Predictability of extreme events in a branching diffusion model
Gabrielov, Andrei; Olsen, Sayaka; Zaliapin, Ilya
2010-01-01
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with immigration. New elements -- observation space and observed events -- are introduced in order to formulate a prediction problem patterned after the geophysical and environmental applications. The problem consists of estimating the likelihood of occurrence of an extreme event given the observations of smaller events while the complete internal dynamics of the system is unknown. We look for premonitory patterns that emerge as an extreme event approaches; those patterns are deviations from the long-term system's averages. We have found a single control parameter that governs multiple spatio-temporal premonitory patterns. For that purpose, we derive i) complete analytic description of time- and space-dependent size distribution of particles generated by a single immigrant; ii) the...
Energy Technology Data Exchange (ETDEWEB)
Shukrinov, Yu.M. [BLTP, JINR, Dubna, Moscow Region, 141980 (Russian Federation) and Physical Technical Institute, Dushanbe 734063 (Tajikistan)]. E-mail: shukrinv@theor.jinr.ru; Mahfouzi, F. [Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Seidel, P. [Institut fuer Festkorperphysik, Friedrich-Schiller-Universitaet Jena, D-07743 Jena (Germany)
2006-11-01
Branch structure in current-voltage characteristics of intrinsic Josephson junctions of HTSC is studied in the framework of two models: capacitively coupled Josephson junctions (CCJJ) model and CCJJ model with diffusion current (CCJJ + DC). We investigate the coupling dependence of the branch's slopes and demonstrate that the equidistance of the branch structure in CCJJ model is broken at enough small values of coupling parameter (at {alpha} << 1). We show that the inclusion of diffusion in the tunneling current through intrinsic Josephson junctions might restore the equidistance of the branch structure. Change of the current-voltage characteristics in CCJJ + DC model under variation of the coupling and McCumber parameters and effect of boundary conditions on the branch structure is analyzed.
Shukrinov, Yu. M.; Mahfouzi, F.; Seidel, P.
2006-11-01
Branch structure in current-voltage characteristics of intrinsic Josephson junctions of HTSC is studied in the framework of two models: capacitively coupled Josephson junctions (CCJJ) model and CCJJ model with diffusion current (CCJJ + DC). We investigate the coupling dependence of the branch’s slopes and demonstrate that the equidistance of the branch structure in CCJJ model is broken at enough small values of coupling parameter (at α ≪ 1). We show that the inclusion of diffusion in the tunneling current through intrinsic Josephson junctions might restore the equidistance of the branch structure. Change of the current-voltage characteristics in CCJJ + DC model under variation of the coupling and McCumber parameters and effect of boundary conditions on the branch structure is analyzed.
Parra-Robles, Juan; Wild, Jim M
2014-02-01
Our extensive investigation of the cylinder model theory through numerical modelling and purpose-designed experiments has demonstrated that it does produce inaccurate estimates of airway dimensions at all diffusion times currently used. This is due to a variety of effects: incomplete treatment of non-Gaussian effects, finite airway size, branching geometry, background susceptibility gradients and diffusion time dependence of the (3)He MR diffusion behaviour in acinar airways. The cylinder model is a good starting point for the development of a lung morphometry technique from (3)He diffusion MR but its limitations need to be understood and documented in the interest of reliable clinical interpretation. PMID:24342570
Energy Technology Data Exchange (ETDEWEB)
Shukrinov, Yu.M. [Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation); Physical Technical Institute, Dushanbe 734063 (Tajikistan)], E-mail: shukrinv@theor.jinr.ru; Mahfouzi, F. [Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Seidel, P. [Institut fuer Festkorperphysik, Friedrich-Schiller-Universitaet Jena, D-07743 Jena (Germany)
2007-09-01
We have solved numerically a system of dynamical equations for the gauge-invariant phase differences between superconducting layers for a stack of N intrinsic junctions and obtained a total branch structure in the current-voltage characteristics (IVC) of the stack. The coupling dependence of the branch's slopes is investigated and demonstrated that the equidistance of the branch structure in capacitively coupled Josephson junctions (CCJJ) model is broken at small values of coupling parameter. Changes in the parameters of the boundary conditions and the use of periodic boundary conditions do not affect this result. In the framework of the CCJJ model with the diffusion current we simulate an experiment and obtain the IV-characteristic with equidistant branch structure at different values of model parameters.
Shukrinov, Yu. M.; Mahfouzi, F.; Seidel, P.
2007-09-01
We have solved numerically a system of dynamical equations for the gauge-invariant phase differences between superconducting layers for a stack of N intrinsic junctions and obtained a total branch structure in the current-voltage characteristics (IVC) of the stack. The coupling dependence of the branch’s slopes is investigated and demonstrated that the equidistance of the branch structure in capacitively coupled Josephson junctions (CCJJ) model is broken at small values of coupling parameter. Changes in the parameters of the boundary conditions and the use of periodic boundary conditions do not affect this result. In the framework of the CCJJ model with the diffusion current we simulate an experiment and obtain the IV-characteristic with equidistant branch structure at different values of model parameters.
Branching diffusions in random environment
Böinghoff, Christian
2011-01-01
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival probability. As in the case of BPREs, there is a phase transition in the subcritical regime due to different survival opportunities. In addition, we characterize the process conditioned to never go extinct and establish a backbone construction. In the strongly subcritical regime, mean offspring numbers are increased but still subcritical in the process conditioned to never go extinct. Here survival is solely due to an immortal individual, whose offspring are the ancestors of additional families. In the weakly subcritical regime, the mean offspring number is supercritical in the process conditioned to never go extinct. Thus this process survives with positive probability even if there was no immortal individual.
Supercritical branching diffusions in random environment
Hutzenthaler, Martin
2011-01-01
Supercritical branching processes in constant environment conditioned on eventual extinction are known to be subcritical branching processes. The case of random environment is more subtle. A supercritical branching diffusion in random environment (BDRE) conditioned on eventual extinction of the population is not a BDRE. However the quenched law of the population size of a supercritical BDRE conditioned on eventual extinction is equal to the quenched law of the population size of a subcritical BDRE. As a consequence, supercritical BDREs have a phase transition which is similar to a well-known phase transition of subcritical branching processes in random environment.
Residence times of branching diffusion processes
Dumonteil, E.; Mazzolo, A.
2016-07-01
The residence time of a branching Brownian process is the amount of time that the mother particle and all its descendants spend inside a domain. Using the Feynman-Kac formalism, we derive the residence-time equation as well as the equations for its moments for a branching diffusion process with an arbitrary number of descendants. This general approach is illustrated with simple examples in free space and in confined geometries where explicit formulas for the moments are obtained within the long time limit. In particular, we study in detail the influence of the branching mechanism on those moments. The present approach can also be applied to investigate other additive functionals of branching Brownian process.
The branching structure of diffusion-limited aggregates
Halsey, T C
1997-01-01
I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the numerically obtained result of B ~ 5.2. In high dimensions, B -> 3.12; the bifurcation ratio is thus a decreasing function of dimensionality. This analysis also determines the scaling properties of the ramification matrix, which describes the hierarchy of branches.
Jochem B. Evers; Vos, Jan
2013-01-01
Cereals and grasses adapt their structural development to environmental conditions and the resources available. The primary adaptive response is a variable degree of branching, called tillering in cereals. Especially for heterogeneous plant configurations the degree of tillering varies per plant. Functional–structural plant modeling (FSPM) is a modeling approach allowing simulation of the architectural development of individual plants, culminating in the emergent behavior at the canopy level....
Some distance bounds of branching processes and their diffusion limits
Kammerer, Niels B
2010-01-01
We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitrary type of criticality). Implications for asymptotic distinguishability behaviour in terms of contiguity and entire separation of the involved GWI are given, too. Furthermore, we determine the corresponding limit quantities for the context in which the two GWI converge to Feller-type branching diffusion processes, as the time-lags between observations tend to zero. Some applications to (static random environment like) Bayesian decision making and Neyman-Pearson testing are presented as well.
Infinite-Scale Percolation in a New Type of Branching Diffusion Processes
Mezhlumian, A.; Molchanov, S. A.
1992-01-01
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes with diffusion on the space of parameters distinguishing the branching `particles' each other.
Measuring neuronal branching patterns using model-based approach.
Luczak, Artur
2010-01-01
Neurons have complex branching systems which allow them to communicate with thousands of other neurons. Thus understanding neuronal geometry is clearly important for determining connectivity within the network and how this shapes neuronal function. One of the difficulties in uncovering relationships between neuronal shape and its function is the problem of quantifying complex neuronal geometry. Even by using multiple measures such as: dendritic length, distribution of segments, direction of branches, etc, a description of three dimensional neuronal embedding remains incomplete. To help alleviate this problem, here we propose a new measure, a shape diffusiveness index (SDI), to quantify spatial relations between branches at the local and global scale. It was shown that growth of neuronal trees can be modeled by using diffusion limited aggregation (DLA) process. By measuring "how easy" it is to reproduce the analyzed shape by using the DLA algorithm it can be measured how "diffusive" is that shape. Intuitively, "diffusiveness" measures how tree-like is a given shape. For example shapes like an oak tree will have high values of SDI. This measure is capturing an important feature of dendritic tree geometry, which is difficult to assess with other measures. This approach also presents a paradigm shift from well-defined deterministic measures to model-based measures, which estimate how well a model with specific properties can account for features of analyzed shape. PMID:21079752
Branching process models of cancer
Durrett, Richard
2015-01-01
This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As a consequence, the authors calculate the probability that mutations that confer resistance to treatment are present at detection and quantify the extent of tumor heterogeneity. As applications, the authors evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis. These notes should be accessible to students who are familiar with Poisson processes and continuous time. Richard Durrett is mathematics professor at Duke University, USA. He is the author of 8 books, over 200 journal articles, and has supervised more than 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.
Parton Branching in Color Mutation Model
Hwa, R C
1999-01-01
The soft production problem in hadronic collisions as described in the eikonal color mutation branching model is improved in the way that the initial parton distribution is treated. Furry branching of the partons is considered as a means of describing the nonperturbative process of parton reproduction in soft interaction. The values of all the moments, and $C_q$, for q=2,...,5, as well as their energy dependences can be correctly determined by the use of only two parameters.
Wilkinson, P; Dimbylow, P J
1985-10-01
A mathematical model has been developed that examines the ingress of radon into houses, through a vertical crack in an otherwise impervious concrete floor. Initially, the model considered the diffusive flow of radon from its soil source and this simulation has highlighted the dependency of the flux of radon into the house on the magnitude of various parameters, such as the diffusion coefficient of radon in soil. A preliminary investigation of the modelling of pressure-driven flow into a building is presented, and the potential of this type of analysis is discussed. PMID:4081719
Measuring neuronal branching patterns using model-based approach
Directory of Open Access Journals (Sweden)
Artur Luczak
2010-10-01
Full Text Available Neurons have complex branching systems which allow them to communicate with thousands of other neurons. Thus understanding neuronal geometry is clearly important for determining connectivity within the network and how this shapes neuronal function. One of the difficulties in uncovering relationships between neuronal shape and its function is the problem of quantifying complex neuronal geometry. Even by using multiple measures such as: dendritic length, topology, distribution of segments, direction of branches, etc, a description of three dimensional neuronal embedding remains incomplete. To help alleviate this problem, here we propose a new measure, a shape diffusiveness index (SDI, to quantify spatial relations between branches at the local and global scale. It was shown that growth of neuronal trees can be modeled by using Diffusion Limited Aggregation (DLA process. By measuring ‘how easy’ it is to reproduce the analyzed shape by using the DLA algorithm it can be measured how ‘diffusive’ is that shape. Intuitively, ‘diffusiveness’ measures how tree-like is a given shape. For example shapes like an oak tree will have high values of SDI. This measure is capturing an important feature of dendritic tree geometry, which is difficult to assess with other measures. This approach also presents a paradigm shift from well-defined deterministic measures to model-based measures, which estimate how well a model with specific properties can account for features of analyzed shape.
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.
Simple statistical model for branched aggregates
DEFF Research Database (Denmark)
Lemarchand, Claire; Hansen, Jesper Schmidt
2015-01-01
We propose a statistical model that can reproduce the size distribution of any branched aggregate, including amylopectin, dendrimers, molecular clusters of monoalcohols, and asphaltene nanoaggregates. It is based on the conditional probability for one molecule to form a new bond with a molecule......, given that it already has bonds with others. The model is applied here to asphaltene nanoaggregates observed in molecular dynamics simulations of Cooee bitumen. The variation with temperature of the probabilities deduced from this model is discussed in terms of statistical mechanics arguments....... The relevance of the statistical model in the case of asphaltene nanoaggregates is checked by comparing the predicted value of the probability for one molecule to have exactly i bonds with the same probability directly measured in the molecular dynamics simulations. The agreement is satisfactory...
Branching process in a stochastic extremal model
Manna, S. S.
2009-08-01
We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the number M of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion. The critical behavior of the SBSM is found to be the same as the BS model in dimensions d=1 and 2. However on the scale-free graphs the critical fitness value is nonzero even in the thermodynamic limit but the critical behavior is mean-field like. Finally ⟨M⟩ has been made even smaller than two by probabilistically updating the mutation zone, which also shows the original BS model behavior. We conjecture that a SBSM on any arbitrary graph with any small branching factor greater than unity will lead to a self-organized critical state.
Dawson, Donald A
2010-01-01
We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of supercritical branching random walks with an additional deathrate which is quadratic in the local number of particles. The former describes a standard two-type population under selection, mutation, the latter models describe a population under scarce resources causing additional death at high local population intensity. Geographic space is modelled by $\\{1, \\cdots, N\\}$. The first process starts in an initial state with only the inferior type present or an exchangeable configuration and the second one with a single initial particle. {This material is a special case of the theory developed in \\cite{DGsel}.} We study the behaviour in two time windows, first between time 0 and $T$ and secondly after a large time when in the Fisher-Wright model the rare mutants succeed respectivel...
3D modelling of branching in plants
Evers, J.B.
2011-01-01
Shoot branching is a key determinant of overall aboveground plant form. During plant development, the number of branches formed strongly influences the amount of light absorbed by the plant, and thus the plant’s competitive strength in terms of light capture in relation to neighbouring plants. Branching is regulated by multiple internal factors which are modulated by different environmental signals. A key environmental signal in the context of a plant population is a low red / far-red intensi...
Econometric Advances in Diffusion Models
Peers, Yuri
2011-01-01
textabstractThis thesis gives new and important insights in modeling diffusion data in marketing. It addresses modeling multiple series instead of just one series such that one can learn from the differences and similarities across products and countries. Additionally, this thesis addresses the current availability of higher frequency diffusion data. The two issues provide challenges for modeling of diffusion processes. In this thesis we provide solutions to these challenges, and we also sugg...
Moehler, S.; Dreizler, S.; LeBlanc, F.; Khalack, V.; Michaud, G.; Richer, J.; Sweigart, Allen V.; Grundahl, F.
2014-01-01
Context. NGC288 is a globular cluster with a well developed blue horizontal branch covering the so-called u-jump which indicates the onset of diffusion. It is therefore well suited to study the effects of diffusion in blue horizontal branch (HB) stars. Aims. We compare observed abundances to predictions from stellar evolution models calculated with diffusion and from stratified atmospheric models. We verify the effect of using stratified model spectra to derive atmospheric parameters. In addition we investigate the nature of the overluminous blue HB stars around the u-jump. Methods. We define a new photometric index sz from uvby measurements that is gravity sensitive between 8 000K and 12 000 K. Using medium-resolution spectra and Stroemgren photometry we determine atmospheric parameters (Teff, logg) and abundances for the blue HB stars. We use both homogeneous and stratified model spectra for our spectroscopic analyses. Results. The atmospheric parameters and masses of the hot HB stars in NGC288 show a behaviour seen also in other clusters for temperatures between 9 000K and 14 000 K. Outside this temperature range, however, they follow rather the results found for such stars in (omega)Cen. The abundances derived from our observations are for most elements (except He and P) within the abundance range expected from evolutionary models that include the effects of atomic diffusion and assume a surface mixed mass of 10(exp -7) M. The abundances predicted by stratified model atmospheres are generally significantly more extreme than observed, except for Mg. The use of stratified model spectra to determine effective temperatures, surface gravities and masses moves the hotter stars to a closer agreement with canonical evolutionary predictions. Conclusions. Our results show definite promise towards solving the long-standing issue of surface gravity and mass discrepancies for hot HB stars, but there is still much work needed to arrive at a self-consistent solution.
