A new model of diffuse brain injury in rats. Part I: Pathophysiology and biomechanics.
Marmarou, A; Foda, M A; van den Brink, W; Campbell, J; Kita, H; Demetriadou, K
1994-02-01
This report describes the development of an experimental head injury model capable of producing diffuse brain injury in the rodent. A total of 161 anesthetized adult rats were injured utilizing a simple weight-drop device consisting of a segmented brass weight free-falling through a Plexiglas guide tube. Skull fracture was prevented by cementing a small stainless-steel disc on the calvaria. Two groups of rats were tested: Group 1, consisting of 54 rats, to establish fracture threshold; and Group 2, consisting of 107 animals, to determine the primary cause of death at severe injury levels. Data from Group 1 animals showed that a 450-gm weight falling from a 2-m height (0.9 kg-m) resulted in a mortality rate of 44% with a low incidence (12.5%) of skull fracture. Impact was followed by apnea, convulsions, and moderate hypertension. The surviving rats developed decortication flexion deformity of the forelimbs, with behavioral depression and loss of muscle tone. Data from Group 2 animals suggested that the cause of death was due to central respiratory depression; the mortality rate decreased markedly in animals mechanically ventilated during the impact. Analysis of mathematical models showed that this mass-height combination resulted in a brain acceleration of 900 G and a brain compression gradient of 0.28 mm. It is concluded that this simple model is capable of producing a graded brain injury in the rodent without a massive hypertensive surge or excessive brain-stem damage.
Al-Shakran, Mohammad; Kibler, Ludwig A.; Jacob, Timo; Ibach, Harald; Beltramo, Guillermo L.; Giesen, Margret
2016-09-01
This is Part I of two closely related papers, where we show that the specific adsorption of anions leads to a failure of the nearest-neighbor Ising model to describe island perimeter curvatures on Au(100) electrodes in dilute KBr, HCl and H2SO4 electrolytes and the therewith derived step diffusivity vs. step orientation. This result has major consequences for theoretical studies aiming at the understanding of growth, diffusion and degradation phenomena. Part I focuses on the experimental data. As shown theoretically in detail in Part II (doi:10.1016/j.susc.2016.03.022), a set of nearest-neighbor and next-nearest-neighbor interaction energies (ɛNN, ɛNNN) can uniquely be derived from the diffusivity of steps along and . We find strong repulsive next-nearest neighbor (NNN) interaction in KBr and HCl, whereas NNN interaction is negligibly for H2SO4. The NNN repulsive interaction energy ɛNNN therefore correlates positively with the Gibbs adsorption energy of the anions. We find furthermore that ɛNNN increases with increasing Br- and Cl- coverage. The results for ɛNN and ɛNNN are quantitatively consistent with the coverage dependence of the step line tension. We thereby establish a sound experimental base for theoretical studies on the energetics of steps in the presence of specific adsorption.
Model of information diffusion
Lande, D V
2008-01-01
The system of cellular automata, which expresses the process of dissemination and publication of the news among separate information resources, has been described. A bell-shaped dependence of news diffusion on internet-sources (web-sites) coheres well with a real behavior of thematic data flows, and at local time spans - with noted models, e.g., exponential and logistic ones.
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
Han, Xuebing; Ouyang, Minggao; Lu, Languang; Li, Jianqiu
2015-03-01
Now the lithium ion batteries are widely used in electrical vehicles (EV). The battery modeling and state estimation is of great significance. The rigorous physic based electrochemical model is too complicated for on-line simulation in vehicle. In this work, the simplification of physics-based model lithium ion battery for application in battery management system (BMS) on real electrical vehicle is proposed. Approximate method for solving the solid phase diffusion and electrolyte concentration distribution problems is introduced. The approximate result is very close to the rigorous model but fewer computations are needed. An extended single particle model is founded based on these approximated results and the on-line state of charge (SOC) estimation algorithm using the extended Kalman filter with this single particle model is discussed. This SOC estimation algorithm could be used in the BMS in real vehicle.
Garaud, P; Verhoeven, J
2016-01-01
Shear-induced turbulence could play a significant role in mixing momentum and chemical species in stellar radiation zones, as discussed by Zahn (1974). In this paper we analyze the results of direct numerical simulations of stratified plane Couette flows, in the limit of rapid thermal diffusion, to measure the turbulent diffusivity and turbulent viscosity as a function of the local shear and the local stratification. We find that the stability criterion proposed by Zahn (1974), namely that the product of the gradient Richardson number and the Prandtl number must be smaller than a critical values $(J\\Pr)_c$ for instability, adequately accounts for the transition to turbulence in the flow, with $(J\\Pr)_c \\simeq 0.007$. This result recovers and confirms the prior findings of Prat et al. (2016). Zahn's model for the turbulent diffusivity and viscosity (Zahn 1992), namely that the mixing coefficient should be proportional to the ratio of the thermal diffusivity to the gradient Richardson number, does not satisfact...
Modelling the Diffusion of Scientific Publications
Ph.H.B.F. Franses (Philip Hans); D. Fok (Dennis)
2007-01-01
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 f
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 f
HUANG Rui Xin
2014-01-01
Study of oceanic circulation and climate requires models which can simulate tracer eddy diffusion and ad-vection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial hori-zontal diffusivity/viscosity due to the incorrect alignment of the axis. Therefore, such models can smear sharp fronts and introduce other numerical artifacts. For simulation with relatively low resolution, large lateral diffusion was explicitly used in models;therefore, such numerical diffusion may not be a problem. However, with the increase of horizontal resolution, the artificial diffusivity/viscosity associated with hori-zontal advection in the commonly used Eulerian coordinates may become one of the most challenging ob-stacles for modeling the ocean circulation accurately. Isopycnal eddy diffusion (mixing) has been widely used in numerical models. The common wisdom is that mixing along isopycnal is energy free. However, a careful examination reveals that this is not the case. In fact, eddy diffusion can be conceptually separated into two steps:stirring and subscale diffusion. Due to the thermobaric effect, stirring, or exchanging water masses, along isopycnal surface is associated with the change of GPE in the mean state. This is a new type of instability, called the thermobaric instability. In addition, due to cabbeling subscale diffusion of water parcels always leads to the release of GPE. The release of GPE due to isopycnal stirring and subscale diffusion may lead to the thermobaric instability.
Modeling Internet Diffusion in Developing Countries
Scott McCoy
2012-04-01
Full Text Available Despite the increasing importance of the Internet, there is little work that addresses the degree to which the models and theories of Internet diffusion in developed countries can be applied to Internet diffusion in developing countries. This paper presents the first attempt to address this issue through theory driven modeling of Internet diffusion. Consistent with previous research, our findings suggest that economic development and technology infrastructure are musts for Internet diffusion. Interestingly, users’ cognition and government policies can accelerate Internet diffusion only after a certain level of human rights has been reached in a developing country.
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy; Kurien, Susan
2016-11-01
A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
Connectionist and diffusion models of reaction time.
Ratcliff, R; Van Zandt, T; McKoon, G
1999-04-01
Two connectionist frameworks, GRAIN (J. L. McClelland, 1993) and brain-state-in-a-box (J. A. Anderson, 1991), and R. Ratcliff's (1978) diffusion model were evaluated using data from a signal detection task. Dependent variables included response probabilities, reaction times for correct and error responses, and shapes of reaction-time distributions. The diffusion model accounted for all aspects of the data, including error reaction times that had previously been a problem for all response-time models. The connectionist models accounted for many aspects of the data adequately, but each failed to a greater or lesser degree in important ways except for one model that was similar to the diffusion model. The findings advance the development of the diffusion model and show that the long tradition of reaction-time research and theory is a fertile domain for development and testing of connectionist assumptions about how decisions are generated over time.
Diffusion in condensed matter methods, materials, models
Kärger, Jörg
2005-01-01
Diffusion as the process of particle transport due to stochastic movement is a phenomenon of crucial relevance for a large variety of processes and materials. This comprehensive, handbook- style survey of diffusion in condensed matter gives detailed insight into diffusion as the process of particle transport due to stochastic movement. Leading experts in the field describe in 23 chapters the different aspects of diffusion, covering microscopic and macroscopic experimental techniques and exemplary results for various classes of solids, liquids and interfaces as well as several theoretical concepts and models. Students and scientists in physics, chemistry, materials science, and biology will benefit from this detailed compilation.
A Single Species Model with Impulsive Diffusion
Jing Hui; Lan-sun Chen
2005-01-01
In most models of population dynamics, diffusion between patches is assumed to be continuous or discrete, but in practice many species diffuse only during a single period. In this paper we propose a single species model with impulsive diffusion between two patches, which provides a more natural description of population dynamics. By using the discrete dynamical system generated by a monotone, concave map for the population,we prove that the map alwayshas a globally stable positive fixed point. This means that a single species system with impulsive diffusion always has a globally stable positive periodic solution. This result is further substantiated by numerical simulation. Under impulsive diffusion the single species survives in the two patches.
Discrete random walk models for space-time fractional diffusion
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
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 {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} 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.
Multipath diffusion: A general numerical model
Lee, J. K. W.; Aldama, A. A.
1992-06-01
The effect of high-diffusivity pathways on bulk diffusion of a solute in a material has been modeled previously for simple geometries such as those in tracer diffusion experiments, but not for the geometries and boundary conditions appropriate for experiments involving bulk exchange. Using a coupled system of equations for simultaneous diffusion of a solute through two families of diffusion pathways with differing diffusivities, a general 1-D finite difference model written in FORTRAN has been developed which can be used to examine the effect of high-diffusivity paths on partial and total concentration profiles within a homogeneous isotropic sphere, infinite cylinder, and infinite slab. The partial differential equations are discretized using the θ-method/central-difference scheme, and an iterative procedure analogous to the Gauss-Seidel method is employed to solve the two systems of coupled equations. Using Fourier convergence analysis, the procedure is shown to be unconditionally convergent. Computer simulations demonstrate that a multipath diffusion mechanism can enhance significantly the bulk diffusivity of a diffusing solute species through a material. The amount of solute escaping from a material is dependent strongly on the exchange coefficients, which govern the transfer of solute from the crystal lattice to the high-diffusivity paths and vice versa. In addition, the exchange coefficients ( ϰ1, and ϰ2) seem to control not only the amount of solute that is lost, but also the shape of the concentration profile. If | K1| < | K2|, concentration profiles generally are non-Fickian in shape, typically having shallow concentration gradients near the center (radius r = 0) and steep gradients towards the outer boundary of the material ( r = R). When | K1| ⩾ | K2| a concentration profile is generated which resembles a Fickian (volume) diffusion profile with an apparent bulk diffusivity between that of the crystal lattice and that of the high-diffusivity pathways
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
DIFFUSION BACKGROUND MODEL FOR MOVING OBJECTS DETECTION
B. V. Vishnyakov
2015-05-01
Full Text Available In this paper, we propose a new approach for moving objects detection in video surveillance systems. It is based on construction of the regression diffusion maps for the image sequence. This approach is completely different from the state of the art approaches. We show that the motion analysis method, based on diffusion maps, allows objects that move with different speed or even stop for a short while to be uniformly detected. We show that proposed model is comparable to the most popular modern background models. We also show several ways of speeding up diffusion maps algorithm itself.
The Bipolar Quantum Drift-diffusion Model
Xiu Qing CHEN; Li CHEN
2009-01-01
A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassical limit describes the relation between quantum and classical drift-diffusion models. Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.
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.
Callison, Daniel
2002-01-01
Defines models and describes information search models that can be helpful to instructional media specialists in meeting users' abilities and information needs. Explains pathfinders and Kuhlthau's information search process, including the pre-writing information search process. (LRW)
Trait Characteristics of Diffusion Model Parameters
Anna-Lena Schubert
2016-07-01
Full Text Available Cognitive modeling of response time distributions has seen a huge rise in popularity in individual differences research. In particular, several studies have shown that individual differences in the drift rate parameter of the diffusion model, which reflects the speed of information uptake, are substantially related to individual differences in intelligence. However, if diffusion model parameters are to reflect trait-like properties of cognitive processes, they have to qualify as trait-like variables themselves, i.e., they have to be stable across time and consistent over different situations. To assess their trait characteristics, we conducted a latent state-trait analysis of diffusion model parameters estimated from three response time tasks that 114 participants completed at two laboratory sessions eight months apart. Drift rate, boundary separation, and non-decision time parameters showed a great temporal stability over a period of eight months. However, the coefficients of consistency and reliability were only low to moderate and highest for drift rate parameters. These results show that the consistent variance of diffusion model parameters across tasks can be regarded as temporally stable ability parameters. Moreover, they illustrate the need for using broader batteries of response time tasks in future studies on the relationship between diffusion model parameters and intelligence.
Agent-based modelling of cholera diffusion
Augustijn, Ellen-Wien; Doldersum, Tom; Useya, Juliana; Augustijn, Denie
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
Agent-based modelling of cholera diffusion
Augustijn, Ellen-Wien; Doldersum, Tom; Useya, Juliana; Augustijn, Denie
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 d
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
Review of Gaussian diffusion-deposition models
Horst, T.W.
1979-01-01
The assumptions and predictions of several Gaussian diffusion-deposition models are compared. A simple correction to the Chamberlain source depletion model is shown to predict ground-level airborne concentrations and dry deposition fluxes in close agreement with the exact solution of Horst.
Numerical modeling of mantle plume diffusion
Krupsky, D.; Ismail-Zadeh, A.
2004-12-01
To clarify the influence of the heat diffusion on the mantle plume evolution, we develop a two-dimensional numerical model of the plume diffusion and relevant efficient numerical algorithm and code to compute the model. The numerical approach is based on the finite-difference method and modified splitting algorithm. We consider both von Neumann and Direchlet conditions at the model boundaries. The thermal diffusivity depends on pressure in the model. Our results show that the plume is disappearing from the bottom up - the plume tail at first and its head later - because of the mantle plume geometry (a thin tail and wide head) and higher heat conductivity in the lower mantle. We study also an effect of a lateral mantle flow associated with the plate motion on the distortion of the diffusing mantle plume. A number of mantle plumes recently identified by seismic tomography seem to disappear in the mid-mantle. We explain this disappearance as the effect of heat diffusion on the evolution of mantle plume.
ORTHOGONAL-DIRECTIONAL FORWARD DIFFUSION IMAGE INPAINTING AND DENOISING MODEL
Wu Jiying; Ruan Qiuqi; An Gaoyun
2008-01-01
In this paper,an orthogonal-directional forward diffusion Partial Differential Equation (PDE) image inpainting and denoising model which processes image based on variation problem is proposed. The novel model restores the damaged information and smoothes the noise in image si-multaneously. The model is morphological invariant which processes image based on the geometrical property. The regularization item of it diffuses along and cross the isophote,and then the known image information is transported into the target region through two orthogonal directions. The cross isophote diffusion part is the TV (Total Variation) equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation. The equivalence between the Helmholtz equation and the inpainting PDEs is proved. The model with the fidelity item which is used in the whole image domain denoises while preserving edges. So the novel model could inpaint and denoise simultaneously. Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper.
A transformation approach to modelling multi-modal diffusions
Forman, Julie Lyng; Sørensen, Michael
2014-01-01
This paper demonstrates that flexible and statistically tractable multi-modal diffusion models can be attained by transformation of simple well-known diffusion models such as the Ornstein–Uhlenbeck model, or more generally a Pearson diffusion. The transformed diffusion inherits many properties...
The Econometrics Of The Bass Diffusion Model
H.P. Boswijk (Peter); Ph.H.B.F. Franses (Philip Hans)
2002-01-01
textabstractWe propose a new empirical representation of the Bass diffusion model, in order to estimate the three key parameters, concerning innovation, imitation and maturity. The representation is based on the notion that the observed data may temporarily deviate from the mean path determined by
A Simplified Diffusion-Deposition Model
Jensen, Niels Otto
1980-01-01
The use of a simple top hat plume model facilitates an analytical treatment of the deposition problem. A necessary constraint, however, is that the diffusion velocity (e.g., in terms of the plume growth-rate) is large compared to the deposition velocity. With these limitations, explicit formulae...
HUANG Rui Xin
2014-01-01
Two important nonlinear properties of seawater thermodynamics linked to changes of water density, cab-beling and elasticity (compressibility), are discussed. Eddy diffusion and advection lead to changes in den-sity;as a result, gravitational potential energy of the system is changed. Therefore, cabbeling and elasticity play key roles in the energetics of lateral eddy diffusion and advection. Vertical eddy diffusion is one of the key elements in the mechanical energy balance of the global oceans. Vertical eddy diffusion can be con-ceptually separated into two steps:stirring and subscale diffusion. Vertical eddy stirring pushes cold/dense water upward and warm/light water downward;thus, gravitational potential energy is increased. During the second steps, water masses from different places mix through subscale diffusion, and water density is increased due to cabbeling. Using WOA01 climatology and assuming the vertical eddy diffusivity is equal to a constant value of 2×103 Pa2/s, the total amount of gravitational potential energy increase due to vertical stirring in the world oceans is estimated at 263 GW. Cabbeling associated with vertical subscale diffusion is a sink of gravitational potential energy, and the total value of energy lost is estimated at 73 GW. Therefore, the net source of gravitational potential energy due to vertical eddy diffusion for the world oceans is estimated at 189 GW.
Modeling diffuse pollution with a distributed approach.
León, L F; Soulis, E D; Kouwen, N; Farquhar, G J
2002-01-01
The transferability of parameters for non-point source pollution models to other watersheds, especially those in remote areas without enough data for calibration, is a major problem in diffuse pollution modeling. A water quality component was developed for WATFLOOD (a flood forecast hydrological model) to deal with sediment and nutrient transport. The model uses a distributed group response unit approach for water quantity and quality modeling. Runoff, sediment yield and soluble nutrient concentrations are calculated separately for each land cover class, weighted by area and then routed downstream. The distributed approach for the water quality model for diffuse pollution in agricultural watersheds is described in this paper. Integrating the model with data extracted using GIS technology (Geographical Information Systems) for a local watershed, the model is calibrated for the hydrologic response and validated for the water quality component. With the connection to GIS and the group response unit approach used in this paper, model portability increases substantially, which will improve non-point source modeling at the watershed scale level.
Diffusion of innovations in Axelrod's model
Tilles, Paulo F C
2015-01-01
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 and two dimensions, we find that initially the innovation spreads linearly with the time $t$ and diffusively in the long time limit, provided its introduction in the community is successful. For finite lattices, the growth curves for the number of adopters are typically concave functions of $t$. Fo...
Optimal information diffusion in stochastic block models
Curato, Gianbiagio
2016-01-01
We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two community structure where the initial set of informed nodes lies only in one of the two communities and we look for optimal network structures, i.e. those maximizing the asymptotic extent of the diffusion. We find that, constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery, or even disassortative. We then look for minimal cost structures, i.e. those such that a minimal fraction of initially informed nodes is needed to trigger a global cascade. We find that the optimal networks are assortative but with a structure very close to a core-periphery graph, i.e. a very dense community linked to a much more sparsely connected periphery.
Wind and diffusion modeling for complex terrain
Cox, R.M.; Sontowski, J.; Fry, R.N. Jr. [and others
1996-12-31
Atmospheric transport and dispersion over complex terrain were investigated. Meteorological and sulfur hexafluoride (SF{sub 6}) concentration data were collected and used to evaluate the performance of a transport and diffusion model coupled with a mass consistency wind field model. Meteorological data were collected throughout April 1995. Both meteorological and concentration data were measured in December 1995. The data included 11 to 15 surface stations, 1 to 3 upper air stations, and 1 mobile profiler. A range of conditions was encountered, including inversion and post-inversion breakup, light to strong winds, and a broad distribution of wind directions. The models used included the SCIPUFF (Second-order Closure Integrated Puff) transport and diffusion model and the MINERVE mass consistency wind model. Evaluation of the models was focused primarily on their effectiveness as a short term (one to four hours) predictive tool. These studies showed how they can be used to help direct emergency response following a hazardous material release. For purposes of the experiments, the models were used to direct the deployment of mobile sensors intended to intercept and measure tracer clouds.
A diffuse interface model with immiscibility preservation
Tiwari, Arpit, E-mail: atiwari2@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Freund, Jonathan B., E-mail: jbfreund@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Pantano, Carlos [Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States)
2013-11-01
A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical-bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results.
A Specification Test of Stochastic Diffusion Models
Shu-lin ZHANG; Zheng-hong WEI; Qiu-xiang BI
2013-01-01
In this paper,we propose a hypothesis testing approach to checking model mis-specification in continuous-time stochastic diffusion model.The key idea behind the development of our test statistic is rooted in the generalized information equality in the context of martingale estimating equations.We propose a bootstrap resampling method to implement numerically the proposed diagnostic procedure.Through intensive simulation studies,we show that our approach is well performed in the aspects of type Ⅰ error control,power improvement as well as computational efficiency.
Creatinine Diffusion Modeling in Capacitive Sensors
Mohabbati-Kalejahi, Elham; Azimirad, Vahid; Bahrami, Manouchehr
2016-12-01
In this paper, creatinine diffusion in capacitive sensors is discussed. The factors influencing the response time of creatinine biosensors are mathematically formulated and then three novel approaches for decreasing the response time are presented. At first, a piezoelectric actuator is used to vibrate the microtube that contains the blood sample, in order to reduce the viscosity of blood, and thus to increase the coefficient of diffusion. Then, the blood sample is assumed to be pushed through a porous medium, and the relevant conditions are investigated. Finally, the effect of the dentate shape of dielectric on response time is studied. The algorithms and the mathematical models are presented and discussed, and the results of simulations are illustrated. The response times for the first, second and third method are 60, 0.036 and about 31 s, respectively. It is also found that pumping results in very fast responses.
NEW CAR DEMAND MODELING AND FORECASTING USING BASS DIFFUSION MODEL
Zuhaimy Ismail
2013-01-01
Full Text Available Forecasting model of new product demand has been developed and applied to forecast new vehicle demand in Malaysia. Since the publication of the Bass model in 1969, innovation of new diffusion theory has sparked considerable research among marketing science scholars, operational researchers and mathematicians. The building of Bass diffusion model for forecasting new product within the Malaysian society is presented in this study. The proposed model represents the spread level of new Proton car among a given set of the society in terms of a simple mathematical function that elapsed since the introduction of the new car. With the limited amount of data available for the new car, a robust Bass model was developed to forecast the sales volume. A procedure of the proposed diffusion model was designed and the parameters were estimated. Results obtained by applying the proposed model and numerical calculation shows that the proposed diffusion model is robust and effective for forecasting demand of new Proton car. The proposed diffusion model is shown to forecast more effectively and accurately even with insufficient previous data on the new product.
Diffusion through thin membranes: Modeling across scales
Aho, Vesa; Mattila, Keijo; Kühn, Thomas; Kekäläinen, Pekka; Pulkkinen, Otto; Minussi, Roberta Brondani; Vihinen-Ranta, Maija; Timonen, Jussi
2016-04-01
From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.
Elements of a Model State Education Agency Diffusion System.
Mojkowski, Charles
A study, presented to the National Dissemination Conference, provides a conceptualization of a model diffusion system as it might exist within a state education agency (SEA) and places this diffusion model within the context of the SEA's expanding role as an educational service. Five conclusions were reached regarding a model diffusion system.…
HUANG Rui Xin
2014-01-01
Gravitational Potential Energy (GPE) change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps:stirring and sub-scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir-ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi-nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule-rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.
Modeling of Reaction Processes Controlled by Diffusion
Revelli, J
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 differe...
ANALYSIS OF THE MECHANISM MODELS OF TECHNOLOGICAL INNOVATION DIFFUSION
XU Jiuping; HU Minan
2004-01-01
This paper analyzes the mechanism and principle of diffusion of technology diffusion on the basis of quantitative analysis. Then it sets up the diffusion model of innovation incorporating price, advertising and distribution, the diffusion model of innovation including various kinds of consumers, and the substitute model between the new technology and the old one applied systems dynamics, optimization method, probabilistic method and simulation method on computer. Finally this paper concludes with some practical observations from a case study.
Reaction-diffusion pulses: a combustion model
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.
Ancestral process and diffusion model with selection
Mano, Shuhei
2008-01-01
The ancestral selection graph in population genetics introduced by Krone and Neuhauser (1997) is an analogue to the coalescent genealogy. The number of ancestral particles, backward in time, of a sample of genes is an ancestral process, which is a birth and death process with quadratic death and linear birth rate. In this paper an explicit form of the number of ancestral particle is obtained, by using the density of the allele frequency in the corresponding diffusion model obtained by Kimura (1955). It is shown that fixation is convergence of the ancestral process to the stationary measure. The time to fixation of an allele is studied in terms of the ancestral process.
The Voter Model and Jump Diffusion
Majmudar, Jimit; Baumgaertner, Bert O; Tyson, Rebecca C
2015-01-01
Opinions, and subsequently opinion dynamics, depend not just on interactions among individuals, but also on external influences such as the mass media. The dependence on local interactions, however, has received considerably more attention. In this paper, we use the classical voter model as a basis, and extend it to include external influences. We show that this new model can be understood using the theory of jump diffusion processes. We derive results pertaining to fixation probability and expected consensus time of the process, and find that the contribution of an external influence significantly dwarfs the contribution of the node-to-node interactions in terms of driving the social network to eventual consensus. This result suggests the potential importance of ``macro-level'' phenomena such as the media influence as compared to the ``micro-level'' local interactions, in modelling opinion dynamics.
Wind and Diffusion Modeling for Complex Terrain.
Cox, Robert M.; Sontowski, John; Fry, Richard N., Jr.; Dougherty, Catherine M.; Smith, Thomas J.
1998-10-01
Atmospheric transport and dispersion over complex terrain were investigated. Meteorological and sulfur hexafluoride (SF6) concentration data were collected and used to evaluate the performance of a transport and diffusion model coupled with a mass consistency wind field model. Meteorological data were collected throughout April 1995. Both meteorological and plume location and concentration data were measured in December 1995. The meteorological data included measurements taken at 11-15 surface stations, one to three upper-air stations, and one mobile profiler. A range of conditions was encountered, including inversion and postinversion breakup, light to strong winds, and a broad distribution of wind directions.The models used were the MINERVE mass consistency wind model and the SCIPUFF (Second-Order Closure Integrated Puff) transport and diffusion model. These models were expected to provide and use high-resolution three-dimensional wind fields. An objective of the experiment was to determine if these models could provide emergency personnel with high-resolution hazardous plume information for quick response operations.Evaluation of the models focused primarily on their effectiveness as a short-term (1-4 h) predictive tool. These studies showed how they could be used to help direct emergency response following a hazardous material release. For purposes of the experiments, the models were used to direct the deployment of mobile sensors intended to intercept and measure tracer clouds.The April test was conducted to evaluate the performance of the MINERVE wind field generation model. It was evaluated during the early morning radiation inversion, inversion dissipation, and afternoon mixed atmosphere. The average deviations in wind speed and wind direction as compared to observations were within 0.4 m s1 and less than 10° for up to 2 h after data time. These deviations increased as time from data time increased. It was also found that deviations were greatest during
Stochastic Modelling of the Diffusion Coefficient for Concrete
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....
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.
Bass-SIR model for diffusion of new products
Fibich, Gadi
2016-01-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the SIR model, but rather by a novel model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from non-adopters to adopters is described by a non-standard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
Voter Model Perturbations and Reaction Diffusion Equations
Cox, J Theodore; Perkins, Edwin
2011-01-01
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins and the second confirms a conjecture of Ohtsuki et al in the ...
Mathematical model for radon diffusion in earthen materials
Nielson, K.K.; Rogers, V.C.
1982-10-01
Radon migration in porous, earthen materials is characterized by diffusion in both the air and water components of the system as well as by the interaction of the radon between the air and water. The size distribution and configuration of the pore spaces and their moisture distributions are key parameters in determining the radon diffusion coefficient for the bulk material. A mathematical model is developed and presented for calculating radon diffusion coefficients solely from the moisture content and pore size distribution of a soil, reducing the need for resorting to radon diffusion measurements. The resulting diffusion coefficients increase with the median pore diameter of the soil and decrease with increasing widths of the pore size distribution. The calculated diffusion coefficients are suitable for use in simple homogeneous-medium diffusion expressions for predicting radon transport and compare well with measured diffusion coefficients and with empirical diffusion coefficient correlations.
Wang, Shifang; Wu, Tao; Deng, Yongju; Zheng, Qiusha; Zheng, Qian
2016-08-01
Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging-diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging-diverging effect included is in good agreement with reported experimental data.
Theoretical Model of Transformation Superlastic Diffusion Bonding for Eutectoid Steel
无
2002-01-01
Based on current theories of diffusion and creep cavity closure at high temperature, a theoretical analysis of phase transformation diffusion bonding for T8/T8 eutectoid steel is carried out. The diffusion bonding is mainly described as two-stage process: Ⅰ The interfacial cavity with shape change from diamond to cylinder.Ⅱ The radius of the cylindrical cavity are reduced and eliminated gradually. A new theoretical model is established for the process of transformation superplastic diffusion bonding (TSDB) ...
Matrix diffusion model. In situ tests using natural analogues
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.
Some Problems in Using Diffusion Models for New Products
Bernhardt, Irwin; Mackenzie, Kenneth D.
1972-01-01
Analyzes some of the problems involved in using diffusion models to formulate marketing strategies for introducing new products. Six models, which remove some of the theoretical and methodological restrictions inherent in current models of the adoption and diffusion process, are presented. (Author/JH)
Models to assess perfume diffusion from skin.
Schwarzenbach, R; Bertschi, L
2001-04-01
Temperature, fragrance concentration on the skin and power of ventilation have been determined as crucial parameters in fragrance diffusion from skin. A tool has been developed to simulate perfume diffusion from skin over time, allowing headspace analysis and fragrance profile assessments in a highly reproducible way.
Wavelet estimation of the diffusion coefficient in time dependent diffusion models
Ping; CHEN; Jin-de; WANG
2007-01-01
The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1-dimensional bounded Lipschitzian function of the state or the time only.There is no previous work for the nonparametric estimation of time-dependent diffusion models where the diffusion coefficient depends on both the state and the time.This paper introduces and studies a wavelet estimation of the time-dependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz function.Using the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the Lr convergence rate.A strong consistency of the estimate is established.With this result one can estimate the time-dependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability measure.For example,in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure.
Comparison of two stochastic models of scalar diffusion in turbulent flow
Rodean, H. C.; Lange, R.; Nasstrom, J. S.; Gavrilov, V. P.
1992-07-01
This report describes and compares two Lagrangian stochastic models for turbulent diffusion: (1) the random velocity increment model based on the Langevin equation; and (2) the random displacement model. We apply both models to identical test problems for one-dimensional (vertical) diffusion, using identical parameterizations of turbulence statistics as inputs. We compare the results and discuss the advantages and disadvantages of each model. This work is part of an effort to improve the ADPIC dispersion model which is based on the eddy diffusivity model. It is also part of a cooperative research effort on the transport and dispersion of hazardous materials in the atmosphere by the Lawrence Livermore National Laboratory and the Institute of Experimental Meteorology (USSR).
Radon diffusion through multilayer earthen covers: models and simulations
Mayer, D.W.; Oster, C.A.; Nelson, R.W.; Gee, G.W.
1981-09-01
A capability to model and analyze the fundamental interactions that influence the diffusion of radon gas through uranium mill tailings and cover systems has been investigated. The purpose of this study is to develop the theoretical basis for modeling radon diffusion and to develop an understanding of the fundamental interactions that influence radon diffusion. This study develops the theoretical basis for modeling radon diffusion in one, two and three dimensions. The theory has been incorporated into three computer models that are used to analyze several tailings and cover configurations. This report contains a discussion of the theoretical basis for modeling radon diffusion, a discussion of the computer models used to analyze uranium mill tailings and multilayered cover systems, and presents the results that have been obtained.
A variable-order fractal derivative model for anomalous diffusion
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
A consistent transported PDF model for treating differential molecular diffusion
Wang, Haifeng; Zhang, Pei
2016-11-01
Differential molecular diffusion is a fundamentally significant phenomenon in all multi-component turbulent reacting or non-reacting flows caused by the different rates of molecular diffusion of energy and species concentrations. In the transported probability density function (PDF) method, the differential molecular diffusion can be treated by using a mean drift model developed by McDermott and Pope. This model correctly accounts for the differential molecular diffusion in the scalar mean transport and yields a correct DNS limit of the scalar variance production. The model, however, misses the molecular diffusion term in the scalar variance transport equation, which yields an inconsistent prediction of the scalar variance in the transported PDF method. In this work, a new model is introduced to remedy this problem that can yield a consistent scalar variance prediction. The model formulation along with its numerical implementation is discussed, and the model validation is conducted in a turbulent mixing layer problem.
Diffusive description of lattice gas models
Fiig, T.; Jensen, H.J.
1993-01-01
in time. We have numerically investigated the power spectrum of the density fluctuations, the lifetime distribution, and the spatial correlation function. We discuss the appropriate Langevin-like diffusion equation which can reproduce our numerical findings. Our conclusion is that the deterministic...... lattice gases are described by a diffusion equation without any bulk noise. The open lattice gas exhibits a crossover behavior as the probability for introducing particles at the edge of the system becomes small. The power spectrum changes from a 1/f to a 1/f2 spectrum. The diffusive description, proven...
Modeling the diffusion of solid copper into liquid solder alloys
Rizvi, M.J. [School of Computing and Mathematical Sciences, University of Greenwich, 30 Park Row, London, SE10 9LS (United Kingdom)], E-mail: rm77@gre.ac.uk; Lu, H.; Bailey, C. [School of Computing and Mathematical Sciences, University of Greenwich, 30 Park Row, London, SE10 9LS (United Kingdom)
2009-01-01
During the soldering process, the copper atoms diffuse into liquid solders. The diffusion process determines integrity and the reworking possibility of a solder joint. In order to capture the diffusion scenarios of solid copper into liquid Sn-Pb and Sn-Cu solders, a computer modeling has been performed for 10 s. An analytical model has also been proposed for calculating the diffusion coefficient of copper into liquid solders. It is found that the diffusion coefficient for Sn-Pb solder is 2.74 x 10{sup -10} m{sup 2}/s and for Sn-Cu solder is 6.44 x 10{sup -9} m{sup 2}/s. The modeling results reveal that the diffusion coefficient is one of the major factors that govern the rate at which solid Cu dissolve in the molten solder. The predicted dissolved amounts of copper into solders have been validated with the help of scanning electron microscopic analysis.
HUANG Rui Xin
2014-01-01
Gravitational potential energy (GPE) source and sink due to stirring and cabbeling associated with sigma dif-fusion/advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography;the exces-sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec-tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu-sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.
A social diffusion model with an application on election simulation.
Lou, Jing-Kai; Wang, Fu-Min; Tsai, Chin-Hua; Hung, San-Chuan; Kung, Perng-Hwa; Lin, Shou-De; Chen, Kuan-Ta; Lei, Chin-Laung
2014-01-01
Issues about opinion diffusion have been studied for decades. It has so far no empirical approach to model the interflow and formation of crowd's opinion in elections due to two reasons. First, unlike the spread of information or flu, individuals have their intrinsic attitudes to election candidates in advance. Second, opinions are generally simply assumed as single values in most diffusion models. However, in this case, an opinion should represent preference toward multiple candidates. Previously done models thus may not intuitively interpret such scenario. This work is to design a diffusion model which is capable of managing the aforementioned scenario. To demonstrate the usefulness of our model, we simulate the diffusion on the network built based on a publicly available bibliography dataset. We compare the proposed model with other well-known models such as independent cascade. It turns out that our model consistently outperforms other models. We additionally investigate electoral issues with our model simulator.
Some Problems in Using Diffusion Models for New Products.
Bernhardt, Irwin; Mackenzie, Kenneth D.
This paper analyzes some of the problems of using diffusion models to formulate marketing strategies for new products. Though future work in this area appears justified, many unresolved problems limit its application. There is no theory for adoption and diffusion processes; such a theory is outlined in this paper. The present models are too…
The Semiclassical Limit in the Quantum Drift-Diffusion Model
Qiang Chang JU
2009-01-01
Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon-ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diffusion model. In addition, we also proved the global existence of weak solutions.
SEMICLASSICAL LIMIT FOR BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL
Ju Qiangchang; Chen Li
2009-01-01
Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit ofthis solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.
Feller Property for a Special Hybrid Jump-Diffusion Model
Jinying Tong
2014-01-01
Full Text Available We consider the stochastic stability for a hybrid jump-diffusion model, where the switching here is a phase semi-Markovian process. We first transform the process into a corresponding jump-diffusion with Markovian switching by the supplementary variable technique. Then we prove the Feller and strong Feller properties of the model under some assumptions.
One-dimensional diffusion model in an Inhomogeneous region
Fedotov, I
2006-01-01
Full Text Available A one-dimensional model is developed to describe atomic diffusion in a graphite tube atomizer for electrothermal atomic adsorption spectrometry. The underlying idea of the model is the solution of an inhomogeneous one-dimensional diffusion equation...
Stochastic modeling of the diffusion coefficient for concrete
Thoft-Christensen, Palle
In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on a physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficient D is strongly dependent on the w/c ratio and the temperature....... A deterministic relationship between the diffusion coefficient and the w/c ratio and the temperature is used for the stochastic modelling. The w/c ratio and the temperature are modelled by log-normally and normally distributed stochastic variables, respectively. It is then shown by Monte Carlo simulation...... that the diffusion coefficient D may be modelled by a normally distributed stochastic variable. The sensitivities of D with regard to the mean values and the standard deviations are evaluated....
Spatial Pattern of an Epidemic Model with Cross-diffusion
LI Li; JIN Zhen; SUN Gui-Quan
2008-01-01
Pattern formation of a spatial epidemic model with both serf- and cross-diffusion is investigated. From the Turing theory, it is well known that Thring pattern formation cannot occur for the equal self-diffusion coefficients.However, combined with cross-diffusion, the system will show emergence of isolated groups, i.e., stripe-like or spotted or coexistence of both, which we show by both mathematical ana/ysis and numerical simulations. Our study shows that the interaction of self- and cross-diffusion can be considered as an important mechanism for the appearance of complex spatiotemporal dynamics in epidemic models.
Asmparts: assembly of biological model parts.
Rodrigo, Guillermo; Carrera, Javier; Jaramillo, Alfonso
2007-12-01
We propose a new computational tool to produce models of biological systems by assembling models from biological parts. Our software not only takes advantage of modularity, but it also enforces standardisation in part characterisation by considering a model of each part. We have used model parts in SBML to design transcriptional networks. Our software is open source, it works in linux and windows platforms, and it could be used to automatically produce models in a server. Our tool not only facilitates model design, but it will also help to promote the establishment of a registry of model parts.
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.
Varakin, A I; Mazur, V V; Arkhipova, N V; Serianov, Iu V
2009-01-01
Mathematical models of the transfer of charged macromolecules have been constructed on the basis of the classical equations of electromigration diffusion of Helmholtz-Smolukhovskii, Goldman, and Goldman-Hodgkin-Katz. It was shown that ion transfer in placental (mimicking lipid-protein barriers) and muscle barriers occurs by different mechanisms. In placental barriers, the electromigration diffusion occurs along lipid-protein channels formed due to the conformational deformation of phospholipid and protein molecules with the coefficients of diffusion D = (2.6-3.6) x 10(-8) cm2/s. The transfer in muscle barriers is due to the migration across charged interfibrillar channels with the negative diffusion activation energy, which is explained by changes in the structure of muscle fibers and expenditures of thermal energy for the extrusion of Cl- from channel walls with the diffusion coefficient D = (6.0-10.0) x 10(-6) cm2/s.
Many-server queues with customer abandonment: Numerical analysis of their diffusion model
Shuangchi He
2013-01-01
Full Text Available We use a multidimensional diffusion process to approximate the dynamics of aqueue served by many parallel servers. Waiting customers in this queue may abandonthe system without service. To analyze the diffusion model, we develop a numericalalgorithm for computing its stationary distribution. A crucial part of the algorithm ischoosing an appropriate reference density. Using a conjecture on the tailbehavior of the limit queue length process, we propose a systematic approach toconstructing a reference density. With the proposed reference density, thealgorithm is shown to converge quickly in numerical experiments. Theseexperiments demonstrate that the diffusion model is a satisfactory approximation formany-server queues, sometimes for queues with as few as twenty servers.
