measured data. Therefore simulations were considered as adequately robust for identifying the major sources of diffuse pollution. The analysis depicted that in Switzerland widespread pollution of streams can be expected. Along more than 18 000 km of the river network one or more simulated substances has a concentration exceeding the AA-EQS. In single stream sections it could be more than 50 different substances. Moreover, the simulations showed that in two-thirds of small streams (Strahler order 1 and 2) at least one AA-EQS is always exceeded. The highest number of substances exceeding the AA-EQS are in areas with large fractions of arable cropping, vineyards and fruit orchards. Urban areas are also of concern even without considering
Lisý, Vladimír; Tóthová, Jana
2018-02-01
Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.
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.
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.
An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach
Wilkerson, Trena L.; Cooper, Susan; Gupta, Dittika; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie; Baker, Betty Ruth; Sharp, Pat T.
2015-01-01
This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in…
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...
Ertas, Gokhan
2018-07-01
To assess the value of joint evaluation of diffusion tensor imaging (DTI) measures by using logistic regression modelling to detect high GS risk group prostate tumors. Fifty tumors imaged using DTI on a 3 T MRI device were analyzed. Regions of interests focusing on the center of tumor foci and noncancerous tissue on the maps of mean diffusivity (MD) and fractional anisotropy (FA) were used to extract the minimum, the maximum and the mean measures. Measure ratio was computed by dividing tumor measure by noncancerous tissue measure. Logistic regression models were fitted for all possible pair combinations of the measures using 5-fold cross validation. Systematic differences are present for all MD measures and also for all FA measures in distinguishing the high risk tumors [GS ≥ 7(4 + 3)] from the low risk tumors [GS ≤ 7(3 + 4)] (P Logistic regression modelling provides a favorable solution for the joint evaluations easily adoptable in clinical practice. Copyright © 2018 Elsevier Inc. All rights reserved.
A review of anisotropic conductivity models of brain white matter based on diffusion tensor imaging.
Wu, Zhanxiong; Liu, Yang; Hong, Ming; Yu, Xiaohui
2018-06-01
The conductivity of brain tissues is not only essential for electromagnetic source estimation (ESI), but also a key reflector of the brain functional changes. Different from the other brain tissues, the conductivity of whiter matter (WM) is highly anisotropic and a tensor is needed to describe it. The traditional electrical property imaging methods, such as electrical impedance tomography (EIT) and magnetic resonance electrical impedance tomography (MREIT), usually fail to image the anisotropic conductivity tensor of WM with high spatial resolution. The diffusion tensor imaging (DTI) is a newly developed technique that can fulfill this purpose. This paper reviews the existing anisotropic conductivity models of WM based on the DTI and discusses their advantages and disadvantages, as well as identifies opportunities for future research on this subject. It is crucial to obtain the linear conversion coefficient between the eigenvalues of anisotropic conductivity tensor and diffusion tensor, since they share the same eigenvectors. We conclude that the electrochemical model is suitable for ESI analysis because the conversion coefficient can be directly obtained from the concentration of ions in extracellular liquid and that the volume fraction model is appropriate to study the influence of WM structural changes on electrical conductivity. Graphical abstract ᅟ.
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
Directory of Open Access Journals (Sweden)
S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
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).
International Nuclear Information System (INIS)
Yuste, Santos Bravo; Abad, Enrique
2011-01-01
We present an iterative method to obtain approximations to Bessel functions of the first kind J p (x) (p > -1) via the repeated application of an integral operator to an initial seed function f 0 (x). The class of seed functions f 0 (x) leading to sets of increasingly accurate approximations f n (x) is considerably large and includes any polynomial. When the operator is applied once to a polynomial of degree s, it yields a polynomial of degree s + 2, and so the iteration of this operator generates sets of increasingly better polynomial approximations of increasing degree. We focus on the set of polynomial approximations generated from the seed function f 0 (x) = 1. This set of polynomials is useful not only for the computation of J p (x) but also from a physical point of view, as it describes the long-time decay modes of certain fractional diffusion and diffusion-wave problems.
Czech Academy of Sciences Publication Activity Database
Ibrahim, I.; Tintěra, J.; Škoch, A.; Jírů, F.; Hluštík, P.; Martinková, Patrícia; Zvára, Karel; Řasová, K.
2011-01-01
Roč. 53, č. 11 (2011), s. 917-926 ISSN 0028-3940 Grant - others:GA MŠk(CZ) 1M0517 Program:1M Institutional research plan: CEZ:AV0Z10300504 Keywords : multiple sclerosis * rehabilitation * facilitation physiotherapy * diffusion tensor imaging * corpus callosum Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.824, year: 2011
Generalized modeling of the fractional-order memcapacitor and its character analysis
Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin
2018-06-01
Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.