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.
Quantification of branching in model three-arm star polyethylene
Ramachandran, Ramnath
2012-01-24
The versatility of a novel scaling approach in quantifying the structure of model well-defined 3-arm star polyethylene molecules is presented. Many commercial polyethylenes have long side branches, and the nature and quantity of these branches varies widely among the various forms. For instance, low-density polyethylene (LDPE) is typically a highly branched structure with broad distributions in branch content, branch lengths and branch generation (in hyperbranched structures). This makes it difficult to accurately quantify the structure and the inherent structure-property relationships. To overcome this drawback, model well-defined hydrogenated polybutadiene (HPB) structures have been synthesized via anionic polymerization and hydrogenation to serve as model analogues to long-chain branched polyethylene. In this article, model 3-arm star polyethylene molecules are quantified using the scaling approach. Along with the long-chain branch content in polyethylene, the approach also provides unique measurements of long-chain branch length and hyperbranch content. Such detailed description facilitates better understanding of the effect of branching on the physical properties of polyethylene. © 2012 American Chemical Society.
Modeling of branching density and branching distribution in low-density polyethylene polymerization
D.M. Kim; P.D. Iedema
2008-01-01
Low-density polyethylene (ldPE) is a general purpose polymer with various applications. By this reason, many publications can be found on the ldPE polymerization modeling. However, scission reaction and branching distribution are only recently considered in the modeling studies due to difficulties i
Biggins, J D
2010-01-01
Results on the behaviour of the rightmost particle in the $n$th generation in the branching random walk are reviewed and the phenomenon of anomalous spreading speeds, noticed recently in related deterministic models, is considered. The relationship between such results and certain coupled reaction-diffusion equations is indicated.
A Data Flow Behavior Constraints Model for Branch Decisionmaking Variables
Directory of Open Access Journals (Sweden)
Lu Yan
2012-06-01
Full Text Available In order to detect the attacks to decision-making variable, this paper presents a data flow behavior constraint model for branch decision-making variables. Our model is expanded from the common control flow model, itemphasizes on the analysis and verification about the data flow for decision-making variables, so that to ensure the branch statement can execute correctly and can also detect the attack to branch decision-making variableeasily. The constraints of our model include the collection of variables, the statements that the decision-making variables are dependent on and the data flow constraint with the use-def relation of these variables. Our experimental results indicate that it is effective in detecting the attacks to branch decision-making variables as well as the attacks to control-data.
Anomalous scaling in an age-dependent branching model
Keller-Schmidt, Stephanie; Tugrul, Murat; Eguíluz, Víctor M.; Hernández-García, Emilio; Klemm, Konstantin
2015-01-01
We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $\\tau$ as $\\tau^{-\\alpha}$. Depending on the exponent $\\alpha$, the scaling of tree depth with tree size $n$ displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition ($\\alpha=1$) tree depth grows as $(\\log n)^2$. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus p...
Anomalous scaling in an age-dependent branching model
Keller-Schmidt, Stephanie; Tugrul, Murat; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Klemm, Konstantin
2010-01-01
We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $\\tau$ as $\\tau^{-\\alpha}$. Depending on the exponent $\\alpha$, the scaling of tree depth with tree size $n$ displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition ($\\alpha=1$) tree depth grows as $(\\log n)^2$. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus p...
A spatially-averaged mathematical model of kidney branching morphogenesis
Zubkov, V.S.
2015-08-01
© 2015 Published by Elsevier Ltd. Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.
Controls on stream network branching angles, tested using landscape evolution models
Theodoratos, Nikolaos; Seybold, Hansjörg; Kirchner, James W.
2016-04-01
Stream networks are striking landscape features. The topology of stream networks has been extensively studied, but their geometry has received limited attention. Analyses of nearly 1 million stream junctions across the contiguous United States [1] have revealed that stream branching angles vary systematically with climate and topographic gradients at continental scale. Stream networks in areas with wet climates and gentle slopes tend to have wider branching angles than in areas with dry climates or steep slopes, but the mechanistic linkages underlying these empirical correlations remain unclear. Under different climatic and topographic conditions different runoff generation mechanisms and, consequently, transport processes are dominant. Models [2] and experiments [3] have shown that the relative strength of channel incision versus diffusive hillslope transport controls the spacing between valleys, an important geometric property of stream networks. We used landscape evolution models (LEMs) to test whether similar factors control network branching angles as well. We simulated stream networks using a wide range of hillslope diffusion and channel incision parameters. The resulting branching angles vary systematically with the parameters, but by much less than the regional variability in real-world stream networks. Our results suggest that the competition between hillslope and channeling processes influences branching angles, but that other mechanisms may also be needed to account for the variability in branching angles observed in the field. References: [1] H. Seybold, D. H. Rothman, and J. W. Kirchner, 2015, Climate's watermark in the geometry of river networks, Submitted manuscript. [2] J. T. Perron, W. E. Dietrich, and J. W. Kirchner, 2008, Controls on the spacing of first-order valleys, Journal of Geophysical Research, 113, F04016. [3] K. E. Sweeney, J. J. Roering, and C. Ellis, 2015, Experimental evidence for hillslope control of landscape scale, Science, 349
A space-averaged model of branched structures
Lopez, Diego; Michelin, Sébastien
2014-01-01
Many biological systems and artificial structures are ramified, and present a high geometric complexity. In this work, we propose a space-averaged model of branched systems for conservation laws. From a one-dimensional description of the system, we show that the space-averaged problem is also one-dimensional, represented by characteristic curves, defined as streamlines of the space-averaged branch directions. The geometric complexity is then captured firstly by the characteristic curves, and secondly by an additional forcing term in the equations. This model is then applied to mass balance in a pipe network and momentum balance in a tree under wind loading.
Coset construction of logarithmic minimal models: branching rules and branching functions
Pearce, Paul A
2013-01-01
Working in the Virasoro picture, it is argued that the logarithmic minimal models LM(p,p')=LM(p,p';1) can be extended to an infinite hierarchy of logarithmic conformal field theories LM(p,p';n) at higher fusion levels n=1,2,3,.... From the lattice, these theories are constructed by fusing together n x n elementary faces of the appropriate LM(p,p') models. It is further argued that all of these logarithmic theories are realized as diagonal cosets (A_1^{(1)})_k \\oplus (A_1^{(1)})_n / (A_1^{(1)})_{k+n} where n is the integer fusion level and k=np/(p'-p)-2 is a fractional level. These cosets mirror the cosets of the higher fusion level minimal models of the form M(m,m';n), but are associated with certain reducible representations. We present explicit branching rules for characters in the form of multiplication formulas arising in the logarithmic limit of the usual Goddard-Kent-Olive coset construction of the non-unitary minimal models M(m,m';n). The limiting branching functions play the role of Kac characters for...
Diffusion models for Knudsen compressors
Aoki, Kazuo; Degond, Pierre; Takata, Shigeru; Yoshida, Hiroaki
2007-01-01
A rarefied gas in a long straight pipe with a periodic structure consisting of alternately arranged narrow and wide pipes and with periodic temperature distribution, which is known as the Knudsen compressor (or pump), is considered. Under the assumption that the pipe is much thinner than the period, a diffusion model that describes the pressure distribution and mass flux of the gas in each pipe element is derived, together with the connection conditions at the junctions of the narrow and wide...
Anomalous scaling in an age-dependent branching model.
Keller-Schmidt, Stephanie; Tuğrul, Murat; Eguíluz, Víctor M; Hernández-García, Emilio; Klemm, Konstantin
2015-02-01
We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ(-α). Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)(2). This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point. PMID:25768548
Anomalous scaling in an age-dependent branching model
Keller-Schmidt, Stephanie; Tugrul, Murat; Víctor M Eguíluz; Hernández-García, Emilio; Klemm, Konstantin
2015-01-01
© 2015 American Physical Society. We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ-α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus provid...
Anomalous scaling in an age-dependent branching model.
Keller-Schmidt, Stephanie; Tuğrul, Murat; Eguíluz, Víctor M; Hernández-García, Emilio; Klemm, Konstantin
2015-02-01
We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ(-α). Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)(2). This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.
Fluctuation induces evolutionary branching in a mathematical model of ecosystems.
Directory of Open Access Journals (Sweden)
Masashi Tachikawa
Full Text Available Ecological systems are always subjected to various environmental fluctuations. They evolve under these fluctuations and the resulting systems are robust against them. The diversity in ecological systems is also acquired through the evolution. How do the fluctuations affect the evolutionary processes? Do the fluctuations have direct impact on the species diversity in ecological systems? In the present paper, we investigate the relation between the environmental fluctuation and the evolution of species diversity with a mathematical model of evolutionary ecology. In the model, individual organisms compete for a single restricted resource and the temporal fluctuation in the resource supply is introduced as the environmental fluctuation. The evolutionary process is represented by the mutational change of genotypes which determines their resource utilization strategies. We found that when the environmental state is switched form static to fluctuating conditions, the initial closely related population distributed around the genotype adapted for the static environment is destabilized and divided into two groups in the genotype space; i.e., the evolutionary branching is induced by the environmental fluctuation. The consequent multiple species structures is evolutionary stable at the presence of the fluctuation. We perform the evolutionary invasion analysis for the phenomena and illustrate the mechanisms of the branchings. The results indicate a novel process of increasing the species diversity via evolutionary branching, and the analysis reveals the mechanisms of the branching process as the response to the environmental fluctuation. The robustness of the evolutionary process is also discussed.
Pen Branch Delta and Savannah River Swamp Hydraulic Model
International Nuclear Information System (INIS)
The proposed Savannah River Site (SRS) Wetlands Restoration Project area is located in Barnwell County, South Carolina on the southwestern boundary of the SRS Reservation. The swamp covers about 40.5 km2 and is bounded to the west and south by the Savannah River and to the north and east by low bluffs at the edge of the Savannah River floodplain. Water levels within the swamp are determined by stage along the Savannah River, local drainage, groundwater seepage, and inflows from four tributaries, Beaver Dam Creek, Fourmile Branch, Pen Branch, and Steel Creek. Historic discharges of heated process water into these tributaries scoured the streambed, created deltas in the adjacent wetland, and killed native vegetation in the vicinity of the delta deposits. Future releases from these tributaries will be substantially smaller and closer to ambient temperatures. One component of the proposed restoration project will be to reestablish indigenous wetland vegetation on the Pen Branch delta that covers about 1.0 km2. Long-term predictions of water levels within the swamp are required to determine the characteristics of suitable plants. The objective of the study was to predict water levels at various locations within the proposed SRS Wetlands Restoration Project area for a range of Savannah River flows and regulated releases from Pen Branch. TABS-MD, a United States Army Corps of Engineer developed two-dimensional finite element open channel hydraulic computer code, was used to model the SRS swamp area for various flow conditions
Pen Branch Delta and Savannah River Swamp Hydraulic Model
Energy Technology Data Exchange (ETDEWEB)
Chen, K.F.
1999-05-13
The proposed Savannah River Site (SRS) Wetlands Restoration Project area is located in Barnwell County, South Carolina on the southwestern boundary of the SRS Reservation. The swamp covers about 40.5 km2 and is bounded to the west and south by the Savannah River and to the north and east by low bluffs at the edge of the Savannah River floodplain. Water levels within the swamp are determined by stage along the Savannah River, local drainage, groundwater seepage, and inflows from four tributaries, Beaver Dam Creek, Fourmile Branch, Pen Branch, and Steel Creek. Historic discharges of heated process water into these tributaries scoured the streambed, created deltas in the adjacent wetland, and killed native vegetation in the vicinity of the delta deposits. Future releases from these tributaries will be substantially smaller and closer to ambient temperatures. One component of the proposed restoration project will be to reestablish indigenous wetland vegetation on the Pen Branch delta that covers about 1.0 km2. Long-term predictions of water levels within the swamp are required to determine the characteristics of suitable plants. The objective of the study was to predict water levels at various locations within the proposed SRS Wetlands Restoration Project area for a range of Savannah River flows and regulated releases from Pen Branch. TABS-MD, a United States Army Corps of Engineer developed two-dimensional finite element open channel hydraulic computer code, was used to model the SRS swamp area for various flow conditions.
Stochastic models of technology diffusion
Energy Technology Data Exchange (ETDEWEB)
Horner, S.M.
1978-01-01
Simple stochastic models of epidemics have often been employed by economists and sociologists in the study of the diffusion of information or new technology. In the present theoretical inquiry the properties of a family of models related to these epidemic processes are investigated, and use of the results in the study of technical change phenomena is demonstrated. A moving limit to the level of productivity of capital is hypothesized, the exact increment is determined exogenously by basic or applied research carried on outside the industry. It is this level of latent productivity (LPRO) which fills the role of the ''disease'' which ''spreads'' through the industry. In the single advance models, LPRO is assumed to have moved forward at some point in time, after which an individual firm may advance to the limit by virtue of its own research and development or through imitation of the successful efforts of another firm. In the recurrent advance models, LPRO is assumed to increase at either a constant absolute or relative rate. The firms, in the course of their research and imitation efforts, follow behind LPRO. Using the methods of stochastic processes, it is shown that these models are equivalent to ergodic Markov chains. Based on an assumption of constant intensity of R and D effort, it is shown how the single and recurrent advance models reflect on Joseph Schumpeter's hypothesis that more concentrated industries tend to be more technologically advanced than less concentrated. The results corroborate the weakest version of the hypothesis: monopoly prices need not be higher than competitive prices.
Implications of an inverse branching aftershock sequence model.
Turcotte, D L; Abaimov, S G; Dobson, I; Rundle, J B
2009-01-01
The branching aftershock sequence (BASS) model is a self-similar statistical model for earthquake aftershock sequences. A prescribed parent earthquake generates a first generation of daughter aftershocks. The magnitudes and times of occurrence of the daughters are obtained from statistical distributions. The first generation daughter aftershocks then become parent earthquakes that generate second generation aftershocks. The process is then extended to higher generations. The key parameter in the BASS model is the magnitude difference Deltam* between the parent earthquake and the largest expected daughter earthquake. In the application of the BASS model to aftershocks Deltam* is positive, the largest expected daughter event is smaller than the parent, and the sequence of events (aftershocks) usually dies out, but an exponential growth in the number of events with time is also possible. In this paper we explore this behavior of the BASS model as Deltam* varies, including when Deltam* is negative and the largest expected daughter event is larger than the parent. The applications of this self-similar branching process to biology and other fields are discussed.
Branched pore kinetic model analysis of geosmin adsorption on super-powdered activated carbon.
Matsui, Yoshihiko; Ando, Naoya; Sasaki, Hiroshi; Matsushita, Taku; Ohno, Koichi
2009-07-01
Super-powdered activated carbon (S-PAC) is activated carbon of much finer particle size than powdered activated carbon (PAC). Geosmin is a naturally occurring taste and odor compound that impairs aesthetic quality in drinking water. Experiments on geosmin adsorption on S-PAC and PAC were conducted, and the results using adsorption kinetic models were analyzed. PAC pulverization, which produced the S-PAC, did not change geosmin adsorption capacity, and geosmin adsorption capacities did not differ between S-PAC and PAC. Geosmin adsorption kinetics, however, were much higher on S-PAC than on PAC. A solution to the branched pore kinetic model (BPKM) was developed, and experimental adsorption kinetic data were analyzed by BPKM and by a homogeneous surface diffusion model (HSDM). The HSDM describing the adsorption behavior of geosmin required different surface diffusivity values for S-PAC and PAC, which indicated a decrease in surface diffusivity apparently associated with activated carbon particle size. The BPKM, consisting of macropore diffusion followed by mass transfer from macropore to micropore, successfully described the batch adsorption kinetics on S-PAC and PAC with the same set of model parameter values, including surface diffusivity. The BPKM simulation clearly showed geosmin removal was improved as activated carbon particle size decreased. The simulation also implied that the rate-determining step in overall mass transfer shifted from intraparticle radial diffusion in macropores to local mass transfer from macropore to micropore. Sensitivity analysis showed that adsorptive removal of geosmin improved with decrease in activated carbon particle size down to 1microm, but further particle size reduction produced little improvement.