A memory diffusion model for molecular anisotropic diffusion in siliceous β-zeolite.
Ji, Xiangfei; An, Zhuanzhuan; Yang, Xiaofeng
2016-01-01
A memory diffusion model of molecules on β-zeolite is proposed. In the model, molecular diffusion in β-zeolites is treated as jumping from one adsorption site to its neighbors and the jumping probability is a compound probability which includes that provided by the transitional state theory as well as that derived from the information about which direction the target molecule comes from. The proposed approach reveals that the diffusivities along two crystal axes on β-zeolite are correlated. The model is tested by molecular dynamics simulations on diffusion of benzene and other simple molecules in β-zeolites. The results show that the molecules with larger diameters fit the prediction much better and that the "memory effects" are important in all cases.
Dynamic hysteresis modeling including skin effect using diffusion equation model
Hamada, Souad; Louai, Fatima Zohra; Nait-Said, Nasreddine; Benabou, Abdelkader
2016-07-01
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Dynamic hysteresis modeling including skin effect using diffusion equation model
Hamada, Souad, E-mail: souadhamada@yahoo.fr [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Louai, Fatima Zohra, E-mail: fz_louai@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Nait-Said, Nasreddine, E-mail: n_naitsaid@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Benabou, Abdelkader, E-mail: Abdelkader.Benabou@univ-lille1.fr [L2EP, Université de Lille1, 59655 Villeneuve d’Ascq (France)
2016-07-15
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
A NEW MODEL FOR THE DETERMINATION OF GRAIN BOUNDARY DIFFUSIVITIES
R LOUAHDI
2001-12-01
Full Text Available A new model, based on a surface saturation technique, is suggested to determine grain boundary diffusivity of impurities. The model is applied to the Ni-S system that is of great practical interest. The initial saturation of nickel grain boundaries with sulphur is obtained by annealing at a temperature which satisfies the thermodynamics criterion for surface saturation. In order to reduce the annealing time, dynamic (non-equilibrium segregation is induced by carrying out the anneal on cold worked nickel (e = 0.2 true strain. Both the grain boundaries and the surface were saturated after only 24 hours of annealing at a temperature as low as 450°C. The heat treatment of the cold rolled material was carried out inside the vacuum chamber of an Auger Electron Spectrometer (AES. The diffusivity, as obtained from the slope of the linear parts of the kinetics curves recorded by the AES, is found to be given by the relationship D = 2.7×10-9exp(-58.700/RT m2s-1 in the temperature range 450 to 700°C.
Anisotropy-resolving models for predicting separation in 3--D asymmetric diffusers
Jeyapaul, Elbert; Durbin, Paul
2011-11-01
All linear eddy-viscosity models are qualitatively incorrect in predicting separation in 3-D asymmetric diffusers. The failure to predict normal stress and shear stress anisotropy at high production-dissipation ratios is the cause. The Explicit algebraic Reynolds stress model (Wallin and Johansson, 2000) predicts the mean flow field in the diffuser accurately, but not the wall pressure and Reynolds stresses. Recalibrating the coefficients of the rapid part of pressure-strain model improves the wall pressure prediction. Including the convective, diffusive, streamline curvature effects on anisotropy has not been beneficial. The model has been tested using a family of diffusers having the same nominal streamwise pressure gradient, LES data is used as a reference. Professor
Diffusion imaging with stimulated echoes: signal models and experiment design
Alexander, Daniel C
2013-01-01
Purpose: Stimulated echo acquisition mode (STEAM) diffusion MRI can be advantageous over pulsed-gradient spin-echo (PGSE) for diffusion times that are long compared to $\\ttwo$. It is important therefore for biomedical diffusion imaging applications at 7T and above where $\\ttwo$ is short. However, imaging gradients in the STEAM sequence contribute much greater diffusion weighting than in PGSE, but are often ignored during post-processing. We demonstrate here that this can severely bias parameter estimates. Method: We present models for the STEAM signal for free and restricted diffusion that account for crusher and slice-select (butterfly) gradients to avoid such bias. The butterfly gradients also disrupt experiment design, typically by skewing gradient-vectors towards the slice direction. We propose a simple compensation to the diffusion gradient vector specified to the scanner that counterbalances the butterfly gradients to preserve the intended experiment design. Results: High-field data fixed monkey brain e...
Modeling dendrite density from magnetic resonance diffusion measurements
Jespersen, Sune Nørhøj; Kroenke, CD; Østergaard, Leif;
2007-01-01
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 in this mo...
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
Nonequilibrium drift-diffusion model for organic semiconductor devices
Felekidis, Nikolaos; Melianas, Armantas; Kemerink, Martijn
2016-07-01
Two prevailing formalisms are currently used to model charge transport in organic semiconductor devices. Drift-diffusion calculations, on the one hand, are time effective but assume local thermodynamic equilibrium, which is not always realistic. Kinetic Monte Carlo models, on the other hand, do not require this assumption but are computationally expensive. Here, we present a nonequilibrium drift-diffusion model that bridges this gap by fusing the established multiple trap and release formalism with the drift-diffusion transport equation. For a prototypical photovoltaic system the model is shown to quantitatively describe, with a single set of parameters, experiments probing (1) temperature-dependent steady-state charge transport—space-charge limited currents, and (2) time-resolved charge transport and relaxation of nonequilibrated photocreated charges. Moreover, the outputs of the developed kinetic drift-diffusion model are an order of magnitude, or more, faster to compute and in good agreement with kinetic Monte Carlo calculations.
Pricing Participating Products under a Generalized Jump-Diffusion Model
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.
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.
Wang, Hsin [ORNL; Porter, Wallace D [ORNL; Bottner, Harold [Fraunhofer-Institute, Freiburg, Germany; Konig, Jan [Fraunhofer-Institute, Freiburg, Germany; Chen, Lidong [Chinese Academy of Sciences; Bai, Shengqiang [Chinese Academy of Sciences; Tritt, Terry M. [Clemson University; Mayolett, Alex [Corning, Inc; Senawiratne, Jayantha [Corning, Inc; Smith, Charlene [Corning, Inc; Harris, Fred [ZT-Plus; Gilbert, Partricia [Marlow Industries, Inc; Sharp, J [Marlow Industries, Inc; Lo, Jason [CANMET - Materials Technology Laboratory, Natural Resources of Canada; Keinke, Holger [University of Waterloo, Canada; Kiss, Laszlo I. [University of Quebec at Chicoutimi
2013-01-01
For bulk thermoelectrics, figure-of-merit, ZT, still needs to improve from the current value of 1.0 - 1.5 to above 2 to be competitive to other alternative technologies. In recent years, the most significant improvements in ZT were mainly due to successful reduction of thermal conductivity. However, thermal conductivity cannot be measured directly at high temperatures. The combined measurements of thermal diffusivity and specific heat and density are required. It has been shown that thermal conductivity is the property with the greatest uncertainty and has a direct influence on the accuracy of the figure of merit. The International Energy Agency (IEA) group under the implementing agreement for Advanced Materials for Transportation (AMT) has conducted two international round-robins since 2009. This paper is Part II of the international round-robin testing of transport properties of bulk bismuth telluride. The main focuses in Part II are on thermal diffusivity, specific heat and thermal conductivity.
Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model
Xiaoqin Wang
2013-01-01
Full Text Available We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.
New Symmetries for a Model of Fast Diffusion
QIN Mao-Chang; XU Xue-Jun; MEI Feng-Xiang
2004-01-01
@@ The new symmetries for a mathematical model of fast diffusion are determined. A new system method is given to search for new symmetries of differential equations written in a conserved form, several new symmetry generators and exact solutions are presented.
Postural control model interpretation of stabilogram diffusion analysis
Peterka, R. J.
2000-01-01
Collins and De Luca [Collins JJ. De Luca CJ (1993) Exp Brain Res 95: 308-318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.
Modeling diffuse reflectance measurements of light scattered by layered tissues
Rohde, Shelley B.
In this dissertation, we first present a model for the diffuse reflectance due to a continuous beam incident normally on a half space composed of a uniform scattering and absorbing medium. This model is the result of an asymptotic analysis of the radiative transport equation for strong scattering, weak absorption and a defined beam width. Through comparison with the diffuse reflectance computed using the numerical solution of the radiative transport equation, we show that this diffuse reflectance model gives results that are accurate for small source-detector separation distances. We then present an explicit model for the diffuse reflectance due to a collimated beam of light incident normally on layered tissues. This model is derived using the corrected diffusion approximation applied to a layered medium, and it takes the form of a convolution with an explicit kernel and the incident beam profile. This model corrects the standard diffusion approximation over all source-detector separation distances provided the beam is sufficiently wide compared to the scattering mean-free path. We validate this model through comparison with Monte Carlo simulations. Then we use this model to estimate the optical properties of an epithelial layer from Monte Carlo simulation data. Using measurements at small source-detector separations and this model, we are able to estimate the absorption coefficient, scattering coefficient and anisotropy factor of epithelial tissues efficiently with reasonable accuracy. Finally, we present an extension of the corrected diffusion approximation for an obliquely incident beam. This model is formed through a Fourier Series representation in the azimuthal angle which allows us to exhibit the break in axisymmetry when combined with the previous analysis. We validate this model with Monte Carlo simulations. This model can also be written in the form of a convolution of an explicit kernel with the incident beam profile. Additionally, it can be used to
A transformation approach to modelling multi-modal diffusions
Forman, Julie Lyng; Sørensen, Michael
2014-01-01
when the diffusion is observed with additional measurement error. The new approach is applied to molecular dynamics data in the form of a reaction coordinate of the small Trp-zipper protein, from which the folding and unfolding rates of the protein are estimated. Because the diffusion coefficient...... is state-dependent, the new models provide a better fit to this type of protein folding data than the previous models with a constant diffusion coefficient, particularly when the effect of errors with a short time-scale is taken into account....
A reaction-diffusion model of human brain development.
Julien Lefèvre
2010-04-01
Full Text Available Cortical folding exhibits both reproducibility and variability in the geometry and topology of its patterns. These two properties are obviously the result of the brain development that goes through local cellular and molecular interactions which have important consequences on the global shape of the cortex. Hypotheses to explain the convoluted aspect of the brain are still intensively debated and do not focus necessarily on the variability of folds. Here we propose a phenomenological model based on reaction-diffusion mechanisms involving Turing morphogens that are responsible for the differential growth of two types of areas, sulci (bottom of folds and gyri (top of folds. We use a finite element approach of our model that is able to compute the evolution of morphogens on any kind of surface and to deform it through an iterative process. Our model mimics the progressive folding of the cortical surface along foetal development. Moreover it reveals patterns of reproducibility when we look at several realizations of the model from a noisy initial condition. However this reproducibility must be tempered by the fact that a same fold engendered by the model can have different topological properties, in one or several parts. These two results on the reproducibility and variability of the model echo the sulcal roots theory that postulates the existence of anatomical entities around which the folding organizes itself. These sulcal roots would correspond to initial conditions in our model. Last but not least, the parameters of our model are able to produce different kinds of patterns that can be linked to developmental pathologies such as polymicrogyria and lissencephaly. The main significance of our model is that it proposes a first approach to the issue of reproducibility and variability of the cortical folding.
A Stochastic Model of Inward Diffusion in Magnetospheric Plasmas
Sato, Naoki
2014-01-01
The inward diffusion of particles, often observed in magnetospheric plasmas (either naturally created stellar ones or laboratory devices) creates a spontaneous density gradient, which seemingly contradicts the entropy principle. We construct a theoretical model of diffusion that can explain the inward diffusion in a dipole magnetic field. The key is the identification of the proper coordinates on which an appropriate diffusion operator can be formulated. The effective phase space is foliated by the adiabatic invariants; on the symplectic leaf, the invariant measure (by which the entropy must be calculated) is distorted, by the inhomogeneous magnetic field, with respect to the conventional Lebesgue measure of the natural phase space. The collision operator is formulated to be consistent to the ergodic hypothesis on the symplectic leaf, i.e., the resultant diffusion must diminish gradients on the proper coordinates. The non-orthogonality of the cotangent vectors of the configuration space causes a coupling betw...
Modelling Urban diffuse pollution in groundwater
Jato, Musa; Smith, Martin; Cundy, Andrew
2017-04-01
Diffuse urban pollution of surface and ground waters is a growing concern in many cities and towns. Traffic-derived pollutants such as salts, heavy metals and polycyclic aromatic hydrocarbons (PAHs) may wash off road surfaces in soluble or particulate forms which later drain through soils and drainage systems into surface waters and groundwater. In Brighton, about 90% of drinking water supply comes from groundwater (derived from the Brighton Chalk block). In common with many groundwater sources the Chalk aquifer has been relatively extensively monitored and assessed for diffuse rural contaminants such as nitrate, but knowledge on the extent of contamination from road run-off is currently lacking. This project examines the transfer of traffic-derived contaminants from the road surface to the Chalk aquifer, via urban drainage systems. A transect of five boreholes have been sampled on a monthly basis and groundwater samples analysed to examine the concentrations of key, mainly road run-off derived, hydrocarbon and heavy metal contaminants in groundwater across the Brighton area. Trace concentrations of heavy metals and phenols have been observed in groundwater. Electrical conductivity changes in groundwater have also been used to assess local changes in ionic strength which may be associated with road-derived contaminants. This has been supplemented by systematic water and sediment sampling from urban gully pots, with further sampling planned from drainage and settlement ponds adjacent to major roads, to examine initial road to drainage system transport of major contaminants.
Theoretical model of blood flow measurement by diffuse correlation spectroscopy
Sakadžić, Sava; Boas, David A.; Carp, Stefan
2017-02-01
Diffuse correlation spectroscopy (DCS) is a noninvasive method to quantify tissue perfusion from measurements of the intensity temporal autocorrelation function of diffusely scattered light. However, DCS autocorrelation function measurements in tissue better match theoretical predictions based on the diffusive motion of the scatterers than those based on a model where the advective nature of blood flow dominates the stochastic properties of the scattered light. We have recently shown using Monte Carlo (MC) simulations and assuming a simplistic vascular geometry and laminar flow profile that the diffusive nature of the DCS autocorrelation function decay is likely a result of the shear-induced diffusion of the red blood cells. Here, we provide theoretical derivations supporting and generalizing the previous MC results. Based on the theory of diffusing-wave spectroscopy, we derive an expression for the autocorrelation function along the photon path through a vessel that takes into account both diffusive and advective scatterer motion, and we provide the solution for the DCS autocorrelation function in a semi-infinite geometry. We also derive the correlation diffusion and correlation transfer equation, which can be applied for an arbitrary sample geometry. Further, we propose a method to take into account realistic vascular morphology and flow profile.
Guillory, J. U.; Terry, R. E.
1984-07-01
This report describes work done under DNA Contract 001-79-C-0189 from February 1982 to June 1983, and some more recent work. Part 1 includes treatments of a simple zero-D implosion code, analytic but very approximate scaling laws for radiation, and a discussion of preliminary work on nonlinear field penetration of plasma. Part 2 contains a discussion of electrodiffusive 1D modeling of annular plasma implosions. The thermoelectrical field, its role in field penetrations, the nonlocal constraints required in field diffusion (and some arising from field diffusion), flux limits and the acceleration process for annular plasmas are discussed.
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
Innovation Diffusion Model in Higher Education: Case Study of E-Learning Diffusion
Buc, Sanjana; Divjak, Blaženka
2015-01-01
The diffusion of innovation (DOI) is critical for any organization and especially nowadays for higher education institutions (HEIs) in the light of vast pressure of emerging educational technologies as well as of the demand of economy and society. DOI takes into account the initial and the implementation phase. The conceptual model of DOI in…
Toward Information Diffusion Model for Viral Marketing in Business
Lulwah AlSuwaidan
2016-02-01
Full Text Available Current obstacles in the study of social media marketing include dealing with massive data and real-time updates have motivated to contribute solutions that can be adopted for viral marketing. Since information diffusion and social networks are the core of viral marketing, this article aims to investigate the constellation of diffusion methods for viral marketing. Studies on diffusion methods for viral marketing have applied different computational methods, but a systematic investigation of these methods has limited. Most of the literature have focused on achieving objectives such as influence maxi-mization or community detection. Therefore, this article aims to conduct an in-depth review of works related to diffusion for viral marketing. Viral marketing has applied to business-to-consumer transactions but has seen limited adoption in business-to-business transactions. The literature review reveals a lack of new diffusion methods, especially in dynamic and large-scale networks. It also offers insights into applying various mining methods for viral marketing. It discusses some of the challenges, limitations, and future research directions of information diffusion for viral marketing. The article also introduces a viral marketing informa-tion diffusion model. The proposed model attempts to solve the dynamicity and large-scale data of social networks by adopting incremental clustering and a stochastic differential equation for business-to-business transactions.
Evaluation of the Thermodynamic Models for the Thermal Diffusion Factor
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 Drickame...
Diffuse Scattering Model of Indoor Wideband Propagation
Franek, Ondrej; Andersen, Jørgen Bach; Pedersen, Gert Frølund
2011-01-01
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...... 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...... intensity in all locations eventually follows exponential decay with the same slope and approximately the same level for given delay. These observations are shown to be in good agreement with theory and previous measurements—the slopes of the decay curves for measurement, simulation and theory are found...
Modeling cation diffusion in compacted water-saturatedNa-bentonite at low ionic strength
Bourg, Ian C.; Sposito, Garrison; Bourg, Alain C.M.
2007-08-28
Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the 'macropore/nanopore' model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the 'surface diffusion' model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm{sup -3} (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.2 kg dm{sup -3}.
Numerical Simulation Model of Laminar Hydrogen/Air Diffusion Flame
于溯源; 吕雪峰
2002-01-01
A numerical simulation model is developed for a laminar hydrogen/air diffusion flame. Nineteen species and twenty chemical reactions are considered. The chemical kinetics package (CHEMKIN) subroutines are employed to calculate species thermodynamic properties and chemical reaction rate constants. The flow field is calculated by simultaneously solving a continuity equation, an axial momentum equation and an energy equation in a cylindrical coordinate system. Thermal diffusion and Brownian diffusion are considered in the radial direction while they are neglected in the axial direction. The results suggest that the main flame is buoyancy-controlled.
Reaction-diffusion-branching models of stock price fluctuations
Tang, Lei-Han; Tian, Guang-Shan
Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ( H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.
Update on Advection-Diffusion Purge Flow Model
Brieda, Lubos
2015-01-01
Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.
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.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
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)
Many-server queues with customer abandonment: numerical analysis of their diffusion models
Dai, J G
2011-01-01
We use multidimensional diffusion processes to approximate the dynamics of a queue served by many parallel servers. The queue is served in the first-in-first-out (FIFO) order and the customers waiting in queue may abandon the system without service. Two diffusion models are proposed in this paper. They differ in how the patience time distribution is built into them. The first diffusion model uses the patience time density at zero and the second one uses the entire patience time distribution. To analyze these diffusion models, we develop a numerical algorithm for computing the stationary distribution of such a diffusion process. A crucial part of the algorithm is to choose an appropriate reference density. Using a conjecture on the tail behavior of a limit queue length process, we propose a systematic approach to constructing a reference density. With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments. These experiments also show that the diffusion models are go...
Cohabitation reaction-diffusion model for virus focal infections
Amor, Daniel R.; Fort, Joaquim
2014-12-01
The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction-diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction-diffusion equations may lead to unrealistic descriptions. We argue that previous virus infection models also have this limitation, because they assume that a virion can simultaneously reproduce inside a cell and diffuse away from it. For this reason, we build a several-species cohabitation model that does not have this limitation. Furthermore, we perform a sensitivity analysis for the most relevant parameters of the model, and we compare the predicted infection speed with observed data for two different strains of the T7 virus.
Knowledge epidemics and population dynamics models for describing idea diffusion
Vitanov, Nikolay K
2012-01-01
The diffusion of ideas is often closely connected to the creation and diffusion of knowledge and to the technological evolution of society. Because of this, knowledge creation, exchange and its subsequent transformation into innovations for improved welfare and economic growth is briefly described from a historical point of view. Next, three approaches are discussed for modeling the diffusion of ideas in the areas of science and technology, through (i) deterministic, (ii) stochastic, and (iii) statistical approaches. These are illustrated through their corresponding population dynamics and epidemic models relative to the spreading of ideas, knowledge and innovations. The deterministic dynamical models are considered to be appropriate for analyzing the evolution of large and small societal, scientific and technological systems when the influence of fluctuations is insignificant. Stochastic models are appropriate when the system of interest is small but when the fluctuations become significant for its evolution...
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
Compact Models for Defect Diffusivity in Semiconductor Alloys.
Wright, Alan F.; Modine, Normand A.; Lee, Stephen R.; Foiles, Stephen M.
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 (QASP R) pro gram since defect di ffusion 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 us ing alloy s such as InGaAs and InGa P . 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, r adiation - 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 c ompute the time dependence of defect ener gies 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 disseminatio n only as authorized to U.S. Government agencies and their contr actors; other requests shall be approved by the originating facility or higher
Langevin equation with fluctuating diffusivity: A two-state model.
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
Modeling Copper Diffusion in Polycrystalline CdTe Solar Cells
Akis, Richard [Arizona State University; Brinkman, Daniel [Arizona State University; Sankin, Igor [First Solar; Fang, Tian [First Solar; Guo, Da [Arizona State Univeristy; Vasileska, Dragica [Arizona State University; Ringhofer, Christain [Arizona State University
2014-06-06
It is well known that Cu plays an important role in CdTe solar cell performance as a dopant. In this work, a finite-difference method is developed and used to simulate Cu diffusion in CdTe solar cells. In the simulations, which are done on a two-dimensional (2D) domain, the CdTe is assumed to be polycrystalline, with the individual grains separated by grain boundaries. When used to fit experimental Cu concentration data, bulk and grain boundary diffusion coefficients and activation energies for CdTe can be extracted. In the past, diffusion coefficients have been typically obtained by fitting data to simple functional forms of limited validity. By doing full simulations, the simplifying assumptions used in those analytical models are avoided and diffusion parameters can thus be determined more accurately
Modeling diffusion of innovations with probabilistic cellular automata
Boccara, N; Boccara, Nino; Fuks, Henryk
1997-01-01
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a second-order phase transition. We show that the number of individuals who eventually keep adopting the innovation strongly depends on connectivity between individuals.
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
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.
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.
Relaxation and diffusion models with non-singular kernels
Sun, HongGuang; Hao, Xiaoxiao; Zhang, Yong; Baleanu, Dumitru
2017-02-01
Anomalous relaxation and diffusion processes have been widely quantified by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to its limitation in describing different kinds of non-exponential decays (e.g. stretched exponential decay). Meanwhile, many efforts by mathematicians and engineers have been made to overcome the singularity of power function kernel in its definition. This study first explores physical properties of relaxation and diffusion models where the temporal derivative was defined recently using an exponential kernel. Analytical analysis shows that the Caputo type derivative model with an exponential kernel cannot characterize non-exponential dynamics well-documented in anomalous relaxation and diffusion. A legitimate extension of the previous derivative is then proposed by replacing the exponential kernel with a stretched exponential kernel. Numerical tests show that the Caputo type derivative model with the stretched exponential kernel can describe a much wider range of anomalous diffusion than the exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes.
Weak diffusion limits of dynamic conditional correlation models
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 dif......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...... for the rate of convergence of the parameters, obtaining time-varying but deterministic variances and/or correlations. A Monte Carlo experiment confirms that the quasi approximate maximum likelihood (QAML) method to estimate the diffusion parameters is inconsistent for any fixed frequency, but that it may...
A coupled model for intragranular deformation and chemical diffusion
Zhong, Xin; Vrijmoed, Johannes; Moulas, Evangelos; Tajčmanová, Lucie
2017-09-01
A coupled model for chemical diffusion and mechanical deformation is developed in analogy to the studies of poroelasticity and thermoelasticity. Nondimensionalization of the governing equations yields a controlling dimensionless parameter, the Deborah number, given by the ratio of the characteristic time for pressure relaxation and concentration homogenization. Using the Deborah number two types of plausible chemical zonation are distinguished, i.e. diffusion controlled, and mechanically controlled. The transition between these two types of chemical zonation is determined at the conditions where the Deborah number equals one. We apply our model to a chemically zoned plagioclase rim in a spherical coordinate frame assuming homogeneous initial pressure. Using thermodynamic data, an experimentally derived diffusion coefficient and a viscous flow law for plagioclase, our numerical simulations show that up to ∼0.6 GPa grain-scale pressure variation is generated during the diffusion-deformation process. Due to the mechanical-chemical coupling, the pressure variations maintain the chemical zonation longer than predicted by the classical diffusion model. The fully coupled mechanical-chemical model provides an alternative explanation for the preservation of chemically zoned minerals, and may contribute to a better understanding of metamorphic processes in the deep Earth interior.
Notes on the Langevin model for turbulent diffusion of ``marked`` particles
Rodean, H.C.
1994-01-26
Three models for scalar diffusion in turbulent flow (eddy diffusivity, random displacement, and on the Langevin equation) are briefly described. These models random velocity increment based Fokker-Planck equation is introduced as are then examined in more detail in the reverse order. The Fokker-Planck equation is the Eulerian equivalent of the Lagrangian Langevin equation, and the derivation of e outlined. The procedure for obtaining the deterministic and stochastic components of the Langevin equation from Kolmogorov`s 1941 inertial range theory and the Fokker-Planck equation is described. it is noted that a unique form of the Langevin equation can be determined for diffusion in one dimension but not in two or three. The Langevin equation for vertical diffusion in the non-Gaussian convective boundary layer is presented and successively simplified for Gaussian inhomogeneous turbulence and Gaussian homogeneous turbulence in turn. The Langevin equation for Gaussian inhomogeneous turbulence is mathematically transformed into the random displacement model. It is shown how the Fokker-Planck equation for the random displacement model is identical in form to the partial differential equation for the eddy diffusivity model. It is noted that the Langevin model is applicable in two cases in which the other two are not valid: (1) very close in time and distance to the point of scalar release and (2) the non-Gaussian convective boundary layer. The two- and three-dimensional cases are considered in Part III.
Modelling on cavitation in a diffuser with vortex generator
Jablonská J.
2013-04-01
Full Text Available Based on cavitation modelling in Laval nozzle results and experience, problem with the diffuser with vortex generator was defined. The problem describes unsteady multiphase flow of water. Different cavitation models were used when modelling in Fluent, flow condition is inlet and pressure condition is outlet. Boundary conditions were specified by Energy Institute, Victor Kaplan’s Department of Fluid Engineering, Faculty of Mechanical Engineering, Brno University of Technology. Numerical modelling is compared with experiment.
Mathematical models of a diffusion-convection in porous media
Anvarbek M. Meirmanov
2012-06-01
Full Text Available Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory. We start with the mathematical model on the microscopic level, which consist of the Stokes system for a weakly compressible viscous liquid occupying a pore space, coupled with a diffusion-convection equation for the admixture. We suppose that the viscosity of the liquid depends on a concentration of the admixture and for this nonlinear system we prove the global in time existence of a weak solution. Next we rigorously fulfil the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous media.
Modeling and Analysis of Epidemic Diffusion with Population Migration
Ming Liu
2013-01-01
Full Text Available An improved Susceptible-Infected-Susceptible (SIS epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease-free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion.
Diffusion model for acid corrosion of cemented materials
Van Dijk, J.C.; De Moel, P.J.; Nooyen, W.F.; Nuiten, P.C.
1986-09-25
The acid corrosion of cemented materials is an important aspect in engineering practice. Corrosion affects the strength of materials and may cause a deterioration of water quality. This article deals with corrosion due to non-erosive acid attacks. A diffusion model is presented in which the depth of attack increases in proportion to the square root of both time, the hydronium ion concentration in the water, and the inverse of the total concentration of lime in the solid phase. Experiments verifying the model are presented. The experiments also reveal that the corrosion of asbestos cement proceeds faster as compared to concrete because of desintegration of the structure of asbestos cement. The diffusion model also worked out to be applicable for corrosion by agressive CO/sub 2/. The lower corrosion rate due to the formation of CaCO/sub 3/ can for this case be described by a lower diffusion coefficient. 4 tabs., 6 figs., 9 refs.
Numerical modelling of swirling diffusive flames
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.
Hierarchical set of models to estimate soil thermal diffusivity
Arkhangelskaya, Tatiana; Lukyashchenko, Ksenia
2016-04-01
Soil thermal properties significantly affect the land-atmosphere heat exchange rates. Intra-soil heat fluxes depend both on temperature gradients and soil thermal conductivity. Soil temperature changes due to energy fluxes are determined by soil specific heat. Thermal diffusivity is equal to thermal conductivity divided by volumetric specific heat and reflects both the soil ability to transfer heat and its ability to change temperature when heat is supplied or withdrawn. The higher soil thermal diffusivity is, the thicker is the soil/ground layer in which diurnal and seasonal temperature fluctuations are registered and the smaller are the temperature fluctuations at the soil surface. Thermal diffusivity vs. moisture dependencies for loams, sands and clays of the East European Plain were obtained using the unsteady-state method. Thermal diffusivity of different soils differed greatly, and for a given soil it could vary by 2, 3 or even 5 times depending on soil moisture. The shapes of thermal diffusivity vs. moisture dependencies were different: peak curves were typical for sandy soils and sigmoid curves were typical for loamy and especially for compacted soils. The lowest thermal diffusivities and the smallest range of their variability with soil moisture were obtained for clays with high humus content. Hierarchical set of models will be presented, allowing an estimate of soil thermal diffusivity from available data on soil texture, moisture, bulk density and organic carbon. When developing these models the first step was to parameterize the experimental thermal diffusivity vs. moisture dependencies with a 4-parameter function; the next step was to obtain regression formulas to estimate the function parameters from available data on basic soil properties; the last step was to evaluate the accuracy of suggested models using independent data on soil thermal diffusivity. The simplest models were based on soil bulk density and organic carbon data and provided different
Groundwater transport modeling with nonlinear sorption and intraparticle diffusion
Singh, Anshuman; Allen-King, Richelle M.; Rabideau, Alan J.
2014-08-01
Despite recent advances in the mechanistic understanding of sorption in groundwater systems, most contaminant transport models provide limited support for nonideal sorption processes such as nonlinear isotherms and/or diffusion-limited sorption. However, recent developments in the conceptualization of "dual mode" sorption for hydrophobic organic contaminants have provided more realistic and mechanistically sound alternatives to the commonly used Langmuir and Freundlich models. To support the inclusion of both nonlinear and diffusion-limited sorption processes in groundwater transport models, this paper presents two numerical algorithms based on the split operator approach. For the nonlinear equilibrium scenario, the commonly used two-step split operator algorithm has been modified to provide a more robust treatment of complex multi-parameter isotherms such as the Polanyi-partitioning model. For diffusion-limited sorption, a flexible three step split-operator procedure is presented to simulate intraparticle diffusion in multiple spherical particles with different sizes and nonlinear isotherms. Numerical experiments confirmed the accuracy of both algorithms for several candidate isotherms. However, the primary advantages of the algorithms are: (1) flexibility to accommodate any isotherm equation including "dual mode" and similar expressions, and (2) ease of adapting existing grid-based transport models of any dimensionality to include nonlinear sorption and/or intraparticle diffusion. Comparisons are developed for one-dimensional transport scenarios with different isotherms and particle configurations. Illustrative results highlight (1) the potential influence of isotherm model selection on solute transport predictions, and (2) the combined effects of intraparticle diffusion and nonlinear sorption on the plume transport and flushing for both single-particle and multi-particle scenarios.
Secondary Cosmic Positrons in an Anisotropic Diffusion Model
Kappl, Rolf
2016-01-01
One aim of cosmic ray measurements is the search for possible signatures of annihilating or decaying dark matter. The so-called positron excess has attracted a lot of attention in this context. On the other hand it has been proposed that the data might challenge the established diffusion model for cosmic ray propagation. We investigate an anisotropic diffusion model by solving the corresponding equations analytically. Depending on the propagation parameters we find that the spectral features of the positron spectrum are affected significantly. We also discuss the influence of the anisotropy on hadronic spectra.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
A WORKING INTEGRATED MODEL FOR THE DIFFUSION OF CONSTRUCTION INNOVATION
Ahmad Rahman Songip
2013-01-01
Full Text Available Construction industry is said to be low in innovation and adoption of innovations is necessary to gain competitive advantage in a liberalized and globalized marketplace. This study investigated the factors that influenced the diffusion of construction innovations and developed an integrated framework to improve the diffusion process. A conceptual model was developed to guide the study and the modification of a questionnaire used in previous study of similar nature. The dependent variable was extent of diffusion and 10 independent factors were identified and categorized into industry characteristics, innovation attributes, adopter innovative characteristics and environmental interventions. A questionnaire survey was conducted on large and established construction firms in Malaysia. A randomized sample of 525 firms was selected and the primary data were collected by self-administered postal survey. The response rate was 28%. Data analysis was carried out using Statistical Package for Social Science (SPSS Version 12. Among the factors, innovative culture was found to be most significant and influenced diffusion positively. In contrast with most of the previous studies conducted in developed countries, this study was conducted in Malaysia. It is likely to benefit the construction industry of developing countries of similar settings. The integrated framework of innovation diffusion will benefit homegrown innovation developers in more successful diffusion of their future construction innovations.
THE SEPARATION OF URANIUM ISOTOPES BY GASEOUS DIFFUSION: A LINEAR PROGRAMMING MODEL,
URANIUM, ISOTOPE SEPARATION), (*GASEOUS DIFFUSION SEPARATION, LINEAR PROGRAMMING ), (* LINEAR PROGRAMMING , GASEOUS DIFFUSION SEPARATION), MATHEMATICAL MODELS, GAS FLOW, NUCLEAR REACTORS, OPERATIONS RESEARCH
Cellular Automata Models for Diffusion of Innovations
Fuks, H; Fuks, Henryk; Boccara, Nino
1997-01-01
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the rule increases, the takeover time for innovation increases and converges toward its mean-field value, which is almost inversely proportional to R when R is large. Exact solutions for R=1 and $R=\\infty$ (mean-field) are presented, as well as simulation results for other values of R. The average local density is found to converge to a certain stationary value, which allows us to obtain a semi-phenomenological solution valid in the vicinity of the fixed point n=1 (for large t).
Background Error Correlation Modeling with Diffusion Operators
2013-01-01
functions defined on the orthogonal curvilin- ear grid of the Navy Coastal Ocean Model (NCOM) [28] set up in the Monterrey Bay (Fig. 4). The number N...H2 = [1 1; 1−1], the HMs with order N = 2n, n= 1,2... can be easily constructed. HMs with N = 12,20 were constructed ” manually ” more than a century
A stellar model with diffusion in general relativity
Alho, Artur
2016-01-01
We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self-similar solution.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
Nonlinear diffusion model for Rayleigh-Taylor mixing.
Boffetta, G; De Lillo, F; Musacchio, S
2010-01-22
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusivity models for the mean temperature profile. It is found that a nonlinear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows us to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Asymmetric diffusion model for oblique-incidence reflectometry
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.
Reaction-diffusion models of decontamination
Hjorth, Poul G.
A contaminant, which also contains a polymer is in the form of droplets on a solid surface. It is to be removed by the action of a decontaminant, which is applied in aqueous solution. The contaminant is only sparingly soluble in water, so the reaction mechanism is that it slowly dissolves...... in the aqueous solution and then is oxidized by the decontaminant. The polymer is insoluble in water, and so builds up near the interface, where its presence can impede the transport of contaminant. In these circumstances, Dstl wish to have mathematical models that give an understanding of the process, and can...
Toxicological Models Part B: Environmental Models
Garric, Jeanne; Thybaud, Eric
Assessment of ecotoxicological risks due to chemical substances is based in part on establishing concentration-response relationships for different organisms, including plants, invertebrates, and vertebrates living on land, fresh water, or sea water. European regulations for assessing the risks due to chemical products thus recommend the measurement of toxic effects on at least three taxons (algae, crustacea, fish) [1]. The assessment becomes more relevant when based upon a variety of different organisms, with a range of different biological and ecological features (autotrophic or heterotrophic, benthic or pelagic habitat, and different modes of reproduction, growth, respiration, or feeding, etc.), but also when it describes the effects of contaminants on sensitive physiological functions such as growth and reproduction, which determine the balance of populations of terrestrial and aquatic species in their environment.
GIS-BASED 1-D DIFFUSIVE WAVE OVERLAND FLOW MODEL
KALYANAPU, ALFRED [Los Alamos National Laboratory; MCPHERSON, TIMOTHY N. [Los Alamos National Laboratory; BURIAN, STEVEN J. [NON LANL
2007-01-17
This paper presents a GIS-based 1-d distributed overland flow model and summarizes an application to simulate a flood event. The model estimates infiltration using the Green-Ampt approach and routes excess rainfall using the 1-d diffusive wave approximation. The model was designed to use readily available topographic, soils, and land use/land cover data and rainfall predictions from a meteorological model. An assessment of model performance was performed for a small catchment and a large watershed, both in urban environments. Simulated runoff hydrographs were compared to observations for a selected set of validation events. Results confirmed the model provides reasonable predictions in a short period of time.
Active Versus Passive: Receiver Model Transforms for Diffusive Molecular Communication
Noel, Adam; Makrakis, Dimitrios; Hafid, Abdelhakim
2016-01-01
This paper presents an analytical comparison of the active and passive receiver models in diffusive molecular communication. In the active model, molecules are absorbed when they collide with the receiver surface. In the passive model, the receiver is a virtual boundary that does not affect molecule behavior. Two approaches are presented to derive transforms between the active and passive receiver signals. As an example, we unify the two models for an unbounded diffusion-only molecular communication system with a spherical receiver. As time increases in the three-dimensional system, the transform functions have constant scaling factors, such that the receiver models are effectively equivalent. Methods are presented to enable the transformation of stochastic simulations, which are used to verify the transforms and demonstrate that transforming the simulation of a passive receiver can be more efficient and more accurate than the direct simulation of an absorbing receiver.
Turing instability in reaction-diffusion models on complex networks
Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya
2016-09-01
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.
Quasineutral limit of a standard drift diffusion model for semiconductors
无
2002-01-01
The limit of vanishing Debye length (charge neutral limit ) in a nonlinear bipolar drift-diffusion model for semiconductors without pn-junction (i.e. without a bipolar background charge ) is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using the weak compactness argument and the so-called entropy functional which yields appropriate uniform estimates.
Modeling intragranular diffusion in low-connectivity granular media
Ewing, Robert P.; Liu, Chongxuan; Hu, Qinhong
2012-03-01
Characterizing the diffusive exchange of solutes between bulk water in an aquifer and water in the intragranular pores of the solid phase is still challenging despite decades of study. Many disparities between observation and theory could be attributed to low connectivity of the intragranular pores. The presence of low connectivity indicates that a useful conceptual framework is percolation theory. The present study was initiated to develop a percolation-based finite difference (FD) model, and to test it rigorously against both random walk (RW) simulations of diffusion starting from nonequilibrium, and data on Borden sand published by Ball and Roberts (1991a,b) and subsequently reanalyzed by Haggerty and Gorelick (1995) using a multirate mass transfer (MRMT) approach. The percolation-theoretical model is simple and readily incorporated into existing FD models. The FD model closely matches the RW results using only a single fitting parameter, across a wide range of pore connectivities. Simulation of the Borden sand experiment without pore connectivity effects reproduced the MRMT analysis, but including low pore connectivity effects improved the fit. Overall, the theory and simulation results show that low intragranular pore connectivity can produce diffusive behavior that appears as if the solute had undergone slow sorption, despite the absence of any sorption process, thereby explaining some hitherto confusing aspects of intragranular diffusion.