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
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.
2012-11-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.; Radwan, Ahmed G.; Salama, Khaled N.; Momani, Shaher M.; Hashim, Ishak
2012-01-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
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
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
Universal block diagram based modeling and simulation schemes for fractional-order control systems.
Bai, Lu; Xue, Dingyü
2017-05-08
Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Amato, Ernesto; Italiano, Antonio; Baldari, Sergio
2014-01-01
We developed a general model for the calculation of absorbed fractions in ellipsoidal volumes of soft tissue uniformly filled with alpha, beta and gamma emitting radionuclides. The approach exploited Monte Carlo simulations with the Geant4 code to determine absorbed fractions in ellipsoids characterized by a wide range of dimensions and ellipticities, for monoenergetic emissions of each radiation type. The so-obtained absorbed fractions were put in an analytical relationship with the 'general...
Directory of Open Access Journals (Sweden)
Yang Xiao-Jun
2017-01-01
Full Text Available In this paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.
N'Doye, Ibrahima
2015-05-25
In this paper, a dynamical fractional viscoelastic fluids convection model in porous media is proposed and its chaotic behavior is studied. A preformed equilibrium points analysis indicates the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.
Energy Technology Data Exchange (ETDEWEB)
Burrowes, Delilah; Deng, Jie [Ann and Robert H. Lurie Children' s Hospital of Chicago, Department of Medical Imaging, Chicago, IL (United States); Northwestern University, Feinberg School of Medicine, Department of Radiology, Chicago, IL (United States); Fangusaro, Jason R. [Ann and Robert H. Lurie Children' s Hospital of Chicago, Department of Hematology/Oncology, Chicago, IL (United States); Northwestern University, Feinberg School of Medicine, Department of Pediatrics-Hematology, Oncology, and Stem Cell Transplantation, Chicago, IL (United States); Nelson, Paige C.; Rozenfeld, Michael J. [Ann and Robert H. Lurie Children' s Hospital of Chicago, Department of Medical Imaging, Chicago, IL (United States); Zhang, Bin [Cincinnati Children' s Hospital Medical Center, Department of Biostatistics and Epidemiology, Cincinnati, OH (United States); Wadhwani, Nitin R. [Ann and Robert H. Lurie Children' s Hospital of Chicago, Department of Pathology and Laboratory Medicine, Chicago, IL (United States); Northwestern University, Feinberg School of Medicine, Department of Pathology, Chicago, IL (United States)
2017-08-15
The purpose of this study was to examine advanced diffusion-weighted magnetic resonance imaging (DW-MRI) models for differentiation of low- and high-grade tumors in the diagnosis of pediatric brain neoplasms. Sixty-two pediatric patients with various types and grades of brain tumors were evaluated in a retrospective study. Tumor type and grade were classified using the World Health Organization classification (WHO I-IV) and confirmed by pathological analysis. Patients underwent DW-MRI before treatment. Diffusion-weighted images with 16 b-values (0-3500 s/mm{sup 2}) were acquired. Averaged signal intensity decay within solid tumor regions was fitted using two-compartment and anomalous diffusion models. Intracellular and extracellular diffusion coefficients (D{sub slow} and D{sub fast}), fractional volumes (V{sub slow} and V{sub fast}), generalized diffusion coefficient (D), spatial constant (μ), heterogeneity index (β), and a diffusion index (index{sub d}iff = μ x V{sub slow}/β) were calculated. Multivariate logistic regression models with stepwise model selection algorithm and receiver operating characteristic (ROC) analyses were performed to evaluate the ability of each diffusion parameter to distinguish tumor grade. Among all parameter combinations, D and index{sub d}iff jointly provided the best predictor for tumor grades, where lower D (p = 0.03) and higher index{sub d}iff (p = 0.009) were significantly associated with higher tumor grades. In ROC analyses of differentiating low-grade (I-II) and high-grade (III-IV) tumors, index{sub d}iff provided the highest specificity of 0.97 and D provided the highest sensitivity of 0.96. Multi-parametric diffusion measurements using two-compartment and anomalous diffusion models were found to be significant discriminants of tumor grading in pediatric brain neoplasms. (orig.)
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
Directory of Open Access Journals (Sweden)
Timurkhan S. Aleroev
2013-12-01
Full Text Available We consider a linear heat equation involving a fractional derivative in time, with a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution for a problem with an over-determining condition of integral type. We prove the existence and uniqueness of the solution, and its continuous dependence on the data.