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 diffusion model for service products
Shi, Xiaohui; Chumnumpan, Pattarin; Fernandes, Kiran
2014-01-01
Purpose – This paper aims to develop a diffusion model that can be used to understand and forecast the market growth of service products in a competitive environment. Despite the fast growth of the service sector, the existing literature has dedicated little effort to modeling the market growth of service products. Design/methodology/approach – The authors propose a choice-type diffusion model that links the issues of service product utility, customers’ choice preference, customer switching b...
A Single Species Model with Impulsive Diffusion
Institute of Scientific and Technical Information of China (English)
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.
DIFFUSION BACKGROUND MODEL FOR MOVING OBJECTS DETECTION
Directory of Open Access Journals (Sweden)
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
Institute of Scientific and Technical Information of China (English)
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.
Stellar yields from metal-rich asymptotic giant branch models
Karakas, Amanda I
2016-01-01
We present new theoretical stellar yields and surface abundances for three grids of metal-rich asymptotic giant branch (AGB) models. Post-processing nucleosynthesis results are presented for stellar models with initial masses between 1$M_{\\odot}$ and 7.5$M_{\\odot}$ for $Z=0.007$, and 1$M_{\\odot}$ and 8$M_{\\odot}$ for $Z=0.014$ (solar) and $Z=0.03$. We include stellar surface abundances as a function of thermal pulse on the AGB for elements from C to Bi and for a selection of isotopic ratios for elements up to Fe and Ni (e.g., $^{12}$C/$^{13}$C), which can be obtained from observations of molecules in stars and from the laboratory analysis of meteoritic stardust grains. Ratios of elemental abundances of He/H, C/O, and N/O are also included, which are useful for direct comparison to observations of AGB stars and their progeny including planetary nebulae. The integrated elemental stellar yields are presented for each model in the grid for hydrogen, helium and all stable elements from C to Bi. Yields of Li are al...
Mathematical Modeling of Branching Morphogenesis and Vascular Tumor Growth
Yan, Huaming
Feedback regulation of cell lineages is known to play an important role in tissue size control, but the effect in tissue morphogenesis has yet to be explored. We first use a non-spatial model to show that a combination of positive and negative feedback on stem and/or progenitor cell self-renewal leads to bistable or bi-modal growth behaviors and ultrasensitivity to external growth cues. Next, a spatiotemporal model is used to demonstrate spatial patterns such as local budding and branching arise in this setting, and are not consequences of Turing-type instabilities. We next extend the model to a three-dimensional hybrid discrete-continuum model of tumor growth to study the effects of angiogenesis, tumor progression and cancer therapies. We account for the crosstalk between the vasculature and cancer stem cells (CSCs), and CSC transdifferentiation into vascular endothelial cells (gECs), as observed experimentally. The vasculature stabilizes tumor invasiveness but considerably enhances growth. A gEC network structure forms spontaneously within the hypoxic core, consistent with experimental findings. The model is then used to study cancer therapeutics. We demonstrate that traditional anti-angiogenic therapies decelerate tumor growth, but make the tumor highly invasive. Chemotherapies help to reduce tumor sizes, but cannot control the invasion. Anti-CSC therapies that promote differentiation or disturb the stem cell niche effectively reduce tumor invasiveness. However, gECs inherit mutations present in CSCs and are resistant to traditional therapies. We show that anti-gEC treatments block the support on CSCs by gECs, and reduce both tumor size and invasiveness. Our study suggests that therapies targeting the vasculature, CSCs and gECs, when combined, are highly synergistic and are capable of controlling both tumor size and shape.
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.
Horton and Tokunaga self-similarity in basic models of branching, aggregation, time series
Zaliapin, I.; Kovchegov, Y.
2012-12-01
Hierarchical branching structures are readily seen in river and drainage networks, lightening, botanical trees, vein structure of leaves, snowflakes, and bronchial passages, to mention but a few. Empirical evidence reveals a surprising similarity among natural hierarchies of diverse origin; many of them are closely approximated by so-called self-similar trees (SSTs). A two-parametric subclass of Tokunaga SSTs plays a special role in theory and applications, as it has been shown to emerge in unprecedented variety of modeled and natural phenomena. The Tokunaga SSTs with a broad range of parameters are seen in studies of river networks, aftershock sequences, vein structure of botanical leaves, numerical analyses of diffusion limited aggregation, two dimensional site percolation, and nearest-neighbor clustering in Euclidean spaces. The omnipresence of Tokunaga self-similarity hints at the existence of universal underlying mechanisms responsible for its appearance and prompts the question: What basic probability models may generate Tokunaga self-similar trees? This paper reviews the existing results on Tokunaga self-similarity of the critical binary Galton-Watson process, also known as Shreve's random topology model or equiprobable binary tree model. We then present new analytic results that establish Horton and Tokunaga self-similarity in (i) level-set tree representation of white noise, (ii) level-set tree representation of random walk and Brownian motion, and (iii) Kingman's coalescent process. We also formulate a conjecture, based on extensive numerical experiments, about Tokunaga self-similarity for the (iv) additive and (v) multiplicative coalescents as well as (vi) fractional Brownian motion. The listed processes are among the essential building blocks in natural and computer sciences modeling. Accordingly, the results of this study may provide at least a partial explanation for the presence of Horton and Tokunaga self-similarity in observed and modeled branching
Review of Gaussian diffusion-deposition models
Energy Technology Data Exchange (ETDEWEB)
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.
Description of the Risoe puff diffusion model
International Nuclear Information System (INIS)
The Risoe National Laboratory, Roskilde, Denmark, atmospheric puff dispersion model is described. This three-dimensional model simulates the release of Gaussian pullutant puffs and predicts their concentration as they are diffused and advected downwind by a horizontally homogeneous, time-dependent wind. Atmospheric characteristics such as turbulence intensity, potential temperature gradient, buoyant heat flux and maximum mixing depth have been considered. (author)
Multiphase Microfluidics The Diffuse Interface Model
2012-01-01
Multiphase flows are typically described assuming that the different phases are separated by a sharp interface, with appropriate boundary conditions. This approach breaks down whenever the lengthscale of the phenomenon that is being studied is comparable with the real interface thickness, as it happens, for example, in the coalescence and breakup of bubbles and drops, the wetting and dewetting of solid surfaces and, in general, im micro-devices. The diffuse interface model resolves these probems by assuming that all quantities can vary continuously, so that interfaces have a non-zero thickness, i.e. they are "diffuse". The contributions in this book review the theory and describe some relevant applications of the diffuse interface model for one-component, two-phase fluids and for liquid binary mixtures, to model multiphase flows in confined geometries.
Analytical boron diffusivity model in silicon for thermal diffusion from boron silicate glass film
Kurachi, Ikuo; Yoshioka, Kentaro
2015-09-01
An analytical boron diffusivity model in silicon for thermal diffusion from a boron silicate glass (BSG) film has been proposed in terms of enhanced diffusion due to boron-silicon interstitial pair formation. The silicon interstitial generation is considered to be a result of the silicon kick-out mechanism by the diffused boron at the surface. The additional silicon interstitial generation in the bulk silicon is considered to be the dissociation of the diffused pairs. The former one causes the surface boron concentration dependent diffusion. The latter one causes the local boron concentration dependent diffusion. The calculated boron profiles based on the diffusivity model are confirmed to agree with the actual diffusion profiles measured by secondary ion mass spectroscopy (SIMS) for a wide range of the BSG boron concentration. This analytical diffusivity model is a helpful tool for p+ boron diffusion process optimization of n-type solar cell manufacturing.
A Model for Locating Branches of Ghavamin Bank
Directory of Open Access Journals (Sweden)
Ali Khatami Firooz Abadi
2012-01-01
Full Text Available Locating branches of finance and credit institutes and banks is one of the most important and strategic decisions in the field of banking. This task is more significant in private institutes than state banks because of budgetary limitations of private institutes. This kind of banking needs acceptance and usage of modern technologies such as GIS in order to increase customer satisfaction. Therefore in this research, viewpoints of 30 managers, chiefs of branches and experienced employees have been considered the city of Rasht with the aim of determining appropriate sites for establishing branches. Both quantitative and qualitative approaches have been used for data analysis. They include one sample t-test for identifying criteria and Analytic Hierarchical Process (AHP for identifying weights of criteria and for this purpose, SPSS, Expert Choice, GIS and LINGO soft wares have been used. Findings imply that other than four existing branches, with respect to achieved criteria and usage of Maximum Coverage Location Problem (MCLP, coverage of 95% of demands in the research area with establishing four branches in the specified points can be achieved.
A Model for Locating Branches of Ghavamin Bank
Directory of Open Access Journals (Sweden)
seyed Mohammad Ali Khatami Firouzabadi
2012-06-01
Full Text Available Locating branches of finance and credit institutes and banks is one of the most important and strategic decisions in the field of banking. This task is more significant in private institutes than state banks because of budgetary limitations of private institutes. This kind of banking needs acceptance and usage of modern technologies such as GIS in order to increase customer satisfaction. Therefore in this research, viewpoints of 30 managers, chiefs of branches and experienced employees have been considered the city of Rasht with the aim of determining appropriate sites for establishing branches. Both quantitative and qualitative approaches have been used for data analysis. They include one sample t-test for identifying criteria and Analytic Hierarchical Process (AHP for identifying weights of criteria and for this purpose, SPSS, Expert Choice, GIS and LINGO soft wares have been used. Findings imply that other than four existing branches, with respect to achieved criteria and usage of Maximum Coverage Location Problem (MCLP, coverage of 95% of demands in the research area with establishing four branches in the specified points can be achieved.
SERVICE QUALITY ASSESSMENT IN SELECTED BRANCHES OF SOCIAL SECURITY ORGANIZATION USING SERVQUAL MODEL
Shirkavand, Fereshteh; Hossein, Seyed Mahdi; Mokhtarihesar, Parisa
2015-01-01
This study aimed to assess the quality of four branches of social security organization in Tehran Province, using SERVQUAL model and assessing the gaps between expectations and perceptions of customers in each branch of the service quality dimensions (factors tangible, reliability, responsiveness, assurance, empathy and diversity). The population study was the daily costumers of four provincial branches, each group 120, total 480 people. Sampling was simple randomize and the study was cross s...
Modelling genetic regulation of growth and form in a branching sponge.
Kaandorp, Jaap A; Blom, Joke G; Verhoef, Jozef; Filatov, Max; Postma, M; Müller, Werner E G
2008-11-22
We present a mathematical model of the genetic regulation controlling skeletogenesis and the influence of the physical environment on a branching sponge with accretive growth (e.g. Haliclona oculata or Lubomirskia baikalensis). From previous work, it is known that high concentrations of silicate induce spicule formation and upregulate the silicatein gene. The upregulation of this gene activates locally the production of spicules in the sponge and the deposition of the skeleton. Furthermore, it is known that the expression of the gene Iroquois induces the formation of an aquiferous system, consisting of exhalant and inhalant pores. We propose a model of the regulatory network controlling the separation in time and space of the skeletogenesis and the formation of the aquiferous system. The regulatory network is closely linked with environmental influences. In building a skeleton, silicate is absorbed from the environment. In our model, silicate is transported by diffusion through the environment and absorbed at the surface of a geometric model of the sponge, resulting in silicate gradients emerging in the neighbourhood of the sponge. Our model simulations predict sponge morphology and the positioning of the exhalant pores over the surface of the sponge.
Modelling Diffusion of a Personalized Learning Framework
Karmeshu; Raman, Raghu; Nedungadi, Prema
2012-01-01
A new modelling approach for diffusion of personalized learning as an educational process innovation in social group comprising adopter-teachers is proposed. An empirical analysis regarding the perception of 261 adopter-teachers from 18 schools in India about a particular personalized learning framework has been made. Based on this analysis,…
A Simplified Diffusion-Deposition Model
DEFF Research Database (Denmark)
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...
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.
NEW CAR DEMAND MODELING AND FORECASTING USING BASS DIFFUSION MODEL
Zuhaimy Ismail; Noratikah Abu
2013-01-01
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...
Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale.
Chau, Viet T; Bažant, Zdeněk P; Su, Yewang
2016-10-13
Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10(5)-10(6) almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcy-type water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in cracks, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, which is transitional between Biot's two-phase medium and Terzaghi's effective stress and introduces the loading of the solid by pressure gradients of diffusing pore water. A computer program, combining finite elements for deformation and fracture with volume elements for water flow, is developed to validate the new model.This article is part of the themed issue 'Energy and the subsurface'.
Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale.
Chau, Viet T; Bažant, Zdeněk P; Su, Yewang
2016-10-13
Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10(5)-10(6) almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcy-type water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in cracks, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, which is transitional between Biot's two-phase medium and Terzaghi's effective stress and introduces the loading of the solid by pressure gradients of diffusing pore water. A computer program, combining finite elements for deformation and fracture with volume elements for water flow, is developed to validate the new model.This article is part of the themed issue 'Energy and the subsurface'. PMID:27597791
Modeling Low Density Polyethylene with Precisely Placed Butyl Branches
Rojas, Giovanni; Wagener, Kenneth B.
Polyethylene (PE) is a commodity produced on a massive scale and also is one of the most studied macromolecules. Crystallinity can be controlled by copolymerizing ethylene with α-olefins, producing a wide range of material responses. Physical properties of PE, obtained via α olefin copolymerization, depend on the branch content that is directly related to the comonomer incorporation into the PE backbone. Materials with unknown primary structures are produced via chaingrowth chemistry, because unwanted side reactions generate defects in the main backbone that alter the morphological behavior and thermal response. Acyclic diene metathesis (ADMET) polymerization/hydrogenation methodology produce perfect sequenced copolymers of ethylene with α-olefins. Synthesis and thermal properties of PE with butyl branches precisely placed along the polymer backbone using ADMET chemistry is described within.
Modeling Demic and Cultural Diffusion: An Introduction.
Fort, Joaquim; Crema, Enrico R; Madella, Marco
2015-07-01
Identifying the processes by which human cultures spread across different populations is one of the most topical objectives shared among different fields of study. Seminal works have analyzed a variety of data and attempted to determine whether empirically observed patterns are the result of demic and/or cultural diffusion. This special issue collects articles exploring several themes (from modes of cultural transmission to drivers of dispersal mechanisms) and contexts (from the Neolithic in Europe to the spread of computer programming languages), which offer new insights that will augment the theoretical and empirical basis for the study of demic and cultural diffusion. In this introduction we outline the state of art in the modeling of these processes, briefly discuss the pros and cons of two of the most commonly used frameworks (equation-based models and agent-based models), and summarize the significance of each article in this special issue. PMID:26932566
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.
A Viral Branching Model for Predicting the Spread of Electronic Word of Mouth
van der Lans, Ralf; Bruggen, Gerrit; Eliashberg, Jehoshua; Wierenga, Berend
2010-01-01
textabstractIn a viral marketing campaign an organization develops a marketing message, and stimulates customers to forward this message to their contacts. Despite its increasing popularity, there are no models yet that help marketers to predict how many customers a viral marketing campaign will reach, and how marketers can influence this process through marketing activities. This paper develops such a model using the theory of branching processes. The proposed Viral Branching Model allows cu...
Diffusive description of lattice gas models
DEFF Research Database (Denmark)
Fiig, T.; Jensen, H.J.
1993-01-01
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......We have investigated a lattice gas model consisting of repulsive particles following deterministic dynamics. Two versions of the model are studied. In one case we consider a Finite open system in which particles can leave and enter the lattice over the edge. In the other case we use periodic...... boundary conditions. In both cases the density fluctuations exhibit a 1/f power spectrum. The individual particles behave asymptotically like ordinary random walkers. The collective behavior of these particles shows that due to the deterministic dynamics the particles behave as if they are correlated...
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.
Relativistic diffusion processes and random walk models
Dunkel, Jörn; Talkner, Peter; Hänggi, Peter
2006-01-01
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) d...