Modeling the diffusion of phosphorus in silicon in 3-D
Baker, K.R. [Univ. of Texas, Austin, TX (United States)
1994-12-31
The use of matrix preconditioning in semiconductor process simulation is examined. The simplified nonlinear single-species model for the diffusion of phosphorus into silicon is considered. The experimental three-dimensional simulator, PEPPER3, which uses finite differences and the numerical method of lines to implement the reaction-diffusion equation is modified to allow NSPCG to be called to solve the linear system in the inner Newton loop. Use of NSPCG allowed various accelerators such as Generalized Minimal Residual (GMRES) and Conjugate Gradient (CG) to be used in conjunction with preconditioners such as Richardson, Jacobi, and Incomplete Cholesky.
The effect of a realistic thermal diffusivity on numerical model of a subducting slab
Maierova, P.; Steinle-Neumann, G.; Cadek, O.
2010-12-01
A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the
Transport Corrections in Nodal Diffusion Codes for HTR Modeling
Abderrafi M. Ougouag; Frederick N. Gleicher
2010-08-01
The cores and reflectors of High Temperature Reactors (HTRs) of the Next Generation Nuclear Plant (NGNP) type are dominantly diffusive media from the point of view of behavior of the neutrons and their migration between the various structures of the reactor. This means that neutron diffusion theory is sufficient for modeling most features of such reactors and transport theory may not be needed for most applications. Of course, the above statement assumes the availability of homogenized diffusion theory data. The statement is true for most situations but not all. Two features of NGNP-type HTRs require that the diffusion theory-based solution be corrected for local transport effects. These two cases are the treatment of burnable poisons (BP) in the case of the prismatic block reactors and, for both pebble bed reactor (PBR) and prismatic block reactor (PMR) designs, that of control rods (CR) embedded in non-multiplying regions near the interface between fueled zones and said non-multiplying zones. The need for transport correction arises because diffusion theory-based solutions appear not to provide sufficient fidelity in these situations.
Diffusion models in experimental psychology: a practical introduction.
Voss, Andreas; Nagler, Markus; Lerche, Veronika
2013-01-01
Stochastic diffusion models (Ratcliff, 1978) can be used to analyze response time data from binary decision tasks. They provide detailed information about cognitive processes underlying the performance in such tasks. Most importantly, different parameters are estimated from the response time distributions of correct responses and errors that map (1) the speed of information uptake, (2) the amount of information used to make a decision, (3) possible decision biases, and (4) the duration of nondecisional processes. Although this kind of model can be applied to many experimental paradigms and provides much more insight than the analysis of mean response times can, it is still rarely used in cognitive psychology. In the present paper, we provide comprehensive information on the theory of the diffusion model, as well as on practical issues that have to be considered for implementing the model.
Bayesian Model Selection with Network Based Diffusion Analysis.
Whalen, Andrew; Hoppitt, William J E
2016-01-01
A number of recent studies have used Network Based Diffusion Analysis (NBDA) to detect the role of social transmission in the spread of a novel behavior through a population. In this paper we present a unified framework for performing NBDA in a Bayesian setting, and demonstrate how the Watanabe Akaike Information Criteria (WAIC) can be used for model selection. We present a specific example of applying this method to Time to Acquisition Diffusion Analysis (TADA). To examine the robustness of this technique, we performed a large scale simulation study and found that NBDA using WAIC could recover the correct model of social transmission under a wide range of cases, including under the presence of random effects, individual level variables, and alternative models of social transmission. This work suggests that NBDA is an effective and widely applicable tool for uncovering whether social transmission underpins the spread of a novel behavior, and may still provide accurate results even when key model assumptions are relaxed.
Macroscopic diffusion models for precipitation in crystalline gallium arsenide
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.)
Solutions to a nonlinear drift-diffusion model for semiconductors
Weifu Fang
1999-05-01
Full Text Available A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
Morgan, D. J.; Chamberlain, K. J.; Wilson, C. J. N.
2014-12-01
Diffusion modelling of elemental gradients across compositional zones within crystals is frequently used to investigate timescales of various magmatic processes. In most cases, however, only a single crystal phase is used for this modelling. The ~0.76 Ma Bishop Tuff (Long Valley, eastern California) in later parts of its eruptive sequence has zoned orthopyroxene, quartz and sanidine. It thus provides an unusual opportunity to compare the modelled timescales from each phase, and assess the limitations of single-phase diffusion modelling in lower-temperature, rhyolitic volcanic systems. The presence of a late-stage compositionally distinct melt (the 'bright-rim' melt) mixing into the lower parts of the Bishop magma chamber has been noted by many authors [e.g. Wark et al. 2007, Geology 35, 235; Roberge et al. 2013, CMP 165, 237; Chamberlain et al. 2014, J Petrol 55, 395] in later-erupted material discharged from vents along the northern ring fracture of the caldera. Here we present the results of 1D diffusion modelling of Ba and Sr in sanidine, Ti in quartz and Fe-Mg interdiffusion in orthopyroxene in samples from later-erupted ignimbrite packages in the tuff. Timescales from diffusion modelling of Fe-Mg interdiffusion in orthopyroxene are Bishop Tuff eruption. We highlight the importance of having a good understanding of the assumptions made and uncertainties in diffusion coefficients when undertaking such modelling, especially in examples where only one phase is available for diffusion modelling.
Chih-Chun Hsieh
2012-01-01
Full Text Available This study performs a precipitation examination of the phase using the general diffusion equation with comparison to the Vitek model in dissimilar stainless steels during multipass welding. Experimental results demonstrate that the diffusivities (, , and of Cr, Ni, and Si are higher in -ferrite than (, , and in the phase, and that they facilitate the precipitation of the σ phase in the third pass fusion zone. The Vitek diffusion equation can be modified as follows: .
Mechanical reaction-diffusion model for bacterial population dynamics
Ngamsaad, Waipot
2015-01-01
The effect of mechanical interaction between cells on the spreading of bacterial population was investigated in one-dimensional space. A nonlinear reaction-diffusion equation has been formulated as a model for this dynamics. In this model, the bacterial cells are treated as the rod-like particles that interact, when contacting each other, through the hard-core repulsion. The repulsion introduces the exclusion process that causes the fast diffusion in bacterial population at high density. The propagation of the bacterial density as the traveling wave front in long time behavior has been analyzed. The analytical result reveals that the front speed is enhanced by the exclusion process---and its value depends on the packing fraction of cell. The numerical solutions of the model have been solved to confirm this prediction.
Fractional Heat Conduction Models and Thermal Diffusivity Determination
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.
Non-invasive measurement of oxygen diffusion in model foods.
Bhunia, Kanishka; Sablani, Shyam S; Tang, Juming; Rasco, Barbara
2016-11-01
In this study, we developed a non-invasive method to determine oxygen diffusivity (DO2) in food gels using an Oxydot luminescence sensor. We designed and fabricated a transparent diffusion cell in order to represent oxygen transfer into foods packaged in an 8-ounce polymeric tray. Oxydots were glued to the sides (side-dot) and bottom (bottom-dot) of the cell and filled with 1, 2, and 3% (w/v) agar gel as a model food. After deoxygenation, local oxygen concentrations in the gels were measured non-invasively at 4, 12 and 22°C. Effective oxygen diffusivities in gels (DO2g) and water (DO2w) were obtained after fitting experimental data to the analytical solution (data from side-dot) and the numerical solution (data from bottom-dot) to Fick's second law. Temperature had significant positive influence (P0.05) was found between the activation energy (Ea) of water and gels (1-3% w/v) for temperatures ranging from 4 to 22°C. We used a combined obstruction and hydrodynamic model to explain why DO2g decreased as gel concentration increased. The method developed in this study can be used to study the oxygen diffusivity in foods. Copyright © 2016 Elsevier Ltd. All rights reserved.
Antiproton Flux in Cosmic Ray Propagation Models with Anisotropic Diffusion
Grajek, Phillip
2010-01-01
Recently a cosmic ray propagation model has been introduced, where anisotropic diffusion is used as a mechanism to allow for $\\mathcal{O}(100)$ km/s galactic winds. This model predicts a reduced antiproton background flux, suggesting an excess is being observed. We implement this model in GALPROP v50.1 and perform a $\\chi^2$ analysis for B/C, $^{10}$Be/$^{9}$Be, and the recent PAMELA $\\bar{p}/p$ datasets. By introducing a power-index parameter $\\alpha$ that dictates the dependence of the diffusion coefficient $D_{xx}$ on height $|z|$ away from the galactic plane, we confirm that isotropic diffusion models with $\\alpha=0$ cannot accommodate high velocity convective winds suggested by ROSAT, while models with $\\alpha=1$ ($D_{xx}\\propto |z|$) can give a very good fit. A fit to B/C and $^{10}$Be/$^{9}$Be data predicts a lower $\\bar{p}/p$ flux ratio than the PAMELA measurement at energies between approximately 2 GeV to 20 GeV. A combined fit including in addition the $\\bar{p}/p$ data is marginal, suggesting only a...
Characterization and modeling of thermal diffusion and aggregation in nanofluids.
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.
A diffusive model for halo width growth during vertical displacement events
Eidietis, N. W.; Humphreys, D. A.
2011-07-01
The electromagnetic loads produced by halo currents during vertical displacement events (VDEs) impose stringent requirements on the strength of ITER in-vessel components. A predictive understanding of halo current evolution is essential for ensuring the robust design of these components. A significant factor determining that evolution is the plasma resistance, which is a function of three quantities: the resistivities of the core and halo regions, and the halo region width. A diffusive model of halo width growth during VDEs has been developed, which provides one part of a physics basis for predictive halo current simulations. The diffusive model was motivated by DIII-D observations that VDEs with cold post-thermal quench plasma and a current decay time much faster than the vertical motion (type I VDE) possess much wider halo region widths than warmer plasma VDEs, where the current decay is much slower than the vertical motion (type II). A 2D finite element code is used to model the diffusion of toroidal halo current during selected type I and type II DIII-D VDEs. The model assumes a core plasma region within the last closed flux surface (LCFS) diffusing current into a halo plasma filling the vessel outside the LCFS. LCFS motion and plasma temperature are prescribed from experimental observations. The halo width evolution produced by this model compares favourably with experimental measurements of type I and type II toroidal halo current width evolution.
Modeling of gas phase diffusion transport during chemical vapor infiltration process
肖鹏; 李娣; 徐永东; 黄伯云
2002-01-01
In order to improve the uniformity of both the concentration of gaseous reagent and the deposition of matrix within micro-pores during the chemical vapor infiltration (CVI) process, a calculation modeling of gas phase diffusion transport within micro-pores was established. Taken CH3SiCl3 as precursor for depositing SiC as example, the diffusion coefficient, decomposing reaction rate, concentration within the reactor, and concentration distributing profiling of MTS within micro-pore were accounted, respectively. The results indicate that, increasing the ratio of diffusion coefficient to decomposition rate constant of precursor MTS is propitious to decrease the densification gradient of parts, and decreasing the aspect ratio (L/D) of micro-pore is favorable to make the concentration uniform within pores.
Performance of turbulence models for transonic flows in a diffuser
Liu, Yangwei; Wu, Jianuo; Lu, Lipeng
2016-09-01
Eight turbulence models frequently used in aerodynamics have been employed in the detailed numerical investigations for transonic flows in the Sajben diffuser, to assess the predictive capabilities of the turbulence models for shock wave/turbulent boundary layer interactions (SWTBLI) in internal flows. The eight turbulence models include: the Spalart-Allmaras model, the standard k - 𝜀 model, the RNG k - 𝜀 model, the realizable k - 𝜀 model, the standard k - ω model, the SST k - ω model, the v2¯ - f model and the Reynolds stress model. The performance of the different turbulence models adopted has been systematically assessed by comparing the numerical results with the available experimental data. The comparisons show that the predictive performance becomes worse as the shock wave becomes stronger. The v2¯ - f model and the SST k - ω model perform much better than other models, and the SST k - ω model predicts a little better than the v2¯ - f model for pressure on walls and velocity profile, whereas the v2¯ - f model predicts a little better than the SST k - ω model for separation location, reattachment location and separation length for strong shock case.
Modeling of diffuse molecular gas applied to HD 102065 observations
Nehme, Cyrine; Boulanger, Francois; Forets, Guillaume Pineau des; Gry, Cecile
2008-01-01
Aims. We model a diffuse molecular cloud present along the line of sight to the star HD 102065. We compare our modeling with observations to test our understanding of physical conditions and chemistry in diffuse molecular clouds. Methods. We analyze an extensive set of spectroscopic observations which characterize the diffuse molecular cloud observed toward HD 102065. Absorption observations provide the extinction curve, H2, C I, CO, CH, and CH+ column densities and excitation. These data are complemented by observations of CII, CO and dust emission. Physical conditions are determined using the Meudon PDR model of UV illuminated gas. Results. We find that all observational results, except column densities of CH, CH+ and H2 in its excited (J > 2) levels, are consistent with a cloud model implying a Galactic radiation field (G~0.4 in Draine's unit), a density of 80 cm-3 and a temperature (60-80 K) set by the equilibrium between heating and cooling processes. To account for excited (J >2) H2 levels column densit...
Water diffusion in bicelles and the mixed bicelle model.
Soong, Ronald; Macdonald, Peter M
2009-01-06
To test a prediction of the mixed bicelle model, stimulated echo (STE) pulsed field gradient (PFG) (1)H nuclear magnetic resonance (NMR) measurements of water diffusion between and across bicellar lamellae were performed in positively and negatively magnetically aligned bicelles, composed of mixtures of DHPC (1,2-dihexanoyl-sn-glycero-3-phosphocholine) and DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine), as a function of temperature and of the proportion of added short-chain lipid DHPC. (31)P NMR spectra obtained for each situation confirmed that the DHPC undergoes fast exchange between curved and planar regions as per the mixed bicelle model and permitted an estimate of the proportion of the two DHPC populations. Water diffusion across the bicellar lamellae was shown to scale directly with q*, the fraction of edge versus planar phospholipid, rather than simply the ratio q, the global fraction of long-chain to short-chain phospholipid. Geometric modeling of the dependence of water diffusion on q* suggested an upper limit of 400 A for the size of DHPC-rich toroidal perforations within the bicelle lamellae. These findings constitute an independent confirmation of the mixed bicelle model in which DHPC is not confined to edge regions but enjoys, instead, a finite miscibility with DMPC.
Zerr, R. Joseph; Azmy, Yousry [The Pennsylvania State University, University Park, PA (United States); Ouisloumen, Mohamed [Westinghouse Electric Company, LLC, Monroeville, PA (United States)
2008-07-01
Studies have been performed to test for significant gains in core design computational accuracy with the added implementation of direction-dependent diffusion coefficients. The DRAGON code was employed to produce two-group homogeneous B{sub 1} diffusion coefficients and direction-dependent diffusion coefficients with the TIBERE module. A three-dimensional diffusion model of a mini-core was analyzed with the resulting cross section data sets to determine if the multiplication factor or node power was noticeably altered with the more accurate representation of neutronic behaviour in a high-void configuration. Results indicate that using direction-dependent diffusion coefficients homogenized over an entire assembly do not produce significant differences in the results compared to the B{sub 1} counterparts and are much more computationally expensive. Direction-dependent diffusion coefficients that are specific to smaller micro-regions may provide more noteworthy gains in the accuracy of core design computations. (authors)
Most current electrostatic surface complexation models describing ionic binding at the particle/water interface rely on the use of Poisson - Boltzmann (PB) theory for relating diffuse layer charge densities to diffuse layer electrostatic potentials. PB theory is known to contain ...
Modeling and Analysis of New Products Diffusion on Heterogeneous Networks
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.
Experimental exploration of diffusion panel labyrinth in scale model
Vance, Mandi M.
Small rehearsal and performance venues often lack the rich reverberation found in larger spaces. Higini Arau-Puchades has designed and implemented a system of diffusion panels in the Orchestra Rehearsal Room at the Great Theatre Liceu and the Tonhalle St. Gallen that lengthen the reverberation time. These panels defy traditional room acoustics theory which holds that adding material to a room will shorten the reverberation time. This work explores several versions of Arau-Puchades' panels and room characteristics in scale model. Reverberation times are taken from room impulse response measurements in order to better understand the unusual phenomenon. Scale modeling enables many tests but has limitations in its accuracy due to the higher frequency range involved. Further investigations are necessary to establish how the sound energy interacts with the diffusion panels and confirm their validity in a range of applications.
Molecular Diffusive Motion in a Monolayer of a Model Lubricant
Diama, A.; Criswell, L.; Mo, H.; Taub, H.; Herwig, K. W.; Hansen, F. Y.; Volkmann, U. G.; Dimeo, R.; Neumann, D.
2003-03-01
Squalane (C_30H_62), a branched alkane of intermediate length consisting of a tetracosane backbone (n-C_24H_50 or C24) and six symmetrically placed methyl sidegroups, is frequently taken as a model lubricant. We have conducted quasielastic neutron scattering (QNS) experiments to investigate the diffusive motion on different time scales in a squalane monolayer adsorbed on the (0001) surfaces of an exfoliated graphite substrate. Unlike tetracosane, high-energy resolution spectra (time scale ˜0.1 - 4 ns) at temperatures of 215 K and 230 K show the energy width of the QNS to have a maximum near Q = 1.2 ÅThis nonmonotonic Q dependence suggests a more complicated diffusive motion than the simple rotation about the long molecular axis believed to occur in a C24 monolayer at this temperature. Lower-energy-resolution spectra (time scale ˜4 - 40 ps) show evidence of two types of diffusive motion whose rates have opposite temperature dependences. The rate of the faster motion decreases as the monolayer is heated, and we speculate that it is due to hindered rotation of the methyl groups. The rate of the slower motion increases with temperature and may involve both uniaxial rotation and translational diffusion. Our experimental results will be compared with molecular dynamics simulations.
Modeling geomagnetic storms on prompt and diffusive time scales
Li, Zhao
The discovery of the Van Allen radiation belts in the 1958 was the first major discovery of the Space Age. There are two belts of energetic particles. The inner belt is very stable, but the outer belt is extremely variable, especially during geomagnetic storms. As the energetic particles are hazardous to spacecraft, understanding the source of these particles and their dynamic behavior driven by solar activity has great practical importance. In this thesis, the effects of magnetic storms on the evolution of the electron radiation belts, in particular the outer zone, is studied using two types of numerical simulation: radial diffusion and magnetohydrodynamics (MHD) test-particle simulation. A radial diffusion code has been developed at Dartmouth, applying satellite measurements to model flux as an outer boundary condition, exploring several options for the diffusion coefficient and electron loss time. Electron phase space density is analyzed for July 2004 coronal mass ejection (CME) driven storms and March-April 2008 co-rotating interaction region (CIR) driven storms, and compared with Global Positioning System (GPS) satellite measurements within 5 degrees of the magnetic equator at L=4.16. A case study of a month-long interval in the Van Allen Probes satellite era, March 2013, confirms that electron phase space density is well described by radial diffusion for the whole month at low first invariant 0.6 MeV by an order of magnitude over 24 hours as observed.
Modelling of diffusion and conductivity relaxation of oxide ceramics
Preis, Wolfgang
2016-12-01
A two-dimensional square grain model has been applied to simulate simultaneously the diffusion process and relaxation of the dc conduction of polycrystalline oxide materials due to a sudden change of the oxygen partial pressure of the surrounding gas phase. The numerical calculations are performed by employing the finite element approach. The grains are squares of equal side length (average grain size) and the grain boundaries may consist of thin slabs of uniform thickness. An additional (space charge) layer adjacent to the grain boundary cores (thin slabs) either blocking (depletion layer) or highly conductive for electronic charge carriers may surround the grains. The electronic transport number of the mixed ionic-electronic conducting oxide ceramics may be close to unity (predominant electronic conduction). If the chemical diffusion coefficient of the neutral mobile component (oxygen) of the grain boundary core regions is assumed to be higher by many orders of magnitude than that in the bulk, the simulated relaxation curves for mass transport (diffusion) and dc conduction can deviate remarkably from each other. Deviations between the relaxation of mass transport and dc conduction are found in the case of considerably different electronic conductivities of grain boundary core regions, space charge layers, and bulk. On the contrary, the relaxation curves of mass transport and electronic conductivity are in perfect coincidence, when either effective medium diffusion occurs or the effective conductivity is unaffected by the individual conductivities of core regions and possible space charge layers, i.e. the grain boundary resistivity is negligible.
A flamelet model for turbulent diffusion combustion in supersonic flow
LEE; ChunHian
2010-01-01
In order to develop a turbulent diffusion combustion model for supersonic flow, the physical argument of the extension of the flamelet model to supersonic flow was presented, and the flow field of a hydrogen/air diffusion combustion generated by axisymmetric supersonic jets was numerically simulated by employing the flamelet model. Using the experimental data, value of the model coefficient of scalar dissipation in the flamelet model was revised specifically for supersonic flow. The computational results of the modified flamelet model were compared with the experimental results, and it was indicated that the precision of the modified flamelet model was satisfying. Based on the numerical results and flamelet theory, the influence mechanisms of turbulence fluctuation on the average state equation and chemical reaction rate were studied for the first time. It was found that the fluctuation correlation of species mass fractions and temperature has little effect on the averaged gas state equation; the temperature fluctuation decreases the product of H2O, but its effect is small; the fluctuation of species mass fractions increases the product of H2O in the region close to oxidizer while decreases the product of H2O in other regions; the fluctuation correlation of species mass fractions and temperature largely decreases the product of H2O.
THE LOS ALAMOS NATIONAL LABORATORY ATMOSPHERIC TRANSPORT AND DIFFUSION MODELS
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.
Two-phase flow with surfactants: Diffuse interface models and their analysis
Abels, Helmut; Lam, Kei Fong; Weber, Josef
2016-01-01
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a particular diffuse interface model.
[Diffusion factor calculation for TIP4P model of water].
Zlenko, D V
2012-01-01
A molecular dynamics study has been undertaken for a model of liquid TIP4P water. Thermal dependencies of water density and radial distribution functions were calculated for model verification. Three methods have been used for calculation of diffusion factor thermal dependencies. Their sensitivity to molecular system size and length of used trajectory has been analyzed. It has been shown that Green-Kubo formula-based approach which associates diffusion factor with speed autocorrelation function integral is preferred in case of short MD simulations. The second approach based on Einstein equation which associates mean square displacement of molecule with time is preferred in case of long simulations. It has been also demonstrated that it is possible to modify the second approach to make it more stable and reliable. This modification is to use a slope of the graph of the mean square displacement on time as the estimation of the diffusion factor instead of the ratio of molecule mean square displacement and time.
Partial Differential Equations of an Epidemic Model with Spatial Diffusion
El Mehdi Lotfi
2014-01-01
Full Text Available The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the eradication of disease from population. When the basic reproduction number is greater than unity, then disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable; in this case the disease persists in the population. Numerical simulations are presented to illustrate our theoretical results.
Symmetric multi-component diffusion modeling for Magnum PSI
Peerenboom, Kim; van Dijk, Jan; Goedheer, Wim; van der Mullen, Joost
2011-10-01
Magnum PSI is a linear plasma generator for studying plasma surface interaction in conditions as expected in the ITER divertor. In Magnum PSI, the diffusive fluxes do not follow the simple Fick law for diffusion, due to coupling of the fluxes between species and directions, and ambipolar and magnetic fields. Instead they are described by the Stefan-Maxwell equations. In our contribution, we will address the numerical issues associated with solving the Stefan-Maxwell equations and the resulting set of continuity equations for the species. In particular, we will present a symmetric approach where all species are treated as independent unknowns and no species are singled out in order to account for mass and charge conservation. Modeling results of Magnum PSI using this approach will be presented.
Charge diffusion in the one-dimensional Hubbard model
Steinigeweg, R.; Jin, F.; De Raedt, H.; Michielsen, K.; Gemmer, J.
2017-08-01
We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time evolution of these nonequilibrium states, by using numerical forward-propagation approaches to chains as long as 20 sites. For a class of typical states, we find excellent agreement with linear-response theory and unveil the existence of remarkably clean charge diffusion in the regime of strong particle-particle interactions. We additionally demonstrate that, in the half-filling sector, this diffusive behavior does not depend on certain details of our initial conditions, i.e., it occurs for five different realizations with random and nonrandom internal degrees of freedom, single and double occupation of the central site, and displacement of spin-up and spin-down particles.
Diffusion Based Modeling of Human Brain Response to External Stimuli
Namazi, Hamidreza
2012-01-01
Human brain response is the overall ability of the brain in analyzing internal and external stimuli in the form of transferred energy to the mind/brain phase-space and thus, making the proper decisions. During the last decade scientists discovered about this phenomenon and proposed some models based on computational, biological, or neuropsychological methods. Despite some advances in studies related to this area of the brain research there was less effort which have been done on the mathematical modeling of the human brain response to external stimuli. This research is devoted to the modeling of human EEG signal, as an alert state of overall human brain activity monitoring, due to receiving external stimuli, based on fractional diffusion equation. The results of this modeling show very good agreement with the real human EEG signal and thus, this model can be used as a strong representative of the human brain activity.
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
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.
Berlowitz, D.R.
1996-11-01
In the last few decades the negative impact by humans on the thin atmospheric layer enveloping the earth, the basis for life on this planet, has increased steadily. In order to halt, or at least slow down this development, the knowledge and study of these anthropogenic influence has to be increased and possible remedies have to be suggested. An important tool for these studies are computer models. With their help the atmospheric system can be approximated and the various processes, which have led to the current situation can be quantified. They also serve as an instrument to assess short or medium term strategies to reduce this human impact. However, to assure efficiency as well as accuracy, a careful analysis of the numerous processes involved in the dispersion of pollutants in the atmosphere is called for. This should help to concentrate on the essentials and also prevent excessive usage of sometimes scarce computing resources. The basis of the presented work is the EUMAC Zooming Model (ETM), and particularly the component calculating the dispersion of pollutants in the atmosphere, the model MARS. The model has two main parts: an explicit solver, where the advection and the horizontal diffusion of pollutants are calculated, and an implicit solution mechanism, allowing the joint computation of the change of concentration due to chemical reactions, coupled with the respective influence of the vertical diffusion of the species. The aim of this thesis is to determine particularly the influence of the horizontal components of the turbulent diffusion on the existing implicit solver of the model. Suggestions for a more comprehensive inclusion of the full three dimensional diffusion operator in the implicit solver are made. This is achieved by an appropriate operator splitting. A selection of numerical approaches to tighten the coupling of the diffusion processes with the calculation of the applied chemical reaction mechanisms are examined. (author) figs., tabs., refs.
Technology diffusion in energy-economy models: The case of Danish vintage models
Klinge Jacobsen, Henrik
2000-01-01
the costs of greenhouse gas mitigation. This paper examines the effect on aggregate energy efficiency of using technological vintage models to describe technology diffusion. The focus is on short- to medium-term issues. Three different models of Danish energy supply and demand are used to illustrate......Technological progress is an important issue in long-term energy demand projections and in environmental analyses. Different assumptions on technological progress and diffusion of new technologies are among the reasons for diverging results obtained using bottom-up and top-down models for analyzing...... of residential heat demand, fuel price increases are found to accelerate diffusion by increasing replacement rates for heating equipment....
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
Application of the evolution theory in modelling of innovation diffusion
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.
Study of Pre-equilibrium Fission Based on Diffusion Model
无
2006-01-01
In terms of numerical method of Smoluchowski equation the behavior of fission process in diffusion model has been described and analyzed, including the reliance upon time, as well as the deformation parameters at several nuclear temperatures in this paper. The fission rates and the residual probabilities inside the saddle point are calculated for fissile nucleus n+238 U reaction and un-fissile nucleus p+208 Pb reaction. The results indicate that there really exists a transient fission process, which means that the pre-equilibrium fission should be taken into account for the fissile nucleus at the high temperature. Oppositely, the pre-equilibrium fission could be neglected for the un-fissile nucleus. In the certain case the overshooting phenomenon of the fission rates will occur, which is mainly determined by the diffusive current at the saddle point. The higher the temperature is, the more obvious the overshooting phenomenon is. However, the emissions of the light particles accompanying the diffusion process may weaken or vanish the overshooting phenomenon.
A Reaction-Diffusion Model of Cholinergic Retinal Waves
Lansdell, Benjamin; Ford, Kevin; Kutz, J. Nathan
2014-01-01
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability. PMID:25474327
Bayesian Model Selection With Network Based Diffusion Analysis
Andrew eWhalen
2016-04-01
Full Text Available A number of recent studies have used Network Based Diffusion Analysis (NBDA to detect the role of social transmission in the spread of a novel behavior through a population. In this paper we present a unified framework for performing NBDA in a Bayesian setting, and demonstrate how the Watanabe Akaike Information Criteria (WAIC can be used for model selection. We present a specific example of applying this method to Time to Acquisition Diffusion Analysis (TADA. To examine the robustness of this technique, we performed a large scale simulation study and found that NBDA using WAIC could recover the correct model of social transmission under a wide range of cases, including under the presence of random effects, individual level variables, and alternative models of social transmission. This work suggests that NBDA is an effective and widely applicable tool for uncovering whether social transmission underpins the spread of a novel behavior, and may still provide accurate results even when key model assumptions are relaxed.
Modeling of 1D Anomalous Diffusion in Fractured Nanoporous Media
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.
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
Flegg, Mark B.
2013-01-01
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, "The two-regime method for optimizing stochastic reaction-diffusion simulations," J. R. Soc., Interface 9, 859-868 (2012)] in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration
2015-03-26
protection in the United States. AFIT-ENP-MS-15-M-100 INVESTIGATION OF FIELD-COLLECTED DATA USING DIFFUSE AND SPECULAR , FORWARD AND REVERSE...RELEASE; DISTRIBUTION UNLIMITED. AFIT-ENP-MS-15-M-100 INVESTIGATION OF FIELD-COLLECTED DATA USING DIFFUSE AND SPECULAR , FORWARD AND REVERSE... specular and diffuse properties of a set of eight materials on diffuse-only and diffuse- specular radiative transfer models in the wavelength range of
Random walk model in case of iso- and diapycnal diffusion
Spivakovskaya, D.; Deleersnijder, E.; Heemink, A.W.
2006-01-01
Large scale diffusion processes in the ocean occur mostly along isopycnal surfaces, i.e. surfaces of equal density. However, there is also diapycnal diffusion, which is associated with a diffusion flux orthogonal to isopycnal surfaces. The diapycnal and isopycnal diffusion fluxes are commonly parame
Powell, Samuel; Arridge, Simon R.; Leung, Terence S.
2015-03-01
Ultrasound-modulated optical tomography is an emerging biomedical imaging modality which uses the spatially localised acoustically-driven modulation of coherent light as a probe of the structure and optical properties of biological tissues. In this work we model the first-harmonic flux generated by the coupled physics using a simple linearised diffusion-style forward model. We derive analytical expressions for the sensitivity of this measurement type with respect to the optical absorption and scattering coefficients. These correlation measurement density functions can be employed as part of an image-reconstruction procedure capable of reconstructing quantitative images of the optical properties of a medium under investigation.
Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling.
Yudovsky, Dmitry; Durkin, Anthony J
2011-07-20
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling
Yudovsky, Dmitry; Durkin, Anthony J.
2011-07-01
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
Wang, Wei; Ma, Wanbiao; Lai, Xiulan
2017-01-01
From a biological perspective, a diffusive virus infection dynamic model with nonlinear functional response, absorption effect and chemotaxis is proposed. In the model, the diffusion of virus consists of two parts, the random diffusion and the chemotactic movement. The chemotaxis flux of virus depends not only on their own density, but also on the density of infected cells, and the density gradient of infected cells. The well posedness of the proposed model is deeply investigated. For the proposed model, the linear stabilities of the infection-free steady state E0 and the infection steady state E* are extensively performed. We show that the threshold dynamics can be expressed by the basic reproduction number R0 of the model without chemotaxis. That is, the infection-free steady state E0 is globally asymptotically stable if R0 virus is uniformly persistent if R0 > 1. In addition, we use the cross iteration method and the Schauder's fixed point theorem to prove the existence of travelling wave solutions connecting the infection-free steady state E0 and the infection steady state E* by constructing a pair of upper-lower solutions. At last, numerical simulations are presented to confirm theoretical findings.
Proposal of a regressive model for the hourly diffuse solar radiation under all sky conditions
Ruiz-Arias, J.A.; Alsamamra, H.; Tovar-Pescador, J.; Pozo-Vazquez, D. [Department of Physics, Building A3-066, University of Jaen, 23071 Jaen (Spain)
2010-05-15
In this work, we propose a new regressive model for the estimation of the hourly diffuse solar irradiation under all sky conditions. This new model is based on the sigmoid function and uses the clearness index and the relative optical mass as predictors. The model performance was compared against other five regressive models using radiation data corresponding to 21 stations in the USA and Europe. In a first part, the 21 stations were grouped into seven subregions (corresponding to seven different climatic regions) and all the models were locally-fitted and evaluated using these seven datasets. Results showed that the new proposed model provides slightly better estimates. Particularly, this new model provides a relative root mean square error in the range 25-35% and a relative mean bias error in the range -15% to 15%, depending on the region. In a second part, the potential global character of the new model was evaluated. To this end, the model was fitted using the whole dataset. Results showed that the global fitting model provides overall better estimates that the locally-fitted models, with relative root mean square error values ranging 20-35% and a relative mean bias error ranging -5% to -12%. Additionally, the new proposed model showed some advantages compared to other evaluated models. Particularly, the sigmoid behaviour of this model is able to provide physically reliable estimates for extreme values of the clearness index even though using less parameter than other tested models. (author)
Modelization and structural analysis of FDM parts
Martínez, J.; Diéguez, J. L.; Ares, J. E.; Pereira, A.; Pérez, J. A.
2012-04-01
Get prototypes from technologies of Rapid Prototyping (RP) is a very important step for the development of new products. In some cases, these prototypes have mechanical properties lower than the final product, which prevents the designers to use all of the potential that these technologies can provide. In this study the RP technology known as FDM (Fused Deposition Modeling) was used to manufacture samples used in tests, in where the orientation of deposition wires in layers were varying depending on manufacturing placement. Mechanical tests were performed to verify the stiffness of the final pieces obtained. The Classical Theory of Laminates (TCL) will be used to predict the mechanical behavior of the parts in different orientations of manufacturing. Thus, this study aims to evaluate the influence of the strategies in the deposition of construction material on the mechanical properties of parts obtained by the FDM and analyzes manufacturing factors for a future generation of a finite elements analytic model that could be used to obtain the structural behavior of parts made by rapid prototyping with FDM technology.
Vestergaard-Poulsen, Peter; Hansen, Brian; Østergaard, Leif
2007-01-01
PURPOSE: 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. MATERIALS AND METHODS: 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...
Global dynamics and diffusion in triaxial galactic models
Papaphilippou, Y.
We apply the Frequency Map Analysis method to the 3--dimensional logarithmic galactic potential in order to clarify the dynamical behaviour of triaxial power--law galactic models. All the fine dynamical details are displayed in the complete frequency map, a direct representation of the system's Arnol'd web. The influence of resonant lines and the extent of the chaotic zones are directly associated with the physical space of the system. Some new results related with the diffusion of galactic orbits are also discussed. This approach reveals many unknown dynamical features of triaxial galactic potentials and provides strong indications that chaos should be an innate characteristic of triaxial configurations.
Parametric pattern selection in a reaction-diffusion model.
Michael Stich
Full Text Available We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.
Debure, Mathieu, E-mail: mathieu.debure@gmail.com [CEA Marcoule, DTCD/SECM/LCLT, BP 17171, 30207 Bagnols-sur-Cèze Cedex (France); Geosciences Dept., Mines-ParisTech, 35 Rue St-Honoré, 77305 Fontainebleau (France); De Windt, Laurent [Geosciences Dept., Mines-ParisTech, 35 Rue St-Honoré, 77305 Fontainebleau (France); Frugier, Pierre; Gin, Stéphane [CEA Marcoule, DTCD/SECM/LCLT, BP 17171, 30207 Bagnols-sur-Cèze Cedex (France)
2013-11-15
Highlights: •Diffusion of dissolved elements in pore water impacts nuclear glass alteration. •The glass/magnesium carbonate system has been studied in diffusion cells. •Glass alteration is enhanced by Mg–silicates precipitation but slowed down by diffusion. •Coupling between dissolution, diffusion and secondary phases controls the glass alteration. •The ability of reactive transport models to simulate the whole processes is investigated. -- Abstract: The influence of diffusion of reactive species in aqueous solutions on the alteration rate of borosilicate glass of nuclear interest in the presence of magnesium carbonate (hydromagnesite: 4MgCO{sub 3}·Mg(OH){sub 2}·4H{sub 2}O) is investigated together with the ability of coupled chemistry/transport models to simulate the processes involved. Diffusion cells in which the solids are separated by an inert stainless steel sintered filter were used to establish parameters for direct comparison with batch experiments in which solids are intimately mixed. The chemistry of the solution and solid phases was monitored over time by various analytical techniques including ICP-AES, XRD, and SEM. The primary mechanism controlling the geochemical evolution of the system remains the consumption of silicon from the glass by precipitation of magnesium silicates. The solution chemistry and the dissolution and precipitation of solid phases are correctly described by 2D modeling with the GRAAL model implemented in the HYTEC reactive transport code. The spatial symmetry of the boron concentrations in both compartments of the cells results from dissolution coupled with simple diffusion, whereas the spatial asymmetry of the silicon and magnesium concentrations is due to strong coupling between dissolution, diffusion, and precipitation of secondary phases. A sensitivity analysis on the modeling of glass alteration shows that the choice of these phases and their thermodynamic constants have only a moderate impact whereas the
Water Diffusion Modelling of CFB Fly Ash Thermoset Composite
Villa Ralph P.
2016-01-01
Full Text Available The shift in coal-fired power plants from pulverized coal (PC boiler technology into the greener circulating fluidized bed (CFB boiler technology resulted into a major deviation in the properties of the waste fly ash generated making it less suitable for its previous application as additives for construction materials. A new market for CFB fly ash had to be found for it not to end up as a zero value by-product. Using CFB fly ash as filler for thermoset composites is a new and remarkable application. Only a few studies, however, have been done to characterize the properties of this new material. Further experimentation and analysis may be costly and time-consuming since common procedures are material destructive. A computer-aided modeling of the composite’s water sorption behavior was done. The effect of particle loading, size and shape were considered. These properties were varied and the resulting overall diffusivities were compared to previous experimental studies. The comparison of the model and experimental diffusivity values showed satisfactory results. This model may then provide a cheaper and more time-efficient method for the characterization of the water sorption properties of CFB fly ash thermoset composites. In the future, this may lead to further studies on its application as a green material.
SHIR competitive information diffusion model for online social media
Liu, Yun; Diao, Su-Meng; Zhu, Yi-Xiang; Liu, Qing
2016-11-01
In online social media, opinion divergences and differentiations generally exist as a result of individuals' extensive participation and personalization. In this paper, a Susceptible-Hesitated-Infected-Removed (SHIR) model is proposed to study the dynamics of competitive dual information diffusion. The proposed model extends the classical SIR model by adding hesitators as a neutralized state of dual information competition. It is both hesitators and stable spreaders that facilitate information dissemination. Researching on the impacts of diffusion parameters, it is found that the final density of stiflers increases monotonically as infection rate increases and removal rate decreases. And the advantage information with larger stable transition rate takes control of whole influence of dual information. The density of disadvantage information spreaders slightly grows with the increase of its stable transition rate, while whole spreaders of dual information and the relaxation time remain almost unchanged. Moreover, simulations imply that the final result of competition is closely related to the ratio of stable transition rates of dual information. If the stable transition rates of dual information are nearly the same, a slightly reduction of the smaller one brings out a significant disadvantage in its propagation coverage. Additionally, the relationship of the ratio of final stiflers versus the ratio of stable transition rates presents power characteristic.
A chaotic model for advertising diffusion problem with competition
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.
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Spill, Fabian; Alarcon, Tomas; Maini, Philip K; Byrne, Helen
2015-01-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains ...