A gravitational diffusion model without dark matter
Britten, Roy J.
1998-01-01
In this model, without dark matter, the flat rotation curves of galaxies and the mass-to-light ratios of clusters of galaxies are described quantitatively. The hypothesis is that the agent of gravitational force is propagated as if it were scattered with a mean free path of approx 5 kiloparsecs. As a result, the force between moderately distant masses, separated by more than the mean free path, diminishes as the inverse first power of the distance, following diffusion equations, and describes...
"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis
Arellano Gustavo; Argil Julián; Azpeitia Eugenio; Benítez Mariana; Carrillo Miguel; Góngora Pedro; Rosenblueth David A.; Alvarez-Buylla Elena R
2011-01-01
Abstract Background In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulat...
A diffuse interface model with immiscibility preservation
Energy Technology Data Exchange (ETDEWEB)
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.
NEW CAR DEMAND MODELING AND FORECASTING USING BASS DIFFUSION MODEL
Directory of Open Access Journals (Sweden)
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.
Why a Particle Physicist is Interested in DNA Branch Migration
Myers, E; Myers, Eric; Bruist, Michael F.
1996-01-01
We describe an explicitly discrete model of the process of DNA branch migration. The model matches the existing data well, but we find that branch migration along long strands of DNA ($N \\simge 40$~bp) is also well modeled by continuum diffusion. The discrete model is still useful for guiding future experiments.
Distributed Wind Diffusion Model Overview (Presentation)
Energy Technology Data Exchange (ETDEWEB)
Preus, R.; Drury, E.; Sigrin, B.; Gleason, M.
2014-07-01
Distributed wind market demand is driven by current and future wind price and performance, along with several non-price market factors like financing terms, retail electricity rates and rate structures, future wind incentives, and others. We developed a new distributed wind technology diffusion model for the contiguous United States that combines hourly wind speed data at 200m resolution with high resolution electricity load data for various consumer segments (e.g., residential, commercial, industrial), electricity rates and rate structures for utility service territories, incentive data, and high resolution tree cover. The model first calculates the economics of distributed wind at high spatial resolution for each market segment, and then uses a Bass diffusion framework to estimate the evolution of market demand over time. The model provides a fundamental new tool for characterizing how distributed wind market potential could be impacted by a range of future conditions, such as electricity price escalations, improvements in wind generator performance and installed cost, and new financing structures. This paper describes model methodology and presents sample results for distributed wind market potential in the contiguous U.S. through 2050.
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...
Reflector modelization for neutronic diffusion calculations
International Nuclear Information System (INIS)
For neutron diffusion calculations in nuclear reactors, it is always difficult to modelize the reflector. There exist different ways to describe the neutrons density in non fissile areas like the reflector, each of them presenting some advantages and difficulties. The first part of this work gives a new reflector problem formulation, replacing the complete diffusion calculation of the reflector by boundary conditions using non-local operators, the Poincare-Steklov ones. They can be used for the eigenvectors and eigenvalues diffusion problem stated on reactive core only. This theoretical treatment of non fissile areas leads, in second part, to a new interpretation of response matrix methods and Green functions methods. These two methods are in fact the main numerical techniques used to treat reflector as boundary conditions, and an other point of view is given by the Poincare-Steklov operators. Then some simple physical cases are studied, giving explicit expressions of the Poincare-Steklov operators, and allowing numerical estimates of the reflector behaviour in a whole core-reflector PWR calculation. Finally, numerical results of Green functions for boundary perturbations illustrate the physical non-locality of the boundary operators. (author). 16 refs., 2 annexes
ANALYSIS OF THE MECHANISM MODELS OF TECHNOLOGICAL INNOVATION DIFFUSION
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-02
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.
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.
Stochastic Modelling of the Diffusion Coefficient for Concrete
DEFF Research Database (Denmark)
Thoft-Christensen, Palle
In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficients D is strongly dependent on the w/c ratio and the temperature....
Stochastic continuous time neurite branching models with tree and segment dependent rates
van Elburg, Ronald A. J.
2011-01-01
In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation fac
Mathematical Modeling of the Process for Microbial Production of Branched Chained Amino Acids
Directory of Open Access Journals (Sweden)
Todorov K.
2009-12-01
Full Text Available This article deals with modelling of branched chained amino acids production. One of important branched chained amino acid is L-valine. The aim of the article is synthesis of dynamic unstructured model of fed-batch fermentation process with intensive droppings for L-valine production. The presented approach of the investigation includes the following main procedures: description of the process by generalized stoichiometric equations; preliminary data processing and calculation of specific rates for main kinetic variables; identification of the specific rates takes into account the dissolved oxygen tension; establishment and optimisation of dynamic model of the process; simulation researches. MATLAB is used as a research environment.
Markov-modulated diffusion risk models
Bäuerle, Nicole; Kötter, Mirko
2009-01-01
In this paper we consider Markov-modulated diffusion risk reserve processes. Using diffusion approximation we show the relation to classical Markov-modulated risk reserve processes. In particular we derive a representation for the adjustment coefficient and prove some comparison results. Among others we show that increasing the volatility of the diffusion increases the probability of ruin.
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 ...
Correlation effects in sequential energy branching: an exactly solvable model of Fano statistics.
Subashiev, Arsen V; Luryi, Serge
2010-02-01
Correlation effects in the fluctuation of the number of particles in the process of energy branching by sequential impact ionizations are studied using an exactly soluble model of random parking on a line. The Fano factor F calculated in an uncorrelated final-state "shot-glass" model does not give an accurate answer even with the exact gap-distribution statistics. Allowing for the nearest-neighbor correlation effects gives a correction to F that brings F very close to its exact value. We discuss the implications of our results for energy resolution of semiconductor gamma detectors, where the value of F is of the essence. We argue that F is controlled by correlations in the cascade energy branching process and hence the widely used final-state model estimates are not reliable--especially in the practically relevant cases when the energy branching is terminated by competition between impact ionization and phonon emission. PMID:20365546
International Nuclear Information System (INIS)
The coupled radiative transport-diffusion model can be used as light transport model in situations in which the diffusion equation is not a valid approximation everywhere in the domain. In the coupled model, light propagation is modelled with the radiative transport equation in sub-domains in which the approximations of the diffusion equation are not valid, such as within low-scattering regions, and the diffusion approximation is used elsewhere in the domain. In this paper, an image reconstruction method for diffuse optical tomography based on using the coupled radiative transport-diffusion model is developed. In the approach, absorption and scattering distributions are estimated by minimising a regularised least-squares error between the measured data and solution of the coupled model. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the coupled radiative transport-diffusion model can be utilised in image reconstruction problem of diffuse optical tomography and that it produces as good quality reconstructions as the full radiative transport equation also in the presence of low-scattering regions.
Energy Technology Data Exchange (ETDEWEB)
Dou Jianhong; Xia Ling; Zhang Yu; Shou Guofa [Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027 (China); Wei Qing; Liu Feng; Crozier, Stuart [School of Information Technology and Electrical Engineering, University of Queensland, St Lucia, Brisbane, Queensland 4072 (Australia)], E-mail: xialing@zju.edu.cn
2009-01-21
Asynchronous electrical activation, induced by bundle branch block (BBB), can cause reduced ventricular function. However, the effects of BBB on the mechanical function of heart are difficult to assess experimentally. Many heart models have been developed to investigate cardiac properties during BBB but have mainly focused on the electrophysiological properties. To date, the mechanical function of BBB has not been well investigated. Based on a three-dimensional electromechanical canine heart model, the mechanical properties of complete left and right bundle branch block (LBBB and RBBB) were simulated. The anatomical model as well as the fiber orientations of a dog heart was reconstructed from magnetic resonance imaging (MRI) and diffusion tensor MRI (DT-MRI). Using the solutions of reaction-diffusion equations and with a strategy of parallel computation, the asynchronous excitation propagation and intraventricular conduction in BBB was simulated. The mechanics of myocardial tissues were computed with time-, sarcomere length-dependent uniaxial active stress initiated at the time of depolarization. The quantification of mechanical intra- and interventricular asynchrony of BBB was then investigated using the finite-element method with an eight-node isoparametric element. The simulation results show that (1) there exists inter- and intraventricular systolic dyssynchrony during BBB; (2) RBBB may have more mechanical synchrony and better systolic function of the left ventricle (LV) than LBBB; (3) the ventricles always move toward the early-activated ventricle; and (4) the septum experiences higher stress than left and right ventricular free walls in BBB. The simulation results validate clinical and experimental recordings of heart deformation and provide regional quantitative estimates of ventricular wall strain and stress. The present work suggests that an electromechanical heart model, incorporating real geometry and fiber orientations, may be helpful for better
Dou, Jianhong; Xia, Ling; Zhang, Yu; Shou, Guofa; Wei, Qing; Liu, Feng; Crozier, Stuart
2009-01-01
Asynchronous electrical activation, induced by bundle branch block (BBB), can cause reduced ventricular function. However, the effects of BBB on the mechanical function of heart are difficult to assess experimentally. Many heart models have been developed to investigate cardiac properties during BBB but have mainly focused on the electrophysiological properties. To date, the mechanical function of BBB has not been well investigated. Based on a three-dimensional electromechanical canine heart model, the mechanical properties of complete left and right bundle branch block (LBBB and RBBB) were simulated. The anatomical model as well as the fiber orientations of a dog heart was reconstructed from magnetic resonance imaging (MRI) and diffusion tensor MRI (DT-MRI). Using the solutions of reaction-diffusion equations and with a strategy of parallel computation, the asynchronous excitation propagation and intraventricular conduction in BBB was simulated. The mechanics of myocardial tissues were computed with time-, sarcomere length-dependent uniaxial active stress initiated at the time of depolarization. The quantification of mechanical intra- and interventricular asynchrony of BBB was then investigated using the finite-element method with an eight-node isoparametric element. The simulation results show that (1) there exists inter- and intraventricular systolic dyssynchrony during BBB; (2) RBBB may have more mechanical synchrony and better systolic function of the left ventricle (LV) than LBBB; (3) the ventricles always move toward the early-activated ventricle; and (4) the septum experiences higher stress than left and right ventricular free walls in BBB. The simulation results validate clinical and experimental recordings of heart deformation and provide regional quantitative estimates of ventricular wall strain and stress. The present work suggests that an electromechanical heart model, incorporating real geometry and fiber orientations, may be helpful for better
Modeling dendrite density from magnetic resonance diffusion measurements
DEFF Research Database (Denmark)
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...... model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (DL) and perpendicular (DT) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.e., in...... extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides an...
Modeling dendrite density from magnetic resonance diffusion measurements
DEFF Research Database (Denmark)
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 model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (DL) and perpendicular (DT) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.......e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides...
Modeling branching effects on source-sink relationships of the cotton plant
Li, Dong; Guo, Yan; De Reffye, P; Zhan, Zhigang
2010-01-01
Compared with classical process-based models, the functional-structural plant models provide more efficient tools to explore the impact of changes in plant structures on plant functioning. In this paper we investigated the effects of branches on the sourcesink interaction for the cotton plant (Gossypium hirsutum L.) based on a two-treatment experiment conducted on cotton grown in the field: the singlestem plants and the plants with only two vegetative branches. It was observed that the branched cotton had more organs for the whole plant but the organs on the trunk were smaller than those on the single-stem cotton. The phytomer production of the branches was four or five growth cycles delayed compared with the main stem. The organs on the trunk had similar dynamics of expansion for both treatments. Effects of branches were evaluated by using the functionalstructural model GREENLAB. It allowed estimating the coefficients of sink strength to differentiate the biomass acquisition abilities of organs between diffe...
Brodnick, Jacob; Richardson, Brian; Ramachandran, Narayanan
2015-01-01
The Low Profile Diffuser (LPD) project originated as an award from the Marshall Space Flight Center (MSFC) Advanced Development (ADO) office to the Main Propulsion Systems Branch (ER22). The task was created to develop and test an LPD concept that could produce comparable performance to a larger, traditionally designed, ullage gas diffuser while occupying a smaller volume envelope. Historically, ullage gas diffusers have been large, bulky devices that occupy a significant portion of the propellant tank, decreasing the tank volume available for propellant. Ullage pressurization of spacecraft propellant tanks is required to prevent boil-off of cryogenic propellants and to provide a positive pressure for propellant extraction. To achieve this, ullage gas diffusers must slow hot, high-pressure gas entering a propellant tank from supersonic speeds to only a few meters per second. Decreasing the incoming gas velocity is typically accomplished through expansion to larger areas within the diffuser which has traditionally led to large diffuser lengths. The Fluid Dynamics Branch (ER42) developed and applied advanced Computational Fluid Dynamics (CFD) analysis methods in order to mature the LPD design from and initial concept to an optimized test prototype and to provide extremely accurate pre-test predictions of diffuser performance. Additionally, the diffuser concept for the Core Stage of the Space Launch System (SLS) was analyzed in a short amount of time to guide test data collection efforts of the qualification of the device. CFD analysis of the SLS diffuser design provided new insights into the functioning of the device and was qualitatively validated against hot wire anemometry of the exterior flow field. Rigorous data analysis of the measurements was performed on static and dynamic pressure data, data from two microphones, accelerometers and hot wire anemometry with automated traverse. Feasibility of the LPD concept and validation of the computational model were
American Association of University Women: Branch Operations Data Modeling Case
Harris, Ranida B.; Wedel, Thomas L.
2015-01-01
A nationally prominent woman's advocacy organization is featured in this case study. The scenario may be used as a teaching case, an assignment, or a project in systems analysis and design as well as database design classes. Students are required to document the system operations and requirements, apply logical data modeling concepts, and design…
Theoretical Model of Transformation Superlastic Diffusion Bonding for Eutectoid Steel
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
Rasilainen, K. [VTT Energy, Espoo (Finland)
1997-11-01
Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories. 98 refs. The thesis includes also eight previous publications by author.
Matrix diffusion model. In situ tests using natural analogues
International Nuclear Information System (INIS)
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
Hendrickson, Eric B; Edgerton, Jeremy R; Jaeger, Dieter
2011-04-01
Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. Therefore, we analyzed the processing capabilities of full or partially branched reduced models. These models were created by collapsing the dendritic tree of a full morphological model of a globus pallidus (GP) neuron while preserving its total surface area and electrotonic length, as well as its passive and active parameters. Dendritic trees were either collapsed into single cables (unbranched models) or the full complement of branch points was preserved (branched models). Both reduction strategies allowed us to compare dynamics between all models using the same channel density settings. Full model responses to somatic inputs were generally preserved by both types of reduced model while dendritic input responses could be more closely preserved by branched than unbranched reduced models. However, features strongly influenced by local dendritic input resistance, such as active dendritic sodium spike generation and propagation, could not be accurately reproduced by any reduced model. Based on our analyses, we suggest that there are intrinsic differences in processing capabilities between unbranched and branched models. We also indicate suitable applications for different levels of reduction, including fast searches of full model parameter space. PMID:20623167
Sedimentary radioactive tracers and diffusive models.
Carroll, J; Lerche, I
2010-08-01
This paper examines the underlying assumptions and consequences of applying a steady-state equation to sediment profiles of radioactive tracers in order to deconvolute sedimentation from bioturbation processes modelled as a diffusive type process. Several factors follow immediately from this investigation: (i) if the observed radioactive concentration increases with depth over any finite depth range then the proposed steady-state, constant flux equation is not applicable. Any increase in radioactive concentration with depth implies a negative mixing coefficient which is a physical impossibility; (ii) when the radioactive concentration systematically decreases with increasing sedimentary depth then solutions to the steady-state conservation equation exist only when either the constant solid state flux to the sediment surface is small enough so that a positive mixing coefficient results or when the mixing coefficient is small enough so that a positive flux results. If the radioactive concentration, porosity and/or density of the solid phase are such that the proposed equation is inappropriate (because no physically acceptable solution exists) then one must abandon the proposed steady-state equation. Further: if the flux of solid sediment to the sediment surface varies with time then, of course, a steady-state conservation equation is also inappropriate. Simple examples illustrate that the assumption of steady-state restricts the applicability of this modelling approach to a relatively small sub-set of expected situations in the real world.
Institute of Scientific and Technical Information of China (English)
夏宁; 李保国; 邓西民; 郭焱
2004-01-01
在不同修剪手法下,对栽培桃树(Prunuspersica(L.)Batsch)不同母枝上的分枝模式进行了比较研究.从分枝模式来看:修剪后的母枝基本由3个不同的区域组成,基部是不萌发的潜伏芽形成的未分枝区域;中部是延迟分枝和多次分枝组成的分枝区域(主要的枝条类型有短枝、长枝和多次枝);顶部是被剪除的部分.我们通过隐式半马尔可夫模型来模拟这一分枝模式,主要是定量描述1次枝和多次枝在母枝上的数量及其分布状况.在上述模型中,未分枝区、延迟分枝区和多次分枝区称为瞬时态,被剪除的部分称为吸收态.模拟的结果与观察的结果进行对比后发现,两者具有很好的一致性.这说明隐式半马尔可夫模型是模拟植物分枝过程的一种有效方法,尽管隐式半马尔可夫链模型只是一个描述性的模型,但仍能对其所描述的生物现象进行解释,在预测修剪手法对母枝分枝模式影响方面比传统的方法具有明显的优势.本研究结果是建立三维虚拟桃树树冠分枝结构的基础.%The shoot branching patterns of the two-year-old branches of peach trees (Prunus parsica (L.) Batsch cv. Elberta) were compared with different pruning measures. The branches were divided into a basal non-branching zone, a proleptic branching zone, a sylleptic branching zone and the part removed. We used the hidden semi-Markov model to capture the branching patterns. The final results showed that theoretical probability distributions of diverse lateral shoots of the parent branches calculated on the basis of the parameters of the hidden semi-Markov chain model were in good agreement with probabilities extracted from the observed data. This paper described the quantitative effects of pruning on branching architecture of a parent branch, taking into account of branch morphology. Results suggest that the hidden semi-Markov model could be used as an effective tool to describe the
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. PMID:18498453
Daskalova, Nina
2011-01-01
2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25. Multitype branching processes (MTBP) have been proven to be very useful models in cell kinetics. A typical example is the process of oligodendrocyte generation in cell culture, which is regarded as two-type branching process. Usually, such a process is not observable in the sense of the whole tree, but only as the "generation" at given moment in time, which consist of the number of cells of every type. An EM-type algorith...
A Branch and Bound Algorithm for the Protein Folding Problem in the HP Lattice Model
Institute of Scientific and Technical Information of China (English)
Mao Chen; Wen-Qi Huang
2005-01-01
A branch and bound algorithm is proposed for the two-dimensional protein folding problem in the HP lattice model. In this algorithm, the benefit of each possible location of hydrophobic monomers is evaluated and only promising nodes are kept for further branching at each level. The proposed algorithm is compared with other well-known methods for 10 benchmark sequences with lengths ranging from 20 to 100 monomers. The results indicate that our method is a very efficient and promising tool for the protein folding problem.
Puzzle of W Leptonic Decay Branching Fractions and Gauge Model of Generation Nonuniversality
Li, Xiao-Yuan; Ma, Ernest
2005-01-01
Lepton generation universality holds very well in Z decays, but appears to be violated in recent LEP data of W leptonic decay branching fractions. If this trend persists, a consistent and natural explanation is a model of generation nonuniversality, based on the gauge group SU(2)_L X U(1)_R X U(1)_{B-L}.
Modelling genetic regulation of growth and form in a branching sponge
Kaandorp, J.A.; Blom, J.G.; Verhoef, J.; Filatov, M.; Postma, M.; Müller, W.E.G.
2008-01-01
We present a mathematical model of the genetic regulation controlling skeletogenesis and the influence of the physical environment on a branching sponge with accretive growth (e.g. Haliclona oculata or Lubomirskia baikalensis). From previous work, it is known that high concentrations of silicate ind
Measurement and Modeling of Solute Diffusion Coefficients in Unsaturated Soils
Chou, Hsin-Yi
2010-01-01
Solute diffusion in unsaturated soils refers to the transport of dissolved constituents in liquid phase from a higher to a lower concentration point. Several empirical and conceptual models were proposed to predict the solute diffusion coefficients in unsaturated soils, but they were not systematically tested and evaluated under the same conditions using soils of different textures. Our experimental data showed that there is no perfect model that can depict the behavior of solute diffusion co...
Finite difference time domain modeling of phase grating diffusion
Kowalczyk K.; Van Walstijn M.
2010-01-01
In this paper, a method for modeling diffusion caused by non-smooth boundary surfaces in simulations of room acoustics using finite difference time domain (FDTD) technique is investigated. The proposed approach adopts the well-known theory of phase grating diffusers to efficiently model sound scattering from rough surfaces. The variation of diffuser well-depths is attained by nesting allpass filters within the reflection filters from which the digital impedance filters used in the boundary im...
Hendrickson, Eric B.; Edgerton, Jeremy R.; Jaeger, Dieter
2010-01-01
Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. T...
A new parameters identification procedure for simplified double layer capacitor two-branch model
Energy Technology Data Exchange (ETDEWEB)
Faranda, R. [Dipartimento di Energia, Politecnico di Milano, Via La Masa 34, 20156 Milano, MI (Italy)
2010-04-15
Supercapacitors are electrical energy storage devices that offer high power density and a high number of charge and discharge cycles. Even though the amount of stored energy they maintain is not comparable that of classical batteries, supercapacitors can offer advantages in several industrial applications. This paper introduces a simplified model, named the ''two-branch'' model, to characterize the electrical behaviour of double layer capacitors (DLCs). This model is similar to some models in literature from a circuit point of view (e.g. three-branch model), but the parameters identification process is easier and faster. Experimental charge and charge-discharge tests have been executed on supercapacitors of two different makes (Epcos and Maxwell) and for several different sizes (between 110 F and 600 F). Moreover a new identification procedure, for describing short-term behaviour, is proposed for the new simplified two-branch model. This new procedure is simpler than for the other lumped models therefore it can be adopted fruitfully also from them. The experimental results and the performed simulations are reported in order to verify the validity of the new simplified proposed model and of the new parameter identification process. (author)
Wavelet estimation of the diffusion coefficient in time dependent diffusion models
Institute of Scientific and Technical Information of China (English)
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.
Radon diffusion through multilayer earthen covers: models and simulations
Energy Technology Data Exchange (ETDEWEB)
Mayer, D.W.; Oster, C.A.; Nelson, R.W.; Gee, G.W.
1981-09-01
A capability to model and analyze the fundamental interactions that influence the diffusion of radon gas through uranium mill tailings and cover systems has been investigated. The purpose of this study is to develop the theoretical basis for modeling radon diffusion and to develop an understanding of the fundamental interactions that influence radon diffusion. This study develops the theoretical basis for modeling radon diffusion in one, two and three dimensions. The theory has been incorporated into three computer models that are used to analyze several tailings and cover configurations. This report contains a discussion of the theoretical basis for modeling radon diffusion, a discussion of the computer models used to analyze uranium mill tailings and multilayered cover systems, and presents the results that have been obtained.
A social diffusion model with an application on election simulation.
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.
Diffuse radiation models and monthly-average, daily, diffuse data for a wide latitude range
International Nuclear Information System (INIS)
Several years of measured data on global and diffuse radiation and sunshine duration for 40 widely spread locations in the latitude range 36° S to 60° N are used to develop and test models for estimating monthly-mean, daily, diffuse radiation on horizontal surfaces. Applicability of the clearness-index (K) and sunshine fraction (SSO) models for diffuse estimation and the effect of combining several variables into a single multilinear equation are tested. Correlations connecting the diffuse to global fraction (HdH) with K and SSO predict Hd values more accurately than their separate use. Among clearness-index and sunshine-fraction models, SSO models are found to have better accuracy if correlations are developed for wide latitude ranges. By including a term for declinations in the correlation, the accuracy of the estimated data can be marginally improved. The addition of latitude to the equation does not help to improve the accuracy further. (author)
SEMICLASSICAL LIMIT FOR BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL
Institute of Scientific and Technical Information of China (English)
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.
The Semiclassical Limit in the Quantum Drift-Diffusion Model
Institute of Scientific and Technical Information of China (English)
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.
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…
A branching model for the spread of infectious animal diseases in varying environments
Trapman, Pieter; Meester, R; Heesterbeek, J A P
2004-01-01
This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in ...
Spatial Pattern of an Epidemic Model with Cross-diffusion
Institute of Scientific and Technical Information of China (English)
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.
"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis
Directory of Open Access Journals (Sweden)
Arellano Gustavo
2011-12-01
Full Text Available Abstract Background In Thomas' formalism for modeling gene regulatory networks (GRNs, branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a asynchrony, (b incompletely specified behavior, and (c interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths. Results We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", http://turing.iimas.unam.mx:8080/AntelopeWEB/, a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche. There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs. Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary
Restricted diffusion in a model acinar labyrinth by NMR: Theoretical and numerical results
Grebenkov, D. S.; Guillot, G.; Sapoval, B.
2007-01-01
A branched geometrical structure of the mammal lungs is known to be crucial for rapid access of oxygen to blood. But an important pulmonary disease like emphysema results in partial destruction of the alveolar tissue and enlargement of the distal airspaces, which may reduce the total oxygen transfer. This effect has been intensively studied during the last decade by MRI of hyperpolarized gases like helium-3. The relation between geometry and signal attenuation remained obscure due to a lack of realistic geometrical model of the acinar morphology. In this paper, we use Monte Carlo simulations of restricted diffusion in a realistic model acinus to compute the signal attenuation in a diffusion-weighted NMR experiment. We demonstrate that this technique should be sensitive to destruction of the branched structure: partial removal of the interalveolar tissue creates loops in the tree-like acinar architecture that enhance diffusive motion and the consequent signal attenuation. The role of the local geometry and related practical applications are discussed.
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.
Large Scale Structure Formation of normal branch in DGP brane world model
Song, Yong-Seon
2007-01-01
In this paper, we study the large scale structure formation of the normal branch in DGP model (Dvail, Gabadadze and Porrati brane world model) by applying the scaling method developed by Sawicki, Song and Hu for solving the coupled perturbed equations of motion of on-brane and off-brane. There is detectable departure of perturbed gravitational potential from LCDM even at the minimal deviation of the effective equation of state w_eff below -1. The modified perturbed gravitational potential weakens the integrated Sachs-Wolfe effect which is strengthened in the self-accelerating branch DGP model. Additionally, we discuss the validity of the scaling solution in the de Sitter limit at late times.
Heat diffusion in a two-dimensional thermal fuse model
Tørå, Glenn; Hansen, Alex
2009-01-01
We present numerical studies of electrical breakdown in disordered materials using a two-dimensional thermal fuse model with heat diffusion. A conducting fuse is heated locally by a Joule heating term. Heat diffuses to neighbouring fuses by a diffusion term. When the temperature reaches a given threshold, the fuse breaks and turns into an insulator. The time dynamics is governed by the time scales related to the two terms, in the presence of quenched disorder in the conductances of the fuses....
THE BANKRUPT RISK IN FEED DISTRIBUTION BRANCH IN DOLJ DISTRICT – FDR MODEL
Directory of Open Access Journals (Sweden)
Ovidiu CĂPRARIU
2010-01-01
Full Text Available Abstract:In this article, we are intending to present a score function in order to calculate the bankrupt risk for a special domain: feed distribution.All analysis models of the bankruptcy risk have at their basis a score function according to which it is determined with approximation whether the company would get bankruptcy or would have performing economic results, in a period immediately following the analysis.Having a personal analysis in feed distribution branch, I elaborated a score function for counting bankrupt risk, based on financial and non-financial studies of many companies and we called this model “Feed Distribution Risk Model” (FDR. The target was to obtain a high level of precision, so I choose the feed industry and more specific only feed distribution branch and I analyzed statistics about the evolution of the feed distribution companies in Romania and about the normal level of some financial or non-financial indicators for these companies.I have choose five feed distribution companies and I counted two international score functions and two Romanian score function with FDR function. Finally, I concluded that the three main differences between the classic models and this one are that the FDR model is for a specified branch – the feed distribution, it uses an important number of indicators and uses non-financial indicators, which explain the shareholders bonity. As directions to continue the investigations, I propose the elaboration of another models for other branches and adjust the financial information with true dates.
Derrida's Generalized Random Energy models; 4, Continuous state branching and coalescents
Bovier, A
2003-01-01
In this paper we conclude our analysis of Derrida's Generalized Random Energy Models (GREM) by identifying the thermodynamic limit with a one-parameter family of probability measures related to a continuous state branching process introduced by Neveu. Using a construction introduced by Bertoin and Le Gall in terms of a coherent family of subordinators related to Neveu's branching process, we show how the Gibbs geometry of the limiting Gibbs measure is given in terms of the genealogy of this process via a deterministic time-change. This construction is fully universal in that all different models (characterized by the covariance of the underlying Gaussian process) differ only through that time change, which in turn is expressed in terms of Parisi's overlap distribution. The proof uses strongly the Ghirlanda-Guerra identities that impose the structure of Neveu's process as the only possible asymptotic random mechanism.
Model of moisture diffusion in fractal media
Fan Jie; Wang Li-Li; Liu Fu-Juan; Liu Zhi; Liu Yong; Zhang Sheng
2015-01-01
Moisture diffusion in fractal media does not obey the classical Fick’s law. In this paper, its fractal partner is proposed to investigate the phenomenon in fractal media. It reveals that the moisture transport strongly depends on fractal dimensions of the media.
March, N. H.; Moreno, A. J.
2016-06-01
The critical exponent ν for randomly branched polymers with dimensionality d equal to 3, is known exactly as 1/2. Here, we invoke an already available string theory model to predict the remaining static critical exponents. Utilizing results of Hsu et al. (Comput Phys Commun. 2005;169:114-116), results are added for d = 8. Experiment plus simulation would now be important to confirm, or if necessary to refine, the proposed values.
The Standard Model Higgs : Discovery Potentials and Branching Fraction Measurements at the NLC
Sachwitz, M.; Schreiber, H. J.; Shichanin, S.
1997-01-01
We discuss discovery potentials for a 140 GeV Standard Model Higgs boson produced in e+e- collisions at 360 GeV, including all potential irreducible and reducible background contributions. In the second part of the study, we estimate the uncertainties expected for the branching fractions of the Higgs into bb-bar, tau+tau-, WW* and into cc-bar+gg including a realistic error estimation of the inclusive bremsstrahlung Higgs production cross section.
Modelling genetic regulation of growth and form in a branching sponge
Kaandorp, Jaap A.; Blom, Joke G.; Verhoef, Jozef; Filatov, Max; Postma, M.; Müller, Werner E. G.
2008-01-01
We present a mathematical model of the genetic regulation controlling skeletogenesis and the influence of the physical environment on a branching sponge with accretive growth (e.g. Haliclona oculata or Lubomirskia baikalensis). From previous work, it is known that high concentrations of silicate induce spicule formation and upregulate the silicatein gene. The upregulation of this gene activates locally the production of spicules in the sponge and the deposition of the skeleton. Furthermore, i...
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...
Multiscale modelling of radiation-enhanced diffusion phenomena in metals
Chang, Zhongwen
2015-01-01
A multiscale modelling framework and an experiment campaign are used to study void swelling and Cu precipitation under irradiation. Several aspects regarding defect and solute diffusion under irradiation have been studied in this thesis. First, a self-diffusion model in bcc Fe has been constructed in order to describe the non-linear effects, especially the magnetic transition, around the Curie temperature. First principles calculations are applied to obtain the parameters in the model. The pa...
Modeling of Two-Phase Flow through a Rotating Tube with Twin Exit Branches
Directory of Open Access Journals (Sweden)
Sun-Wen Cheng
2000-01-01
Full Text Available A numerical model is proposed to determine the dynamic behavior of single-phase and twophase, two-component flows through a horizontal rotating tube with identical twin exit branches. The working fluid, oil, enters the tube through a radial duct attached at one end and exits into open air through the twin radial branches, one located at midway and the other at the end of the tube. The branch-to-tube diameter ratio, rotational speed, and total oil flow rate are varied. It is experimentally revealed in previous study that the air cavitation occurs at lower speeds, leading to a two-phase flow with the air-oil ratio (void fraction varying with the rotating speed. A unique characteristic in two-phase flow, i.e., hysteresis, is found to exist in both oil flow rates and inlet pressure. In theoretical modeling, the governing flow equations are incorporated by empirical equations for hydraulic head losses. The predicted and measured exit oil flow rates are compared with good agreement in both the single-phase and annular flow regimes. Only qualitative agreement is achieved in the bubbly and bubbly-slug flow regimes. The model can be applied to improve the design and thus enhance the performance of automatic transmission lines, and the cooling efficiency of rotating machines and petroleum drilling process.