Jyothi, D.; Murty, T.V.R.; Sarma, V.V.; Rao, D.P.
of Marine Sciences Vol. 29, June 2000, pp. 185-187 Short Communication Computation of diffusion coefficients for waters of Gauthami Godavari estuary using one-dimensional advection-diffusion model D Jyothi, T V Ramana Murty, V V Sarma & D P Rao National.... - Jan.) Y2(x) = 8.55283 x + 17.5469 (Jan. - April) These equations would be more useful to get diffusion coefficients for any point along the channel axis, which in turn, helps to compute the concentration of pollutant along the axis of estuary. Thus...
Multi-parameter models of innovation diffusion on complex networks
McCullen, Nicholas J; Bale, Catherine S E; Foxon, Tim J; Gale, William F
2012-01-01
A model, applicable to a range of innovation diffusion applications with a strong peer to peer component, is developed and studied, along with methods for its investigation and analysis. A particular application is to individual households deciding whether to install an energy efficiency measure in their home. The model represents these individuals as nodes on a network, each with a variable representing their current state of adoption of the innovation. The motivation to adopt is composed of three terms, representing personal preference, an average of each individual's network neighbours' states and a system average, which is a measure of the current social trend. The adoption state of a node changes if a weighted linear combination of these factors exceeds some threshold. Numerical simulations have been carried out, computing the average uptake after a sufficient number of time-steps over many realisations at a range of model parameter values, on various network topologies, including random (Erdos-Renyi), s...
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.
Agent-based multi-optional model of innovations diffusion
Laciana, Carlos E
2013-01-01
We propose a formalism that allows the study of the process of diffusion of several products competing in a common market. It is based on the generalization of the statistics Ising model (Potts model). For the implementation, agent based modeling is used, applied to a problem of three options; to adopt a product A, a product B, or non-adoption. A launching strategy is analyzed for one of the two products, which delays its launching with the objective of competing with improvements. The proportion reached by one and another product is calculated at market saturation. The simulations are produced varying the social network topology, the uncertainty in the decision, and the population's homogeneity.
Moisture in Self-levelling Flooring Compounds. Part I. Water Vapour Diffusion Coefficients
Anderberg, Anders; Wadsö, Lars
2004-01-01
Diffusion coefficients of three self-levelling flooring compounds (SLC) and water vapour resistance of a primer have been measured with the cup method. The results show that the diffusion coefficient is dependent not only on the vapour content (relative humidity), but also on the absolute moisture content, i.e., there is a hysteresis effect on moisture transport. At RH lower than approximately 90 %, SLC have higher diffusion coefficients than a standard concrete (w/c 0.7 OPC), but the opposit...
Hybrid approaches for multiple-species stochastic reaction–diffusion models
Spill, Fabian, E-mail: fspill@bu.edu [Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Guerrero, Pilar [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Alarcon, Tomas [Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Maini, Philip K. [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Byrne, Helen [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Computational Biology Group, Department of Computer Science, University of Oxford, Oxford OX1 3QD (United Kingdom)
2015-10-15
Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.
Stochastic model of forecasting spare parts demand
Ivan S. Milojević
2012-01-01
hypothesis of the existence of phenomenon change trends, the next step in the methodology of forecasting is the determination of a specific growth curve that describes the regularity of the development in time. These curves of growth are obtained by the analytical representation (expression of dynamic lines. There are two basic stages in the process of expression and they are: - The choice of the type of curve the shape of which corresponds to the character of the dynamic order variation - the determination of the number of values (evaluation of the curve parameters. The most widespread method of forecasting is the trend extrapolation. The basis of the trend extrapolation is the continuing of past trends in the future. The simplicity of the trend extrapolation process, on the one hand, and the absence of other information on the other hand, are the main reasons why the trend extrapolation is used for forecasting. The trend extrapolation is founded on the following assumptions: - The phenomenon development can be presented as an evolutionary trajectory or trend, - General conditions that influenced the trend development in the past will not undergo substantial changes in the future. Spare parts demand forecasting is constantly being done in all warehouses, workshops, and at all levels. Without demand forecasting, neither planning nor decision making can be done. Demand forecasting is the input for determining the level of reserve, size of the order, ordering cycles, etc. The question that arises is the one of the reliability and accuracy of a forecast and its effects. Forecasting 'by feeling' is not to be dismissed if there is nothing better, but in this case, one must be prepared for forecasting failures that cause unnecessary accumulation of certain spare parts, and also a chronic shortage of other spare parts. All this significantly increases costs and does not provide a satisfactory supply of spare parts. The main problem of the application of this model is that each
Modeling of diffusion with partitioning in stratum corneum using a finite element model.
Barbero, Ana M; Frasch, H F
2005-09-01
Partitioning and diffusion of chemicals in skin is of interest to researchers in areas such as transdermal penetration and drug disposition, either for risk assessment or transdermal delivery. In this study a finite element method is used to model diffusion in the skin's outermost layer, the stratum corneum (SC). The SC is considered to be a finite two-dimensional composite having different diffusivity values in each medium as well as a partition coefficient at the interfaces between media. A commercial finite element package with thermal analysis capabilities is selected due to the flexibility of this software to handle irregular geometries. Partitioning is accommodated through a change of variables technique. This technique is validated by comparison of model results with analytical solutions of steady-state flux, transient concentration profiles, and time lag for diffusion in laminates. Two applications are presented. Diffusion is solved in a two-dimensional "brick and mortar" geometry that is a simplification of human stratum corneum, with a partition coefficient between corneocyte and lipid. Results are compared to the diffusion in multiple laminates to examine effects of the partition coefficient. The second application is the modeling of diffusion with partitioning through an irregular geometry which is obtained from a micrograph of hairless mouse stratum corneum.
The ADR model developed in Part I of this study was successfully validated with experimenta data obtained for the inactivation of C. parvum and C. muris oocysts with a pilot-scale ozone-bubble diffuser contactor operated with treated Ohio River water. Kinetic parameters, required...
A numerical model of stress driven grain boundary diffusion
Sethian, J. A.; Wilkening, Jon
2004-01-01
The stress driven grain boundary diffusion problem is a continuum model of mass transport phenomena in microelectronic circuits due to high current densities (electromigration) and gradients in normal stress along grain boundaries. The model involves coupling many different equations and phenomena, and difficulties such as non-locality, stiffness, complex geometry, and singularities in the stress tensor near corners and junctions make the problem difficult to analyze rigorously and simulate numerically. We present a new numerical approach to this problem using techniques from semigroup theory to represent the solution. The generator of this semigroup is the composition of a type of Dirichlet to Neumann map on the grain boundary network with the Laplace operator on the network. To compute the former, we solve the equations of linear elasticity several times, once for each basis function on the grain boundary. We resolve singularities in the stress field near corners and junctions by adjoining special singular basis functions to both finite element spaces (2d for elasticity, 1d for grain boundary functions). We develop data structures to handle jump discontinuities in displacement across grain boundaries, singularities in the stress field, complicated boundary conditions at junctions and interfaces, and the lack of a natural ordering for the nodes on a branching grain boundary network. The method is used to study grain boundary diffusion for several geometries.
Pharmacokinetic modeling of ascorbate diffusion through normal and tumor tissue.
Kuiper, Caroline; Vissers, Margreet C M; Hicks, Kevin O
2014-12-01
Ascorbate is delivered to cells via the vasculature, but its ability to penetrate into tissues remote from blood vessels is unknown. This is particularly relevant to solid tumors, which often contain regions with dysfunctional vasculature, with impaired oxygen and nutrient delivery, resulting in upregulation of the hypoxic response and also the likely depletion of essential plasma-derived biomolecules, such as ascorbate. In this study, we have utilized a well-established multicell-layered, three-dimensional pharmacokinetic model to measure ascorbate diffusion and transport parameters through dense tissue in vitro. Ascorbate was found to penetrate the tissue at a slightly lower rate than mannitol and to travel via the paracellular route. Uptake parameters into the cells were also determined. These data were fitted to the diffusion model, and simulations of ascorbate pharmacokinetics in normal tissue and in hypoxic tumor tissue were performed with varying input concentrations, ranging from normal dietary plasma levels (10-100 μM) to pharmacological levels (>1 mM) as seen with intravenous infusion. The data and simulations demonstrate heterogeneous distribution of ascorbate in tumor tissue at physiological blood levels and provide insight into the range of plasma ascorbate concentrations and exposure times needed to saturate all regions of a tumor. The predictions suggest that supraphysiological plasma ascorbate concentrations (>100 μM) are required to achieve effective delivery of ascorbate to poorly vascularized tumor tissue.
Analysis of a diffuse interface model of multispecies tumor growth
Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.
2017-04-01
We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726-54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.
Pre-Clinical Models of Diffuse Intrinsic Pontine Glioma
Oren J Becher
2015-07-01
Full Text Available Diffuse Intrinsic Pontine Glioma (DIPG is a rare and incurable brain tumor that arises in the brainstem of children predominantly between the ages of six and eight. Its intricate morphology and involvement of normal pons tissue precludes surgical resection, and the standard of care today remains fractionated radiation alone. In the past 30 years, there have been no significant advances made in the treatment of DIPG. This is largely because we lack good models of DIPG and therefore have little biological basis for treatment. In recent years however, due to increased biopsy and acquisition of autopsy specimens, research is beginning to unravel the genetic and epigenetic drivers of DIPG. Insight gleaned from these studies has led to improvements in approaches to both model these tumors in the lab, as well as to potentially treat them in the clinic. This review will detail the initial strides towards modeling DIPG in animals, which included allograft and xenograft rodent models using non-DIPG glioma cells. Important advances in the field came with the development of in vitro cell and in vivo xenograft models derived directly from autopsy material of DIPG patients or from human embryonic stem cells. Lastly, we will summarize the progress made in the development of genetically engineered mouse models of DIPG. Cooperation of studies incorporating all of these modeling systems to both investigate the unique mechanisms of gliomagenesis in the brainstem and to test potential novel therapeutic agents in a preclinical setting will result in improvement in treatments for DIPG patients.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
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.
An HBV model with diffusion and time delay.
Xu, Rui; Ma, Zhien
2009-04-07
In this paper, a hepatitis B virus (HBV) model with spatial diffusion and saturation response of the infection rate is investigated, in which the intracellular incubation period is modelled by a discrete time delay. By analyzing the corresponding characteristic equations, the local stability of an infected steady state and an uninfected steady state is discussed. By comparison arguments, it is proved that if the basic reproductive number is less than unity, the uninfected steady state is globally asymptotically stable. If the basic reproductive number is greater than unity, by successively modifying the coupled lower-upper solution pairs, sufficient conditions are obtained for the global stability of the infected steady state. Numerical simulations are carried out to illustrate the main results.
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)
Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
Rigas, G; Brackston, R D; Morrison, J F
2015-01-01
A modelling methodology to reproduce the experimental measurements of a turbulent flow under the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake- flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries which occur at the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.
Diffusion and sorption on hardened cement pastes - experiments and modelling results
Jakob, A.; Sarott, F.-A.; Spieler, P.
1999-08-01
Large parts of repositories for low and intermediate level radioactive waste consist of cementitious materials. Radionuclides are transported by diffusion in the cement matrix or, in case of fractured or highly permeable cement, by advection and dispersion. In this work we aim at a mechanistic understanding of diffusion processes of some reactive tracers. On the laboratory scale, ten through-diffusion experiments were performed to study these processes for Cl{sup -}, I{sup -}, Cs{sup +} and Ni{sup 2+} ions in a Sulphate Resisting Portland Cement (SRPC) equilibrated with an artificial pore water. Some of the experiments continued up to nearly three years with daily measurements. In all the experiments, a cement disk initially saturated with an artificial pore water was exposed on one side to a highly diluted solution containing the species of interest. On the second side, a near-zero concentration boundary was maintained to drive through-diffusion of the tracer. The changes of concentrations on both sides of the samples were monitored, allowing careful mass balances. From these data, values of the diffusive flux and the mass of tracer taken up by the cementitious material were determined as a function of time. In the subsequent modelling, the time histories of these tracer breakthroughs were fitted using five different models. The simplest model neglects all retarding mechanisms except pure diffusion. More complex models either account for instantaneous equilibrium sorption in form of linear or non-linear (Freundlich) sorption or for first-order sorption kinetics where the forward reaction may be linear or non-linear according to the Freundlich isotherm, while the back-reaction is linear. Hence, the analysis allows the extraction of the diffusion coefficient and parameter values for the sorption isotherm or rate-constants for sorption and desorption. The fits to the experimental data were carried out by an automated Marquardt-Levenberg procedure yielding error
Rule-based spatial modeling with diffusing, geometrically constrained molecules
Lohel Maiko
2010-06-01
Full Text Available Abstract Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined. For our implementation (based on LAMMPS, we have chosen an already existing formalism (BioNetGen for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided. Results Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules. When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa. Conclusions We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial
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
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.
2014-01-01
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.
Magnetic field diffusion modeling of a small enclosed firing system
Warne, L.K.; Merewether, K.O.
1996-01-01
Intense magnetic fields exist in the immediate vicinity of a lightning strike (and near power lines). Conducting barriers increase the rise time (and thus decrease the rise rate) interior to the barrier, but typically do not prevent penetration of the magnetic field, since the lightning current fall time may be larger than the barrier diffusion time. Thus, substantial energy is present in the interior field, although the degradation of rise rate makes it more difficult to couple into electrical circuits. This report assesses the threat posed by the diffusive magnetic field to interior components and wire loops (where voltages are induced). Analytical and numerical bounding analyses are carried out on a pill box shaped conducting barrier to develop estimates for the worst case magnetic field threats inside the system. Worst case induced voltages and energies are estimated and compared with threshold charge voltages and energies on the output capacitor of the system. Variability of these quantities with respect to design parameters are indicated. The interior magnetic field and induced voltage estimates given in this report can be used as excitations for more detailed interior and component models.
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S A; Kugeiko, M M; Firago, V A [Belarusian State University, Minsk (Belarus); Sobchuk, A N [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus)
2014-01-31
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)
Diffusion Modeling: A Study of the Diffusion of “Jatropha Curcas ...
Diffusion of innovation is a versatile social science theory which typically ... Jatropha Curcas based diesel oil (Jacodiesel) in the context of a specific social environment. ... Innovation, Communicative Influence, Multi-media and Communication ...
Weak solutions for a non-Newtonian diffuse interface model with different densities
Abels, Helmut; Breit, Dominic
2016-11-01
We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a nonhomogenouos generalized Navier-Stokes system and a Cahn-Hilliard equation. For the Cahn-Hilliard part a smooth free energy density and a constant, positive mobility is assumed. Using the {{L}∞} -truncation method we prove existence of weak solutions for a power-law exponent p>\\frac{2d+2}{d+2} , d = 2, 3.
A kinetic model for molecular diffusion through pores.
D'Agostino, Tommaso; Salis, Samuele; Ceccarelli, Matteo
2016-07-01
The number of pathogens developing multiple drug resistance is ever increasing. The impact on healthcare systems is huge and the need for novel antibiotics as well a new way to develop them is urgent, especially against Gram-negative bacteria. The first defense of these bacteria is the outer membrane, where unspecific protein channels (porins) modulate nutrients passive diffusion. Also polar antibiotics enter through this path and down-regulation and/or mutation of porins are very common in drug resistant strains. Our inability to come up with novel effective antibiotics mostly relies upon the insufficient comprehension of the key molecular features enabling better penetration through porins. Molecular dynamics simulations offer an extraordinary tool in the study of the dynamics of biological systems; however, one of the major drawbacks of this method is that its use is currently restricted to study time scales of the order of microsecond. Enhanced sampling methods like Metadynamics have been recently used to investigate the diffusion of antibiotics through bacterial porins. The main limitation is that dynamical properties cannot be estimated because of the different potential that the systems under study are experiencing. Recently, the scope of Metadynamics has been extended. By applying an a posteriori analysis one can obtain rates of transitions and rate-limiting steps of the process under study, directly comparable with kinetic data extracted from electrophysiology experiments. In this work, we apply this method to the study of the permeability of Escherichia coli's OmpF with respect to Meropenem, finding good agreement with the residence time obtained analyzing experimental current noise. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.
The Geometric Modelling of Furniture Parts and Its Application
张福炎; 蔡士杰; 王玉兰; 居正文
1989-01-01
In this paper, a 3-D solid modelling method appropriate for the design of furniture parts, which has been used in FCAD (Computer Aided Design for Furniture Structure )system, is introduced. Some interactive functions for modifying part models and deriving a variety of practical parts are described. Finally. the application of the modelling method to computer aided manufacturing of furniture parts is prospected.
Araruna, F. D.; Braz e Silva, P.; Carvalho, R. R.; Rojas-Medar, M. A.
2015-06-01
We consider the motion of a viscous incompressible fluid consisting of two components with a diffusion effect obeying Fick's law in ℝ3. We prove that there exists a small time interval where the fluid variables converge uniformly as the viscosity and the diffusion coefficient tend to zero. In the limit, we find a non-homogeneous, non-viscous, incompressible fluid governed by an Euler-like system.
A policy model for diffusion of electricity saving technologies
Heimdal, Sverre Inge; Bjoernstad, Even (Even Enova SF (Norway))
2009-07-01
This paper discusses an integrated model for information and marketing tools combined with various subsidy elements developed for achieving electricity savings and improved energy efficiency in the Norwegian residential sector. The model represents the framework within which current Norwegian policies within this field are based. A central element of the model is the way marketing and subsidy elements are combined in different phases of the market diffusion process of the relevant technologies, and how market distortions are sought minimized through criteria for entry and exit to the scheme. The paper further gives examples of applications of the model. In 2003 Norwegian parliament launched a one-shot Household Subsidy Programme for heating and efficiency technologies in the residential sector. The evaluation report of the subsidy scheme as well as the IEA national report on Norway in 2005 concluded that the subsidy scheme had been a great success. This programme was reinstated on a permanent basis in 2006, and the paper uses data from these programmes as illustrations to the theoretical model.
Hébert, M.; Becker, J.-M.
2008-01-01
This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelka's layering model describes the multiple reflections and transmissions of light taking place between various superposed diffusing layers (disc...
Solving the Advection-Diffusion Equations in Biological Contexts using the Cellular Potts Model
Dan, D; Chen, K; Glazier, J A; Dan, Debasis; Mueller, Chris; Chen, Kun; Glazier, James A.
2005-01-01
The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference schemes suffer numerical instabilities solving the resulting advection-diffusion equations. To circumvent these problems we simulate advection-diffusion within the framework of the CPM using off-lattice finite-difference methods. We define a set of generalized fluid particles which detach advection and diffusion from the lattice. Diffusion occurs between neighboring fluid particles by local averaging rules which approxi...
Technology diffusion in energy-economy models: The case of Danish vintage models
Klinge Jacobsen, Henrik
2000-01-01
the consequences of the vintage modelling approach. The fluctuating utilization rates for power capacity in Denmark are found to have a significant impact on average fuel efficiencies. Diffusion of electric appliances is linked to economic activity and saturation levels for each appliance. In the sector......Technological progress is an important issue in long-term energy demand projections and in environmental analyses. Different assumptions on technological progress and diffusion of new technologies are among the reasons for diverging results obtained using bottom-up and top-down models for analyzing...... the costs of greenhouse gas mitigation. This paper examines the effect on aggregate energy efficiency of using technological vintage models to describe technology diffusion. The focus is on short- to medium-term issues. Three different models of Danish energy supply and demand are used to illustrate...
Acoustic Predictions in Industrial Spaces Using a Diffusion Model
Alexis Billon
2012-01-01
Full Text Available Industrial spaces are known to be very noisy working environment. This noise exposure can be uncomfortable, tiring, or even harmful, at worst. Industrial spaces have several characteristics: they are often huge flat volumes fitted with many obstacles and sound sources. Moreover, they are usually surrounded by rooms where low noise levels are required. The existing prediction tools can seldom model all these phenomena accurately. In this paper, a prediction model based on a diffusion equation is presented. The successive developments carried out to deal with the various propagating phenomena met in industrial spaces are shown. For each phenomenon, numerical or experimental examples are given to highlight the validity of this model. It is also shown that its computation load is very little in comparison to ray-tracing-based methods. In addition, this model can be used as a reliable and flexible tool to study the physics of the coupling between rooms. Finally, an application to a virtual factory is presented.
Long Term Potentials and Costs of RES - Part I: Potentials, Diffusion and Technological learning
Hoefnagels, E.T.A.; Junginger, H.M.; Panzer, C.; Resch, G.; Held, A.
2011-01-01
Europe requires a long term vision for Renewable Energy Sources (RES) in order to pave the way for a successful and in the mid-term stable RES deployment beyond 2020. This encompasses, on the one hand, an assessment of the mid-term potentials and diffusion constraints for the broad basket of RES opt
Modelling of sand transport under wave-generated sheet flows with a RANS diffusion model
Hassan, Wael; Ribberink, Jan S.
2010-01-01
A 1DV-RANS diffusion model is used to study sand transport processes in oscillatory flat-bed/sheet flow conditions. The central aim is the verification of the model with laboratory data and to identify processes controlling the magnitude and direction (‘onshore’/‘offshore’) of the net time-averaged
Tudor Barbu
2014-06-01
Full Text Available A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explaining the mathematical reasons behind it. Also, we perform a rigorous mathematical investigation on of the existence and uniqueness of the solution of our nonlinear diffusion equation. This PDE-based noise removal approach outperforms most diffusion-based methods, producing considerably better smoothing results and providing a much better edge preservation.
The dynamics of multimodal integration: The averaging diffusion model.
Turner, Brandon M; Gao, Juan; Koenig, Scott; Palfy, Dylan; L McClelland, James
2017-03-08
We combine extant theories of evidence accumulation and multi-modal integration to develop an integrated framework for modeling multimodal integration as a process that unfolds in real time. Many studies have formulated sensory processing as a dynamic process where noisy samples of evidence are accumulated until a decision is made. However, these studies are often limited to a single sensory modality. Studies of multimodal stimulus integration have focused on how best to combine different sources of information to elicit a judgment. These studies are often limited to a single time point, typically after the integration process has occurred. We address these limitations by combining the two approaches. Experimentally, we present data that allow us to study the time course of evidence accumulation within each of the visual and auditory domains as well as in a bimodal condition. Theoretically, we develop a new Averaging Diffusion Model in which the decision variable is the mean rather than the sum of evidence samples and use it as a base for comparing three alternative models of multimodal integration, allowing us to assess the optimality of this integration. The outcome reveals rich individual differences in multimodal integration: while some subjects' data are consistent with adaptive optimal integration, reweighting sources of evidence as their relative reliability changes during evidence integration, others exhibit patterns inconsistent with optimality.
Distributed-order diffusion equations and multifractality: Models and solutions
Sandev, Trifce; Chechkin, Aleksei V.; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M.; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Diffusion in Liquids: Equilibrium Molecular Simulations and Predictive Engineering Models
Liu, X.
2013-01-01
The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations. From a practical point of view, systems consisting more than two components are more interesting. However, experimental and simulation data on transport diffusion for such systems are scarce. There...
Abdelmadjid Atif
2010-01-01
Full Text Available The paper refers to the analysis of interactions between the impeller and the vaned diffuser on the air model of a radial flow pump. The study deals with a numerical simulation of the flow for a full 360° entire impeller and diffuser. The task is carried out close to design operating conditions and for one particular position of the impeller blade with respect to diffuser frame. Among all the results, it has been decided to mainly focus on the flow pattern at the exit part inside the impeller coming from the diffuser vanes interactions. The results are compared to the available PIV measurements.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Ndanou, S., E-mail: serge.ndanou@univ-amu.fr; Favrie, N., E-mail: nicolas.favrie@univ-amu.fr; Gavrilyuk, S., E-mail: sergey.gavrilyuk@univ-amu.fr
2015-08-15
We extend the model of diffuse solid–fluid interfaces developed earlier by authors of this paper to the case of arbitrary number of interacting hyperelastic solids. Plastic transformations of solids are taken into account through a Maxwell type model. The specific energy of each solid is given in separable form: it is the sum of a hydrodynamic part of the energy depending only on the density and the entropy, and an elastic part of the energy which is unaffected by the volume change. It allows us to naturally pass to the fluid description in the limit of vanishing shear modulus. In spite of a large number of governing equations, the model has a quite simple mathematical structure: it is a duplication of a single visco-elastic model. The model is well posed both mathematically and thermodynamically: it is hyperbolic and compatible with the second law of thermodynamics. The resulting model can be applied in the situations involving an arbitrary number of fluids and solids. In particular, we show the ability of the model to describe spallation and penetration phenomena occurring during high velocity impacts.
Quasineutral limit of a standard drift diffusion model for semiconductors
XIAO; Ling
2002-01-01
［1］Brenier, Y., Grenier, E., Limite singuliere de Vlasov-Poisson dans le regime de quasi neutralite: le cas independent du temps, C. R. Acad. Sci. Paris, 1994, 318: 121-124.［2］Cordier, S., Grenier, E., Quasineutral limit of Euler-Poisson system arising from plasma physics, Commun. in P. D. E., 2000, 23: 1099-1113.［3］Jüungel, A., Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci., 1995, 5: 497-518.［4］Chen, F., Introduction to Plasma Physics and Controlled Fusion, Vol. 1, New York: Plenum Press, 1984.［5］Ringhofer, C., An asymptotic analysis of a transient p-n-junction model, SIAM J. Appl. Math., 1987, 47: 624-642.［6］Cordier, S., Degond, P., Markowich, P. A. et al., Traveling waves analysis and jump relations for the Euler-Poisson model in the quasineutral limit, Asymptotic Anal., 1995, 11: 209-224.［7］Brézis, H., Golse, F., Sentis, R., Analyse asymptotique de l'équation de Poisson couplée la relation de Boltzmann, Quasi-neutralité des plasmas, C. R. Acad. Sci. Paris, 1995, 321: 953-959.［8］Simon, J., Compact set in the space Lp(0, T; B), Anal. Math. Pure Appl., 1987, 166: 65-96.［9］Lions, J. L., Quelques méthodes des Résolution des Problémes aux Limites non Linéaires, Paris: Dunod-Gauthier-Villard, 1969.
Diffusion in Liquids: Equilibrium Molecular Simulations and Predictive Engineering Models
Liu, X.
2013-01-01
The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations.
Perceptual decision making: Drift-diffusion model is equivalent to a Bayesian model
Sebastian eBitzer
2014-02-01
Full Text Available Behavioural data obtained with perceptual decision making experiments are typically analysed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence towards a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses.
Synchronized stability in a reaction–diffusion neural network model
Wang, Ling; Zhao, Hongyong, E-mail: hongyongz@126.com
2014-11-14
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability.
Simulating Radiotherapy Effect in High-Grade Glioma by Using Diffusive Modeling and Brain Atlases
Alexandros Roniotis
2012-01-01
Full Text Available Applying diffusive models for simulating the spatiotemporal change of concentration of tumour cells is a modern application of predictive oncology. Diffusive models are used for modelling glioblastoma, the most aggressive type of glioma. This paper presents the results of applying a linear quadratic model for simulating the effects of radiotherapy on an advanced diffusive glioma model. This diffusive model takes into consideration the heterogeneous velocity of glioma in gray and white matter and the anisotropic migration of tumor cells, which is facilitated along white fibers. This work uses normal brain atlases for extracting the proportions of white and gray matter and the diffusion tensors used for anisotropy. The paper also presents the results of applying this glioma model on real clinical datasets.
Empirically Grounded Agent-Based Models of Innovation Diffusion: A Critical Review
Zhang, Haifeng
2016-01-01
Innovation diffusion has been studied extensively in a variety of disciplines, including sociology, economics, marketing, ecology, and computer science. Traditional literature on innovation diffusion has been dominated by models of aggregate behavior and trends. However, the agent-based modeling (ABM) paradigm is gaining popularity as it captures agent heterogeneity and enables fine-grained modeling of interactions mediated by social and geographic networks. While most ABM work on innovation diffusion is theoretical, empirically grounded models are increasingly important, particularly in guiding policy decisions. We present a critical review of empirically grounded agent-based models of innovation diffusion, developing a categorization of this research based on types of agent models as well as applications. By connecting the modeling methodologies in the fields of information and innovation diffusion, we suggest that the maximum likelihood estimation framework widely used in the former is a promising paradigm...
Spatiotemporal Patterns Induced by Cross-Diffusion in a Three-Species Food Chain Model
Ma, Zhan-Ping; Li, Wan-Tong; Wang, Yu-Xia
This paper focuses on a three-species Lotka-Volterra food chain model with cross-diffusion under homogeneous Neumann boundary conditions. The known results indicate that no spatiotemporal patterns happen in the corresponding reaction-diffusion system. When some cross-diffusion terms are introduced in the system, the existence of nonconstant positive steady-states as well as the Hopf bifurcation is studied. Our result shows that cross-diffusion plays a crucial role in the formation of spatiotemporal patterns, that is, it can create not only stationary patterns but also spatially inhomogeneous periodic oscillatory patterns, which is a strong contrast to the case without cross-diffusion.
A simple model for diffusion-induced dislocations during the lithiation of crystalline materials
Fuqian Yang
2014-01-01
Full Text Available Assuming that the lithiation reaction occurs randomly in individual small particles in the vicinity of the reaction front, a simple model of diffusion-induced dislocations was developed. The diffusion-induced dislocations are controlled by the misfit strain created by the diffusion of solute atoms or the phase transformation in the vicinity of the reaction front. The dislocation density is proportional to the total surface area of the “lithiated particle” and inversely proportional to the particle volume. The diffusion-induced dislocations relieve the diffusion-induced stresses.
Spike neural models (part I: The Hodgkin-Huxley model
Johnson, Melissa G.
2017-05-01
Full Text Available Artificial neural networks, or ANNs, have grown a lot since their inception back in the 1940s. But no matter the changes, one of the most important components of neural networks is still the node, which represents the neuron. Within spiking neural networks, the node is especially important because it contains the functions and properties of neurons that are necessary for their network. One important aspect of neurons is the ionic flow which produces action potentials, or spikes. Forces of diffusion and electrostatic pressure work together with the physical properties of the cell to move ions around changing the cell membrane potential which ultimately produces the action potential. This tutorial reviews the Hodkgin-Huxley model and shows how it simulates the ionic flow of the giant squid axon via four differential equations. The model is implemented in Matlab using Euler's Method to approximate the differential equations. By using Euler's method, an extra parameter is created, the time step. This new parameter needs to be carefully considered or the results of the node may be impaired.
Developing A Laser Shockwave Model For Characterizing Diffusion Bonded Interfaces
James A. Smith; Jeffrey M. Lacy; Barry H. Rabin
2014-07-01
12. Other advances in QNDE and related topics: Preferred Session Laser-ultrasonics Developing A Laser Shockwave Model For Characterizing Diffusion Bonded Interfaces 41st Annual Review of Progress in Quantitative Nondestructive Evaluation Conference QNDE Conference July 20-25, 2014 Boise Centre 850 West Front Street Boise, Idaho 83702 James A. Smith, Jeffrey M. Lacy, Barry H. Rabin, Idaho National Laboratory, Idaho Falls, ID ABSTRACT: The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) which is assigned with reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU. The new LEU fuel is based on a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to complete the fuel qualification process, the laser shock technique is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. The Laser Shockwave Technique (LST) is being investigated to characterize interface strength in fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However the deposition of laser energy into the containment layer on specimen’s surface is intractably complex. The shock wave energy is inferred from the velocity on the backside and the depth of the impression left on the surface from the high pressure plasma pulse created by the shock laser. To help quantify the stresses and strengths at the interface, a finite element model is being developed and validated by comparing numerical and experimental results for back face velocities and front face depressions with experimental results. This paper will report on initial efforts to develop a finite element model for laser
Poornesh, K. K.; Cho, C. D.; Lee, G. B.; Tak, Y. S.
In PEM fuel cell, gas-diffusion electrode (GDE) plays very significant role in force transmission from bipolar plate to the membrane. This paper investigates the effects of geometrical heterogeneities of gas-diffusion electrode layer (gas-diffusion layer (GDL) and catalyst layer (CL)) on mechanical damage evolution and propagation. We present a structural integrity principle of membrane electrode assembly (MEA) based on the interlayer stress transfer capacity and corresponding cell layer material response. Commonly observable damages such as rupture of hydrophobic coating and breakage of carbon fiber in gas-diffusion layer are attributed to the ductile to brittle phase transition within a single carbon fiber. Effect of material inhomogeneity on change in modulus, hardness, contact stiffness, and electrical contact resistance is also discussed. Fracture statistics of carbon fiber and variations in flexural strength of GDL are studied. The damage propagation in CL is perceived to be influenced by the type of gradation and the vicinity from which crack originates. Cohesive zone model has been proposed based on the traction-separation law to investigate the damage propagation throughout the two interfaces (carbon fiber/CL and CL/membrane).
An electrodynamics-based model for ion diffusion in microbial polysaccharides.
Liu, Chongxuan; Zachara, John M; Felmy, Andrew; Gorby, Yuri
2004-10-10
An electrodynamics-based model was formulated for simulation of ion diffusion in microbial polysaccharides. The fixed charges and electrostatic double layers that may associate with microbial polysaccharides and their effects on ion diffusion were explicitly built into the model. The model extends a common multicomponent ion diffusion formulation that is based on irreversible thermodynamics under a zero ionic charge flux condition, which is only applicable to the regions without fixed charges and electrostatic double layers. An efficient numerical procedure was presented to solve the differential equations in the model. The model well described key features of experimental observations of ion diffusion in negatively charged microbial polysaccharides including accelerated diffusive transport of cations, exclusion of anions, and increased rate of cation transport with increasing negative charge density. The simulated diffusive fluxes of cations and anions were consistent with a cation exchange diffusion concept in negatively charged polysaccharides at the interface of plant roots and soils; and the developed model allows to mathematically study such diffusion phenomena. An illustrative example was also provided to simulate dynamic behavior of ionic current during ion diffusion within a charged bacterial cell wall polysaccharide and the effects of the ionic current on the compression or expansion of the bacterial electrostatic double layer at the interface of the cell wall and bulk solution.
Film rupture in the diffuse interface model coupled to hydrodynamics.
Thiele, U; Velarde, M G; Neuffer, K; Pomeau, Y
2001-09-01
The process of dewetting of a thin liquid film is usually described using a long-wave approximation yielding a single evolution equation for the film thickness. This equation incorporates an additional pressure term-the disjoining pressure-accounting for the molecular forces. Recently a disjoining pressure was derived coupling hydrodynamics to the diffuse interface model [L. M. Pismen and Y. Pomeau, Phys. Rev. E 62, 2480 (2000)]. Using the resulting evolution equation as a generic example for the evolution of unstable thin films, we examine the thickness ranges for linear instability and metastability for flat films, the families of stationary periodic and localized solutions, and their linear stability. The results are compared to simulations of the nonlinear time evolution. From this we conclude that, within the linearly unstable thickness range, there exists a well defined subrange where finite perturbations are crucial for the time evolution and the resulting structures. In the remainder of the linearly unstable thickness range the resulting structures are controlled by the fastest flat film mode assumed up to now for the entire linearly unstable thickness range. Finally, the implications for other forms of disjoining pressure in dewetting and for spinodal decomposition are discussed.
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-01
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch-Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients.
Allgood, Daniel C.; Graham, Jason S.; Ahuja, Vineet; Hosangadi, Ashvin
2010-01-01
Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence
LIXiangbin; ZHAOYuechun; 等
2002-01-01
A new model,phase equilibrium-kinetics model(PEKM),for estimation of diffusion coefficient was proposed in this paper.Kinetic exeriments of phenol desorption on NKAII resin in the presence and the absence of ultrasound wree separately conducted,and diffusion coefficients of phenol within an adsorbent particle were estimated by means of proposed PEKM and classic simplified model.Results show that the use of ultrasound not only changes the phase equilibrium state of NKAII resin/phenol/water system which had been equilibrium at normal condition,but also enhances diffusion of phenol within the resin.The diffusion coefficient of phenol in the resin in the field of ultrasound increases in an order of magnitude in comparison with the diffusion coefficient determined under no ultrasound.Experimental results also indicated that the diffusion coefficients estimated by PEKM were more accurate than that estimated by the classic simplified mode.
Baup, S; Wolbert, D; Laplanche, A
2002-10-01
Three pesticides (atrazine, bromoxynil and diuron) and two granular activated carbons are involved in equilibrium and kinetic adsorption experiments. Equilibrium is represented by Freundlich isotherm law and kinetic is described by the Homogeneous Surface Diffusion Model, based on external mass transfer and intraparticle surface diffusion. Equilibrium and long-term experiments are conducted to compare Powdered Activated Carbon and Granular Activated Carbon. These first investigations show that crushing GAC into PAC improves the accessibility of the adsorption sites without increasing the number of these sites. In a second part, kinetics experiments are carried out using a Differential Column Batch Reactor. Thanks to this experimental device, the external mass transfer coefficient k(f) is calculated from empirical correlation and the effect of external mass transfer on adsorption is likely to be minimized. In order to obtain the intraparticle surface diffusion coefficient D. for these pesticides, comparisons between experimental kinetic data and simulations are conducted and the best agreement leads to the Ds coefficient. This procedure appears to be an efficient way to acquire surface diffusion coefficients for the adsorption of pesticides onto GAC. Finally it points out the role of surface diffusivity in the adsorption rate. As a matter of fact, even if the amount of the target-compound that could be potentially adsorbed is really important, its surface diffusion coefficient may be small, so that its adsorption may not have enough contact time to be totally achieved.
DIFFUSION MODEL OF CREAMY- AND VEGETABLE SPREADS MIXING
A. N. Ostrikov
2015-01-01
Full Text Available Summary .A mathematical model of the process of mixing cream- and vegetable spread was developed. In modeling the diffusion understanding of the nature of the process were used, allowing escape from the apparatus geometry. After turning on the mixer the mixing process begins. Its duration can be determined by the behavior of the tracer particles introduced into the agitated medium in a predetermined quantity through the free liquid surface within a short period of time. If tracer particles have the same density with the surrounding bulk liquid phase, then the path of movement of the particles and the fluid are identical. The degree of homogeneity of the composition can be stirred calculated by the coefficient of variation, which is identified by the local concentrations of tracer particles in the volume of stirred medium. The task of a one-dimensional particle transport in the plane layer of the mixed liquid is solved for their calculation. The calculated ratios obtained allow us to calculate the particle concentration at any point in the volume being mixed at random times. Based on the experiment effective mixing coefficients are identified and relations for their assessment, depending on the Reynolds number of the mixer in the range studied variations of process are offered. Using the time dependence of the variation coefficient characterizing the homogenity of the system being mixed, it is possible to determine the duration of mixing to obtain the product with the desired uniformity and homogeneity of the product under the definition of a predetermined duration of the mixing process. The variation coefficient %, indicating a sufficiently good uniformity of the spread composition was found for the spread №1, being mixed with a stirrer rotating at a speed of n=150 rev / min, and the dimensionless length of the process Fo =0,0935 for obtaining estimated relations. Using the proposed calculation algorithm one can estimate the homogeneity of the
Osei, Frank B.; Osei, F.B.; Duker, Alfred A.; Stein, A.
2011-01-01
This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint
Osei, Frank B.; Duker, Alfred A.; Stein, Alfred
2011-01-01
This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint
Paper-Based Assessment of the Effects of Aging on Response Time: A Diffusion Model Analysis
Judith Dirk
2017-04-01
Full Text Available The effects of aging on response time were examined in a paper-based lexical-decision experiment with younger (age 18–36 and older (age 64–75 adults, applying Ratcliff’s diffusion model. Using digital pens allowed the paper-based assessment of response times for single items. Age differences previously reported by Ratcliff and colleagues in computer-based experiments were partly replicated: older adults responded more conservatively than younger adults and showed a slowing of their nondecision components of RT by 53 ms. The rates of evidence accumulation (drift rate showed no age-related differences. Participants with a higher score in a vocabulary test also had higher drift rates. The experiment demonstrates the possibility to use formal processing models with paper-based tests.