A branching model for the spread of infectious animal diseases in varying environments.
Trapman, Pieter; Meester, Ronald; Heesterbeek, Hans
2004-12-01
This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in a changing (but not random) environment. With this branching process, we estimate the probability of extinction and the expected number of infected individuals for different control measures. We also use this branching process to calculate the generating function of the number of infected individuals at any given moment. The model and methods are designed using important infections of farmed animals, such as classical swine fever, foot-and-mouth disease and avian influenza as motivating examples, but have a wider application, for example to emerging human infections that lead to strict quarantine of cases and suspected cases (e.g. SARS) and contact and movement restrictions. PMID:15565446
Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models
Yoder, Dennis A.
2016-01-01
This paper will include a detailed comparison of heat transfer models that rely upon the thermal diffusivity. The goals are to inform users of the development history of the various models and the resulting differences in model formulations, as well as to evaluate the models on a variety of validation cases so that users might better understand which models are more broadly applicable.
Rapidity distribution and duality of a phase-space branching model for multiparticle production
International Nuclear Information System (INIS)
A branching model is developed for the description of multiparticle production processes at high energy. The starting point is the essential phenomenological validity of approximate KNO scaling. A quasirapidity variable is introduced, in terms of which the exclusive distribution of the produced particles can be calculated. The model is then described in the context of s- and t-channel duality. The dual picture lends itself to a physical interpretation of the model, the contrast of which from dual topological unitarization is pointed out
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
Directory of Open Access Journals (Sweden)
Tak Kuen Siu
2008-01-01
Full Text Available We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.
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.
New Symmetries for a Model of Fast Diffusion
Institute of Scientific and Technical Information of China (English)
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.
A transformation approach to modelling multi-modal diffusions
DEFF Research Database (Denmark)
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....
Weak diffusion limits of dynamic conditional correlation models
DEFF Research Database (Denmark)
Hafner, Christian M.; Laurent, Sebastien; Violante, Francesco
The properties of dynamic conditional correlation (DCC) models are still not entirely understood. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized...... by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a non-degenerate diffusion limit can be obtained. Alternative sets of conditions are considered...
Branching Brownian motion with selection of the N right-most particles: An approximate model
Maillard, Pascal
2011-01-01
We present an approximation to the Brunet--Derrida model of supercritical branching Brownian motion on the real line with selection of the $N$ right-most particles, valid when the population size $N$ is large. It consists of introducing a random space-time barrier at which particles are instantaneously killed in such a way that the population size stays almost constant over time. We prove that the suitably recentered position of this barrier converges at the $\\log^3 N$ timescale to a L\\'evy process, which we identify. This validates the physicists' predictions about the fluctuations in the Brunet--Derrida model.
International Nuclear Information System (INIS)
It is important to understand the coupled processes of sorption and diffusion of radionuclides (RNs) in compacted bentonite, and to develop mechanistic models that can aid in the prediction of the long-term performance of geological disposal systems of radioactive waste. The integrated sorption and diffusion (ISD) model was developed based on the consistent combination of clay–water interaction, sorption and diffusion models. The diffusion model based on the electrical double layer theory describing relative ionic concentrations and viscoelectric effects at the negatively charged clay surface was coupled with porewater chemistry and sorption models. This ISD model was successfully tested for various actinides with a complex chemistry (Np(V), Am(III), U(VI) under conditions where variably charged carbonate complexes are formed) considered in Part 1, by using published diffusion and sorption data (Da, De, Kd) as a function of partial montmorillonite density. Quantitative agreements were observed by considering uncertainty in porewater chemistry and dominant aqueous species. It can therefore be concluded that the ISD model developed here is able to adequately explain the sorption and diffusion behavior of various RNs with a complex chemistry in compacted bentonites. The performed modeling indicates that uncertainties are mainly related to porewater chemistry and RN speciation and that these parameters need to be carefully evaluated. (author)
Reflector modelization for neutronic diffusion and parameters identification
International Nuclear Information System (INIS)
Physical parameters of neutronic diffusion equations can be adjusted to decrease calculations-measurements errors. The reflector being always difficult to modelize, we choose to elaborate a new reflector model and to use the parameters of this model as adjustment coefficients in the identification procedure. Using theoretical results, and also the physical behaviour of neutronic flux solutions, the reflector model consists then in its replacement by boundary conditions for the diffusion equations on the core only. This theoretical result of non-local operator relations leads then to some discrete approximations by taking into account the multiscaled behaviour, on the core-reflector interface, of neutronic diffusion solutions. The resulting model of this approach is then compared with previous reflector modelizations, and first results indicate that this new model gives the same representation of reflector for the core than previous
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...
Zhigao Liao; Jiuping Xu; Liming Yao
2013-01-01
This paper studies the innovation diffusion problem with the affection of urbanization, proposing a dynamical innovation diffusion model with fuzzy coefficient, and uses the shifting rate of people from rural areas stepping into urban areas to show the process of urbanization. The numerical simulation shows the diffusion process for telephones in China with Genetic Algorithms and this model is effective to show the process of innovation diffusion with the condition of urbanization process.
Evaluation of the Thermodynamic Models for the Thermal Diffusion Factor
DEFF Research Database (Denmark)
Gonzalez-Bagnoli, Mariana G.; Shapiro, Alexander; Stenby, Erling Halfdan
2003-01-01
Over the years, several thermodynamic models for the thermal diffusion factors for binary mixtures have been proposed. The goal of this paper is to test some of these models in combination with different equations of state. We tested the following models: those proposed by Rutherford and Drickamer...
Bento, Ricardo Ferreira; Salomone, Raquel; Nascimento, Silvia Bona do; Ferreira, Ricardo Jose Rodriguez; Silva, Ciro Ferreira da; Costa, Heloisa Juliana Zabeu Rossi
2014-07-01
Introduction The ideal animal model for nerve regeneration studies is the object of controversy, because all models described by the literature have advantages and disadvantages. Objective To describe the histologic and functional patterns of the mandibular branch of the facial nerve of Wistar rats to create a new experimental model of facial nerve regeneration. Methods Forty-two male rats were submitted to a nerve conduction test of the mandibular branch to obtain the compound muscle action potential. Twelve of these rats had the mandibular branch surgically removed and submitted to histologic analysis (number, partial density, and axonal diameter) of the proximal and distal segments. Results There was no statistically significant difference in the functional and histologic variables studied. Conclusion These new histologic and functional standards of the mandibular branch of the facial nerve of rats establish an objective, easy, and greatly reproducible model for future facial nerve regeneration studies. PMID:25992106
Institute of Scientific and Technical Information of China (English)
WU Qiye
1995-01-01
The Rouse-Zimm model with slippage was improved and the basic parameters of modelwere modified to explain the rheological properties of star-type branched polymersolutions. The theoretical results show good agreement with experimental data.
Scaling in the Diffusion Limited Aggregation Model
Menshutin, Anton
2012-01-01
We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/Rdep(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/Rdep) function on an ensemble with 1000 clusters of 5×107 particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.
Toward Information Diffusion Model for Viral Marketing in Business
Directory of Open Access Journals (Sweden)
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.
Jump-Diffusion Models for Option Pricing versus the Black Scholes Model
Storeng, Håkon Båtnes
2014-01-01
In general, the daily logarithmic returns of individual stocks are not normally distributed. This poses a challenge when trying to compute the most accurate option prices. This thesis investigates three different models for option pricing, The Black Scholes Model (1973), the Merton Jump-Diffusion Model (1975) and the Kou Double-Exponential Jump-Diffusion Model (2002). The jump-diffusion models do not make the same assumption as the Black Scholes model regarding the behavior of the underlyi...
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…
GLOBAL ATTRACTIVITY OF POPULATION MODELS WITH DELAYS AND DIFFUSION
Institute of Scientific and Technical Information of China (English)
QIU Zhipeng
2005-01-01
In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patchΩand periodic environment and with delays recruitment, the second models a single species dispersal among the m patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators.Some earlier results are extended to population models with delays and diffusion.
Numerical Simulation Model of Laminar Hydrogen/Air Diffusion Flame
Institute of Scientific and Technical Information of China (English)
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.
Energy Technology Data Exchange (ETDEWEB)
Capdebosq, Y
1999-09-01
In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)
Institute of Scientific and Technical Information of China (English)
TENG Hong-Hui; JIANG Zong-Lin
2011-01-01
@@ One-dimensional detonation waves are simulated with the three-step chain branching reaction model, and the instability criterion is studied.The ratio of the induction zone length and the reaction zone length may be used to decide the instability, and the detonation becomes unstable with the high ratio.However, the ratio is not invariable with different heat release values.The critical ratio, corresponding to the transition from the stable detonation to the unstable detonation, has a negative correlation with the heat release.An empirical relation of the Chapman-Jouguet Mach number and the length ratio is proposed as the instability criterion.
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.
Tang, Justin
2012-01-01
The problem of shock induced ignition by a piston is addressed in the framework of Fickett's model for reactive compressible flows, i.e., the reactive form of Burgers' equation. An induction-reaction two-step chain-branching model is used to study the coupling between the energy release and the compressible hydrodynamics occurring during the shock ignition transient leading to a detonation. Owing to the model's simplicity, the ignition and acceleration mechanism is explained using the two families of characteristics admitted by the model. The energy release along the particle paths provides the amplification of forward-travelling pressure waves. These waves pre-compress the medium in the induction layer ahead of the reaction zone, therefore changing the induction delays of successive particles. The variation of the induction delay provides the modulation of the amplification of the forward travelling pressure waves by controlling the residence time of the pressure waves in the reaction zone. A closed form ana...
Saichev, A
2005-01-01
Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold $m_d$) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to investigate how the statistical properties of observable earthquakes differ from the statistics of all events. The ETAS (epidemic-type aftershock sequence) model assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. The triggering efficiency of earthquakes is assumed to vanish below a lower magnitude limit $m_0$, in order to ensure the convergence of the theory and may reflect the physics of state-and-velocity frictional rupture. We show that, to a good approximation, the ETAS model is renormalized onto itself under what amounts to a decimation procedure $m_...
[Comparative analysis of the monopodial and sympodial models of bulb branching in Galanthus L].
Chub, V V; Kozhevnikova, A D
2000-01-01
We have examined sympodial and monopodial models of bulb branching in Galanthus. The issue of the position of the reduced prophyll is discussed. We proposed a method of formal interpretation: parts of the plant were positioned on diagrams; several variants of axial schemes were matched to each diagram; the schemes were divided into two classes, monopodial and sympodial ones, and stability of each class was estimated. In order to decide about the model of Galanthus bulb branching, we have examined plants with additional inflorescences and plants with additional leaf series. We have shown that the sympodial model predicts the presence of the reduced prophyll at the base of the innovation bud in all studied cases. Consecutive stages of prophyll reduction (prophyll of the innovation bud) can be followed in Amaryllidaceae in the following sequence: Zephyranthes, a well-developed large prophyll with green lamina; Vallota, a developed prophyll with reduced green lamina; Haemanthus, a thin chaffy short-living prophyll. At the end of this sequence is Galanthus with completely reduced prophyll at the innovation bud.
A Generalized Norton-Bass Model for Multigeneration Diffusion
Zhengrui Jiang; Dipak C. Jain
2012-01-01
The Norton-Bass (NB) model is often credited as the pioneering multigeneration diffusion model in marketing. However, as acknowledged by the authors, when counting the number of adopters who substitute an old product generation with a new generation, the NB model does not differentiate those who have already adopted the old generation from those who have not. In this study, we develop a generalized Norton-Bass (GNB) model that separates the two different types of substitutions. The GNB model ...
Ostwald ripening on a substrate : modeling local interparticle diffusion
Zheng, Xin; Bigot, Bernard
1994-01-01
A model with local interparticle diffusion is considered, in contrast with the classical model of Ostwald ripening (the mean field model) and its multiparticle extensions which have long range interactions. Simulations of the evolution of the system show that the asymptotic behavior obeys a power law. It is also found that the scaled asymptotic distribution of particle radii is broader than in the previous models, even at low initial coverage where the multiparticle models have the same narro...
Diffuse Scattering Model of Indoor Wideband Propagation
DEFF Research Database (Denmark)
Franek, Ondrej; Andersen, Jørgen Bach; Pedersen, Gert Frølund
2011-01-01
to be 18 dB, 19.4 dB and 20.2 dB per 100 ns, respectively. The remaining differences are further discussed and an additional case of spherical room is used to demonstrate the influence of the room shape on the results. It is concluded that the presented method is valid as a simple tool for use in indoor......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...... 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...
A comparison of Gaussian and diffusivity models of atmospheric dispersion
International Nuclear Information System (INIS)
The Gaussian plume diffusion model of Smith and a diffusivity model by Maul are compared over the full range of atmospheric stability. The models' predictions for ground level concentration are found to agree well a) for ground level releases of materials, and b) for elevated releases of material at distances comparable to or greater than the distance of maximum ground level concentration. Surface layer, ground roughness, and dry deposition effects are examined and a simple ground deposition model used in the Gaussian plume model is found to be adequate over most of the stability range. Uncertainties due to the models themselves and the meteorological input data are estimated and the advantages and limitations of both types of model are discussed. It is concluded that the models are suitable for a variety of applications and that they are fast and inexpensive to run as computer models. (author)
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.
RETADD: a Regional Trajectory And Diffusion-Deposition model
Energy Technology Data Exchange (ETDEWEB)
Begovich, C. L.; Murphy, B. D.; Nappo, Jr., C. J.
1978-06-01
The Regional Trajectory and Diffusion-Deposition Model (RETADD) is based upon a version of the National Oceanic and Atmospheric Administration Air Resources Laboratory's Regional-Continental Scale Transport, Diffusion, and Deposition Model. The FORTRAN IV computer model uses a trajectory analysis technique for estimating the transport and long-range diffusion of material emitted from a point source. The wind trajectory portion of the code uses observed upper air winds to compute the transport of the material. Ground level concentrations and depositions are computed by using the Gaussian plume equation for wind trajectories projected forward in time. Options are included to specify an upper bound for the mixed layer and a chemical decomposition rate for the effluent. The limitations to the technique are discussed, the equations and model are described, and listings of the program, input, and output are included.
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...
Numerical modelling of swirling diffusive flames
Parra-Santos Teresa; Perez Ruben; Szasz Robert Z.; Gutkowski Artur N.; Castro Francisco
2016-01-01
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...
Modelling and simulation of diffusive processes methods and applications
Basu, SK
2014-01-01
This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport
A spatial model of the diffusion of mobile communications within the European Union
Frank, Lauri Dieter
2002-01-01
Innovation diffusion studies have been popular. However, usually the focus has been on two dimensions: Either the innovation's diffusion is studied on the micro level by examining the individual's adoption of an innovation, or on the macro-level by modelling the sigmoid diffusion curve. The third dimension of the diffusion of an innovation, spatial diffusion, has gained less attention. Spatial diffusion models mostly base on the effect of distance on an innovation's diffusion process. General...
International Nuclear Information System (INIS)
The advection of thermonuclear ashes by magnetized domains emerging near the H shell was suggested to explain asymptotic giant branch (AGB) star abundances. Here we verify this idea quantitatively through exact MHD models. Starting with a simple two-dimensional (2D) geometry and in an inertia frame, we study plasma equilibria avoiding the complications of numerical simulations. We show that below the convective envelope of an AGB star, variable magnetic fields induce a natural expansion, permitted by the almost ideal MHD conditions, in which the radial velocity grows as the second power of the radius. We then study the convective envelope, where the complexity of macroturbulence allows only for a schematic analytical treatment. Here the radial velocity depends on the square root of the radius. We then verify the robustness of our results with 3D calculations for the velocity, showing that for both studied regions the solution previously found can be seen as a planar section of a more complex behavior, in which the average radial velocity retains the same dependency on the radius found in 2D. As a final check, we compare our results to approximate descriptions of buoyant magnetic structures. For realistic boundary conditions, the envelope crossing times are sufficient to disperse in the huge convective zone any material transported, suggesting magnetic advection as a promising mechanism for deep mixing. The mixing velocities are smaller than for convection but larger than for diffusion and adequate for extra mixing in red giants.