Models and measures of mixing and effective diffusion
Lin, Zhi; Doering, Charles R
2010-01-01
Mixing a passive scalar field by stirring can be measured in a variety of ways including tracer particle dispersion, via the flux-gradient relationship, or by suppression of scalar concentration variations in the presence of inhomogeneous sources and sinks. The mixing efficiency or efficacy of a particular flow is often expressed in terms of enhanced diffusivity and quantified as an effective diffusion coefficient. In this work we compare and contrast several notions of effective diffusivity. We thoroughly examine the fundamental case of a steady sinusoidal shear flow mixing a scalar sustained by a steady sinusoidal source-sink distribution to explore apparent quantitative inconsistencies among the measures. Ultimately the conflicts are attributed to the noncommutative asymptotic limits of large P$\\acute{\\text{e}}$clet number and large length-scale separation. We then propose another approach, a generalization of Batchelor's 1949 theory of diffusion in homogeneous turbulence, that helps unify the particle dis...
Fu-Kwun Wang; Yu-Yao Hsiao; Ku-Kuang Chang
2012-01-01
It is important for executives to predict the future trends. Otherwise, their companies cannot make profitable decisions and investments. The Bass diffusion model can describe the empirical adoption curve for new products and technological innovations. The Grey model provides short-term forecasts using four data points. This study develops a combined model based on the rolling Grey model (RGM) and the Bass diffusion model to forecast motherboard shipments. In addition, we investigate evolutio...
Fu-Kwun Wang; Yu-Yao Hsiao; Ku-Kuang Chang
2012-01-01
It is important for executives to predict the future trends. Otherwise, their companies cannot make profitable decisions and investments. The Bass diffusion model can describe the empirical adoption curve for new products and technological innovations. The Grey model provides short-term forecasts using four data points. This study develops a combined model based on the rolling Grey model (RGM) and the Bass diffusion model to forecast motherboard shipments. In addition, we investigate evolutio...
Moustafa, Ahmed A; Kéri, Szabolcs; Somlai, Zsuzsanna; Balsdon, Tarryn; Frydecka, Dorota; Misiak, Blazej; White, Corey
2015-09-15
In this study, we tested reward- and punishment learning performance using a probabilistic classification learning task in patients with schizophrenia (n=37) and healthy controls (n=48). We also fit subjects' data using a Drift Diffusion Model (DDM) of simple decisions to investigate which components of the decision process differ between patients and controls. Modeling results show between-group differences in multiple components of the decision process. Specifically, patients had slower motor/encoding time, higher response caution (favoring accuracy over speed), and a deficit in classification learning for punishment, but not reward, trials. The results suggest that patients with schizophrenia adopt a compensatory strategy of favoring accuracy over speed to improve performance, yet still show signs of a deficit in learning based on negative feedback. Our data highlights the importance of applying fitting models (particularly drift diffusion models) to behavioral data. The implications of these findings are discussed relative to theories of schizophrenia and cognitive processing.
Nonlocal-response diffusion model of holographic recording in photopolymer
Sheridan, John T.; Lawrence, Justin R.
2000-01-01
The standard one-dimensional diffusion equation is extended to include nonlocal temporal and spatial medium responses. How such nonlocal effects arise in a photopolymer is discussed. It is argued that assuming rapid polymer chain growth, any nonlocal temporal response can be dealt with so that the response can be completely understood in terms of a steady-state nonlocal spatial response. The resulting nonlocal diffusion equation is then solved numerically, in low-harmonic approximation, to de...
Michaud, Georges; Richer, Jacques
2015-01-01
This book gives an overview of atomic diffusion, a fundamental physical process, as applied to all types of stars, from the main sequence to neutron stars. The superficial abundances of stars as well as their evolution can be significantly affected. The authors show where atomic diffusion plays an essential role and how it can be implemented in modelling. In Part I, the authors describe the tools that are required to include atomic diffusion in models of stellar interiors and atmospheres. An important role is played by the gradient of partial radiative pressure, or radiative acceleration, which is usually neglected in stellar evolution. In Part II, the authors systematically review the contribution of atomic diffusion to each evolutionary step. The dominant effects of atomic diffusion are accompanied by more subtle effects on a large number of structural properties throughout evolution. One of the goals of this book is to provide the means for the astrophysicist or graduate student to evaluate the importanc...
Dharmawan, Komang
2017-03-01
It has been claimed in many literatures that the prices of some agriculture commodities tend to follow mean reversion. However, when dealing with the prices of agriculture commodities, is mean-reversion realistic enough without incorporating seasonality and jump diffusion? This research tries to answer the question. The combination between mean-reversion feature, jump and seasonal components are applied to model the behavior of agriculture commodity prices. A jump and seasonal components are added to the standard mean-reverting process in order to reproduce the spiky or jump behaviors. This model has been well applied on simulating the electricity prices but it has not been applied to investigate the behavior of agriculture commodity prices yet. This paper discusses the performance of the model when it is used to price European call options. First, the deterministic seasonality part is calibrated using the least square method. The second stage is to calibrate the stochastic part based on historical prices. The parameters are calibrated by discretizing the model. Hence, the discretized model allows us to perform Monte Carlo simulation on the commodity price under real-word probability. The analysis is conducted using 2 future price of Crude Palm Oil and Coffee Bean on standard payoff functions, a Basket, a Spread, Best of Call, and Worst of Call Options.
Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model
Xinze Lian
2012-01-01
Full Text Available This paper presents a theoretical analysis of evolutionary process that involves organisms distribution and their interaction of spatial distribution of the species with self- and cross-diffusion in a Holling-III ratio-dependent predator-prey model. The diffusion instability of the positive equilibrium of the model with Neumann boundary conditions is discussed. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spots, stripes, and spiral wave pattern replication, which show that reaction-diffusion model is useful to reveal the spatial predation dynamics in the real world.
A reaction diffusion model of pattern formation in clustering of adatoms on silicon surfaces
Trilochan Bagarti
2012-12-01
Full Text Available We study a reaction diffusion model which describes the formation of patterns on surfaces having defects. Through this model, the primary goal is to study the growth process of Ge on Si surface. We consider a two species reaction diffusion process where the reacting species are assumed to diffuse on the two dimensional surface with first order interconversion reaction occuring at various defect sites which we call reaction centers. Two models of defects, namely a ring defect and a point defect are considered separately. As reaction centers are assumed to be strongly localized in space, the proposed reaction-diffusion model is found to be exactly solvable. We use Green's function method to study the dynamics of reaction diffusion processes. Further we explore this model through Monte Carlo (MC simulations to study the growth processes in the presence of a large number of defects. The first passage time statistics has been studied numerically.
COUPLED PHYSICAL-ECOLOGICAL MODELLING OF THE CENTRAL PART OF JIAOZHOU BAY I. PHYSICAL MODELLING
无
2000-01-01
Sharples's 1-D physical model, employing tide-wind driven turbulence closure and surface heating-cooling physics, was used to simulate the evolution of seawater temperature in the central part of Jiaozhou Bay. The results were consistent with observation after application of a large value of vertical eddy diffusivity to the upper layer in the case of rainy season. The simulated bottom seawater temperature varies regularly in sinusoidal pattern. The simulated surface seawater temperature clearly indicates that stratification begins in the middle of April, lasting about 6 days, and ends in later August, lasting only 2 days; and that the strongest stratification occurs in June, when the surface net heat flux is close to zero. Since the rainfall process not considered in the present model could cause very strong vertical mixing in the upper layer of bay water, the physical meaning of applying a larger vertical eddy diffusivity is supposed to be a parametrization of the rainfall created mixing in the upper layer. To prove this hypothesis more complex models have to be used and more observations have to be made in future study.
Carrillo-Hermosilla, J.
2007-07-01
Conventional models of technology diffusion have typically focused on the question of the rate of diffusion at which one new technology is fully adopted. The model described here provides a broader approach, from the perspective the extension of the diffusion of multiple technologies, and the related phenomenon of standardization. Moreover, most conventional research has characterized the diffusion process in terms of technology attributes or adopting firms attributes. Alternatively, we propose here a wide-ranging and consistent taxonomy of the relationships between the circumstances of an industry and the attributes of the technology standardization processes taking place within it. (Author) 100 refs.
Spatiotemporal Pattern in a Self- and Cross-Diffusive Predation Model with the Allee Effect
Feng Rao
2013-01-01
Full Text Available This paper proposes and analyzes a mathematical model for a predator-prey interaction with the Allee effect on prey species and with self- and cross-diffusion. The effect of diffusion which can drive the model with zero-flux boundary conditions to Turing instability is investigated. We present numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spotted and striped-like coexisting and spotted pattern replication. Moreover, we discuss the effect of cross-diffusivity on the stability of the nontrivial equilibrium of the model, which depends upon the magnitudes of the self- and cross-diffusion coefficients. The obtained results show that cross-diffusion plays an important role in the pattern formation of the predator-prey model. It is also useful to apply the reaction-diffusion model to reveal the spatial predation in the real world.
Mathematical Model of a pH-gradient Creation at Isoelectrofocusing. Part IV. Theory
Shiryaeva, E V; Zhukov, M Yu
2013-01-01
The mathematical model describing the non-stationary natural pH-gradient arising under the action of an electric field in an aqueous solution of ampholytes (amino acids) is constructed. The model is a part of a more general model of the isoelectrofocusing (IEF) process. The presented model takes into account: 1) general Ohm's law (electric current flux includes the diffusive electric current); 2) dissociation of water; 3) difference between isoelectric point (IEP) and isoionic point (PZC -- point of zero charge). We also study the Kohlraush's function evolution and discuss the role of the Poisson-Boltzmann equation.
Aminfar, Habib; Mohammadpourfard, Mousa; Khajeh, Kosar
2017-03-01
It is well-known that the Low Density Lipoprotein (LDL) can accumulate and penetrate into the arterial wall. Here, we have investigated the diffusion rate of macromolecules across the porous layer of blood vessel under the effects of magnetic force. By using a finite volume technique, it was found that magnetic field makes alterations in diffusion rate of LDLs, also surface concentration of macromolecules on the walls. As well, the influence of different value of Re and Sc number in the presence of a magnetic field have shown as nondimensional concentration profiles. Magnetic field considered as a body force, porous layer simulated by using Darcy's law and the blood regarded as nano fluid which was examined as a single phase model.
RESEARCH ON VIRTUAL-PART-BASED CONNECTING ELEMENT MODELING
无
2003-01-01
Based on the inner character analysis of interpart, detail modification and assembly relation of mechanical connecting element, the idea, which extends the feature modeling of part to the interpart feature modeling for assembly purpose, is presented, and virtual-part-based connecting element modeling is proposed. During the assembly modeling, base parts are modified by the Boolean subtraction between the virtual part and the part to be connected. Dynamic matching algorithm, which is based on list database, is designed for dynamic extension and off-line editing of connecting part and virtual part, and design rules of connecting element is encapsulated by the virtual part. A prototyped software module for rapid design of connecting elements is implemented under self-developed CAD/CAM platform-SuperMan.
Nonexistence of nonconstant steady-state solutions in a triangular cross-diffusion model
Lou, Yuan; Tao, Youshan; Winkler, Michael
2017-05-01
In this paper we study the Shigesada-Kawasaki-Teramoto model for two competing species with triangular cross-diffusion. We determine explicit parameter ranges within which the model exclusively possesses constant steady state solutions.
Stalled-Flow and Head-Loss Model for Diffuser Pumps
Meng, S. Y.
1984-01-01
Modeling procedure approximates inlet transition zone (blade leading edge to blade throat) of diffuser pump as two-dimensional cascade, properties of which are well known. Model applied to stators as well as rotors. Procedure much faster than previous methods.
Stalled-Flow and Head-Loss Model for Diffuser Pumps
Meng, S. Y.
1984-01-01
Modeling procedure approximates inlet transition zone (blade leading edge to blade throat) of diffuser pump as two-dimensional cascade, properties of which are well known. Model applied to stators as well as rotors. Procedure much faster than previous methods.
Bass-SIR model for diffusion of new products in social networks.
Fibich, Gadi
2016-09-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
Bass-SIR model for diffusion of new products in social networks
Fibich, Gadi
2016-09-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
Development of a hydrogen diffusion gothic model of MARK III-containment
Hung, Zhen-Yu [National Tsing Hua Univ., Dept. of Engineering and System Science, Hsinchu, Taiwan (China); Huang, Yu-Kai; Pei, Bau-Shei [National Tsing Hua Univ., Inst. of Nuclear Engineering Science, Hsinchu, Taiwan (China); Hsu, Wen-Sheng [National Tsing Hua Univ., Nuclear Science and Technology Development Center, Hsinchu, Taiwan (China); Chen, Yen-Shu [Institute of Nuclear Energy Research, Nuclear Engineering Div., Taiyuan County, Taiwan (China)
2015-07-15
The accident that occurred at the Fukushima Daiichi Nuclear Power Plant is a reminder of the danger of hydrogen explosion within a reactor building. Sufficiently high hydrogen concentration may cause an explosion that could damage the structure, resulting in the release of radioisotopes into the environment. In the first part of this study, a gas diffusion experiment was performed, in which helium was used as the working fluid. An analytical model was also developed using the GOTHIC code and the model predictions of the helium distribution were found to be in good agreement with the experimentally measured data. In the second part of the study, a model of the Mark III containment of the Kuosheng Plant in Taiwan was developed, and was applied to a long-term station blackout (SBO) accident similar to that of the Fukushima plant. The hydrogen generation was calculated using the Modular Accident Analysis Program and was used as the boundary condition for the GOTHIC containment model. The simulation results revealed that the hydrogen concentration at the first floor of the wetwell in the containment reached 4 % 9.7 h after the accident. This indicated the possibility of dangerous conditions inside the containment. Although active hydrogen ignitors are already installed in the Kuosheng plant, the findings of this study indicate that it may be necessary to add passive recombiners to prolong an SBO event.
Climate stability for a Sellers-type model. [atmospheric diffusive energy balance model
Ghil, M.
1976-01-01
We study a diffusive energy-balance climate model governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. We consider also models similar to the main one studied, and determine the number of their steady states. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. We investigate the stability under small perturbations of the main model's climates. A stability criterion is derived, and its application shows that the 'present climate' and the 'deep freeze' are stable, whereas the model's glacial is unstable. A variational principle is introduced to confirm the results of this stability analysis. For a sufficient decrease in solar radiation (about 2%) the glacial and interglacial solutions disappear, leaving the ice-covered earth as the only possible climate.
Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay
Boli Xie
2014-01-01
Full Text Available A predator-prey model with both cross diffusion and time delay is considered. We give the conditions for emerging Turing instability in detail. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits a delay and diffusion controlled formation growth not only of spots and stripe-like patterns, but also of the two coexist. The obtained results show that this system has rich dynamics; these patterns show that it is useful for the diffusive predation model with a delay effect to reveal the spatial dynamics in the real model.
A Fractional Fokker-Planck Model for Anomalous Diffusion
anderson, Johan; Moradi, Sara
2014-01-01
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 observing the transition from a Gaussian distribution to a L\\'evy distribution. The statistical properties of the distribution functions are assessed by a generalized 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.
Purchasing policy model based on components／parts unification
SunXiaolin; ZhongDeqiang; ManDaqing; BinSheng
2003-01-01
This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different prices and quality characteristics. Because of the buyer's quality preference and suppliers' discount rates for bulky purchases, the model assists the procurement manager to determine how best to purchase the components/parts to meet its demand while minimizing the total acquisition costs.
Eitzinger Bernhard
2014-07-01
Full Text Available The diffusion capacity of cigarette paper has been reported to be an important parameter in relation to the self-extinguishment of cigarettes and also in relation to carbon monoxide yields. Although the diffusion capacity is routinely measured and instruments for this measurement have been available for several years, differences between measured values obtained on the same paper sample but on different instruments or in different laboratories may be substantial and may make it difficult to use these values, for example, as a basis for paper specifications. Among several reasons, deviations of temperature and pressure from standard conditions, especially within the measurement chamber of the instrument, may contribute to the high variation in diffusion capacity data. Deviations of temperature and pressure will have an influence on the gas flow rates, the diffusion processes inside the measurement chamber and consequently the measured CO2 concentration. Generally, the diffusion capacity is determined from a mathematical model, which describes the diffusion processes inside the measurement chamber. Such models provide the CO2 concentration in the outflow gas for a given diffusion capacity. For practical applications the inverse model is needed, that is, the diffusion capacity shall be determined from a measured CO2 concentration. Often such an inverse model is approximated by a polynomial, which, however, is only valid for standard temperature and pressure. It is shown that relative approximation errors from such polynomials, even without temperature and pressure deviations, cannot always be neglected and it is proposed to eliminate such errors by direct inversion of the model with a comparably simple iterative method. A model which includes temperature and pressure effects is described and the effects of temperature and pressure deviations on the diffusion capacity are theoretically estimated by comparing the output of a model with and without
Compressor Part I: Measurement and Design Modeling
Thomas W. Bein
1999-01-01
method used to design the 125-ton compressor is first reviewed and some related performance curves are predicted based on a quasi-3D method. In addition to an overall performance measurement, a series of instruments were installed on the compressor to identify where the measured performance differs from the predicted performance. The measurement techniques for providing the diagnostic flow parameters are also described briefly. Part II of this paper provides predictions of flow details in the areas of the compressor where there were differences between the measured and predicted performance.
Wu, Hao; Noé, Frank
2011-03-01
Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.
Ho, C.K.; Webb, S.W.
1996-05-01
A review of mechanisms, models, and data relevant to the postulated phenomenon of enhanced vapor-phase diffusion in porous media is presented. Information is obtained from literature spanning two different disciplines (soil science and engineering) to gain a diverse perspective on this topic. Findings indicate that while enhanced vapor diffusion tends to correct the discrepancies observed between past theory and experiments, no direct evidence exists to support the postulated processes causing enhanced vapor diffusion. Numerical modeling analyses of experiments representative of the two disciplines are presented in this paper to assess the sensitivity of different systems to enhanced vapor diffusion. Pore-scale modeling is also performed to evaluate the relative significance of enhanced vapor diffusion mechanisms when compared to Fickian diffusion. The results demonstrate the need for additional experiments so that more discerning analyses can be performed.
Kee, Kerk F; Sparks, Lisa; Struppa, Daniele C; Mannucci, Mirco A; Damiano, Alberto
2016-01-01
By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that coexist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data.
Hidden variable models for quantum mechanics can have local parts
Larsson, Jan-Ake
2009-01-01
We present an explicit nonlocal nonsignaling model which has a nontrivial local part and is compatible with quantum mechanics. This model constitutes a counterexample to Colbeck and Renner's statement [Phys. Rev. Lett. 101, 050403 (2008)] that "any hidden variable model can only be compatible with quantum mechanics if its local part is trivial". Furthermore, we examine Colbeck and Renner's definition of "local part" and find that, in the case of models reproducing the quantum predictions for the singlet state, it is a restriction equivalent to the conjunction of nonsignaling and trivial local part.
Modeling of the magnetic free energy of self-diffusion in bcc Fe
Sandberg, N.; Chang, Z.; Messina, L.; Olsson, P.; Korzhavyi, P.
2015-11-01
A first-principles based approach to calculating self-diffusion rates in bcc Fe is discussed with particular focus on the magnetic free energy associated with diffusion activation. First, the enthalpies and entropies of vacancy formation and migration in ferromagnetic bcc Fe are calculated from standard density functional theory methods in combination with transition state theory. Next, the shift in diffusion activation energy when going from the ferromagnetic to the paramagnetic state is estimated by averaging over random spin states. Classical and quantum mechanical Monte Carlo simulations within the Heisenberg model are used to study the effect of spin disordering on the vacancy formation and migration free energy. Finally, a quasiempirical model of the magnetic contribution to the diffusion activation free energy is applied in order to connect the current first-principles results to experimental data. The importance of the zero-point magnon energy in modeling of diffusion in bcc Fe is stressed.
Simulation of levulinic acid adsorption in packed beds using parallel pore/surface diffusion model
Zeng, L.; Mao, J. [Zhejiang Provincial Key Laboratory for Chemical and Biological Processing Technology of Farm Products, Zhejiang University of Science and Technology, Hangzhou (China); Ren, Q. [National Laboratory of Secondary Resources Chemical Engineering, Zhejiang University, Hangzhou (China); Liu, B.
2010-07-15
The adsorption of levulinic acid in fixed beds of basic polymeric adsorbents at 22 C was studied under various operating conditions. A general rate model which considers pore diffusion and parallel pore/surface diffusion was solved numerically by orthogonal collocation on finite elements to describe the experimental breakthrough data. The adsorption isotherms, and the pore and surface diffusion coefficients were determined independently in batch adsorption studies. The external film resistance and the axial dispersion coefficient were estimated by the Wilson-Geankoplis equation and the Chung-Wen equation, respectively. Simulation elucidated that the model which considers parallel diffusion successfully describes the breakthrough behavior and gave a much better prediction than the model which considers pore diffusion. The results obtained in this work are applicable to design and optimizes the separation process. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Scrape-off layer modeling with kinetic or diffusion description of charge-exchange atoms
Tokar, M. Z.
2016-12-01
Hydrogen isotope atoms, generated by charge-exchange (c-x) of neutral particles recycling from the first wall of a fusion reactor, are described either kinetically or in a diffusion approximation. In a one-dimensional (1-D) geometry, kinetic calculations are accelerated enormously by applying an approximate pass method for the assessment of integrals in the velocity space. This permits to perform an exhaustive comparison of calculations done with both approaches. The diffusion approximation is deduced directly from the velocity distribution function of c-x atoms in the limit of charge-exchanges with ions occurring much more frequently than ionization by electrons. The profiles across the flux surfaces of the plasma parameters averaged along the main part of the scrape-off layer (SOL), beyond the X-point and divertor regions, are calculated from the one-dimensional equations where parallel flows of charged particles and energy towards the divertor are taken into account as additional loss terms. It is demonstrated that the heat losses can be firmly estimated from the SOL averaged parameters only; for the particle loss the conditions in the divertor are of importance and the sensitivity of the results to the so-called "divertor impact factor" is investigated. The coupled 1-D models for neutral and charged species, with c-x atoms described either kinetically or in the diffusion approximation, are applied to assess the SOL conditions in a fusion reactor, with the input parameters from the European DEMO project. It is shown that the diffusion approximation provides practically the same profiles across the flux surfaces for the plasma density, electron, and ion temperatures, as those obtained with the kinetic description for c-x atoms. The main difference between the two approaches is observed in the characteristics of these species themselves. In particular, their energy flux onto the wall is underestimated in calculations with the diffusion approximation by 20 %-30
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
Stochastic modelling and diffusion modes for POD models and small-scale flow analysis
Resseguier, Valentin; Heitz, Dominique; Chapron, Bertrand
2016-01-01
We introduce a stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a decomposition of the velocity in terms of a smooth large-scale velocity component and a rough, highly oscillating, component gives rise, without any supplementary assumption, to a large-scale flow dynamics that includes a modified advection term together with an inhomogeneous diffusion term. Both of those terms, related respectively to turbophoresis and mixing effects, depend on the variance of the unre-solved small-scale velocity component. They bring to the reduced system an explicit subgrid term enabling to take into account the action of the truncated modes. Besides, a decomposition of the variance tensor in terms of diffusion modes provides a meaningful statistical representation of the stationary or nonstationary structuration of the small-scale velocity and of its action on the reso...
Allgood, Daniel C.; Graham, Jason S.; Ahuja, Vineet; Hosangadi, Ashvin
2008-01-01
Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence
S-matrix Fluctuations in a model with Classical Diffusion and Quantum Localization
Borgonovi, F; Borgonovi, Fausto; Guarneri, Italo
1993-01-01
Abstract: The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix theoretic predictions is discussed in the various regimes (ballistic, diffusive, localized).
A vintage model of technology diffusion: The effects of returns to disversity and learning by using
H.L.F. de Groot (Henri); M.W. Hofkes; P. Mulder (Peter)
2003-01-01
textabstractThe diffusion of new technologies is a lengthy process and many firms continue to invest in relatively old technologies. This paper develops a vintage model of technology adoption and diffusion that aims at explaining these two phenomena. Our explanation for these phenomena emphasises th
Geophysical modelling of 3D electromagnetic diffusion with multigrid
Mulder, W.A.
2008-01-01
The performance of a multigrid solver for time-harmonic electromagnetic problems in geophysical settings was investigated. With the low frequencies used in geophysical surveys for deeper targets, the light-speed waves in the earth can be neglected. Diffusion of induced currents is the dominant physi
Anomalous chain diffusion in unentangled model polymer nanocomposites
Schneider, G.; Nusser, K.; Neueder, S.; Brodeck, M.; Willner, L.; Farago, B.; Holderer, O.; Briels, W.J.; Richter, D.
2013-01-01
We studied unentangled poly(ethylene-alt-propylene) (PEP) in a composite with hydrophobic silica particles as a function of the filler concentration. Our neutron spin echo (NSE) experiments cover both the internal dynamics as well as the center of mass diffusion beyond the Rouse time. The key experi
A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Walker, Christoph
2011-01-01
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
Two-dimensional MHD model of the reconnection diffusion region
N. V. Erkaev
2002-01-01
Full Text Available Magnetic reconnection is an important process providing a fast conversion of magnetic energy into thermal and kinetic plasma energy. In this concern, a key problem is that of the resistive diffusion region where the reconnection process is initiated. In this paper, the diffusion region is associated with a nonuniform conductivity localized to a small region. The nonsteady resistive incompressible MHD equations are solved numerically for the case of symmetric reconnection of antiparallel magnetic fields. A Petschek type steady-state solution is obtained as a result of time relaxation of the reconnection layer structure from an arbitrary initial stage. The structure of the diffusion region is studied for various ratios of maximum and minimum values of the plasma resistivity. The effective length of the diffusion region and the reconnection rate are determined as functions of the length scale and the maximum of the resistivity. For sufficiently small length scale of the resistivity, the reconnection rate is shown to be consistent with Petschek's formula. By increasing the resistivity length scale and decreasing the resistivity maximum, the reconnection layer tends to be wider, and correspondingly, the reconnection rate tends to be more consistent with that of the Parker-Sweet regime.
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
Model assessment of protective barriers: Part 3
Fayer, M.J.; Rockhold, M.L.; Holford, D.J.
1992-02-01
Radioactive waste exists at the US Department of Energy's (DOE's) Hanford Site in a variety of locations, including subsurface grout and tank farms, solid waste burial grounds, and contaminated soil sites. Some of these waste sites may need to be isolated from percolating water to minimize the potential for transport of the waste to the ground water, which eventually discharges to the Columbia River. Multilayer protective barriers have been proposed as a means of limiting the flow of water through the waste sites (DOE 1987). A multiyear research program (managed jointly by Pacific Northwest Laboratory (PNL) and Westinghouse Hanford Company for the DOE) is aimed at assessing the performance of these barriers. One aspect of this program involves the use of computer models to predict barrier performance. Three modeling studies have already been conducted and a test plan was produced. The simulation work reported here was conducted by PNL and extends the previous modeling work. The purpose of this report are to understand phenomena that have been observed in the field and to provide information that can be used to improve hydrologic modeling of the protective barrier. An improved modeling capability results in better estimates of barrier performance. Better estimates can be used to improve the design of barriers and the assessment of their long-term performance.
Diffusion on a hypersphere: application to the Wright-Fisher model
Maruyama, Kishiko; Itoh, Yoshiaki
2016-04-01
The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a hypersphere is transformed into the diffusion for the Wright-Fisher model with a particular mutation rate. We use the Ito calculus considering stochastic differential equations. The expansion gives a simple interpretation of the Griffiths eigenfunction expansion for the Wright-Fisher model. Our representation is useful to simulate the Wright-Fisher model as well as Brownian motion on a hypersphere.
John A. Norton; Frank M. Bass
1987-01-01
This study deals with the dynamic sales behavior of successive generations of high-technology products. New technologies diffuse through a population of potential buyers over time. Therefore, diffusion theory models are related to this demand growth. Furthermore, successive generations of a technology compete with earlier ones, and that behavior is the subject of models of technological substitution. Building upon the Bass (Bass, F. M. 1969. A new-product growth model for consumer durables. M...
Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion
Xinze Lian
2013-01-01
Full Text Available We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.
D. J. Goossens
2015-01-01
Full Text Available Diffuse scattering from a crystal contains valuable information about the two-body correlations (related to the nanoscale order in the material. Despite years of development, the detailed analysis of single crystal diffuse scattering (SCDS has yet to become part of the everyday toolbox of the structural scientist. Recent decades have seen the pair distribution function approach to diffuse scattering (in fact, total scattering from powders become a relatively routine tool. However, analysing the detailed, complex, and often highly anisotropic three-dimensional distribution of SCDS remains valuable yet rare because there is no routine method for undertaking the analysis. At present, analysis requires significant investment of time to develop specialist expertise, which means that the analysis of diffuse scattering, which has much to offer, is not incorporated thorough studies of many compounds even though it has the potential to be a very useful adjunct to existing techniques. This article endeavours to outline in some detail how the diffuse scattering from a molecular crystal can be modelled relatively quickly and largely using existing software tools. It is hoped this will provide a template for other studies. To enable this, the entire simulation is included as deposited material.
Tarlow, S.; Lev, E.; Zappa, C. J.; Karson, J.; Wysocki, B.
2011-12-01
Observation and investigation of surface cooling rates of active lava flows can help constrain thermal parameters necessary for creating of more precise lava flow models. To understand how the lava cools, temperature data was collected using an infrared video camera. We explored three models of the release of heat from lava stream; one based on heat conduction, another based on crust thickness and radiation, and a third model based on radiative cooling and variable crust thickness. The lava flow, part of the Syracuse University Lava Project (http://lavaproject.syr.edu), was made by pouring molten basalt at 1300 Celsius from a furnace into a narrow trench of sand. Hanging roughly 2 m over the trench, the infrared camera, records the lava's surface temperature for the duration of the flow. We determine the average surface temperature of the lava flow at a fixed location downstream as the mean of the lateral cross section of each frame of the IR imagery. From the recorded IR frames, we calculate the mean cross-channel temperature for each downstream distance. We then examine how this mean temperature evolves over time, and plot cooling curves for selected down-stream positions. We then compared the observed cooling behavior to that predicted by three cooling models: a conductive cooling model, a radiative cooling model with constant crust thickness, and a radiative cooling model with variable crust thickness. All three models are solutions to the one-dimensional heat equation. To create the best fit for the conductive model, we constrained thermal diffusivity and to create the best fit for the radiative model, we constrained crust thickness. From the comparison of our data to the models we can conclude that the lava flow's cooling is primarily driven by radiation.
Modeling and Analysis of Epidemic Diffusion within Small-World Network
Ming Liu
2012-01-01
Full Text Available To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.
Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates
Marcus C. Christiansen
2013-10-01
Full Text Available In the actuarial literature, it has become common practice to model future capital returns and mortality rates stochastically in order to capture market risk and forecasting risk. Although interest rates often should and mortality rates always have to be non-negative, many authors use stochastic diffusion models with an affine drift term and additive noise. As a result, the diffusion process is Gaussian and, thus, analytically tractable, but negative values occur with positive probability. The argument is that the class of Gaussian diffusions would be a good approximation of the real future development. We challenge that reasoning and study the asymptotics of diffusion processes with affine drift and a general noise term with corresponding diffusion processes with an affine drift term and an affine noise term or additive noise. Our study helps to quantify the error that is made by approximating diffusive interest and mortality rate models with Gaussian diffusions and affine diffusions. In particular, we discuss forward interest and forward mortality rates and the error that approximations cause on the valuation of life insurance claims.
DISCRETIZATION APPROACH USING RAY-TESTING MODEL IN PARTING LINE AND PARTING SURFACE GENERATION
HAN Jianwen; JIAN Bin; YAN Guangrong; LEI Yi
2007-01-01
Surface classification, 3D parting line, parting surface generation and demoldability analysis which is helpful to select optimal parting direction and optimal parting line are involved in automatic cavity design based on the ray-testing model. A new ray-testing approach is presented to classify the part surfaces to core/cavity surfaces and undercut surfaces by automatic identifying the visibility of surfaces. A simple, direct and efficient algorithm to identify surface visibility is developed. The algorithm is robust and adapted to rather complicated geometry, so it is valuable in computer-aided mold design systems. To validate the efficiency of the approach, an experimental program is implemented. Case studies show that the approach is practical and valuable in automatic parting line and parting surface generation.
Nie, Qi-Yang; Maurer, Mara; Müller, Hermann J; Conci, Markus
2016-05-01
Illusory Kanizsa figures demonstrate that a perceptually completed whole is more than the sum of its composite parts. In the current study, we explored part/whole relationships in object completion using the configural superiority effect (CSE) with illusory figures (Pomerantz & Portillo, 2011). In particular, we investigated to which extent the CSE is modulated by closure in target and distractor configurations. Our results demonstrated a typical CSE, with detection of a configural whole being more efficient than the detection of a corresponding part-level target. Moreover, the CSE was more pronounced when grouped objects were presented in distractors rather than in the target. A follow-up experiment systematically manipulated closure in whole target or, respectively, distractor configurations. The results revealed the effect of closure to be again stronger in distractor, rather than in target configurations, suggesting that closure primarily affects the inhibition of distractors, and to a lesser extent the selection of the target. In addition, a drift-diffusion model analysis of our data revealed that efficient distractor inhibition expedites the rate of evidence accumulation, with closure in distractors particularly speeding the drift toward the decision boundary. In sum, our findings demonstrate that the CSE in Kanizsa figures derives primarily from the inhibition of closed distractor objects, rather than being driven by a conspicuous target configuration. Altogether, these results support a fundamental role of inhibition in driving configural superiority effects in visual search.
Modelling Gas Diffusion from Breaking Coal Samples with the Discrete Element Method
Dan-Ling Lin
2015-01-01
Full Text Available Particle scale diffusion is implemented in the discrete element code, Esys-Particle. We focus on the question of how to calibrate the particle scale diffusion coefficient. For the regular 2D packing, theoretical relation between micro- and macrodiffusion coefficients is derived. This relation is then verified in several numerical tests where the macroscopic diffusion coefficient is determined numerically based on the half-time of a desorption scheme. To further test the coupled model, we simulate the diffusion and desorption in the circular sample. The numerical results match the analytical solution very well. An example of gas diffusion and desorption during sample crushing and fragmenting is given at the last. The current approach is the first step towards a realistic and comprehensive modelling of coal and gas outbursts.
Modelling Ti in-diffusion in LiNbO sub 3
Silva-Filho, H F D; Dias-Nunes, F
1997-01-01
This work presents theoretical results on the modelling of Ti in-diffusion in LiNbO sub 3 assuming the Ti activation energy to be spatially dependent along the diffusion depth direction as consequence of the Li concentration depletion due to its out-diffusion. The model also considers that Ti diffusion occurs as an ion exchange process in which Ti sup 4 sup + ions substitute Nb sup 5 sup + ions located in Li sites. The resulting diffusion equation is numerically solved according to initial and boundary conditions chosen to describe as close as possible the experimental scenario. The results show that this approach leads to highly asymmetrical Ti concentration profiles within the LiNbO sub 3 crystal, as already determined experimentally. (author)
Bifurcation and Turing patterns of reaction-diffusion activator-inhibitor model
Wu, Ranchao; Zhou, Yue; Shao, Yan; Chen, Liping
2017-09-01
Gierer-Meinhardt system is one of prototypical pattern formation models. Turing instability could induce various patterns in this system. Hopf bifurcation analysis and its direction are performed on such diffusive model in this paper, by employing normal form and center manifold reduction. The effects of diffusion on the stability of equilibrium point and the bifurcated limit cycle from Hopf bifurcation are investigated. It is found that under some conditions, diffusion-driven instability, i.e, Turing instability, about the equilibrium point and the bifurcated limit cycle will happen, which are stable without diffusion. Those diffusion-driven instabilities will lead to the occurrence of spatially nonhomogeneous solutions. As a result, some patterns, like stripe and spike solutions, will form. The explicit criteria about the stability and instability of the equilibrium point and the limit cycle in the system are derived, which could be readily applied. Further, numerical simulations are presented to illustrate theoretical analysis.
Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.
Bendahmane, Mostafa; Ruiz-Baier, Ricardo; Tian, Canrong
2016-05-01
In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.
Diffusive flux in a model of stochastically gated oxygen transport in insect respiration
Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.
2016-05-01
Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.
The Water-Induced Linear Reduction Gas Diffusivity Model Extended to Three Pore Regions
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......An existing gas diffusivity model developed originally for sieved, repacked soils was extended to characterize gas diffusion in differently structured soils and functional pore networks. A gas diffusivity-derived pore connectivity index was used as a measure of soil structure development...... developed for sieved, repacked soil was extended to two simple, linear regions to characterize gas diffusion and functional pore-network structure also in intact, structured soil systems. Based on the measurements in soils with markedly different pore regions, we showed that the two linear regions can...
Hierarchical Bass model: a product diffusion model considering a diversity of sensitivity to fashion
Tashiro, Tohru
2016-11-01
We propose a new product diffusion model including the number of how many adopters or advertisements a non-adopter met until he/she adopts the product, where (non-)adopters mean people (not) possessing it. By this effect not considered in the Bass model, we can depict a diversity of sensitivity to fashion. As an application, we utilize the model to fit the iPod and the iPhone unit sales data, and so the better agreement is obtained than the Bass model for the iPod data. We also present a new method to estimate the number of advertisements in a society from fitting parameters of the Bass model and this new model.
A STUDY ON NEW PRODUCT DEMAND FORECASTING BASED ON BASS DIFFUSION MODEL
Zuhaimy Ismail
2013-01-01
Full Text Available A forecasting model of new product demand has been developed and applied to forecast new vehicle demand in Malaysia. Since the publication of the Bass model in 1969, innovation of new diffusion theory has sparked considerable research among marketing science scholars, operational researchers and mathematicians. This study considers the Bass Model for forecasting the diffusion of new products or an innovation in the Malaysian society. The objective of the proposed model is to represent the level of spread on new products among a given set of society in terms of a simple mathematical function that elapsed since the introduction of new products. With limited amount of data available for new products, a robust Bass model was developed to forecast the sales volume. A procedure of the proposed diffusion model was designed and the parameters were estimated. Results obtained by applying the proposed model and numerical calculation show that the proposed Bass diffusion model is robust and effective for forecasting demand of new products. This study concludes that the newly developed bass diffusion of demand function has significantly contributed for forecasting the diffusion of new products.
29 CFR Appendix A to Part 4011 - Model Participant Notice
2010-07-01
... 29 Labor 9 2010-07-01 2010-07-01 false Model Participant Notice A Appendix A to Part 4011 Labor... DISCLOSURE REQUIREMENTS DISCLOSURE TO PARTICIPANTS Pt. 4011, App. A Appendix A to Part 4011—Model Participant..., the Internal Revenue Service may grant a funding waiver that permits the company to...
Xu, X; Sumption, M D
2016-01-12
In this work we explore the compositions of non-stoichiometric intermediate phases formed by diffusion reactions: a mathematical framework is developed and tested against the specific case of Nb3Sn superconductors. In the first part, the governing equations for the bulk diffusion and inter-phase interface reactions during the growth of a compound are derived, numerical solutions to which give both the composition profile and growth rate of the compound layer. The analytic solutions are obtained with certain approximations made. In the second part, we explain an effect that the composition characteristics of compounds can be quite different depending on whether it is the bulk diffusion or grain boundary diffusion that dominates in the compounds, and that "frozen" bulk diffusion leads to unique composition characteristics that the bulk composition of a compound layer remains unchanged after its initial formation instead of varying with the diffusion reaction system; here the model is modified for the case of grain boundary diffusion. Finally, we apply this model to the Nb3Sn superconductors and propose approaches to control their compositions.
Optimal prediction for moment models: crescendo diffusion and reordered equations
Seibold, Benjamin; Frank, Martin
2009-12-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to generally study the moment closure within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, such as P N , diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered P N equations, that are similar to the simplified P N equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.
Cellular automata models for diffusion of information and highway traffic flow
Fuks, Henryk
In the first part of this work we study a family of deterministic models for highway traffic flow which generalize cellular automaton rule 184. This family is parameterized by the speed limit m and another parameter k that represents degree of 'anticipatory driving'. We compare two driving strategies with identical maximum throughput: 'conservative' driving with high speed limit and 'anticipatory' driving with low speed limit. Those two strategies are evaluated in terms of accident probability. We also discuss fundamental diagrams of generalized traffic rules and examine limitations of maximum achievable throughput. Possible modifications of the model are considered. For rule 184, we present exact calculations of the order parameter in a transition from the moving phase to the jammed phase using the method of preimage counting, and use this result to construct a solution to the density classification problem. In the second part we propose a probabilistic cellular automaton model for the spread of innovations, rumors, news, etc., in a social system. We start from simple deterministic models, for which exact expressions for the density of adopters are derived. For a more realistic model, based on probabilistic cellular automata, we study the influence of a range of interaction R on the shape of the adoption curve. When the probability of adoption is proportional to the local density of adopters, and individuals can drop the innovation with some probability p, the system exhibits a second order phase transition. Critical line separating regions of parameter space in which asymptotic density of adopters is positive from the region where it is equal to zero converges toward the mean-field line when the range of the interaction increases. In a region between R=1 critical line and the mean-field line asymptotic density of adopters depends on R, becoming zero if R is too small (smaller than some critical value). This result demonstrates the importance of connectivity in
A Functional Model for Teaching Osmosis-Diffusion to Biology Students
Olsen, Richard W.; Petry, Douglas E.
1976-01-01
Described is a maternal-fetal model, operated by the student, to teach osmosis-diffusion to biology students. Included are materials needed, assembly instructions, and student operating procedures. (SL)
Woo, Jiyoung; Chen, Hsinchun
2016-01-01
As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums.
Wu Qiong; Li Shu-Suo; Ma Yue; Gong Sheng-Kai
2012-01-01
The diffusion coefficients of several alloying elements (Al,Mo,Co,Ta,Ru,W,Cr,Re) in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor (Do) and the activation energy (Q) of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order:DAl ＞ DCr ＞ DCo ＞ DTa ＞DMo ＞ DRu ＞ DW ＞ DRe.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair (E1).The value of E2-E1 (E2 is the solute diffusion energy) and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.
Diffusion of PAH in potato and carrot slices and application for a potato model.
Trapp, Stefan; Cammarano, Anita; Capri, Ettore; Reichenberg, Fredrik; Mayer, Philipp
2007-05-01
A method for quantifying the effect of medium composition on the diffusive mass transfer of hydrophobic organic chemicals through thin layers was applied to plant tissue. The method employs two silicone disks, one serving as source and one as sink for a series of PAHs diffusing through thin layers of water, potato tissue, and carrot tissue. Naphthalene, phenanthrene, anthracene, and fluoranthene served as model substances. Their transfer from source to sink disk was measured by HPLC to determine a velocity rate constant proportional to the diffusive conductivity. The diffusive flux through the plant tissue was modeled using Fick's first law of diffusion. Both the experimental results and the model suggest that mass transfer through plant tissue occurs predominantly through pore water and that, therefore, the mass transfer ratio between plant tissue and water is independent of the hydrophobicity of the chemical. The findings of this study provide a convenient method to estimate the diffusion of nonvolatile organic chemicals through various plant materials. The application to a radial diffusion model suggests that "growth dilution" rendersthe concentration of highly hydrophobic chemicals in potatoes below their equilibrium partitioning level. This is in agreement with field results for the bioconcentration of PAHs in potatoes.
Fu-Kwun Wang
2012-01-01
Full Text Available It is important for executives to predict the future trends. Otherwise, their companies cannot make profitable decisions and investments. The Bass diffusion model can describe the empirical adoption curve for new products and technological innovations. The Grey model provides short-term forecasts using four data points. This study develops a combined model based on the rolling Grey model (RGM and the Bass diffusion model to forecast motherboard shipments. In addition, we investigate evolutionary optimization algorithms to determine the optimal parameters. Our results indicate that the combined model using a hybrid algorithm outperforms other methods for the fitting and forecasting processes in terms of mean absolute percentage error.
Numerical Solution of Fractional Diffusion Equation Model for Freezing in Finite Media
R. S. Damor
2013-01-01
Full Text Available Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.
A Mathematic Model of Gas-diffusion Electrodes in Contact with Liquid Electrolytes
LI Jun; XI Dan-li; SHI Yong; WU Xi-hui
2008-01-01
A mathematic model is developed which is applied to analyze the main factors that affect electrode performance and to account for the process of reaction and mass transfer in gas-diffusion electrodes in contact with liquid electrolytes. Electrochemical Thiele modulus φ2 and electrochemical effectiveness factor ηD are introduced to elucidate the effects of diffusion on electrochemical reaction and utilization of the gas-diffusion electrode.Profile of the reactant along axial direction is discussed,dependence of electrode potential V on current density J.are predicated by means of the newly developed mathematical model.
Sysun, V. I.; Bute, I. V.; Boriskov, P. P.
2016-09-01
The transition process from the low resistance state into the high resistance state in a Pt/NiO/Pt memory switching structure has been studied by numerical modeling. Detailed analysis shows, that thermally induced diffusion oxidation by nickel vacancies is the key factor for distortion of the channel metallic conductivity. Spatial dynamics of the process of oxidation defines channel narrowing mainly in its central part, and also sets the critical current through the structure sufficient for final rupture of the channel and the transition to high resistance state. The increase in critical current above the limit even by 10% reduces the switching time by an order of magnitude, which is in agreement with experiments. The developed radial diffusion model of conductive channel (or filaments) oxidation may be suitable for the analysis of switching effect a number of other ReRAM oxide structures.
A model of modulated diffusion. II. Numerical results on statistical properties
Bazzani, A.; Siboni, S.; Turchetti, G. [dell`Universita Bologna (Italy)] [and others
1994-08-01
We investigate numerically the statistical properties of a model of modulated diffusion for which we have already computed analytically the diffusion coefficient D. Our model is constructed by adding a deterministic or random noise to the frequency of an integrable isochronous system. We consider in particular the central limit theorem and the invariance principle and we show that they follow whenever D is positive and for any magnitude of the noise; we also investigate the asymptotic distribution in a case when D=0.
AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL
闫振亚; 张鸿庆
2001-01-01
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known.Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine- cosine method, more exact solutions are found which contain soliton solutions.
Efficient simulation of diffusion-based choice RT models on CPU and GPU.
Verdonck, Stijn; Meers, Kristof; Tuerlinckx, Francis
2016-03-01
In this paper, we present software for the efficient simulation of a broad class of linear and nonlinear diffusion models for choice RT, using either CPU or graphical processing unit (GPU) technology. The software is readily accessible from the popular scripting languages MATLAB and R (both 64-bit). The speed obtained on a single high-end GPU is comparable to that of a small CPU cluster, bringing standard statistical inference of complex diffusion models to the desktop platform.
Sigalotti, Leonardo Di G; Troconis, Jorge; Sira, Eloy; Peña-Polo, Franklin; Klapp, Jaime
2014-07-01
We study numerically liquid-vapor phase separation in two-dimensional, nonisothermal, van der Waals (vdW) liquid drops using the method of smoothed particle hydrodynamics (SPH). In contrast to previous SPH simulations of drop formation, our approach is fully adaptive and follows the diffuse-interface model for a single-component fluid, where a reversible, capillary (Korteweg) force is added to the equations of motion to model the rapid but smooth transition of physical quantities through the interface separating the bulk phases. Surface tension arises naturally from the cohesive part of the vdW equation of state and the capillary forces. The drop models all start from a square-shaped liquid and spinodal decomposition is investigated for a range of initial densities and temperatures. The simulations predict the formation of stable, subcritical liquid drops with a vapor atmosphere, with the densities and temperatures of coexisting liquid and vapor in the vdW phase diagram closely matching the binodal curve. We find that the values of surface tension, as determined from the Young-Laplace equation, are in good agreement with the results of independent numerical simulations and experimental data. The models also predict the increase of the vapor pressure with temperature and the fitting to the numerical data reproduces very well the Clausius-Clapeyron relation, thus allowing for the calculation of the vaporization pressure for this vdW fluid.
Shaviv, Avi; Raban, Smadar; Zaidel, Elina
2003-05-15
A comprehensive model describing the complex and "non-Fickian" (mathematically nonlinear) nature of the release from single granules of membrane coated, controlled release fertilizers (CRFs) is proposed consisting of three stages: i. a lag period during which water penetrates the coating of the granule dissolving part of the solid fertilizer in it ii. a period of linear release during which water penetration into and release out occur concomitantly while the total volume of the granules remains practically constant; and iii. a period of "decaying release", starting as the concentration inside the granule starts to decrease. A mathematical model was developed based on vapor and nutrient diffusion equations. The model predicts the release stages in terms of measurable geometrical and chemophysical parameters such as the following: the product of granule radius and coating thickness, water and solute permeability, saturation concentration of the fertilizer, and its density. The model successfully predicts the complex and "sigmoidal" pattern of release that is essential for matching plant temporal demand to ensure high agronomic and environmental effectiveness. It also lends itself to more complex statistical formulations which account for the large variability within large populations of coated CRFs and can serve for further improving CRF production and performance.
Introduction to stochastic models of transportation flows. Part I
Malyshev, V A
2011-01-01
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having visual simplicity and simple (but rigorous) formulation, the main objects being cars not abstract flows. The papers consists of three parts. First part considers mainly linear flows on short time scale - dynamics of the flow due to changing driver behavior. Second part studies linear flow on longer time scales - individual car trajectory from entry to exit from the road. Part three considers collective car movement in complex transport networks.
A diffuse plate boundary model for Indian Ocean tectonics
Wiens, D. A.; Demets, C.; Gordon, R. G.; Stein, S.; Argus, D.
1985-01-01
It is suggested that motion along the virtually aseismic Owen fracture zone is negligible, so that Arabia and India are contained within a single Indo-Arabian plate divided from the Australian plate by a diffuse boundary. The boundary is a zone of concentrated seismicity and deformation commonly characterized as 'intraplate'. The rotation vector of Australia relative to Indo-Arabia is consistent with the seismologically observed 2 cm/yr of left-lateral strike-slip along the Ninetyeast Ridge, north-south compression in the Central Indian Ocean, and the north-south extension near Chagos.
Self-diffusion in liquid gallium and hard sphere model
Blagoveshchenskii Nikolay
2015-01-01
Full Text Available Incoherent and coherent components of quasielastic neutron scattering have been studied in the temperature range of T = 313 K – 793 K aiming to explore the applicability limits of the hard-sphere approach for the microscopic dynamics of liquid gallium, which is usually considered as a non-hard-sphere system. It was found that the non-hard-sphere effects come into play at the distances shorter than the average interatomic distance. The longer range diffusive dynamics of liquid Ga is dominated by the repulsive forces between the atoms.
Comparison and analysis of theoretical models for diffusion-controlled dissolution.
Wang, Yanxing; Abrahamsson, Bertil; Lindfors, Lennart; Brasseur, James G
2012-05-07
Dissolution models require, at their core, an accurate diffusion model. The accuracy of the model for diffusion-dominated dissolution is particularly important with the trend toward micro- and nanoscale drug particles. Often such models are based on the concept of a "diffusion layer." Here a framework is developed for diffusion-dominated dissolution models, and we discuss the inadequacy of classical models that are based on an unphysical constant diffusion layer thickness assumption, or do not correctly modify dissolution rate due to "confinement effects": (1) the increase in bulk concentration from confinement of the dissolution process, (2) the modification of the flux model (the Sherwood number) by confinement. We derive the exact mathematical solution for a spherical particle in a confined fluid with impermeable boundaries. Using this solution, we analyze the accuracy of a time-dependent "infinite domain model" (IDM) and "quasi steady-state model" (QSM), both formally derived for infinite domains but which can be applied in approximate fashion to confined dissolution with proper adjustment of a concentration parameter. We show that dissolution rate is sensitive to the degree of confinement or, equivalently, to the total concentration C(tot). The most practical model, the QSM, is shown to be very accurate for most applications and, consequently, can be used with confidence in design-level dissolution models so long as confinement is accurately treated. The QSM predicts the ratio of diffusion layer thickness to particle radius (the Sherwood number) as a constant plus a correction that depends on the degree of confinement. The QSM also predicts that the time required for complete saturation or dissolution in diffusion-controlled dissolution experiments is singular (i.e., infinite) when total concentration equals the solubility. Using the QSM, we show that measured differences in dissolution rate in a diffusion-controlled dissolution experiment are a result of
Jakob, A
2004-07-01
In this report a comprehensive overview on the matrix diffusion of solutes in fractured crystalline rocks is presented. Some examples from observations in crystalline bedrock are used to illustrate that matrix diffusion indeed acts on various length scales. Fickian diffusion is discussed in detail followed by some considerations on rock porosity. Due to the fact that the dual-porosity medium model is a very common and versatile method for describing solute transport in fractured porous media, the transport equations and the fundamental assumptions, approximations and simplifications are discussed in detail. There is a variety of geometrical aspects, processes and events which could influence matrix diffusion. The most important of these, such as, e.g., the effect of the flow-wetted fracture surface, channelling and the limited extent of the porous rock for matrix diffusion etc., are addressed. In a further section open issues and unresolved problems related to matrix diffusion are mentioned. Since matrix diffusion is one of the key retarding processes in geosphere transport of dissolved radionuclide species, matrix diffusion was consequently taken into account in past performance assessments of radioactive waste repositories in crystalline host rocks. Some issues regarding matrix diffusion are site-specific while others are independent of the specific situation of a planned repository for radioactive wastes. Eight different performance assessments from Finland, Sweden and Switzerland were considered with the aim of finding out how matrix diffusion was addressed, and whether a consistent picture emerges regarding the varying methodology of the different radioactive waste organisations. In the final section of the report some conclusions are drawn and an outlook is given. An extensive bibliography provides the reader with the key papers and reports related to matrix diffusion. (author)
Perpendicular Diffusion of Solar Energetic Particles: Model Results and Implications for Electrons
Strauss, R. Du Toit; Dresing, Nina; Engelbrecht, N. Eugene
2017-03-01
The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model that includes perpendicular diffusion. By implementing, as far as possible, the most reasonable estimates of the transport (diffusion) coefficients, we compare our results, in a qualitative manner, to recent observations at energies of 55–105 keV, focusing on the longitudinal distribution of the peak intensity, the maximum anisotropy, and the onset time. By using transport coefficients that are derived from first principles, we limit the number of free parameters in the model to (i) the probability of SEPs following diffusing magnetic field lines, quantified by a\\in [0,1], and (ii) the broadness of the Gaussian injection function. It is found that the model solutions are extremely sensitive to the magnitude of the perpendicular diffusion coefficient and relatively insensitive to the form of the injection function as long as a reasonable value of a = 0.2 is used. We illustrate the effects of perpendicular diffusion on the model solutions and discuss the viability of this process as a dominant mechanism by which SEPs are transported in longitude. Lastly, we try to quantity the effectiveness of perpendicular diffusion as an interplay between the magnitude of the relevant diffusion coefficient and the SEP intensity gradient driving the diffusion process. It follows that perpendicular diffusion is extremely effective early in an SEP event when large intensity gradients are present, while the effectiveness quickly decreases with time thereafter.
Preliminary Hybrid Modeling of the Panama Canal: Operations and Salinity Diffusion
Luis Rabelo
2012-01-01
Full Text Available This paper deals with the initial modeling of water salinity and its diffusion into the lakes during lock operation on the Panama Canal. A hybrid operational model was implemented using the AnyLogic software simulation environment. This was accomplished by generating an operational discrete-event simulation model and a continuous simulation model based on differential equations, which modeled the salinity diffusion in the lakes. This paper presents that unique application and includes the effective integration of lock operations and its impact on the environment.
Fractal Modeling of Pore Structure and Ionic Diffusivity for Cement Paste
Yun Gao
2016-01-01
Full Text Available Pore structure in cement based composites is of paramount importance to ionic diffusivity. In this paper, pore structure in cement paste is modeled by means of the recently proposed solid mass fractal model. Moreover, an enhanced Maxwell homogenization method that incorporates the solid mass fractal model is proposed to determine the associated ionic diffusivity. Experiments are performed to validate the modeling, that is, mercury intrusion porosimetry and rapid chloride migration. Results indicate that modeling agrees well with those obtained from experiments.
Optimal prediction for moment models: Crescendo diffusion and reordered equations
Seibold, Benjamin
2009-01-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to study moment closure generally within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, e.g. $P_N$, diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered $P_N$ equations, that are similar to the simplified $P_N$ equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived...
Impact of Social Network and Business Model on Innovation Diffusion of Electric Vehicles in China
D. Y. Kong
2014-01-01
Full Text Available The diffusion of electric vehicles (EVs involves not only the technological development but also the construction of complex social networks. This paper uses the theory of network control to analyze the influence of network forms on EV diffusion in China, especially focusing on the building of EV business models (BMs and the resulting effects and control on the diffusion of EVs. The Bass model is adopted to forecast the diffusion process of EVs and genetic algorithm is used to estimate the parameters based on the diffusion data of Hybrid Electric Vehicle (HEV in the United States and Japan. Two different social network forms and BMs are selected, that is, battery leasing model and vehicle purchasing model, to analyze how different network forms may influence the innovation coefficient and imitation coefficient in the Bass model, which will in turn result in different diffusion results. Thereby, we can find the appropriate network forms and BMs for EVs which is suitable to the local market conditions.
CAD Parts-Based Assembly Modeling by Probabilistic Reasoning
Zhang, Kai-Ke
2016-04-11
Nowadays, increasing amount of parts and sub-assemblies are publicly available, which can be used directly for product development instead of creating from scratch. In this paper, we propose an interactive design framework for efficient and smart assembly modeling, in order to improve the design efficiency. Our approach is based on a probabilistic reasoning. Given a collection of industrial assemblies, we learn a probabilistic graphical model from the relationships between the parts of assemblies. Then in the modeling stage, this probabilistic model is used to suggest the most likely used parts compatible with the current assembly. Finally, the parts are assembled under certain geometric constraints. We demonstrate the effectiveness of our framework through a variety of assembly models produced by our prototype system. © 2015 IEEE.
MO-G-BRF-07: Anomalously Fast Diffusion of Carbon Nanotubes Carriers in 3D Tissue Model
Wang, Y; Bahng, J; Kotov, N [University of Michigan, Ann Arbor, MI (United States)
2014-06-15
Purpose: We aim to investigate and understand diffusion process of carbon nanotubes (CNTs) and other nanoscale particles in tissue and organs. Methods: In this research, we utilized a 3D model tissue of hepatocellular carcinoma (HCC)cultured in inverted colloidal crystal (ICC) scaffolds to compare the diffusivity of CNTs with small molecules such as Rhodamine and FITC in vitro, and further investigated the transportation of CNTs with and without targeting ligand, TGFβ1. The real-time permeation profiles of CNTs in HCC tissue model with high temporal and spatial resolution was demonstrated by using standard confocal microscopy. Quantitative analysis of the diffusion process in 3D was carried out using luminescence intensity in a series of Z-stack images obtained for different time points of the diffusion process after initial addition of CNTs or small molecules to the cell culture and the image data was analyzed by software ImageJ and Mathematica. Results: CNTs display diffusion rate in model tissues substantially faster than small molecules of the similar charge such as FITC, and the diffusion rate of CNTs are significantly enhanced with targeting ligand, TGFβ1. Conclusion: In terms of the advantages of in-vitro model, we were able to have access to measuring the rate of CNT penetration at designed conditions with variable parameters. And the findings by using this model, changed our understanding about advantages of CNTs as nanoscale drug carriers and provides design principles for making new drug carriers for both treatment and diagnostics. Additionally the fast diffusion opens the discussion of the best possible drug carriers to reach deep parts of cancerous tissues, which is often a prerequisite for successful cancer treatment. This work was supported by the Center for Photonic and Multiscale Nanomaterials funded by National Science Foundation Materials Research Science and Engineering Center program DMR 1120923. The work was also partially supported by NSF
Diffusion of a Sustainable Farming Technique in Sri Lanka: An Agent-Based Modeling Approach
Jacobi, J. H.; Gilligan, J. M.; Carrico, A. R.; Truelove, H. B.; Hornberger, G.
2012-12-01
We live in a changing world - anthropogenic climate change is disrupting historic climate patterns and social structures are shifting as large scale population growth and massive migrations place unprecedented strain on natural and social resources. Agriculture in many countries is affected by these changes in the social and natural environments. In Sri Lanka, rice farmers in the Mahaweli River watershed have seen increases in temperature and decreases in precipitation. In addition, a government led resettlement project has altered the demographics and social practices in villages throughout the watershed. These changes have the potential to impact rice yields in a country where self-sufficiency in rice production is a point of national pride. Studies of the climate can elucidate physical effects on rice production, while research on social behaviors can illuminate the influence of community dynamics on agricultural practices. Only an integrated approach, however, can capture the combined and interactive impacts of these global changes on Sri Lankan agricultural. As part of an interdisciplinary team, we present an agent-based modeling (ABM) approach to studying the effects of physical and social changes on farmers in Sri Lanka. In our research, the diffusion of a sustainable farming technique, the system of rice intensification (SRI), throughout a farming community is modeled to identify factors that either inhibit or promote the spread of a more sustainable approach to rice farming. Inputs into the ABM are both physical and social and include temperature, precipitation, the Palmer Drought Severity Index (PDSI), community trust, and social networks. Outputs from the ABM demonstrate the importance of meteorology and social structure on the diffusion of SRI throughout a farming community.
A Bayesian hierarchical diffusion model decomposition of performance in Approach-Avoidance Tasks.
Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan
2015-01-01
Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach-Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest.
Ying Liu
2015-01-01
Full Text Available Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.
M Wahab Amjad
Full Text Available Biomolecules have been widely investigated as potential therapeutics for various diseases. However their use is limited due to rapid degradation and poor cellular uptake in vitro and in vivo. To address this issue, we synthesized a new nano-carrier system comprising of cholic acid-polyethylenimine (CA-PEI copolymer micelles, via carbodiimide-mediated coupling for the efficient delivery of small interfering ribonucleic acid (siRNA and bovine serum albumin (BSA as model protein. The mean particle size of siRNA- or BSA-loaded CA-PEI micelles ranged from 100-150 nm, with zeta potentials of +3-+11 mV, respectively. Atomic force, transmission electron and field emission scanning electron microscopy demonstrated that the micelles exhibited excellent spherical morphology. No significant morphology or size changes were observed in the CA-PEI micelles after siRNA and BSA loading. CA-PEI micelles exhibited sustained release profile, the effective diffusion coefficients were successfully estimated using a mathematically-derived cylindrical diffusion model and the release data of siRNA and BSA closely fitted into this model. High siRNA and BSA binding and loading efficiencies (95% and 70%, respectively were observed for CA-PEI micelles. Stability studies demonstrated that siRNA and BSA integrity was maintained after loading and release. The CA-PEI micelles were non cytotoxic to V79 and DLD-1 cells, as shown by alamarBlue and LIVE/DEAD cell viability assays. RT-PCR study revealed that siRNA-loaded CA-PEI micelles suppressed the mRNA for ABCB1 gene. These results revealed the promising potential of CA-PEI micelles as a stable, safe, and versatile nano-carrier for siRNA and the model protein delivery.
Wang, Jing [Iowa State Univ., Ames, IA (United States)
2013-01-11
We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.
Diffusion of a collaborative care model in primary care: a longitudinal qualitative study
Vedel Isabelle
2013-01-01
Full Text Available Background Although collaborative team models (CTM improve care processes and health outcomes, their diffusion poses challenges related to difficulties in securing their adoption by primary care clinicians (PCPs. The objectives of this study are to understand: (1 how the perceived characteristics of a CTM influenced clinicians' decision to adopt -or not- the model; and (2 the model's diffusion process. Methods We conducted a longitudinal case study based on the Diffusion of Innovations Theory. First, diffusion curves were developed for all 175 PCPs and 59 nurses practicing in one borough of Paris. Second, semi-structured interviews were conducted with a representative sample of 40 PCPs and 15 nurses to better understand the implementation dynamics. Results Diffusion curves showed that 3.5 years after the start of the implementation, 100% of nurses and over 80% of PCPs had adopted the CTM. The dynamics of the CTM's diffusion were different between the PCPs and the nurses. The slopes of the two curves are also distinctly different. Among the nurses, the critical mass of adopters was attained faster, since they adopted the CTM earlier and more quickly than the PCPs. Results of the semi-structured interviews showed that these differences in diffusion dynamics were mostly founded in differences between the PCPs' and the nurses' perceptions of the CTM's compatibility with norms, values and practices and its relative advantage (impact on patient management and work practices. Opinion leaders played a key role in the diffusion of the CTM among PCPs. Conclusion CTM diffusion is a social phenomenon that requires a major commitment by clinicians and a willingness to take risks; the role of opinion leaders is key. Paying attention to the notion of a critical mass of adopters is essential to developing implementation strategies that will accelerate the adoption process by clinicians.
A novel rumor diffusion model considering the effect of truth in online social media
Sun, Ling; Liu, Yun; Zeng, Qing-An; Xiong, Fei
2015-12-01
In this paper, we propose a model to investigate how truth affects rumor diffusion in online social media. Our model reveals a relation between rumor and truth — namely, when a rumor is diffusing, the truth about the rumor also diffuses with it. Two patterns of the agents used to identify rumor, self-identification and passive learning are taken into account. Combining theoretical proof and simulation analysis, we find that the threshold value of rumor diffusion is negatively correlated to the connectivity between nodes in the network and the probability β of agents knowing truth. Increasing β can reduce the maximum density of the rumor spreaders and slow down the generation speed of new rumor spreaders. On the other hand, we conclude that the best rumor diffusion strategy must balance the probability of forwarding rumor and the probability of agents losing interest in the rumor. High spread rate λ of rumor would lead to a surge in truth dissemination which will greatly limit the diffusion of rumor. Furthermore, in the case of unknown λ, increasing β can effectively reduce the maximum proportion of agents who do not know the truth, but cannot narrow the rumor diffusion range in a certain interval of β.
Maurin, D
2001-02-01
Dark matter is present at numerous scale of the universe (galaxy, cluster of galaxies, universe in the whole). This matter plays an important role in cosmology and can not be totally explained by conventional physic. From a particle physic point of view, there exists an extension of the standard model - supersymmetry - which predicts under certain conditions the existence of new stable and massive particles, the latter interacting weakly with ordinary matter. Apart from direct detection in accelerators, various indirect astrophysical detection are possible. This thesis focuses on one particular signature: disintegration of these particles could give antiprotons which should be measurable in cosmic rays. The present study evaluates the background corresponding to this signal i. e. antiprotons produced in the interactions between these cosmic rays and interstellar matter. In particular, uncertainties of this background being correlated to the uncertainties of the diffusion parameter, major part of this thesis is devoted to nuclei propagation. The first third of the thesis introduces propagation of cosmic rays in our galaxy, emphasizing the nuclear reaction responsibles of the nuclei fragmentation. In the second third, different models are reviewed, and in particular links between the leaky box model and the diffusion model are recalled (re-acceleration and convection are also discussed). This leads to a qualitative discussion about information that one can infer from propagation of these nuclei. In the last third, we finally present detailed solutions of the bidimensional diffusion model, along with constrains obtained on the propagation parameters. The latter is applied on the antiprotons background signal and it concludes the work done in this thesis. The propagation code for nuclei and antiprotons used here has proven its ability in data analysis. It would probably be of interest for the analysis of the cosmic ray data which will be taken by the AMS experiment on
The EZ diffusion model provides a powerful test of simple empirical effects
van Ravenzwaaij, Don; Donkin, Chris; Vandekerckhove, Joachim
Over the last four decades, sequential accumulation models for choice response times have spread through cognitive psychology like wildfire. The most popular style of accumulator model is the diffusion model (Ratcliff Psychological Review, 85, 59–108, 1978), which has been shown to account for data
O. H. Kapitonov
2010-05-01
Full Text Available A mathematical model of coulostatic relaxation of the potential for solid metallic electrode was presented. The solution in the case of limiting diffusion current was obtained. On the basis of this model the technique of concentration measurements for heavy metal ions in diluted solutions was suggested. The model adequacy was proved by experimental data.
Sliding drops in the diffuse interface model coupled to hydrodynamics.
Thiele, U; Velarde, M G; Neuffer, K; Bestehorn, M; Pomeau, Y
2001-12-01
Using a film thickness evolution equation derived recently combining long-wave approximation and diffuse interface theory [L. M. Pismen and Y. Pomeau, Phys. Rev. E 62, 2480 (2000)] we study one-dimensional surface profiles for a thin film on an inclined plane. We discuss stationary flat film and periodic solutions including their linear stability. Flat sliding drops are identified as universal profiles, whose main properties do not depend on mean film thickness. The flat drops are analyzed in detail, especially how their velocity, advancing and receding dynamic contact angles and plateau thicknesses depend on the inclination of the plane. A study of nonuniversal drops shows the existence of a dynamical wetting transition with hysteresis between droplike solutions and a flat film with small amplitude nonlinear waves.
Modeling diffusion of adsorbed polymer with explicit solvent.
Desai, Tapan G; Keblinski, Pawel; Kumar, Sanat K; Granick, Steve
2007-05-25
Computer simulations of a polymer chain of length N strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the N dependence of the polymer lateral diffusion coefficient, D(||). We find that surface roughness has a large influence, and D(||) scales as D(||) approximately N(-x), with x approximately 3/4 and x approximately 1 for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a "particle" of radius of gyration R(G) approximately N(nu) (nu=0.75) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.
A hybrid transport-diffusion model for radiative transfer in absorbing and scattering media
Roger, M., E-mail: maxime.roger@insa-lyon.fr [Université de Lyon, CNRS, INSA-Lyon, CETHIL, UMR5008, F-69621 Villeurbanne (France); Caliot, C. [PROMES-UPR CNRS 6144, 7 rue du Four Solaire, 66120 Font Romeu Odeillo (France); Crouseilles, N. [INRIA-Rennes Bretagne-Atlantique (IPSO Project) and Université de Rennes 1 (IRMAR), Campus de Beaulieu, 35042 Rennes Cedex (France); Coelho, P.J. [Mechanical Engineering Department, LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001, Lisboa (Portugal)
2014-10-15
A new multi-scale hybrid transport-diffusion model for radiative transfer is proposed in order to improve the efficiency of the calculations close to the diffusive regime, in absorbing and strongly scattering media. In this model, the radiative intensity is decomposed into a macroscopic component calculated by the diffusion equation, and a mesoscopic component. The transport equation for the mesoscopic component allows to correct the estimation of the diffusion equation, and then to obtain the solution of the linear radiative transfer equation. In this work, results are presented for stationary and transient radiative transfer cases, in examples which concern solar concentrated and optical tomography applications. The Monte Carlo and the discrete-ordinate methods are used to solve the mesoscopic equation. It is shown that the multi-scale model allows to improve the efficiency of the calculations when the medium is close to the diffusive regime. The proposed model is a good alternative for radiative transfer at the intermediate regime where the macroscopic diffusion equation is not accurate enough and the radiative transfer equation requires too much computational effort.
Using a Quasipotential Transformation for Modeling Diffusion Media inPolymer-Electrolyte Fuel Cells
Weber, Adam Z.; Newman, John
2008-08-29
In this paper, a quasipotential approach along with conformal mapping is used to model the diffusion media of a polymer-electrolyte fuel cell. This method provides a series solution that is grid independent and only requires integration along a single boundary to solve the problem. The approach accounts for nonisothermal phenomena, two-phase flow, correct placement of the electronic potential boundary condition, and multilayer media. The method is applied to a cathode diffusion medium to explore the interplay between water and thermal management and performance, the impact of the rib-to-channel ratio, and the existence of diffusion under the rib and flooding phenomena.
Qualitative analysis on a diffusive prey-predator model with ratio-dependent functional response
2008-01-01
In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.
Using a Quasipotential Transformation for Modeling Diffusion Media inPolymer-Electrolyte Fuel Cells
Weber, Adam Z.; Newman, John
2008-08-29
In this paper, a quasipotential approach along with conformal mapping is used to model the diffusion media of a polymer-electrolyte fuel cell. This method provides a series solution that is grid independent and only requires integration along a single boundary to solve the problem. The approach accounts for nonisothermal phenomena, two-phase flow, correct placement of the electronic potential boundary condition, and multilayer media. The method is applied to a cathode diffusion medium to explore the interplay between water and thermal management and performance, the impact of the rib-to-channel ratio, and the existence of diffusion under the rib and flooding phenomena.
Assessing Cognitive Processes with Diffusion Model Analyses: A Tutorial based on fast-dm-30
Andreas eVoss
2015-03-01
Full Text Available Diffusion models can be used to infer cognitive processes involved in fast binary decision tasks. The model assumes that information is accumulated continuously until one of two thresholds is hit. In the analysis, response time distributions from numerous trials of the decision task are used to estimate a set of parameters mapping distinct cognitive processes. In recent years, diffusion model analyses have become more and more popular in different fields of psychology. This increased popularity is based on the recent development of several software solutions for the parameter estimation. Although these programs make the application of the model relatively easy, there is a shortage of knowledge about different steps of a state-of-the-art diffusion model study. In this paper, we give a concise tutorial on diffusion modelling, and we present fast-dm-30, a thoroughly revised and extended version of the fast-dm software (Voss & Voss, 2007 for diffusion model data analysis. The most important improvement of the fast-dm version is the possibility to choose between different optimization criteria (i.e., Maximum Likelihood, Chi-Square, and Kolmogorov-Smirnov, which differ in applicability for different data sets.
Numerical Simulation of Water Jet Flow Using Diffusion Flux Mixture Model
Zhi Shang
2014-01-01
Full Text Available A multidimensional diffusion flux mixture model was developed to simulate water jet two-phase flows. Through the modification of the gravity using the gradients of the mixture velocity, the centrifugal force on the water droplets was able to be considered. The slip velocities between the continuous phase (gas and the dispersed phase (water droplets were able to be calculated through multidimensional diffusion flux velocities based on the modified multidimensional drift flux model. Through the numerical simulations, comparing with the experiments and the simulations of traditional algebraic slip mixture model on the water mist spray, the model was validated.
Bernard Wong
2009-01-01
martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.
Qinghui Zhou
2011-06-01
Full Text Available A new phenomenological model, the TP (Temperature Phase model, is presented to carry out optimization calculations for turbulent diffusion combustion in a high-pressure common rail diesel engine. Temperature is the most important parameter in the TP model, which includes two parts: an auto-ignition and a soot model. In the auto-ignition phase, different reaction mechanisms are built for different zones. For the soot model, different methods are used for different temperatures. The TP model is then implemented in KIVA code instead of original model to carry out optimization. The results of cylinder pressures, the corresponding heat release rates, and soot with variation of injection time, variation of rail pressure and variation of speed among TP model, KIVA standard model and experimental data are analyzed. The results indicate that the TP model can carry out optimization and CFD (computational fluid dynamics and can be a useful tool to study turbulent diffusion combustion.
Ingo, Carson; Sui, Yi; Chen, Yufen; Parrish, Todd; Webb, Andrew; Ronen, Itamar
2015-03-01
In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifications of the Mittag-Leffler function. For the case of time-fractional subdiffusion, we compute the kurtosis for the Mittag-Leffler function, which provides both a connection and physical context to the much-used approach of diffusional kurtosis imaging. We provide Monte Carlo simulations to illustrate the concepts of anomalous diffusion as stochastic processes of the random walk. Finally, we demonstrate the clinical utility of the Mittag-Leffler function as a model to describe tissue microstructure through estimations of subdiffusion and kurtosis with diffusion MRI measurements in the brain of a chronic ischemic stroke patient.
Modelling the impact of an invasive insect via reaction-diffusion.
Roques, Lionel; Auger-Rozenberg, Marie-Anne; Roques, Alain
2008-11-01
An exotic, specialist seed chalcid, Megastigmus schimitscheki, has been introduced along with its cedar host seeds from Turkey to southeastern France during the early 1990s. It is now expanding in plantations of Atlas Cedar (Cedrus atlantica). We propose a model to predict the expansion and impact of this insect. This model couples a time-discrete equation for the ovo-larval stage with a two-dimensional reaction-diffusion equation for the adult stage, through a formula linking the solution of the reaction-diffusion equation to a seed attack rate. Two main diffusion operators, of Fokker-Planck and Fickian types, are tested. We show that taking account of the dependence of the insect mobility with respect to spatial heterogeneity, and choosing the appropriate diffusion operator, are critical factors for obtaining good predictions.
Generalized Density-Corrected Model for Gas Diffusivity in Variably Saturated Soils
Chamindu, Deepagoda; Møldrup, Per; Schjønning, Per
2011-01-01
Accurate predictions of the soil-gas diffusivity (Dp/Do, where Dp is the soil-gas diffusion coefficient and Do is the diffusion coefficient in free air) from easily measureable parameters like air-filled porosity (ε) and soil total porosity (φ) are valuable when predicting soil aeration...... and the emission of greenhouse gases and gaseous-phase contaminants from soils. Soil type (texture) and soil density (compaction) are two key factors controlling gas diffusivity in soils. We extended a recently presented density-corrected Dp(ε)/Do model by letting both model parameters (α and β) be interdependent...... and also functions of φ. The extension was based on literature measurements on Dutch and Danish soils ranging from sand to peat. The parameter α showed a promising linear relation to total porosity, while β also varied with α following a weak linear relation. The thus generalized density-corrected (GDC...
M. M. Becker
2013-01-01
Full Text Available Common fluid models used for the description of electron transport in nonthermal discharge plasmas are subject to substantial restrictions if the electron energy transport significantly influences the discharge behaviour. A drift-diffusion approach is presented which is based on a multiterm approximation of the electron velocity distribution function and overcomes some of these restrictions. It is validated using a benchmark model and applied for the analysis of argon discharge plasmas at low and atmospheric pressure. The results are compared to those of common drift-diffusion models as well as to experimental data. It is pointed out that fluid models are able to describe nonlocal phenomena caused by electron energy transport, if the energy transport is consistently described. Numerical difficulties that frequently occur when the conventional drift-diffusion model is consistently applied are avoided by the proposed method.
Ocampo-Perez, Raul; Leyva-Ramos, Roberto; Mendoza-Barron, Jovita; Guerrero-Coronado, Rosa M
2011-12-01
The concentration decay curves for the adsorption of phenol on organobentonite were obtained in an agitated tank batch adsorber. The experimental adsorption rate data were interpreted with diffusional models as well as first-order, second-order and Langmuir kinetic models. The surface diffusion model adjusted the data quite well, revealing that the overall rate of adsorption was controlled by surface diffusion. Furthermore, the surface diffusion coefficient increased raising the mass of phenol adsorbed at equilibrium and was independent of the particle diameter in the range 0.042-0.0126 cm. It was demonstrated that the overall rate of adsorption was essentially not affected by the external mass transfer. The second-order and the Langmuir kinetic models fitted the experimental data quite well; however, the kinetic constants of both models varied without any physical meaning while increasing the particle size and the mass of phenol adsorbed at equilibrium. Copyright © 2011 Elsevier Inc. All rights reserved.
Modeling and Uncertainty Quantification of Vapor Sorption and Diffusion in Heterogeneous Polymers
Sun, Yunwei [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Harley, Stephen J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Glascoe, Elizabeth A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-08-13
A high-fidelity model of kinetic and equilibrium sorption and diffusion is developed and exercised. The gas-diffusion model is coupled with a triple-sorption mechanism: Henry’s law absorption, Langmuir adsorption, and pooling or clustering of molecules at higher partial pressures. Sorption experiments are conducted and span a range of relative humidities (0-95 %) and temperatures (30-60 °C). Kinetic and equilibrium sorption properties and effective diffusivity are determined by minimizing the absolute difference between measured and modeled uptakes. Uncertainty quantification and sensitivity analysis methods are described and exercised herein to demonstrate the capability of this modeling approach. Water uptake in silica-filled and unfilled poly(dimethylsiloxane) networks is investigated; however, the model is versatile enough to be used with a wide range of materials and vapors.