Energy Technology Data Exchange (ETDEWEB)
Nucci, M. C. [Department of Mathematics and Informatics, University of Perugia, via Vanvitelli 1, Perugia, I-06123 (Italy); Busso, M., E-mail: mariaclara.nucci@unipg.it, E-mail: busso@fisica.unipg.it [INFN, Section of Perugia, via Pascoli, Perugia, I-06123 (Italy)
2014-06-01
The advection of thermonuclear ashes by magnetized domains emerging near the H shell was suggested to explain asymptotic giant branch (AGB) star abundances. Here we verify this idea quantitatively through exact MHD models. Starting with a simple two-dimensional (2D) geometry and in an inertia frame, we study plasma equilibria avoiding the complications of numerical simulations. We show that below the convective envelope of an AGB star, variable magnetic fields induce a natural expansion, permitted by the almost ideal MHD conditions, in which the radial velocity grows as the second power of the radius. We then study the convective envelope, where the complexity of macroturbulence allows only for a schematic analytical treatment. Here the radial velocity depends on the square root of the radius. We then verify the robustness of our results with 3D calculations for the velocity, showing that for both studied regions the solution previously found can be seen as a planar section of a more complex behavior, in which the average radial velocity retains the same dependency on the radius found in 2D. As a final check, we compare our results to approximate descriptions of buoyant magnetic structures. For realistic boundary conditions, the envelope crossing times are sufficient to disperse in the huge convective zone any material transported, suggesting magnetic advection as a promising mechanism for deep mixing. The mixing velocities are smaller than for convection but larger than for diffusion and adequate for extra mixing in red giants.
The parton model for the diffusion
International Nuclear Information System (INIS)
We analyze the Buchmueller-Hebecker model for diffraction processes, point out its predictions to the diffractive structure function FD(3)2 (xIP, β,Q2). The break of factorization for the FD93)2 present in recent H1 data is well described introducing an extra soft (reggeon) contribution as an extension to the model. (author)
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. PMID:27575079
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.
THREE-DIMENSIONAL NUMERICAL MODEL FOR WINDING TIDAL RIVER WITH BRANCHES
Institute of Scientific and Technical Information of China (English)
YANG Li-ling; WANG Yun-hong; ZHU Zhi-xia; XU Feng-jun; DENG Jia-quan; YANG Fang
2007-01-01
Natural rivers are usually winding with branches and shoals, which are difficult to be simulated with rectangular grids. A 3-D current numerical model was established based on the orthogonal curvilinear coordinate system and vertical σ coordinate system. The equations were discretisized using a semi-implicit scheme. The "predictor" and "corrector" steps were applied for the horizontal momentum equations to meet the basic requirement that the depth-integrated currents obtained from the equations for 2-D and 3-D modes have identical values. And a modification of traditional method of dry/wet discriminance was proposed to determine accurately the boundary and ensure the continuity of variable boundary in the simulation. This model was verified with the data measured in a winding tidal river with branches in April, 2004. The simulated data of water levels and velocities agree well with the measured ones, and the computed results reveal well the practical flow characteristics, including the vertical secondary flow in a winding reach.
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
Institute of Scientific and Technical Information of China (English)
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.
Diffusion approximation for modeling of 3-D radiation distributions
International Nuclear Information System (INIS)
A three-dimensional transport code DIF3D, based on the diffusion approximation, is used to model the spatial distribution of radiation energy arising from volumetric isotropic sources. Future work will be concerned with the determination of irradiances and modeling of realistic scenarios, relevant to the battlefield conditions. 8 refs., 4 figs
A combinatorial model of malware diffusion via bluetooth connections.
Directory of Open Access Journals (Sweden)
Stefano Merler
Full Text Available We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy and closed form (more complex but efficiently computable expression.
Modeling Copper Diffusion in Polycrystalline CdTe Solar Cells
Energy Technology Data Exchange (ETDEWEB)
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
N. Yaghini; P.D. Iedema
2014-01-01
We present a comprehensive model to predict the molecular weight distribution (MWD),(1) and branching distribution of low-density polyethylene (IdPE),(2) for free radical polymerization system in a continuous stirred tank reactor (CSTR).(3) The model accounts for branching, by branching moment or ps
Numerical modelling of swirling diffusive flames
Directory of Open Access Journals (Sweden)
Parra-Santos Teresa
2016-01-01
Full Text Available Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing in mind the annular jet has swirl number over 0.5, a vortex breakdown appears in the axis of the burner. Besides, the sudden expansion with a ratio of 2 in diameter between nozzle exits and the test chamber produces the boundary layer separation with the corresponding torus shape recirculation. Contrasting the mixing and combustion models, the last one produces the reduction of the vortex breakdown.
Numerical modelling of swirling diffusive flames
Parra-Santos, Teresa; Perez, Ruben; Szasz, Robert Z.; Gutkowski, Artur N.; Castro, Francisco
2016-03-01
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.
COMPUTATION OF GREEKS FOR JUMP-DIFFUSION MODELS
M'Hamed Eddahbi; SIDI MOHAMED LALAOUI BEN CHERIF; ABDELAZIZ NASROALLAH
2015-01-01
In the present paper, we compute the Greeks for a class of jump diffusion models by using Malliavin calculus techniques. More precisely, the model under consideration is governed by a Brownian component and a jump part described by a compound Poisson process. Our approach consists of approximating the compound Poisson process by a suitable sequence of standard Poisson processes. The Greeks of the original model are obtained as limits or weighted limits of the Greeks of the approximate model. ...
Modelling on cavitation in a diffuser with vortex generator
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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
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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
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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
Energy Technology Data Exchange (ETDEWEB)
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.
Near Critical Catalyst Reactant Branching Processes with Controlled Immigration
Budhiraja, Amarjit
2012-01-01
Near critical catalyst-reactant branching processes with controlled immigration are studied. The reactant population evolves according to a branching process whose branching rate is proportional to the total mass of the catalyst. The bulk catalyst evolution is that of a classical continuous time branching process; in addition there is a specific form of immigration. Immigration takes place exactly when the catalyst population falls below a certain threshold, in which case the population is instantaneously replenished to the threshold. Such models are motivated by problems in chemical kinetics where one wants to keep the level of a catalyst above a certain threshold in order to maintain a desired level of reaction activity. A diffusion limit theorem for the scaled processes is presented, in which the catalyst limit is described through a reflected diffusion, while the reactant limit is a diffusion with coefficients that are functions of both the reactant and the catalyst. Stochastic averaging principles under ...
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.
Modeling Dynamics of Diffusion Across Heterogeneous Social Networks: News Diffusion in Social Media
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Peter Christen
2013-10-01
Full Text Available Diverse online social networks are becoming increasingly interconnected by sharing information. Accordingly, emergent macro-level phenomena have been observed, such as the synchronous spread of information across different types of social media. Attempting to analyze the emergent global behavior is impossible from the examination of a single social platform, and dynamic influences between different social networks are not negligible. Furthermore, the underlying structural property of networks is important, as it drives the diffusion process in a stochastic way. In this paper, we propose a macro-level diffusion model with a probabilistic approach by combining both the heterogeneity and structural connectivity of social networks. As real-world phenomena, we explore instances of news diffusion across different social media platforms from a dataset that contains over 386 million web documents covering a one-month period in early 2011. We find that influence between different media types is varied by the context of information. News media are the most influential in the arts and economy categories, while social networking sites (SNS and blog media are in the politics and culture categories, respectively. Furthermore, controversial topics, such as political protests and multiculturalism failure, tend to spread concurrently across social media, while entertainment topics, such as film releases and celebrities, are more likely driven by interactions within single social platforms. We expect that the proposed model applies to a wider class of diffusion phenomena in diverse fields and that it provides a way of interpreting the dynamics of diffusion in terms of the strength and directionality of influences among populations.
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.
Underwood, Thomas; Loebner, Keith; Cappelli, Mark
2015-11-01
Detailed measurements of the thermodynamic and electrodynamic plasma state variables within the plume of a pulsed plasma accelerator are presented. A quadruple Langmuir probe operating in current-saturation mode is used to obtain time resolved measurements of the plasma density, temperature, potential, and velocity along the central axis of the accelerator. This data is used in conjunction with a fast-framing, intensified CCD camera to develop and validate a model predicting the existence of two distinct types of ionization waves corresponding to the upper and lower solution branches of the Hugoniot curve. A deviation of less than 8% is observed between the quasi-steady, one-dimensional theoretical model and the experimentally measured plume velocity. This work is supported by the U.S. Department of Energy Stewardship Science Academic Program in addition to the National Defense Science Engineering Graduate Fellowship.
ORTHOGONAL-DIRECTIONAL FORWARD DIFFUSION IMAGE INPAINTING AND DENOISING MODEL
Institute of Scientific and Technical Information of China (English)
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 WORKING INTEGRATED MODEL FOR THE DIFFUSION OF CONSTRUCTION INNOVATION
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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.
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).
A Vertical Two-Dimensional Model to Simulate Tidal Hydrodynamics in A Branched Estuary
Institute of Scientific and Technical Information of China (English)
LIU Wen-Cheng; WU Chung-Hsing
2005-01-01
A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The governing equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are governed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations,tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
Institute of Scientific and Technical Information of China (English)
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.
Directory of Open Access Journals (Sweden)
Harlow Timothy J
2005-01-01
Full Text Available Abstract Background Bayesian phylogenetic inference holds promise as an alternative to maximum likelihood, particularly for large molecular-sequence data sets. We have investigated the performance of Bayesian inference with empirical and simulated protein-sequence data under conditions of relative branch-length differences and model violation. Results With empirical protein-sequence data, Bayesian posterior probabilities provide more-generous estimates of subtree reliability than does the nonparametric bootstrap combined with maximum likelihood inference, reaching 100% posterior probability at bootstrap proportions around 80%. With simulated 7-taxon protein-sequence datasets, Bayesian posterior probabilities are somewhat more generous than bootstrap proportions, but do not saturate. Compared with likelihood, Bayesian phylogenetic inference can be as or more robust to relative branch-length differences for datasets of this size, particularly when among-sites rate variation is modeled using a gamma distribution. When the (known correct model was used to infer trees, Bayesian inference recovered the (known correct tree in 100% of instances in which one or two branches were up to 20-fold longer than the others. At ratios more extreme than 20-fold, topological accuracy of reconstruction degraded only slowly when only one branch was of relatively greater length, but more rapidly when there were two such branches. Under an incorrect model of sequence change, inaccurate trees were sometimes observed at less extreme branch-length ratios, and (particularly for trees with single long branches such trees tended to be more inaccurate. The effect of model violation on accuracy of reconstruction for trees with two long branches was more variable, but gamma-corrected Bayesian inference nonetheless yielded more-accurate trees than did either maximum likelihood or uncorrected Bayesian inference across the range of conditions we examined. Assuming an exponential
Forecasting with a Repeat Purchase Diffusion Model
Ambar G. Rao; Masataka Yamada
1988-01-01
A methodology for forecasting the sales of an ethical drug as a function of marketing effort before any sales data are available and for updating the forecast with a few periods of sales data is presented. Physicians' perceptions of the drug on a number of attributes, e.g. effectiveness, range of ailments for which appropriate, frequency of prescriptions, are used to estimate the parameters of a model originally proposed by Lilien, Rao and Kalish (Lilien, G. L., A. G. Rao, S. Kalish. 1981. Ba...
Asymmetric diffusion model for oblique-incidence reflectometry
Institute of Scientific and Technical Information of China (English)
Yaqin Chen; Liji Cao; Liqun Sun
2011-01-01
A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectom-etry. By fitting to this asymmetric diffusion model, the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10% from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp') away from the incident point; particularly, μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10% accuracy. The method is verified by Monte Carlo simulations and experimentally tested on a phantom.%A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectometry.By fitting to this asymmetric diffusion model,the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10％ from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp')away from the incident point;particularly,μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10％ accuracy.The method is verified by Monte Carlo simulations and experimentally tested on a phantom.Knowledge about the optical properties,including the absorption coefficient (μa) and the reduced scattering coefficient (μ's =μs(1-g)),where μs is the scattering coefficient and g is the anisotropy factor of scattering,of biological tissues plays an important role for optical therapeutic and diagnostic techniques in medicine.
Modelling the sound transmission through partition walls using a diffusion model
Billon, A.; Foy, C; VALEAU, V; Picaut, J.; Sakout, A.
2007-01-01
The diffusion model has been used successfully to evaluate the acoustic behaviour of a system of coupled rooms connected through a coupling aperture. In this paper, an extension of this model is proposed to deal with the propagation of sound energy through a partition wall. The diffusion model can be considered as a extension of the statistical theory to none diffuse sound fields. Numerical comparisons with the statistical theory are then carried out. The following parameters are varied : its...
Directory of Open Access Journals (Sweden)
Omid Arjmandi-Tash
2012-12-01
Full Text Available Introduction: Atherosclerosis is a focal disease that susceptibly forms near bifurcations, anastomotic joints, side branches, and curved vessels along the arterial tree. In this study, pulsatile blood flow in a bifurcation model with a non-planar branch is investigated. Methods: Wall shear stress (WSS distributions along generating lines on vessels for different bifurcation angles are calculated during the pulse cycle. Results: The WSS at the outer side of the bifurcation plane vanishes especially for higher bifurcation angles but by increasing the bifurcation angle low WSS region squeezes. At the systolic phase there is a high possibility of formation of a separation region at the outer side of bifurcation plane for all the cases. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these peaks drop as bifurcation angle is increased. Conclusion: It was found that non-planarity of the daughter vessel lowers the minimum WSS at the outer side of the bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky.
A Patient-Specific Airway Branching Model for Mechanically Ventilated Patients
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Nor Salwa Damanhuri
2014-01-01
Full Text Available Background. Respiratory mechanics models have the potential to guide mechanical ventilation. Airway branching models (ABMs were developed from classical fluid mechanics models but do not provide accurate models of in vivo behaviour. Hence, the ABM was improved to include patient-specific parameters and better model observed behaviour (ABMps. Methods. The airway pressure drop of the ABMps was compared with the well-accepted dynostatic algorithm (DSA in patients diagnosed with acute respiratory distress syndrome (ARDS. A scaling factor (α was used to equate the area under the pressure curve (AUC from the ABMps to the AUC of the DSA and was linked to patient state. Results. The ABMps recorded a median α value of 0.58 (IQR: 0.54–0.63; range: 0.45–0.66 for these ARDS patients. Significantly lower α values were found for individuals with chronic obstructive pulmonary disease (P<0.001. Conclusion. The ABMps model allows the estimation of airway pressure drop at each bronchial generation with patient-specific physiological measurements and can be generated from data measured at the bedside. The distribution of patient-specific α values indicates that the overall ABM can be readily improved to better match observed data and capture patient condition.
GIS-BASED 1-D DIFFUSIVE WAVE OVERLAND FLOW MODEL
Energy Technology Data Exchange (ETDEWEB)
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.
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.
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.
A Short Note on Non-isothermal Diffusion Models
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T. Ficker
2003-01-01
Full Text Available Asymptotic behaviour of the DIAL and DRAL non-isothermal models, derived previously for the diffusion of water vapour through a porous building structure, is studied under the assumption that the initially non-isothermal structure becomes purely isothermal.
Mathematical modeling of clearing liquid drop diffusion after intradermal injection
Stolnitz, Mikhail M.; Bashkatov, Alexey N.; Genina, Elina A.; Tuchin, Valery V.
2007-05-01
The mathematical model of clearing agent diffusion after intradermal injection has been developed. Skin was presented as multilayer medium, but one layer with proper boundary conditions is considered. Analytical solution of the boundary problem for small and large time intervals is obtained.