Modeling chemistry in and above snow at Summit, Greenland – Part 1: Model description and results
J. L. Thomas
2010-12-01
Full Text Available Sun-lit snow is increasingly recognized as a chemical reactor that plays an active role in uptake, transformation, and release of atmospheric trace gases. Snow is known to influence boundary layer air on a local scale, and given the large global surface coverage of snow may also be significant on regional and global scales.
We present a new detailed one-dimensional snow chemistry module that has been coupled to the 1-D atmospheric boundary layer model MISTRA, we refer to the coupled model as MISTRA-SNOW. The new 1-D snow module, which is dynamically coupled to the overlaying atmospheric model, includes heat transport in the snowpack, molecular diffusion, and wind pumping of gases in the interstitial air. The model includes gas phase photochemistry and chemical reactions both in the interstitial air and the atmosphere. Heterogeneous and multiphase chemistry on atmospheric aerosol is considered explicitly. The chemical interaction of interstitial air with snow grains is simulated assuming chemistry in a liquid (aqueous layer on the grain surface. The model was used to investigate snow as the source of nitrogen oxides (NO_{x} and gas phase reactive bromine in the atmospheric boundary layer in the remote snow covered Arctic (over the Greenland ice sheet as well as to investigate the link between halogen cycling and ozone depletion that has been observed in interstitial air. The model is validated using data taken 10 June–13 June, 2008 as part of the Greenland Summit Halogen-HO_{x} experiment (GSHOX. The model predicts that reactions involving bromide and nitrate impurities in the surface snow at Summit can sustain atmospheric NO and BrO mixing ratios measured at Summit during this period.
Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage
Allen, Rebecca
2015-04-01
ABSTRACT Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage Rebecca Allen Geological CO2 storage is an engineering feat that has been undertaken around the world for more than two decades, thus accurate modeling of flow and transport behavior is of practical importance. Diffusive and convective transport are relevant processes for buoyancy-driven convection of CO2 into underlying fluid, a scenario that has received the attention of numerous modeling studies. While most studies focus on Darcy-scale modeling of this scenario, relatively little work exists at the pore-scale. In this work, properties evaluated at the pore-scale are used to investigate the transport behavior modeled at the Darcy-scale. We compute permeability and two different forms of tortuosity, namely hydraulic and diffusive. By generating various pore ge- ometries, we find hydraulic and diffusive tortuosity can be quantitatively different in the same pore geometry by up to a factor of ten. As such, we emphasize that these tortuosities should not be used interchangeably. We find pore geometries that are characterized by anisotropic permeability can also exhibit anisotropic diffusive tortuosity. This finding has important implications for buoyancy-driven convection modeling; when representing the geological formation with an anisotropic permeabil- ity, it is more realistic to also account for an anisotropic diffusivity. By implementing a non-dimensional model that includes both a vertically and horizontally orientated 5 Rayleigh number, we interpret our findings according to the combined effect of the anisotropy from permeability and diffusive tortuosity. In particular, we observe the Rayleigh ratio may either dampen or enhance the diffusing front, and our simulation data is used to express the time of convective onset as a function of the Rayleigh ratio. Also, we implement a lattice Boltzmann model for thermal convective flows, which we treat as an analog for
Qualitative Analysis on a Reaction-Diffusion Prey Predator Model and the Corresponding Steady-States
Qunyi BIE; Rui PENG
2009-01-01
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem.The local and global stability of the positive constant steady-state are discussed,and then some results for nonexistence of positive non-constant steady-states are derived.
Diffusion of PAH in potato and carrot slices and application for a potato model
Trapp, Stefan; Cammarano, A.; Capri, E.; Reichenberg, F.; Mayer, Philipp
2007-01-01
A method for quantifying the effect of medium composition on the diffusive mass transfer of hydrophobic organic chemicals through thin layers was applied to plant tissue. The method employs two silicone disks, one serving as source and one as sink for a series of PAHs diffusing through thin layers of water, potato tissue, and carrot tissue. Naphthalene, phenanthrene, anthracene, and fluoranthene served as model substances. Their transfer from source to sink disk was measured by HPLC to determ...
Lauret, A J P; Boyer, H; Adelard, L; Garde, F
2012-01-01
As part of our efforts to complete the software CODYRUN validation, we chose as test building a block of flats constructed in Reunion Island, which has a humid tropical climate. The sensitivity analysis allowed us to study the effects of both diffuse and direct solar radiation on our model of this building. With regard to the choice and location of sensors, this stage of the study also led us to measure the solar radiation falling on the windows. The comparison of measured and predicted radiation clearly showed that our predictions over-estimated the incoming solar radiation, and we were able to trace the problem to the algorithm which calculates diffuse solar radiation. By calculating view factors between the windows and the associated shading devices, changes to the original program allowed us to improve the predictions, and so this article shows the importance of sensitivity analysis in this area of research.
Testing and modeling of diffusion bonded prototype optical windows under ITER conditions
Jacobs, M. [Flemish Inst. for Technological Research, Mol (Belgium); Van Oost, G. [Dept. of Applied Physics, Ghent Univ., Ghent (Belgium); Degrieck, J.; De Baere, I. [Dept. of Materials Science and Engineering, Ghent Univ., Ghent (Belgium); Gusarov, A. [Belgian Nuclear Research Center, Mol (Belgium); Gubbels, F. [TNO, Eindhoven (Netherlands); Massaut, V. [Belgian Nuclear Research Center, Mol (Belgium)
2011-07-01
Glass-metal joints are a part of ITER optical diagnostics windows. These joints must be leak tight for the safety (presence of tritium in ITER) and to preserve the vacuum. They must also withstand the ITER environment: temperatures up to 220 deg.C and fast neutron fluxes of {approx}3.10{sup 9} n/cm{sup 2}.s. At the moment, little information is available about glass-metal joints suitable for ITER. Therefore, we performed mechanical and thermal tests on some prototypes of an aluminium diffusion bonded optical window. Finite element modeling with Abaqus code was used to understand the experimental results. The prototypes were helium leaking probably due to very tiny cracks in the interaction layer between the steel and the aluminium. However, they were all able to withstand a thermal cycling test up to 200 deg. C; no damage could be seen after the tests by visual inspection. The prototypes successfully passed push-out test with a 500 N load. During the destructive push-out tests the prototypes broke at a 6-12 kN load between the aluminium layer and the steel or the glass, depending on the surface quality of the glass. The microanalysis of the joints has also been performed. The finite element modeling of the push-out tests is in a reasonable agreement with the experiments. According to the model, the highest thermal stress is created in the aluminium layer. Thus, the aluminium joint seems to be the weakest part of the prototypes. If this layer is improved, it will probably make the prototype helium leak tight and as such, a good ITER window candidate. (authors)
Modeling and Implementing ISO 13584-based Part Library
杨东; 肖丽雯; 何援军; 张申生
2004-01-01
ISO 13584 (I.e. PLIB) is an international standard for the representation and exchange of CAD part libraries. It aims to provide an application-independent mechanism to enable the share of part library information between applications. In this paper, the approach of modeling part library conforming to ISO 13584 is presented. Also, a prototype of part library management system, I.e. BYL-PLIB, whose implementation is in agreement with ISO 13854 is developed to demonstrate the usefulness of proposed approach.
Optimization Model for Refinery Hydrogen Networks Part II
Enrique E. Tarifa
2016-10-01
Full Text Available In the first part of this work, a model of optimization was presented that minimizes the consumption of the hydrogen of a refinery. In this second part, the model will be augmented to take into account the length of the pipelines, the addition of purification units and the installation of new compressors, all features of industrial real networks. The model developed was implemented in the LINGO software environment. For data input and results output, an Excel spreadsheet was developed that interfaces with LINGO. The model is currently being used in YPFLuján de Cuyo refinery (Mendoza, Argentina
Porth, O.; Vorster, M. J.; Lyutikov, M.; Engelbrecht, N. E.
2016-08-01
We study the transport of high-energy particles in pulsar wind nebulae (PWN) using three-dimensional magnetohydrodynamic (MHD) and test-particle simulations, as well as a Fokker-Planck particle transport model. The latter includes radiative and adiabatic losses, diffusion, and advection on the background flow of the simulated MHD nebula. By combining the models, the spatial evolution of flux and photon index of the X-ray synchrotron emission is modelled for the three nebulae G21.5-0.9, the inner regions of Vela, and 3C 58, thereby allowing us to derive governing parameters: the magnetic field strength, average flow velocity, and spatial diffusion coefficient. For comparison, the nebulae are also modelled with the semi-analytic Kennel & Coroniti model but the Porth et al. model generally yields better fits to the observational data. We find that high velocity fluctuations in the turbulent nebula (downstream of the termination shock) give rise to efficient diffusive transport of particles, with average Péclet number close to unity, indicating that both advection and diffusion play an important role in particle transport. We find that the diffusive transport coefficient of the order of ˜ 2 × 1027(Ls/0.42 Ly) cm2 s- 1 (Ls is the size of the termination shock) is independent of energy up to extreme particle Lorentz factors of γp ˜ 1010.
Xuefang, L.; Liu, Y.
2015-12-01
Huang et al (2010) found that Fe, Ca and Mg isotope fractionations of high-temperature silicate melts are only associated with the temperature gradients in thermal diffusion processes and are independent of compositions and mean temperatures [1]. Richter et al (2010) doubted that the existing data are sufficient to obtain such conclusion [2]. A few theoretical models have been proposed for explaining isotopic fractionations in these processes under high temperatures [3, 4]. However, molecular-level mechanisms and theoretical treatments of these processes are still under debating. Here we provide a unified theory based on the local thermodynamic equilibrium treatment (LTE) of statistical mechanics for evaluating thermal isotopic fractionations under a wide range of temperatures. Under high temperatures, our theory however can be reasonably approximated to this equation: where A and B are constants which are related to specific isotope systems and chemical compositions of silicate melts. If the thermal gradient is not very large and the mean temperature is high, the second part of the above equation can be safely neglected and obtain an extremely simple equation which is linearly depended on temperatures, agreeing with what Huang et al (2010) concluded. Based on this terse equation, we can not only easily provide isotope fractionation data for almost all kinds of isotope systems, but also can provide the mechanisms of isotope fractionation in thermal diffusion processes. [1] Huang et al (2010) Nature 464, 396-400. [2] Richter et al (2010) Nature 472, E1-E1. [3] Dominguez et al (2011) Nature 473, 70-73.
Gallego, Sergi; Ortuño, Manuel; Neipp, Cristian; Márquez, Andrés; Beléndez, Augusto; Pascual, Inmaculada
2005-10-01
Several theoretical models have been proposed to predict the behavior of photopolymers as holographic recording materials. Basically these models have been applied to study thin layers (around 100 µm thick). The increasing importance of holographic memories recorded in photopolymers (thickness of >500 µm) makes it necessary to extend the ideas proposed by these models to study thick photopolymer layers. We calculate the temporal evolution of the diffraction efficiencies for thick layers using a first-harmonic diffusion model, and the results obtained are compared with the corresponding values for thin layers. Furthermore, the values of the average diffusivity of the polymer chains after the grating is formed are also obtained. In general, we find that the monomer and polymer diffusivity increases when higher values of thickness are used.
Density-corrected models for gas diffusivity and air permeability in unsaturated soil
Deepagoda Thuduwe Kankanamge Kelum, Chamindu; Møldrup, Per; Schjønning, Per
2011-01-01
. Also, a power-law ka model with exponent 1.5 (derived from analogy with a previous gas diffusivity model) used in combination with the D-C approach for ka,100 (reference point) seemed promising for ka(e) predictions, with good accuracy and minimum parameter requirements. Finally, the new D-C model......Accurate prediction of gas diffusivity (Dp/Do) and air permeability (ka) and their variations with air-filled porosity (e) in soil is critical for simulating subsurface migration and emission of climate gases and organic vapors. Gas diffusivity and air permeability measurements from Danish soil...... profile data (total of 150 undisturbed soil samples) were used to investigate soil type and density effects on the gas transport parameters and for model development. The measurements were within a given range of matric potentials (-10 to -500 cm H2O) typically representing natural field conditions...
Density-Corrected Models for Gas Diffusivity and Air Permeability in Unsaturated Soil
Chamindu, Deepagoda; Møldrup, Per; Schjønning, Per
2011-01-01
Accurate prediction of gas diffusivity (Dp/Do) and air permeability (ka) and their variations with air-filled porosity (e) in soil is critical for simulating subsurface migration and emission of climate gases and organic vapors. Gas diffusivity and air permeability measurements from Danish soil...... in subsurface soil. The data were regrouped into four categories based on compaction (total porosity F 0.4 m3 m-3) and soil texture (volume-based content of clay, silt, and organic matter 15%). The results suggested that soil compaction more than soil type was the major control on gas...... diffusivity and to some extent also on air permeability. We developed a density-corrected (D-C) Dp(e)/Do model as a generalized form of a previous model for Dp/ Do at -100 cm H2O of matric potential (Dp,100/Do). The D-C model performed well across soil types and density levels compared with existing models...
Chemical kinetic modeling of a methane opposed flow diffusion flame and comparison to experiments
Marinov, N.M., Pitz, W.J.; Westbrook, C.K. [Lawrence Livermore National Lab., CA (United States); Vincitore, A.M.; Senka, S.M. [Univ. of California, Los Angeles, CA (United States); Lutz, A.E. [Sandia National Labs., Livermore, CA (United States)
1998-01-01
The chemical structure of an opposed flow, methane diffusion flame is studied using a chemical kinetic model and the results are compared to experimental measurements. The chemical kinetic paths leading to aromatics and polycyclic aromatics hydrocarbons (PAHs) in the diffusion flame are identified. These paths all involve resonantly stabilized radicals which include propargyl, allyl, cyclopentadienyl, and benzyl radicals. The modeling results show reasonable agreement with the experimental measurements for the large hydrocarbon aliphatic compounds, aromatics, and PAHs. the benzene was predicted to be formed primarily by the reaction sequence of Allyl plus Propargyl equals Fulvene plus H plus H followed by fulvene isomerization to benzene. Naphthalene was modeled using the reaction of benzyl with propargyl, while the combination of cyclopentadienyl radicals were shown to be a minor contributor in the diffusion flame. The agreement between the model and experiment for the four-ring PAHs was poor.
A comparison between the fission matrix method, the diffusion model and the transport model
Dehaye, B.; Hugot, F. X.; Diop, C. M. [Commissariat a l' Energie Atomique et aux Energies Alternatives, Direction de l' Energie Nucleaire, Departement de Modelisation des Systemes et Structures, CEA DEN/DM2S, PC 57, F-91191 Gif-sur-Yvette cedex (France)
2013-07-01
The fission matrix method may be used to solve the critical eigenvalue problem in a Monte Carlo simulation. This method gives us access to the different eigenvalues and eigenvectors of the transport or fission operator. We propose to compare the results obtained via the fission matrix method with those of the diffusion model, and an approximated transport model. To do so, we choose to analyse the mono-kinetic and continuous energy cases for a Godiva-inspired critical sphere. The first five eigenvalues are computed with TRIPOLI-4{sup R} and compared to the theoretical ones. An extension of the notion of the extrapolation distance is proposed for the modes other than the fundamental one. (authors)
Quasi-Brittle Fracture Modeling of Preflawed Bitumen Using a Diffuse Interface Model
Yue Hou
2016-01-01
Full Text Available Fundamental understandings on the bitumen fracture mechanism are vital to improve the mixture design of asphalt concrete. In this paper, a diffuse interface model, namely, phase-field method is used for modeling the quasi-brittle fracture in bitumen. This method describes the microstructure using a phase-field variable which assumes one in the intact solid and negative one in the crack region. Only the elastic energy will directly contribute to cracking. To account for the growth of cracks, a nonconserved Allen-Cahn equation is adopted to evolve the phase-field variable. Numerical simulations of fracture are performed in bituminous materials with the consideration of quasi-brittle properties. It is found that the simulation results agree well with classic fracture mechanics.
Effect of a protection zone in the diffusive Leslie predator-prey model
Du, Yihong; Peng, Rui; Wang, Mingxin
In this paper, we consider the diffusive Leslie predator-prey model with large intrinsic predator growth rate, and investigate the change of behavior of the model when a simple protection zone Ω for the prey is introduced. As in earlier work [Y. Du, J. Shi, A diffusive predator-prey model with a protection zone, J. Differential Equations 229 (2006) 63-91; Y. Du, X. Liang, A diffusive competition model with a protection zone, J. Differential Equations 244 (2008) 61-86] we show the existence of a critical patch size of the protection zone, determined by the first Dirichlet eigenvalue of the Laplacian over Ω and the intrinsic growth rate of the prey, so that there is fundamental change of the dynamical behavior of the model only when Ω is above the critical patch size. However, our research here reveals significant difference of the model's behavior from the predator-prey model studied in [Y. Du, J. Shi, A diffusive predator-prey model with a protection zone, J. Differential Equations 229 (2006) 63-91] with the same kind of protection zone. We show that the asymptotic profile of the population distribution of the Leslie model is governed by a standard boundary blow-up problem, and classical or degenerate logistic equations.
Wang Shaoli; Feng Xinlong; He Yinnian
2011-01-01
This article proposes a diffused hepatitis B virus (HBV) model with CTLimmune response and nonlinear incidence for the control of viral infections.By means of different Lyapunov functions,the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained.Global stability of the positive equilibrium of the model is also considered.The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.
Pattern selection in a predation model with self and cross diffusion
Wang Wei-Ming; Wang Wen-Juan; Lin Ye-Zhi; Tan Yong-Ji
2011-01-01
In this paper, we present the amplitude equations for the excited modes in a cross-diffusive predator-prey model with zero-flux boundary conditions. From these equations, the stability of patterns towards uniform and inhomogenous perturbations is determined. Furthermore, we present novel numerical evidence of six typical turing patterns, and find that the model dynamics exhibits complex pattern replications: for μ1 μ4, the stripe pattern emerges. This may enrich the pattern formation in the cross-diffusive predator-prey model.
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Chirkunov, Yu. A., E-mail: chr101@mail.ru [Novosibirsk State Technical University, Marks Avenue 20, Novosibirsk 630073 (Russian Federation)
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
Stoffers, N.H.; Brandsch, R.; Bradley, E.L.; Cooper, I.; Dekker, M.; Störmer, A.; Franz, R.
2005-01-01
This paper describes the second part of a project whose main objective was to develop the know-how to produce certified reference materials (CRMs) for specific migration testing. Certification parameters discussed are the diffusion coefficient, DP, the respective polymer-specific coefficient, AP, of
Nonlinear diffusion model for Rayleigh-Taylor mixing
Boffetta, G; Musacchio, S
2010-01-01
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Forecasting turbulent modes with nonparametric diffusion models: Learning from noisy data
Berry, Tyrus; Harlim, John
2016-04-01
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the availability of a noise-free training data set observing the full state space of the dynamics, in real applications we often have only partial observations which are corrupted by noise. To alleviate these practical issues, following the theory of embedology, the diffusion model is built using the delay-embedding coordinates of the data. We show that this delay embedding biases the geometry of the data in a way which extracts the most stable component of the dynamics and reduces the influence of independent additive observation noise. The resulting diffusion forecast model approximates the semigroup solutions of the generator of the underlying dynamics in the limit of large data and when the observation noise vanishes. As in any standard forecasting problem, the forecasting skill depends crucially on the accuracy of the initial conditions. We introduce a novel Bayesian method for filtering the discrete-time noisy observations which works with the diffusion forecast to determine the forecast initial densities. Numerically, we compare this nonparametric approach with standard stochastic parametric models on a wide-range of well-studied turbulent modes, including the Lorenz-96 model in weakly chaotic to fully turbulent regimes and the barotropic modes of a quasi-geostrophic model with baroclinic instabilities. We show that when the only available data is the low-dimensional set of noisy modes that are being modeled, the diffusion forecast is indeed competitive to the perfect model.
Akimoto, Takuma; Yamamoto, Eiji
2016-12-01
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the time-averaged diffusion coefficients are intrinsically random (irreproducible) even in the long-time measurements in non-equilibrium situations. Furthermore, the distribution of the time-averaged diffusion coefficients converges to a universal distribution in the sense that it does not depend on initial conditions. Our findings pave the way for a theoretical understanding of distributional behavior of the time-averaged diffusion coefficients in disordered systems.
Memory Effects and Coverage Dependence of Surface Diffusion in a Model Adsorption System
Vattulainen, Ilpo Tapio; Ying, S. C.; Ala-Nissila, T.
1999-01-01
diffusion is found to decay following a power law after an initial transient period. This behavior persists until the hydrodynamic regime is reached, after which the memory effect decays exponentially. The time required to reach the hydrodynamical regime and the related exponential decay is strongly......We study the coverage dependence of surface diffusion coefficients for a strongly interacting adsorption system O/W(110) via Monte Carlo simulations of a lattice-gas model. In particular, we consider the nature and emergence of memory effects as contained in the corresponding correlation factors...... influenced by both the critical effects related to long-wavelength fluctuations and the local order in the overlayer. We also analyze the influence of the memory effects on the effective diffusion barriers extracted from the Arrhenius analysis. For tracer diffusion, we find that the contribution from memory...
Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
Desvillettes, Laurent
2010-01-01
We study a continuous coagulation-fragmentation model with constant kernels for reacting polymers (see [M. Aizenman and T. Bak, Comm. Math. Phys., 65 (1979), pp. 203-230]). The polymers are set to diffuse within a smooth bounded one-dimensional domain with no-flux boundary conditions. In particular, we consider size-dependent diffusion coefficients, which may degenerate for small and large cluster-sizes. We prove that the entropy-entropy dissipation method applies directly in this inhomogeneous setting. We first show the necessary basic a priori estimates in dimension one, and second we show faster-than-polynomial convergence toward global equilibria for diffusion coefficients which vanish not faster than linearly for large sizes. This extends the previous results of [J.A. Carrillo, L. Desvillettes, and K. Fellner, Comm. Math. Phys., 278 (2008), pp. 433-451], which assumes that the diffusion coefficients are bounded below. © 2009 Society for Industrial and Applied Mathematics.
Rare events and their impact on velocity diffusion in a stochastic Fermi-Ulam model.
Karlis, A K; Diakonos, F K; Constantoudis, V; Schmelcher, P
2008-10-01
A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards.
DSOM: a novel self-organizing model based on NO dynamic diffusing mechanism
YIN Junsong; HU Dewen; CHEN Shuang; ZHOU Zongtan
2005-01-01
In this paper the four-dimensional dynamic diffusing mechanism and the enhancement in Long-Term Potentiation (LTP) of intrinsic nitric oxide (NO) in nervous system are studied computationally. A novel unsupervised Diffusing Self-Organizing Maps (DSOM) model is presented on the union of SOM with NO diffusing mechanism. Based on the spatial prototype mapping, temporal enhancement is introduced in DSOM and the fine-tuning manner is improved by the simplified NO diffusing mechanism. Furthermore, the quantization error of optimal weights is valuated and the detailed noise analysis of DSOM is presented. Finally some typical stimulation experiments are presented to illustrate how DSOM gracefully handles time warping and multiple patterns with overlapping reference vectors.
Fricke-agarose dosimeter gels: ion diffusion modelling and microdensitometry alternative to MRI
De Pasquale, F.; Barone, P.; Sebastiani, G. [CNR. Istituto per le Applicazioni del Calcolo, Rome (Italy); D' Errico, F. [Yale Univ. School of Medicine, Yale (United States). Department of Therapeutic Radiology; Egger, E. [Paul Scheller Institut, Villigen (Switzerland). Department of Radiation Medicine; Luciani, A.M.; Pacilio, M.; Guidoni, L.; Votti, V. [Istituto Superiore della Sanita' , Rome (Italy). Laboratorio di Fisica; INFN, Rome (Italy)
2002-07-01
Ferric ion diffusion is one of the main problems that still restrains the dosimetric application of Fricke-agarose gels. In this work, we model this process within finite length gel samples. The temporal evolution of the ion concentration as a function of the initial concentration is derived by solving Fick's second law in two dimensions with boundary reflections. The influence of ion concentration gradient, elapsed time, diffusion coefficient and spatial resolution is studied. Due to the main drawbacks of MRI for studying these systems, i.e. high cost and acquisition time often non-negligible compared to diffusion time, we also investigate the possibility of using a microdensitometer. The application of this technique for Fricke gel dosimetry is proposed here for the first time. The estimate of the ion diffusion coefficient is in a very agreement with those reported in literature.
Modelling Of Eco-innovation Diffusion: The EU Eco-label
KIJEK TOMASZ
2015-03-01
Full Text Available The aim of this article is to carry out a theoretical and empirical analysis of the process of eco-label diffusion. Eco-labels allow consumers to identify products and services that have a reduced environmental impact during their life cycle. Thus, they are aimed at diminishing the information gap between sellers and buyers. The results of the estimation using the Bass model indicate that the diffusion of the EU eco-label has been most dynamic in countries such as Hungary, Poland, Denmark, Germany and France. In turn, the scope of diffusion (absolute saturation level reached the highest value for companies in France and Italy. In addition, the results of the study confirm the stimulating impact of the scope of eco-label diffusion on consumer awareness of environmental issues. This finding points to the need for environmental education among consumers, which could in turn encourage firms to undertake pro-environmental actions.
Jump diffusion models and the evolution of financial prices
Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, University of Brasilia (Brazil); Silva, Sergio da [Department of Economics, Federal University of Santa Catarina (Brazil); Gleria, Iram, E-mail: iram@pq.cnpq.br [Institute of Physics, Federal University of Alagoas (Brazil)
2011-08-08
We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior. -- Highlights: → We analyze a stochastic model to describe the evolution of financial prices. → The stochastic term is considered as a sum of the Wiener noise and a jump process. → The process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. → We extend the De Finetti functions to a generalized nonlinear model.
Modeling in biomedical informatics - An exploratory analysis (Part 1)
A. Hasman; R. Haux
2006-01-01
Objectives: Modeling is a significant part of research, education and practice in biomedical and health informatics. Our objective was to explore, which types of models of processes are used in current biomedical/health informatics research, as reflected in publications of scientific journals in thi
Donkin, C.; Brown, S.; Heathcote, A.; Wagenmakers, E.-J.
2011-01-01
Quantitative models for response time and accuracy are increasingly used as tools to draw conclusions about psychological processes. Here we investigate the extent to which these substantive conclusions depend on whether researchers use the Ratcliff diffusion model or the Linear Ballistic
On the well posedness and further regularity of a diffusive three species aquatic model
Parshad, R.D.
2012-01-01
We consider Upadhay\\'s three species aquatic food chain model, with the inclusion of spatial spread. This is a well established food chain model for the interaction of three given aquatic species. It exhibits rich dynamical behavior, including chaos. We prove the existence of a global weak solution to the diffusive system, followed by existence of local mild and strong solution.
Barbante, Paolo [Dipartimento di Matematica, Politecnico di Milano - Piazza Leonardo da Vinci 32 - 20133 Milano (Italy); Frezzotti, Aldo; Gibelli, Livio [Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano - Via La Masa 34 - 20156 Milano (Italy)
2014-12-09
The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviations of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.
A time-periodic reaction-diffusion epidemic model with infection period
Zhang, Liang; Wang, Zhi-Cheng
2016-10-01
In this paper, we propose a time-periodic and diffusive SIR epidemic model with constant infection period. By introducing the basic reproduction number R_0 via a next generation operator for this model, we show that the disease goes extinction if R_0 1.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Wagenmakers, E.-J.
2009-01-01
The Ratcliff diffusion model for simple two-choice decisions (e.g., Ratcliff, 1978; Ratcliff & McKoon, 2008) has two outstanding advantages. First, the model generally provides an excellent fit to the observed data (i.e., response accuracy and the shape of RT distributions, both for correct and erro
Proposing an Educational Scaling-and-Diffusion Model for Inquiry-Based Learning Designs
Hung, David; Lee, Shu-Shing
2015-01-01
Education cannot adopt the linear model of scaling used by the medical sciences. "Gold standards" cannot be replicated without considering process-in-learning, diversity, and student-variedness in classrooms. This article proposes a nuanced model of educational scaling-and-diffusion, describing the scaling (top-down supports) and…
Proposing an Educational Scaling-and-Diffusion Model for Inquiry-Based Learning Designs
Hung, David; Lee, Shu-Shing
2015-01-01
Education cannot adopt the linear model of scaling used by the medical sciences. "Gold standards" cannot be replicated without considering process-in-learning, diversity, and student-variedness in classrooms. This article proposes a nuanced model of educational scaling-and-diffusion, describing the scaling (top-down supports) and…
Spreading Speed for a Periodic Reaction-diffusion Model with Nonmonotone Birth Function
HUANG Ye-hui; WENG Pei-xuan
2012-01-01
A reaction-diffusion model for a single spccies with age structure and nonlocal reaction for periodic time t is derived.Some results about the model with monotone birth function are firstly introduced,and then by constructing two auxiliary equations and squeezing method,the spreading speed for the system with nonmonotone birth function is obtained.
Weak localization as a definitive test of diffusive models in the Casimir effect
Allocca, Andrew; Wilson, Justin; Galitski, Victor
2015-03-01
Results from many measurements of the Casimir effect suggest that the metallic plates in these experiments should be modeled with the plasma model of free electrons as opposed to the naive diffusive Drude model, while other experiments seem to indicate the exact opposite, with results more in line with a diffusive model. We study the Casimir effect at low temperatures between a thick disordered plate and purely two-dimensional disordered system where the Drude conductivity decreases logarithmically at low temperatures due to weak localization. This effect can be tuned with either temperature or applied magnetic field leading to a measurable change in the Casimir force. On the other hand, a ballistic model cannot experience such an effect and is only weakly dependent on temperature and magnetic field. As a result, we propose that an experiment would unambiguously differentiate between diffusive and ballistic models by measuring the effect at low temperatures with an applied magnetic field. Additionally, we calculate the impact that fluctuations in the disorder distribution have on the Casimir effect. Assuming the validity of a diffusive model, we find that the Drude model is a good approximation of a more exact treatment of disorder. This work was supported by the DOE-BES (Grant No. DESC0001911) (A.A. and V.G.), the JQI-PFC (J.W.), and the Simons Foundation.
Jakob, A
2002-12-01
In this report, the procedure and the results of an inverse modelling study on the through-diffusion of tritiated water (HTO) and {sup 2}2Na{sup +}-ions are presented using high-porous hardened cement pastes with a water/cement ratio of 1.3 in the first stage of the cement degradation. For the analysis two alternative models were applied: 1) a diffusion model where a possible sorption of the tracer was entirely neglected, and 2) a diffusion model with linear sorption. The analysis of the through-diffusion phase allowed extracting values for the effective diffusion coefficient (D{sub e}) and the rock-capacity factor ({alpha}). Both models could fit the breakthrough curves equally well, and also mass-balance considerations did not allow to clearly preferring one of the two competing models to the other. But blind-predictions for tracer out-diffusion using the best-fit parameter values deduced from analysing the former through-diffusion phase gave a clear indication that linear sorption had to be included in the diffusion model. The extracted K{sub d} values for HTO are in excellent agreement with values from batch sorption experiments and are of the order of 0.8. 10{sup -3} m{sup 3}/kg. Those for {sup 2}2Na{sup +} are of the order of 1.0. 10{sup -3} m{sup 3}/kg and are by a factor of two larger than values from batch sorption experiments. The values for the effective diffusion coefficients for HTO are of the order of (2-3).10{sup -1}0 m{sup 2}/s, and those for sodium are roughly by a factor of two smaller than values for HTO. On the one hand, the observed tracer uptake could only partially be addressed to isotope exchange; the most obvious process which could account for the remaining part of the uptaken tracer mass is diffusion into a second type of porosity, the dead-end pores. On the other hand, the results and conclusions drawn are encouraging for future investigations; therefore no major deficiency concerning the applied equipment and the modelling methodology
Improvement of the One-dimensional Vertical Advection-diffusion Model in Seawater
王保栋; 单宝田; 战闰; 王修林
2003-01-01
The classical 1-D vertical advection-diffusion model was improved in this work. Themain advantages of the improved model over the previous one are: 1 ) The applicable condition ofthe 1-D model is made clear in the improved model, in that it is substantively applicable only to avertical domain on which two end-member water masses are mixing. 2) The substitution of parame-ter f(z) in the equation of the classical 1-D model with end-member fraction f1 makes the modelmore precisely and easily solved. 3 ) All the terms in the improved model equation have specificphysical meanings, which makes the model easily understood. Practical application of the improvedmodel to predict the vertical profiles of dissolved oxygen and micronutrients in abyssal ocean waterof the North Pacific proved that the improvement of the 1-D advection-diffusion model is successfuland practicable.
Effects of spatial diffusion on nonequilibrium steady states in a model for prebiotic evolution
Intoy, B. F.; Wynveen, A.; Halley, J. W.
2016-10-01
Effects of spatial diffusion in a Kauffman-like model for prebiotic evolution previously studied in a "well-mixed" limit are reported. The previous model was parametrized by a parameter p defined as the probability that a possible reaction in a network of reactions characterizing the artificial chemistry actually appears in the chemical network. In the model reported here, we numerically study a grid of such well-mixed reactors on a two-dimensional spatial lattice in which the model chemical constituents can hop between neighboring reactors at a rate controlled by a second parameter η . We report the frequency of appearance of three distinct types of nonequilibrium steady states, characterized as "diffusively alive locally dead" (DALD), "diffusively dead locally alive" (DDLA) and "diffusively alive locally alive" (DALA). The types are defined according to whether they are chemically equilibrated at each site, diffusively equilibrated between sites, or neither, respectively. With our parametrization of the definitions of these nonequilibrium states, many of the DALA states are growing rapidly in population due to the explosive population growth of a few sites, while their entropy remains well below its equilibrium value. Sharp temporal transitions occur as exploding sites appear. DALD states occur less commonly than the other types and also usually harbor a few explosively growing sites but transitions are less sharp than in DALA systems.
Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue.
Srinivasan, R Srini; Gerth, Wayne A; Powell, Michael R
2003-04-01
Models of gas bubble dynamics employed in probabilistic analyses of decompression sickness incidence in man must be theoretically consistent and simple, if they are to yield useful results without requiring excessive computations. They are generally formulated in terms of ordinary differential equations that describe diffusion-limited gas exchange between a gas bubble and the extravascular tissue surrounding it. In our previous model (Ann. Biomed. Eng. 30: 232-246, 2002), we showed that with appropriate representation of sink pressures to account for gas loss or gain due to heterogeneous blood perfusion in the unstirred diffusion region around the bubble, diffusion-limited bubble growth in a tissue of finite volume can be simulated without postulating a boundary layer across which gas flux is discontinuous. However, interactions between two or more bubbles caused by competition for available gas cannot be considered in this model, because the diffusion region has a fixed volume with zero gas flux at its outer boundary. The present work extends the previous model to accommodate interactions among multiple bubbles by allowing the diffusion region volume of each bubble to vary during bubble evolution. For given decompression and tissue volume, bubble growth is sustained only if the bubble number density is below a certain maximum.
Jump diffusion models and the evolution of financial prices
Figueiredo, Annibal; de Castro, Marcio T.; da Silva, Sergio; Gleria, Iram
2011-08-01
We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior.
Multi-view and 3D deformable part models.
Pepik, Bojan; Stark, Michael; Gehler, Peter; Schiele, Bernt
2015-11-01
As objects are inherently 3D, they have been modeled in 3D in the early days of computer vision. Due to the ambiguities arising from mapping 2D features to 3D models, 3D object representations have been neglected and 2D feature-based models are the predominant paradigm in object detection nowadays. While such models have achieved outstanding bounding box detection performance, they come with limited expressiveness, as they are clearly limited in their capability of reasoning about 3D shape or viewpoints. In this work, we bring the worlds of 3D and 2D object representations closer, by building an object detector which leverages the expressive power of 3D object representations while at the same time can be robustly matched to image evidence. To that end, we gradually extend the successful deformable part model [1] to include viewpoint information and part-level 3D geometry information, resulting in several different models with different level of expressiveness. We end up with a 3D object model, consisting of multiple object parts represented in 3D and a continuous appearance model. We experimentally verify that our models, while providing richer object hypotheses than the 2D object models, provide consistently better joint object localization and viewpoint estimation than the state-of-the-art multi-view and 3D object detectors on various benchmarks (KITTI [2] , 3D object classes [3] , Pascal3D+ [4] , Pascal VOC 2007 [5] , EPFL multi-view cars[6] ).
On strongly degenerate convection-diffusion Problems Modeling sedimentation-consolidation Processes
Buerger, R.; Evje, S.; Karlsen, S. Hvistendahl
1999-10-01
This report investigates initial-boundary value problems for a quasilinear strongly degenerate convection-diffusion equation with a discontinuous diffusion coefficient. These problems come from the mathematical modelling of certain sedimentation-consolidation processes. Existence of entropy solutions belonging to BV is shown by the vanishing viscosity method. The existence proof for one of the models includes a new regularity result for the integrated diffusion coefficient. New uniqueness proofs for entropy solutions are also presented. These proofs rely on a recent extension to second order equations of Kruzkov`s method of `doubling of the variables`. The application to a sedimentation-consolidation model is illustrated by two numerical examples. 25 refs., 2 figs.
Dermic diffusion and stratum corneum: a state of the art review of mathematical models.
Couto, Ana; Fernandes, Rúben; Cordeiro, M Natália S; Reis, Sara S; Ribeiro, Rogério T; Pessoa, Ana M
2014-03-10
Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives. Copyright © 2013 Elsevier B.V. All rights reserved.
Mutual diffusion coefficient models for polymer-solvent systems based on the Chapman-Enskog theory
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.
Analytical solution of diffusion model for nutrient release from controlled release fertilizer
Ameenuddin Irfan, Sayed; Razali, Radzuan; KuShaari, KuZilati; Mansor, Nurlidia; Azeem, Babar
2017-09-01
An analytical method has been developed to solve the initial value problem which arises from Fick’s diffusion equation encountered in the modelling of the Controlled Release Fertilizers. The proposed analytical solution is developed using the modified Adomian decomposition method. This method does not require the discretization method, reliability and efficiency of this method is more and it also reduces the calculation time. The model has predicted the effect of granule radius and diffusion coefficient on the nutrient release and total release time of Controlled Release Fertilizer. Model has predicted that increase in the radius of granule reduces the release and vice versa in case of diffusion coefficient. Detailed understanding of these parameters helps in improved designing of Controlled Release Fertilizer.
Wang, Junjian; Kang, Qinjun; Rahman, Sheik S
2016-01-01
Gas flow in shale is associated with both organic matter (OM) and inorganic matter (IOM) which contain nanopores ranging in size from a few to hundreds of nanometers. In addition to the noncontinuum effect which leads to an apparent permeability of gas higher than the intrinsic permeability, the surface diffusion of adsorbed gas in organic pores also can influence the apparent permeability through its own transport mechanism. In this study, a generalized lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed shale matrix consisting of OM and IOM. The Expectation-Maximization (EM) algorithm is used to assign the pore size distribution to each component, and the dusty gas model (DGM) and generalized Maxwell-Stefan model (GMS) are adopted to calculate the apparent permeability accounting for multiple transport mechanisms including viscous flow, Knudsen diffusion and surface diffusion. Effects of pore radius and pressure on permeability of both IOM and OM as well as effects of Langmuir ...
Lin, Guoxing
2017-02-01
Pulsed field gradient (PFG) technique is a noninvasive tool, and has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is much more complicated than normal diffusion. In this paper, a fractal derivative model based modified Gaussian phase distribution method is proposed to describe PFG anomalous diffusion. By using the phase distribution obtained from the effective phase shift diffusion method based on fractal derivatives, and employing some of the traditional Gaussian phase distribution approximation techniques, a general signal attenuation expression for free fractional diffusion is derived. This expression describes a stretched exponential function based attenuation, which is distinct from both the exponential attenuation for normal diffusion obtained from conventional Gaussian phase distribution approximation, and the Mittag-Leffler function based attenuation for anomalous diffusion obtained from fractional derivative. The obtained signal attenuation expression can analyze the finite gradient pulse width (FGPW) effect. Additionally, it can generally be applied to all three types of PFG fractional diffusions classified based on time derivative order α and space derivative order β. These three types of fractional diffusions include time-fractional diffusion with { 0 reported results based on effective phase shift diffusion equation method and instantaneous signal attenuation method. This method provides a new, convenient approximation formalism for analyzing PFG anomalous diffusion experiments. The expression that can simultaneously interpret general fractional diffusion and FGPW effect could be especially important in PFG MRI, where the narrow gradient pulse limit cannot be satisfied.
无
2001-01-01
Natural gas diffusion through the cap rock is mainly by means ofdissolving in water, so its concentration can be replaced by solubility, which varies with temperature, pressure and salinity in strata. Under certain geological conditions the maximal solubility is definite, so the diffusion com-putation can be handled approximately by stable state equation. Furthermore, on the basis of the restoration of the paleo-buried history, the diffusion is calculated with the dynamic method, and the result is very close to the real diffusion value in the geological history.
American Society for Testing and Materials. Philadelphia
2008-01-01
1.1 This test method provides procedures for measuring the leach rates of elements from a solidified matrix material, determining if the releases are controlled by mass diffusion, computing values of diffusion constants based on models, and verifying projected long-term diffusive releases. This test method is applicable to any material that does not degrade or deform during the test. 1.1.1 If mass diffusion is the dominant step in the leaching mechanism, then the results of this test can be used to calculate diffusion coefficients using mathematical diffusion models. A computer program developed for that purpose is available as a companion to this test method (Note 1). 1.1.2 It should be verified that leaching is controlled by diffusion by a means other than analysis of the leach test solution data. Analysis of concentration profiles of species of interest near the surface of the solid waste form after the test is recommended for this purpose. 1.1.3 Potential effects of partitioning on the test results can...
A diffusion-precipitation model for gaseous nitriding of Fe-2 wt.% V alloy
Kouba, R., E-mail: r_kouba11@yahoo.fr [Departement SDM, Laboratoire de Technologie des Materiaux, Faculte de Genie Mecanique et Genie des Procedes, USTHB, BP 32 El-Alia, 16111 Alger (Algeria); Keddam, M. [Departement SDM, Laboratoire de Technologie des Materiaux, Faculte de Genie Mecanique et Genie des Procedes, USTHB, BP 32 El-Alia, 16111 Alger (Algeria); Djeghlal, M.E. [Laboratoire LSGM, Departement de Metallurgie, Ecole Nationale Polytechnique, 10 Avenue Hassen Badi, BP 182-16200 El Harrach (Algeria)
2012-09-25
Highlights: Black-Right-Pointing-Pointer Simulation of binary Fe-V nitriding was realized on the diffusion zone. Black-Right-Pointing-Pointer The model takes into account nitrogen diffusion in ferrite and VN precipitation. Black-Right-Pointing-Pointer VN precipitation was considered via thermodynamic equilibrium calculation. Black-Right-Pointing-Pointer The model predicts nitrogen profile and highlights nitrogen excess phenomenon. Black-Right-Pointing-Pointer The model was validated by using experimental data available on literature. - Abstract: A diffusion-precipitation model for gaseous nitriding of a Fe-2 wt.% V binary alloy has been presented. The nitriding treatment is assumed to be completely realized in the ferritic zone. The model takes into account both nitrogen diffusion and vanadium nitride precipitation. The VN precipitation was obtained with the assumption that it exists a local thermodynamic equilibrium between the matrix phase and the precipitate. The thermodynamic equilibrium calculations are based on Gibbs energies minimization, which were performed by the Thermocalc software. The suggested model allowed the prediction of the nitrogen profiles, and also takes into account the nitrogen excess phenomenon. This nitrogen excess has been explained by the presence of iron atoms within the precipitate. The theoretical results of the model have been compared to the experimental data given in the literature. A good agreement was then noticed between the experimental data and the numerical results.
Jacquemet, Vincent
2010-09-01
Microscale electrical propagation in the heart can be modeled by a reaction-diffusion system, describing cell and tissue electrophysiology. Macroscale features of wavefront propagation can be reproduced by an eikonal model, a reduced formulation involving only wavefront shape. In this paper, these two approaches are combined to incorporate global information about reentrant pathways into a reaction-diffusion model. The eikonal-diffusion formulation is generalized to handle reentrant activation patterns and wavefront collisions. Boundary conditions are used to specify pathways of reentry. Finite-element-based numerical methods are presented to solve this nonlinear equation on a coarse triangular mesh. The macroscale eikonal model serves to construct an initial condition for the microscale reaction-diffusion model. Electrical propagation simulated from this initial condition is then compared to the isochrones predicted by the eikonal model. Results in 2-D and thin 3-D test-case geometries demonstrate the ability of this technique to initiate anatomical and functional reentries along prescribed pathways, thus facilitating the development of dedicated models aimed at better understanding clinical case reports.
Coupled nonlinear-diffusion color image sharpening based on the chromaticity-brightness model
Saito, Takahiro; Nosaka, Reina; Komatsu, Takashi
2006-01-01
Previously we have presented a selective image sharpening method based on the coupled nonlinear diffusion process composed of a nonlinear diffusion term, a fidelity term and an isotropic peaking term, and it can sharpen only blurred edges without increasing the noise visibility. Our previously presented prototypal color-image sharpening methods based on the coupled nonlinear-diffusion process have been formulated on the linear color models, namely, the channel-bychannel model and the 3D vectorial model. Our prototypal methods can sharpen blurred color step edges, but they do not necessarily enhance contrasts of signal variations in complex texture image regions so well as in simple step-edge regions. To remedy the drawback, this paper extends our coupled nonlinear-diffusion color-image sharpening method to the nonlinear non-flat color model, namely, the chromaticity-brightness model, which is known to be closely relating to human color perception. We modify our time-evolution PDE's for the non-flat space of the chromaticity vector and present its digital implementations. Through experimental simulations, we compare our new color-image sharpening method based on the chromaticity-brightness model with our prototypal color-image sharpening methods based on the linear color models.
Konukoglu, Ender; Clatz, Olivier; Menze, Bjoern H; Stieltjes, Bram; Weber, Marc-André; Mandonnet, Emmanuel; Delingette, Hervé; Ayache, Nicholas
2010-01-01
Reaction-diffusion based tumor growth models have been widely used in the literature for modeling the growth of brain gliomas. Lately, recent models have started integrating medical images in their formulation. Including different tissue types, geometry of the brain and the directions of white matter fiber tracts improved the spatial accuracy of reaction-diffusion models. The adaptation of the general model to the specific patient cases on the other hand has not been studied thoroughly yet. In this paper, we address this adaptation. We propose a parameter estimation method for reaction-diffusion tumor growth models using time series of medical images. This method estimates the patient specific parameters of the model using the images of the patient taken at successive time instances. The proposed method formulates the evolution of the tumor delineation visible in the images based on the reaction-diffusion dynamics; therefore, it remains consistent with the information available. We perform thorough analysis of the method using synthetic tumors and show important couplings between parameters of the reaction-diffusion model. We show that several parameters can be uniquely identified in the case of fixing one parameter, namely the proliferation rate of tumor cells. Moreover, regardless of the value the proliferation rate is fixed to, the speed of growth of the tumor can be estimated in terms of the model parameters with accuracy. We also show that using the model-based speed, we can simulate the evolution of the tumor for the specific patient case. Finally, we apply our method to two real cases and show promising preliminary results.
Modeling photovoltaic diffusion: an analysis of geospatial datasets
Davidson, Carolyn; Drury, Easan; Lopez, Anthony; Elmore, Ryan; Margolis, Robert
2014-07-01
This study combines address-level residential photovoltaic (PV) adoption trends in California with several types of geospatial information—population demographics, housing characteristics, foreclosure rates, solar irradiance, vehicle ownership preferences, and others—to identify which subsets of geospatial information are the best predictors of historical PV adoption. Number of rooms, heating source and house age were key variables that had not been previously explored in the literature, but are consistent with the expected profile of a PV adopter. The strong relationship provided by foreclosure indicators and mortgage status have less of an intuitive connection to PV adoption, but may be highly correlated with characteristics inherent in PV adopters. Next, we explore how these predictive factors and model performance varies between different Investor Owned Utility (IOU) regions in California, and at different spatial scales. Results suggest that models trained with small subsets of geospatial information (five to eight variables) may provide similar explanatory power as models using hundreds of geospatial variables. Further, the predictive performance of models generally decreases at higher resolution, i.e., below ZIP code level since several geospatial variables with coarse native resolution become less useful for representing high resolution variations in PV adoption trends. However, for California we find that model performance improves if parameters are trained at the regional IOU level rather than the state-wide level. We also find that models trained within one IOU region are generally representative for other IOU regions in CA, suggesting that a model trained with data from one state may be applicable in another state.
First-harmonic diffusion-based model applied to a polyvinyl-alcohol- acrylamide-based photopolymer
Neipp, Cristian; Gallego, Sergi; Ortun~O, Manuel; Márquez, Andrés; Alvarez, Mariela L.; Beléndez, Augusto; Pascual, Inmaculada
2003-10-01
The photopolymerization diffusion models give accurate comprehension of the mechanism of hologram formation inside photopolymer materials. Although several models have been proposed, these models share the common assumption that there is an interplay between the processes of monomer polymerization and monomer diffusion. Nevertheless, most of the studies to check the validity of the theoretical models have been done by using photopolymers of the DuPont™ type, or photopolymer materials with values of the monomer diffusion time similar to those of the DuPont material. We check the applicability of a modified diffusion-based model to a polyvinyl alcohol-acrylamide photopolymer. This material has the property of longer diffusion times for the monomer to travel from the unexposed to the exposed zones than in the case of other polymeric materials. Some interesting effects are observed and theoretically treated by using the modified first-harmonic diffusion-based model we propose.
Intelligent control of HVAC systems. Part I: Modeling and synthesis
Adrian TOADER
2013-03-01
Full Text Available This is the first part of a work on intelligent type control of Heating, Ventilating and Air-Conditioning (HVAC systems. The study is performed from the perspective of giving a unitary control method to ensure high energy efficiency and air quality improving. To illustrate the proposed HVAC control technique, in this first part it is considered as benchmark problem a single thermal space HVAC system. The construction of the mathematical model is performed only with a view to obtain a framework of HVAC intelligent control validation by numerical simulations. The latter will be reported in a second part of the study.
Sabeeha Hasnain
Full Text Available A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD, with hydrodynamic interactions (HI accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion are the main cause for anomalous diffusion, with a secondary contribution from HI.
A Jump-Diffusion Model with Stochastic Volatility and Durations
Wei, Wei; Pelletier, Denis
Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price...... jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate Ornstein-Ulenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps....... The algorithm provides smoothed estimates of the latent variables such as spot volatility, conditional duration, jump times, and jump sizes. We apply this model to IBM data and find that volatility and conditional duration are interdependent. We also find that jumps play an important role in return variation...
Density of capillaries and the oxygen diffusion model in the porous silk fibroin film
BAI Lun; XU Jianmei; SUN Qilong; DI Chuanxia; ZUO Baoqi; GUAN Guoping; WU Zhenyu
2007-01-01
In order to obtain porous silk fibroin films(PSFFs)fit for the repair of different tissues and organs and design the configuration of the PSFFs more rationally,a model of the oxygen diffusing system of the capillary was built,and also the equations of the model were solved.Moreover,the relationships between the distribution of the oxygen concentration and each affecting factors were discussed,a method was developed to estimate the density of the capillaries in the tissue,and hereby discussed the characteristics of the oxygen diffusion in the tissues around the open capillaries.
Fitting the CDO correlation skew: a tractable structural jump-diffusion model
Willemann, Søren
2007-01-01
We extend a well-known structural jump-diffusion model for credit risk to handle both correlations through diffusion of asset values and common jumps in asset value. Through a simplifying assumption on the default timing and efficient numerical techniques, we develop a semi-analytic framework...... allowing for instantaneous calibration to heterogeneous CDS curves and fast computation of CDO tranche spreads. We calibrate the model to CDX and iTraxx data from February 2007 and achieve a satisfactory fit. To price the senior tranches for both indices, we require a risk-neutral probability of a market...
Inhomogeneous diffusion model for recent data on high-energy cosmic rays
Tomassetti, Nicola
2015-01-01
The AMS Collaboration has recently released precision data on cosmic ray (CR) leptons and protons at high energies. Interesting progresses have also been made on the measurement of CR nuclei, such as the boron-to-carbon ratio or the lithium spectrum, up to TeV/nucleon energies. In order to provide a description these data, I consider a diffusion model of CR propagation which allows for latitudinal variations of the CR diffusion properties in the Galactic halo. I discuss the role of high-precision data on light CR nuclei in resolutely testing this model and the key propagation parameters.
Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion.
Ramirez, J C; Beckermann, C; Karma, A; Diepers, H-J
2004-05-01
A phase-field model is developed for simulating quantitatively microstructural pattern formation in solidification of dilute binary alloys with coupled heat and solute diffusion. The model reduces to the sharp-interface equations in a computationally tractable thin-interface limit where (i). the width of the diffuse interface is about one order of magnitude smaller than the radius of curvature of the interface but much larger than the real microscopic width of a solid-liquid interface, and (ii). kinetic effects are negligible. A recently derived antitrapping current [Phys. Rev. Lett. 87, 115701 (2001)
Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric
2003-03-01
We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.
Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
Li, Shanbing; Wu, Jianhua; Dong, Yaying
2015-09-01
In this paper, we consider a reaction-diffusion model with Degn-Harrison reaction scheme. Some fundamental analytic properties of nonconstant positive solutions are first investigated. We next study the stability of constant steady-state solution to both ODE and PDE models. Our result also indicates that if either the size of the reactor or the effective diffusion rate is large enough, then the system does not admit nonconstant positive solutions. Finally, we establish the global structure of steady-state bifurcations from simple eigenvalues by bifurcation theory and the local structure of the steady-state bifurcations from double eigenvalues by the techniques of space decomposition and implicit function theorem.
Modeling of Diffusive Convective and Electromechanical Processes in PEM fuel cells
Bang, Mads
and chemical species. Since analytical solutions to these three dimensional convections diffusion problems can rarely be obtained, the CFX code makes use of a finite volume discretization and numerical techniques, in order to obtain a solution. The model developed solves the convective and diffusive transport...... the fuel cells polarization curve and efficiency under operation. It is shown that the conductivity and the effective porosity of the catalyst layer, may strongly affect the performance of the fuel cell, and that it therefore should be considered when fuel cell models are made....
High-Resolution Numerical Model for Shallow Water Flows and Pollutant Diffusions
王嘉松; 何友声
2002-01-01
A finite-volume high-resolution numerical model for coupling the shallow water flows and pollutant diffusions was presented based on using a hybrid TVD scheme in space discretization and a Runge-Kutta method in time discretization. Numerical simulations for modelling dam- break, enlarging open channel flow and pollutant dispersion were implemented and compared with experimental data or other published computations. The validation of this method shows that it can not only deal with the problem involving discontinuities and unsteady flows, but also solve the general shallow water flows and pollutant diffusions.
Parameters estimation using the first passage times method in a jump-diffusion model
Khaldi, K.; Meddahi, S.
2016-06-01
The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic Jump-Diffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton Jump-Diffusion (MJD) model.
Continuous-time random-walk model for anomalous diffusion in expanding media
Le Vot, F.; Abad, E.; Yuste, S. B.
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Social Content Recommendation Based on Spatial-Temporal Aware Diffusion Modeling in Social Networks
Farman Ullah
2016-09-01
Full Text Available User interactions in online social networks (OSNs enable the spread of information and enhance the information dissemination process, but at the same time they exacerbate the information overload problem. In this paper, we propose a social content recommendation method based on spatial-temporal aware controlled information diffusion modeling in OSNs. Users interact more frequently when they are close to each other geographically, have similar behaviors, and fall into similar demographic categories. Considering these facts, we propose multicriteria-based social ties relationship and temporal-aware probabilistic information diffusion modeling for controlled information spread maximization in OSNs. The proposed social ties relationship modeling takes into account user spatial information, content trust, opinion similarity, and demographics. We suggest a ranking algorithm that considers the user ties strength with friends and friends-of-friends to rank users in OSNs and select highly influential injection nodes. These nodes are able to improve social content recommendations, minimize information diffusion time, and maximize information spread. Furthermore, the proposed temporal-aware probabilistic diffusion process categorizes the nodes and diffuses the recommended content to only those users who are highly influential and can enhance information dissemination. The experimental results show the effectiveness of the proposed scheme.
Yao, Yi; Berkowitz, Max L; Kanai, Yosuke
2015-12-28
The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na(+) and K(+) ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.
Diffusion of active particles with stochastic torques modeled as α-stable noise
Nötel, Jörg; Sokolov, Igor M.; Schimansky-Geier, Lutz
2017-01-01
We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a Lévy-stable noise. Two situations are investigated. First, we study white Lévy noise where the constant speed and the angular noise generate a persistent motion characterized by the persistence time {τ }D. At this time scale the crossover from ballistic to normal diffusive behavior is observed. The corresponding diffusion coefficient can be obtained analytically for the whole class of symmetric α-stable noises. As typical for models with noise-driven angular dynamics, the diffusion coefficient depends non-monotonously on the angular noise intensity. As second example, we study angular noise as described by an Ornstein–Uhlenbeck process with correlation time {τ }c driven by the Cauchy white noise. We discuss the asymptotic diffusive properties of this model and obtain the same analytical expression for the diffusion coefficient as in the first case which is thus independent on {τ }c. Remarkably, for {τ }c\\gt {τ }D the crossover from a non-Gaussian to a Gaussian distribution of displacements takes place at a time {τ }G which can be considerably larger than the persistence time {τ }D.
Automatic Modelling of Photograhed Parts in CATIA CAD Environment
Yunus Kayır
2014-04-01
Full Text Available In this study, a system was developed that can model parts in CATIA CAD program automatically by using photographic images obtained from the parts. The system, called ImageCAD, can use very kind of photography that was taken for prismatic and cylindrical parts. It can recognize geometric entities, such as lines, circles, arc and free curve, in the image by according to the selection of the user. ImageCAD can save generated knowledge of the entities in a suitable format for the CATIA program. ImageCAD, is controlled by using menus that were done in the CATIA interface, turn whatever you want photographs into 3B CAD models. The obtained CAD models have suitable structure that can be used for all CATIA application. Visual Basic programing language was preferred to design the system.
Hood, L. L.
1983-01-01
A modeling analysis is carried out of six experimental phase space density profiles for nearly equatorially mirroring protons using methods based on the approach of Thomsen et al. (1977). The form of the time-averaged radial diffusion coefficient D(L) that gives an optimal fit to the experimental profiles is determined under the assumption that simple satellite plus Ring E absorption of inwardly diffusing particles and steady-state radial diffusion are the dominant physical processes affecting the proton data in the L range that is modeled. An extension of the single-satellite model employed by Thomsen et al. to a model that includes multisatellite and ring absorption is described, and the procedures adopted for estimating characteristic satellite and ring absorption times are defined. The results obtained in applying three representative solid-body absorption models to evaluate D(L) in the range where L is between 4 and 16 are reported, and a study is made of the sensitivity of the preferred amplitude and L dependence for D(L) to the assumed model parameters. The inferred form of D(L) is then compared with that which would be predicted if various proposed physical mechanisms for driving magnetospheric radial diffusion are operative at Saturn.
J. Y. Tang
2014-01-01
Full Text Available Representation of gaseous diffusion in variably saturated near-surface soils is becoming more common in land biogeochemical models, yet the formulations and numerical solution algorithms applied vary widely. We present three different but equivalent formulations of the dual-phase (gaseous and aqueous tracer diffusion transport problem that is relevant to a wide class of volatile tracers in land biogeochemical models. Of these three formulations (i.e., the gas-primary, aqueous-primary, and bulk tracer based formulations, we contend the gas-primary formulation is the most convenient for modeling tracer dynamics in biogeochemical models. We then provide finite volume approximation to the gas-primary equation and evaluate its accuracy against three analytical models: one for steady-state soil CO2 dynamics, one for steady-state soil CO2 dynamics, and one for transient tracer diffusion from a constant point source into two different sequentially aligned medias. All evaluations demonstrated good accuracy of the numerical approximation. We expect our result will standardize an efficient mechanistic numerical method for solving relatively simple, multi-phase, one-dimensional diffusion problems in land models.
The Reactive-Diffusive Length of OH and Ozone in Model Organic Aerosols.
Lee, Lance; Wilson, Kevin
2016-09-01
A key step in the heterogeneous oxidation of atmospheric aerosols is the reaction of ozone (O3) and hydroxyl radicals (OH) at the gas-particle interface. The formation of reaction products and free radical intermediates and their spatial distribution inside the particle is a sensitive function of the length over which these oxidants diffuse prior to reaction. The reactive-diffusive length of OH and ozone at organic aerosol interfaces is determined by observing the change in the effective uptake coefficient for size-selected model aerosols comprising a reactive core and a thin nanometer-sized (0-12 nm) organic shell. The core and shell materials are selected so that they are immiscible and adopt an assumed core-shell configuration. The results indicate a reactive-diffusive length of 1.4 nm for hydroxyl (OH) radicals in squalane and 1.0 nm for ozone in squalene. Measurements for a purely diffusive system allow for an estimate for diffusion constant (1.6 × 10(-6) cm(2)/s) of ozone in squalane to be determined. The reactive-diffusive length offers a simple first order estimate of how shielding of aerosols by immiscible layers can alter estimates of oxidative lifetimes of aerosols in the atmosphere.
Maxwell's Law Based Models for Liquid and Gas Phase Diffusivities in Variably-Saturated Soil
Mamamoto, Shoichiro; Møldrup, Per; Kawamoto, Ken
2012-01-01
particles (clay and organic matter), FINESvol. The resulting LIquid and GAs diffusivity and tortuosity (LIGA) models were tested against D-s,D-g and D-s,D-l data for differently-textured soils and performed well against the measured data across soil types. A sensitivity analysis using the new Maxwell's Law......The gas diffusion coefficient (D-s,D-g) and solute diffusion coefficient (D-s,D-l) and their dependencies on fluid content (kappa) (equal to soil-air content theta for D-s,D-g and soil-water content epsilon for D-s,D-l) are controlling factors for gas and solute transport in variably saturated......-s,D-l). Different percolation threshold terms adopted from recent studies for gas (D-s,D-g) and solute (D-s,D-l) diffusion were applied. For gas diffusion, epsilon(th) was a function of bulk density (total porosity), while for solute diffusion theta(th) was best described by volumetric content of finer soil...
Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models
Isaacson, Samuel A.; Mauro, Ava J.; Newby, Jay
2016-10-01
The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013), 10.1103/PhysRevE.88.012820] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent.
An analytical model for estimating water exchange rate in white matter using diffusion MRI.
Davoodi-Bojd, Esmaeil; Chopp, Michael; Soltanian-Zadeh, Hamid; Wang, Shiyang; Ding, Guangliang; Jiang, Quan
2014-01-01
Substantial effort is being expended on using micro-structural modeling of the white matter, with the goal of relating diffusion weighted magnetic resonance imaging (DWMRI) to the underlying structure of the tissue, such as axonal density. However, one of the important parameters affecting diffusion is the water exchange rate between the intra- and extra-axonal space, which has not been fully investigated and is a crucial marker of brain injury such as multiple sclerosis (MS), stroke, and traumatic brain injury (TBI). To our knowledge, there is no diffusion analytical model which includes the Water eXchange Rate (WXR) without the requirement of short gradient pulse (SGP) approximation. We therefore propose a new analytical model by deriving the diffusion signal for a permeable cylinder, assuming a clinically feasible pulse gradient spin echo (PGSE) sequence. Simulations based on Markov Random Walk confirm that the exchange parameter included in our model has a linear correlation (R2>0.88) with the actual WXR. Moreover, increasing WXR causes the estimated values of diameter and volume fraction of the cylinders to increase and decrease, respectively, which is consistent with our findings from histology measurements in tissues near TBI regions. This model was also applied to the diffusion signal acquired from ex vivo brains of 14 male (10 TBI and 4 normal) rats using hybrid diffusion imaging. The estimated values of axon diameter and axonal volume fraction are in agreement with their corresponding histological measurements in normal brains, with 0.96 intra-class correlation coefficient value resulting from consistency analysis. Moreover, a significant increase (p = 0.001) in WXR and diameter and decrease in axonal volume fraction in the TBI boundary were detected in the TBI rats compared with the normal rats.
STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies
Hepburn Iain
2012-05-01
Full Text Available Abstract Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins, conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates
Fluid particle diffusion in a semidilute suspension of model micro-organisms.
Ishikawa, Takuji; Locsei, J T; Pedley, T J
2010-08-01
We calculate non-Brownian fluid particle diffusion in a semidilute suspension of swimming micro-organisms. Each micro-organism is modeled as a spherical squirmer, and their motions in an infinite suspension otherwise at rest are computed by the Stokesian-dynamics method. In calculating the fluid particle motions, we propose a numerical method based on a combination of the boundary element technique and Stokesian dynamics. We present details of the numerical method and examine its accuracy. The limitation of semidiluteness is required to ensure accuracy of the fluid particle velocity calculation. In the case of a suspension of non-bottom-heavy squirmers the spreading of fluid particles becomes diffusive in a shorter time than that of the squirmers, and the diffusivity of fluid particles is smaller than that of squirmers. It is confirmed that the probability density distribution of fluid particles also shows diffusive properties. The effect of tracer particle size is investigated by inserting some inert spheres of the same radius as the squirmers, instead of fluid particles, into the suspension. The diffusivity for inert spheres is not less than one tenth of that for fluid particles, even though the particle size is totally different. Scaling analysis indicates that the diffusivity of fluid particles and inert spheres becomes proportional to the volume fraction of squirmers in the semidilute regime provided that there is no more than a small recirculation region around a squirmer, which is confirmed numerically. In the case of a suspension of bottom-heavy squirmers, horizontal diffusivity decreases considerably even with small values of the bottom heaviness, which indicates the importance of bottom heaviness in the diffusion phenomena. We believe that these fundamental findings will enhance our understanding of the basic mechanics of a suspension of swimming micro-organisms.
A fractional diffusion equation model for cancer tumor
Iyiola, Olaniyi Samuel; Zaman, F. D.
2014-10-01
In this article, we consider cancer tumor models and investigate the need for fractional order derivative as compared to the classical first order derivative in time. Three different cases of the net killing rate are taken into account including the case where net killing rate of the cancer cells is dependent on the concentration of the cells. At first, we use a relatively new analytical technique called q-Homotopy Analysis Method on the resulting time-fractional partial differential equations to obtain analytical solution in form of convergent series with easily computable components. Our numerical analysis enables us to give some recommendations on the appropriate order (fractional) of derivative in time to be used in modeling cancer tumor.
Minimal model for short-time diffusion in periodic potentials.
Emary, Clive; Gernert, Robert; Klapp, Sabine H L
2012-12-01
We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the density field, that is, average position and the mean-squared displacement, show nontrivial (nondiffusive) short-time behavior characterized by the appearance of plateaus. We demonstrate that this "cage-like" dynamics can be well described by a discretized master equation model involving two states (related to two positions) within each potential valley. Nontrivial predictions of our approach include analytic expressions for the plateau heights and an estimate of the "de-caging time" obtained from the study of deviations from Gaussian behavior. The simplicity of our approach means that it offers a minimal model to describe the short-time behavior of systems with hindered dynamics.
Rule-based spatial modeling with diffusing, geometrically constrained molecules
Lohel Maiko; Lenser Thorsten; Ibrahim Bashar; Gruenert Gerd; Hinze Thomas; Dittrich Peter
2010-01-01
Abstract Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction net...
Garrido-Baserba, Manel; Sobhani, Reza; Asvapathanagul, Pitiporn; McCarthy, Graham W; Olson, Betty H; Odize, Victory; Al-Omari, Ahmed; Murthy, Sudhir; Nifong, Andrea; Godwin, Johnnie; Bott, Charles B; Stenstrom, Michael K; Shaw, Andrew R; Rosso, Diego
2017-03-15
This research systematically studied the behavior of aeration diffuser efficiency over time, and its relation to the energy usage per diffuser. Twelve diffusers were selected for a one year fouling study. Comprehensive aeration efficiency projections were carried out in two WRRFs with different influent rates, and the influence of operating conditions on aeration diffusers' performance was demonstrated. This study showed that the initial energy use, during the first year of operation, of those aeration diffusers located in high rate systems (with solids retention time - SRT-less than 2 days) increased more than 20% in comparison to the conventional systems (2 > SRT). Diffusers operating for three years in conventional systems presented the same fouling characteristics as those deployed in high rate processes for less than 15 months. A new procedure was developed to accurately project energy consumption on aeration diffusers; including the impacts of operation conditions, such SRT and organic loading rate, on specific aeration diffusers materials (i.e. silicone, polyurethane, EPDM, ceramic). Furthermore, it considers the microbial colonization dynamics, which successfully correlated with the increase of energy consumption (r(2):0.82 ± 7). The presented energy model projected the energy costs and the potential savings for the diffusers after three years in operation in different operating conditions. Whereas the most efficient diffusers provided potential costs spanning from 4900 USD/Month for a small plant (20 MGD, or 74,500 m(3)/d) up to 24,500 USD/Month for a large plant (100 MGD, or 375,000 m(3)/d), other diffusers presenting less efficiency provided spans from 18,000USD/Month for a small plant to 90,000 USD/Month for large plants. The aim of this methodology is to help utilities gain more insight into process mechanisms and design better energy efficiency strategies at existing facilities to reduce energy consumption. Copyright © 2016 Elsevier Ltd. All
The Illumination Model of the Valley Based on the Diffuse Reflect of Forest
He Guoliang
2016-01-01
Full Text Available In this paper, models are build to evaluate the impact of the forest on the valley’s illumination. Based on the assumes that all the light reach the ground comes from the diffuse reflection which comes from the sun directly and from the diffuse reflection of other points, One model is build to consider the impact of time and latitude on the direction of the sunlight. So we can get the direction of the sunlight at different time and latitude through the model. Besides, this paper develops a illumination model to evaluate the intensity of illumination of the ground. Combining the models above, this paper get a complete model which can not only evaluate the overall light intensity of the valley but also convert the light intensity to the intensity of illumination. Simulation of the intensity illumination of some basic terrains and finally gives a comprehensive results which is practical and close to the common sense.
Hui-Chih Hung
2017-01-01
Full Text Available We attempt to develop an effective forecasting model for the diffusion and substitution of multigeneration Dynamic Random Access Memory (DRAM processing technologies. We consider market share data and propose a modified Lotka–Volterra model, in which an additional constraint on the summation of market share is introduced. The mean absolute error is used to measure the accuracy of our market share predictions. Market share data in DRAM industries from quarter one (Q1 of 2005 to 2013 Q4 is collected to validate the prediction accuracy. Our model significantly outperforms other benchmark forecasting models of both revenue and market share data, including the Bass and Lotka–Volterra models. Compared to prior studies on forecasting the diffusion and substitution of multigeneration technologies, our model has two new perspectives: (1 allowing undetermined number of multigeneration technologies and inconsecutive adoption of new technologies and (2 requiring less data for forecasting newborn technologies.
The Buffer and Backfill Handbook. Part 3: Models for calculation of processes and behaviour
Pusch, Roland [Geodevelopment AB, Lund (Sweden)
2003-01-15
The present document collects conceptual and mathematical models that have been proposed for describing the performance of buffers and backfills and processes in them that are related to their function under repository conditions. As in the preceding parts the following types of sealing components are defined. By definition, the buffer shall be so composed that radionuclide transport in the clay-based barriers takes place by diffusion and not by water flow, which makes it important to predict the extent and rate of diffusive transport of such elements through the buffer. It depends strongly on the density and homogeneity of the buffer, which in turn depend on the maturation rate and the ultimate degree of homogeneity of the buffer. They are influenced by the temperature and temperature gradient that exist in the initial phase of water saturation, in which the hydraulic interaction with the near field rock is also important. Design of suitable buffer and backfills hence requires that their performance can be quantified, which requires that the various processes can be modeled conceptually and expressed in mathematical form. Based on the present knowledge this can only be made for some of the involved mechanisms and for coupled processes there is still a very limited number of mathematically expressed computational codes. The models referred to here are conceptual in the first place, defining the respective processes and material property parameters. The quick development of computational tools, numerical as well as analytical, makes it irrelevant to give detailed descriptions of them, while the various assumptions on which they are based - especially the conceptual models - have been considered in some detail. The models of practical use are only described in general terms and examples at the end of the respective chapter illustrate how they can be utilized. A very important fact is that transport and rheological processes in a repository are hardly ever of simple
A Model of Sequence Dependent Rna-Polymerase Diffusion Along Dna
Barbi, M; Popkov, V; Salerno, M; Barbi, Maria; Place, Christophe; Popkov, Vladislav; Salerno, Mario
2001-01-01
We introduce a probabilistic model for the RNA-polymerase sliding motion along DNA during the promoter search. The model accounts for possible effects due to sequence-dependent interactions between the nonspecific DNA and the enzyme. We focus on T7 RNA-polymerase and exploit the available information about its interaction at the promoter site in order to investigate the influence of bacteriophage T7 DNA sequence on the dynamics of the sliding process. Hydrogen bonds in the major groove are used as the main sequence-dependent interaction between the RNA-polymerase and the DNA. The resulting dynamical properties and the possibility of an experimental validation are discussed in details. We show that, while at large times the process reaches a pure diffusive regime, it initially displays a sub-diffusive behavior. The crossover from anomalous to normal diffusion may occur at times large enough to be of biological interest.
DePalma, Glen; Turnidge, John; Craig, Bruce A
2017-02-01
The determination of diffusion test breakpoints has become a challenging issue due to the increasing resistance of microorganisms to antibiotics. Currently, the most commonly-used method for determining these breakpoints is the modified error-rate bounded method. Its use has remained widespread despite the introduction of several model-based methods that have been shown superior in terms of precision and accuracy. However, the computational complexities associated with these new approaches has been a significant barrier for clinicians. To remedy this, we developed and examine the utility of a free online software package designed for the determination of diffusion test breakpoints: dBETS (diffusion Breakpoint Estimation Testing Software). This software package allows clinicians to easily analyze data from susceptibility experiments through visualization, error-rate bounded, and model-based approaches. We analyze four publicly available data sets from the Clinical and Laboratory Standards Institute using dBETS.
MODELING OF SUPERCRITICAL FLUID EXTRACTION KINETIC OF FLAXSEED OIL BY DIFFUSION CONTROL METHOD
Emir Zafer HOŞGÜN
2013-06-01
Full Text Available In this study, Flaxseed oil was extracted by Supercritical Carbondioxide Extraction, and extractionkinetics was modelled using diffusion controlled method.The effect of process parameters, such as pressure (20, 35, 55 MPa, temperature (323 and 343 K, and CO2 flow rate (1 and 3 L CO2 /min on the extraction yield and effective diffusivity (De was investigated. The effective diffusion coefficient varied between 2.4 x10-12 and 10.8 x10-12 m2s-1 for the entire range of experiments and increased with the pressure and flow rate. The model fitted well theexperimental data (ADD varied between 2.35 and 7.48%.
A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model
L. Päivärinta
2011-12-01
Full Text Available In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM. Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT is applied to enlarge the convergence region and rate of solution series given by the HAM.
Muñoz-Jaramillo, Andrés; Martens, Petrus C H
2010-01-01
The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main featur...
Spatially explicit control of invasive species using a reaction-diffusion model
Bonneau, Mathieu; Johnson, Fred A.; Romagosa, Christina M.
2016-01-01
Invasive species, which can be responsible for severe economic and environmental damages, must often be managed over a wide area with limited resources, and the optimal allocation of effort in space and time can be challenging. If the spatial range of the invasive species is large, control actions might be applied only on some parcels of land, for example because of property type, accessibility, or limited human resources. Selecting the locations for control is critical and can significantly impact management efficiency. To help make decisions concerning the spatial allocation of control actions, we propose a simulation based approach, where the spatial distribution of the invader is approximated by a reaction–diffusion model. We extend the classic Fisher equation to incorporate the effect of control both in the diffusion and local growth of the invader. The modified reaction–diffusion model that we propose accounts for the effect of control, not only on the controlled locations, but on neighboring locations, which are based on the theoretical speed of the invasion front. Based on simulated examples, we show the superiority of our model compared to the state-of-the-art approach. We illustrate the use of this model for the management of Burmese pythons in the Everglades (Florida, USA). Thanks to the generality of the modified reaction–diffusion model, this framework is potentially suitable for a wide class of management problems and provides a tool for managers to predict the effects of different management strategies.
Turbulence modelling of the aerodynamic interaction ofOGV wakes and diffuser flow
LI Jing-hua; Page Gary; McGuirk Jim
2011-01-01
Different turbulence closures were used to predict the flow interaction between the wakes created by compressor outlet guide vanes（OGVs） and a downstream annular pre-diffuser.Two statistical turbulence models were tested based on the classical Reynolds-averaged Navier-Stokes（RANS） approach.Both high-Re and low-Re（Launder-Sharma） versions of the k-ε model were applied to a selected test problem for OGV wake/diffuser flows.The test problem was specifically chosen because experimentally determined inlet conditions and both profile and performance data were available to validate predictions.A preliminary study was also reported of the more advanced large eddy simulation（LES） approach.The LES sub-grid-scale（SGS） model was the basic Smagorinsky eddy viscosity assumption,with a Van-Driest damping function for improved capture of near-wall viscous behaviour.Comparison between the two RANS models showed little difference in terms of velocity contours at OGV trailing edge and diffuser exit.In terms of overall diffuser performance（static pressure recovery and total pressure loss coefficients）,the high-Re model was shown to agree well with experimental data.The preliminary LES study indicates the highly unsteady character of the OGV wake flow,but requires improved treatment of inlet conditions.
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
Baudron, Anne-Marie A -M; Maday, Yvon; Riahi, Mohamed Kamel; Salomon, Julien
2014-01-01
We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for the space discretization, our implementation provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner (LMW) benchmark [1].
2012-01-01
Diffuse alopecia is mainly caused by telogen effluvium, diffuse androgenetic alopecia (femalepattern hair loss) and diffuse alopecia areata. Differential diagnosis between the three disorders may be difficult in several occasions. In this second part of our study, chronic telogen effluvium and diffuse alopecia areata are discussed in detail, including clinical, dermoscopic and histological aspects. A flowchart presents a practical and objective differential diagnostic approach to diffuse alop...
Approximation of epidemic models by diffusion processes and their statistical inference.
Guy, Romain; Larédo, Catherine; Vergu, Elisabeta
2015-02-01
Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an
Tsuchikawa, Satoru; Siesler, H W
2003-06-01
Fourier transform near-infrared (FT-NIR) transmission spectroscopy was applied to monitor the diffusion process of deuterium-labeled molecules in hardwood (Beech). The results are compared with previous data obtained on softwood (Sitka spruce) in order to consistently understand the state of order in cellulose of wood. The saturation accessibility and diffusion rate varied characteristically with the OH groups in different states of order in the wood substance, the diffusants, and the wood species, respectively. The variation of saturation accessibility should be associated with the fundamental difference of the fine structure such as the microfibrils in the wood substance. The effect of the anatomical cellular structure on the accessibility was reflected in the variation of the diffusion rate with the wood species. The size effect of the diffusants also played an important role for the diffusion process in wood. Since the volumetric percentage of wood fibers and wood rays is relatively similar, the dichroic effects due to the anisotropy of the cellulose chains were apparently diminished. Finally, we proposed a new interpretation of the fine structure of the microfibrils in the cell wall by comparing a series of results from hardwood and softwood. Each elementary fibril in the hardwood has a more homogeneous arrangement in the microfibrils compared to that in the softwood.