Traveling Wave Solutions in a Reaction-Diffusion Epidemic Model
Sheng Wang; Wenbin Liu; Zhengguang Guo; Weiming Wang
2013-01-01
We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.
Diffusion model of delayed hydride cracking in zirconium alloys
Shmakov, AA; Kalin, BA; Matvienko, YG; Singh, RN; De, PK
2004-01-01
We develop a method for the evaluation of the rate of delayed hydride cracking in zirconium alloys. The model is based on the stationary solution of the phenomenological diffusion equation and the detailed analysis of the distribution of hydrostatic stresses in the plane of a sharp tensile crack. Th
Probability of induced nuclear fission in diffusion model
International Nuclear Information System (INIS)
The apparatus of the fission diffusion model taking into account nonequilibrium stage of the process as applied to the description of the probability of induced nuclear fission is described. The results of calculation of the energy dependence of 212Po nuclear fissility according to the new approach are presented
Quasineutral limit of a standard drift diffusion model for semiconductors
Institute of Scientific and Technical Information of China (English)
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.
Decomposing Task-Switching Costs with the Diffusion Model
Schmitz, Florian; Voss, Andreas
2012-01-01
In four experiments, task-switching processes were investigated with variants of the alternating runs paradigm and the explicit cueing paradigm. The classical diffusion model for binary decisions (Ratcliff, 1978) was used to dissociate different components of task-switching costs. Findings can be reconciled with the view that task-switching…
A Mixed-Culture Biofilm Model with Cross-Diffusion.
Rahman, Kazi A; Sudarsan, Rangarajan; Eberl, Hermann J
2015-11-01
We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system.
Computational Modeling of Turbulent Swirling Diffusion Flames
Vondál, Jiří
2012-01-01
Schopnost predikovat tepelné toky do stěn v oblasti spalování, konstrukce pecí a procesního průmyslu je velmi důležitá pro návrh těchto zařízení. Je to často klíčový požadavek pro pevnostní výpočty. Cílem této práce je proto získat kvalitní naměřená data na experimentálním zařízení a využít je pro validaci standardně využívaných modelů počítačového modelování turbulentního vířivého difúzního spalování zemního plynu. Experimentální měření bylo provedeno na vodou chlazené spalovací komoře průmy...
Modeling the diffusion of phosphorus in silicon in 3-D
Energy Technology Data Exchange (ETDEWEB)
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.
Two ARCH Models and Their Limitations as Diffusion Processes
Institute of Scientific and Technical Information of China (English)
杨海波; 叶俊
2002-01-01
Two typical ARCH models: the ASDARCH model and the APARCH model are analyzed. Let Yk and σ2k denote the log returns and the volatility. When the time interval h goes to zero, (Yk,σ2k), as a discrete time Markov chain system, weakly converges to a continuous time diffusion process. The continuous time approximation of the ASDARCH model is done using two different methods. With some transformation, these two results are equivalent to high frequency data. The continuous time approximation of the APARCH model is obtained by a different procedure.
A hierarchy of models related to nanoflows and surface diffusion
Aoki, Kazuo; Degond, Pierre
2010-01-01
In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to analyze the mechanisms that determine mobility of molecules in nanoscale channels. This approach proved to be remarkably useful to give new insight on these issues, such as density dependence of the diffusion coefficient. In this paper we revisit these works to derive the kinetic and diffusion models introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker by using classical tools of kinetic theory such as scaling and systematic asymptotic analysis. Some results are extended to less restrictive hypothesis.
Macroscopic diffusion models for precipitation in crystalline gallium arsenide
Energy Technology Data Exchange (ETDEWEB)
Kimmerle, Sven-Joachim Wolfgang
2009-09-21
Based on a thermodynamically consistent model for precipitation in gallium arsenide crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose two different mathematical models to describe the size evolution of liquid droplets in a crystalline solid. The first model treats the diffusion-controlled regime of interface motion, while the second model is concerned with the interface-controlled regime of interface motion. Our models take care of conservation of mass and substance. These models generalise the well-known Mullins- Sekerka model for Ostwald ripening. We concentrate on arsenic-rich liquid spherical droplets in a gallium arsenide crystal. Droplets can shrink or grow with time but the centres of droplets remain fixed. The liquid is assumed to be homogeneous in space. Due to different scales for typical distances between droplets and typical radii of liquid droplets we can derive formally so-called mean field models. For a model in the diffusion-controlled regime we prove this limit by homogenisation techniques under plausible assumptions. These mean field models generalise the Lifshitz-Slyozov-Wagner model, which can be derived from the Mullins-Sekerka model rigorously, and is well understood. Mean field models capture the main properties of our system and are well adapted for numerics and further analysis. We determine possible equilibria and discuss their stability. Numerical evidence suggests in which case which one of the two regimes might be appropriate to the experimental situation. (orig.)
A Lattice Boltzmann model for diffusion of binary gas mixtures
Bennett, Sam
2010-01-01
This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multi-component model used in the subsequent chapters. Commonly used single component LB methods use a non-physical equation of state, in which the relationship between pressure and density varies according to the sca...
Institute of Scientific and Technical Information of China (English)
Hui-Yong Jiang; Zhong-Xi Huang; Xue-Feng Zhang; Richard Desper; Tong Zhao
2007-01-01
AIM: To construct tree models for classification of diffuse large B-cell lymphomas (DLBCL) by chromosome copy numbers, to compare them with cDNA microarray classification, and to explore models of multi-gene, multi-step and multi-pathway processes of DLBCL tumorigenesis.METHODS: Maximum-weight branching and distance based models were constructed based on the comparative genomic hybridization (CGH) data of 123 DLBCL samples using the established methods and software of Desper et al. A maximum likelihood tree model was also used to analyze the data. By comparing with the results reported in literature, values of tree models in the classification of DLBCL were elucidated.RESULTS: Both the branching and the distance-based trees classified DLBCL into three groups. We combined the classification methods of the two models and classified DLBCL into three categories according to their characteristics. The first group was marked by +Xq, +Xp, -17p and +13q; the second group by +3q, +18q and +18p; and the third group was marked by -6q and +6p. This chromosomal classification was consistent with cDNA classification. It indicated that -6q and +3q were two main events in the tumorigenesis of lymphoma.CONCLUSION: Tree models of lymphoma established from CGH data can be used in the classification of DLBCL. These models can suggest multi-gene, multi-step and multi-pathway processes of tumorigenesis.Two pathways, -6q preceding +6q and +3q preceding +18q, may be important in understanding tumorigenesis of DLBCL. The pathway, -6q preceding +6q, may have a close relationship with the tumorigenesis of non-GCB DLBCL.
Do Coupled Climate Models Correctly SImulate the Upward Branch of the Deept Ocean Global Conveyor?
Energy Technology Data Exchange (ETDEWEB)
Sarmiento, Jorge L; Downes, Stephanie; Bianchi, Daniele
2013-01-17
The large-scale meridional overturning circulation (MOC) connects the deep ocean, a major reservoir of carbon, to the other components of the climate system and must therefore be accurately represented in Earth System Models. Our project aims to address the specific question of the pathways and mechanisms controlling the upwelling branch of the MOC, a subject of significant disagreement between models and observational syntheses, and among general circulation models. Observations of these pathways are limited, particularly in regions of complex hydrography such as the Southern Ocean. As such, we rely on models to examine theories of the overturning circulation, both physically and biogeochemically. This grant focused on a particular aspect of the meridional overturning circulation (MOC) where there is currently significant disagreement between models and observationally based analyses of the MOC, and amongst general circulation models. In particular, the research focused on addressing the following questions: 1. Where does the deep water that sinks in the polar regions rise to the surface? 2. What processes are responsible for this rise? 3. Do state-of-the-art coupled GCMs capture these processes? Our research had three key components: observational synthesis, model development and model analysis. In this final report we outline the key results from these areas of research for the 2007 to 2012 grant period. The research described here was carried out primarily by graduate student, Daniele Bianchi (now a Postdoc at McGill University, Canada), and Postdoc Stephanie Downes (now a Research Fellow at The Australian national University, Australia). Additional support was provided for programmers Jennifer Simeon as well as Rick Slater.
Pouch, Alison M; Tian, Sijie; Takebe, Manabu; Yuan, Jiefu; Gorman, Robert; Cheung, Albert T; Wang, Hongzhi; Jackson, Benjamin M; Gorman, Joseph H; Gorman, Robert C; Yushkevich, Paul A
2015-12-01
Deformable modeling with medial axis representation is a useful means of segmenting and parametrically describing the shape of anatomical structures in medical images. Continuous medial representation (cm-rep) is a "skeleton-first" approach to deformable medial modeling that explicitly parameterizes an object's medial axis and derives the object's boundary algorithmically. Although cm-rep has effectively been used to segment and model a number of anatomical structures with non-branching medial topologies, the framework is challenging to apply to objects with branching medial geometries since branch curves in the medial axis are difficult to parameterize. In this work, we demonstrate the first clinical application of a new "boundary-first" deformable medial modeling paradigm, wherein an object's boundary is explicitly described and constraints are imposed on boundary geometry to preserve the branching configuration of the medial axis during model deformation. This "boundary-first" framework is leveraged to segment and morphologically analyze the aortic valve apparatus in 3D echocardiographic images. Relative to manual tracing, segmentation with deformable medial modeling achieves a mean boundary error of 0.41 ± 0.10 mm (approximately one voxel) in 22 3DE images of normal aortic valves at systole. Deformable medial modeling is additionally demonstrated on pathological cases, including aortic stenosis, Marfan syndrome, and bicuspid aortic valve disease. This study demonstrates a promising approach for quantitative 3DE analysis of aortic valve morphology.
Branching Dynamics of Viral Information Spreading
Iribarren, José Luis
2011-01-01
Despite its importance for rumors or innovations propagation, peer-to-peer collaboration, social networking or Marketing, the dynamics of information spreading is not well understood. Since the diffusion depends on the heterogeneous patterns of human behavior and is driven by the participants' decisions, its propagation dynamics shows surprising properties not explained by traditional epidemic or contagion models. Here we present a detailed analysis of our study of real Viral Marketing campaigns where tracking the propagation of a controlled message allowed us to analyze the structure and dynamics of a diffusion graph involving over 31,000 individuals. We found that information spreading displays a non-Markovian branching dynamics that can be modeled by a two-step Bellman-Harris Branching Process that generalizes the static models known in the literature and incorporates the high variability of human behavior. It explains accurately all the features of information propagation under the "tipping-point" and can...
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Directory of Open Access Journals (Sweden)
Monika Žecová
2015-01-01
Full Text Available The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.
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.
Bayesian 2D Deconvolution: A Model for Diffuse Ultrasound Scattering
Directory of Open Access Journals (Sweden)
Oddvar Husby
2001-10-01
Full Text Available Observed medical ultrasound images are degraded representations of the true acoustic tissue reflectance. The degradation is due to blur and speckle, and significantly reduces the diagnostic value of the images. In order to remove both blur and speckle we have developed a new statistical model for diffuse scattering in 2D ultrasound radio-frequency images, incorporating both spatial smoothness constraints and a physical model for diffuse scattering. The modeling approach is Bayesian in nature, and we use Markov chain Monte Carlo methods to obtain the restorations. The results from restorations of some real and simulated radio-frequency ultrasound images are presented and compared with results produced by Wiener filtering.
Evolution and nucleosynthesis of helium-rich asymptotic giant branch models
Shingles, Luke J; Karakas, Amanda I; Stancliffe, Richard J; Lattanzio, John C; Lugaro, Maria
2015-01-01
There is now strong evidence that some stars have been born with He mass fractions as high as $Y \\approx 0.40$ (e.g., in $\\omega$ Centauri). However, the advanced evolution, chemical yields, and final fates of He-rich stars are largely unexplored. We investigate the consequences of He-enhancement on the evolution and nucleosynthesis of intermediate-mass asymptotic giant branch (AGB) models of 3, 4, 5, and 6 M$_\\odot$ with a metallicity of $Z = 0.0006$ ([Fe/H] $\\approx -1.4$). We compare models with He-enhanced compositions ($Y=0.30, 0.35, 0.40$) to those with primordial He ($Y=0.24$). We find that the minimum initial mass for C burning and super-AGB stars with CO(Ne) or ONe cores decreases from above our highest mass of 6 M$_\\odot$ to $\\sim$ 4-5 M$_\\odot$ with $Y=0.40$. We also model the production of trans-Fe elements via the slow neutron-capture process (s-process). He-enhancement substantially reduces the third dredge-up efficiency and the stellar yields of s-process elements (e.g., 90% less Ba for 6 M$_\\o...
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...
Chih-Chun Hsieh; Weite Wu
2012-01-01
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: .
Directory of Open Access Journals (Sweden)
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: .
Characterization and modeling of thermal diffusion and aggregation in nanofluids.
Energy Technology Data Exchange (ETDEWEB)
Gharagozloo, Patricia E.; Goodson, Kenneth E. (Stanford University, Stanford, CA)
2010-05-01
Fluids with higher thermal conductivities are sought for fluidic cooling systems in applications including microprocessors and high-power lasers. By adding high thermal conductivity nanoscale metal and metal oxide particles to a fluid the thermal conductivity of the fluid is enhanced. While particle aggregates play a central role in recent models for the thermal conductivity of nanofluids, the effect of particle diffusion in a temperature field on the aggregation and transport has yet to be studied in depth. The present work separates the effects of particle aggregation and diffusion using parallel plate experiments, infrared microscopy, light scattering, Monte Carlo simulations, and rate equations for particle and heat transport in a well dispersed nanofluid. Experimental data show non-uniform temporal increases in thermal conductivity above effective medium theory and can be well described through simulation of the combination of particle aggregation and diffusion. The simulation shows large concentration distributions due to thermal diffusion causing variations in aggregation, thermal conductivity and viscosity. Static light scattering shows aggregates form more quickly at higher concentrations and temperatures, which explains the increased enhancement with temperature reported by other research groups. The permanent aggregates in the nanofluid are found to have a fractal dimension of 2.4 and the aggregate formations that grow over time are found to have a fractal dimension of 1.8, which is consistent with diffusion limited aggregation. Calculations show as aggregates grow the viscosity increases at a faster rate than thermal conductivity making the highly aggregated nanofluids unfavorable, especially at the low fractal dimension of 1.8. An optimum nanoparticle diameter for these particular fluid properties is calculated to be 130 nm to optimize the fluid stability by reducing settling, thermal diffusion and aggregation.
Setegn, S. G.; Mahmoudi, M.; Lawrence, A.; Duque, N.
2015-12-01
The Applied Research Center at Florida International University (ARC-FIU) is supporting the soil and groundwater remediation efforts of the U.S. Department of Energy (DOE) Savannah River Site (SRS) by developing a surface water model to simulate the hydrology and the fate and transport of contaminants and sediment in the Tims Branch watershed. Hydrological models are useful tool in water and land resource development and decision-making for watershed management. Moreover, simulation of hydrological processes improves understanding of the environmental dynamics and helps to manage and protect water resources and the environment. MIKE SHE, an advanced integrated modeling system is used to simulate the hydrological processes of the Tim Branch watershed with the objective of developing an integrated modeling system to improve understanding of the physical, chemical and biological processes within the Tims Branch watershed. MIKE SHE simulates water flow in the entire land based phase of the hydrological cycle from rainfall to river flow, via various flow processes such as, overland flow, infiltration, evapotranspiration, and groundwater flow. In this study a MIKE SHE model is developed and applied to the Tim branch watershed to study the watershed response to storm events and understand the water balance of the watershed under different climatic and catchment characteristics. The preliminary result of the integrated model indicated that variation in the depth of overland flow highly depend on the amount and distribution of rainfall in the watershed. The ultimate goal of this project is to couple the MIKE SHE and MIKE 11 models to integrate the hydrological component in the land phase of hydrological cycle and stream flow process. The coupled MIKE SHE/MIKE 11 model will further be integrated with an Ecolab module to represent a range of water quality, contaminant transport, and ecological processes with respect to the stream, surface water and groundwater in the Tims
Pareto genealogies arising from a Poisson branching evolution model with selection.
Huillet, Thierry E
2014-02-01
We study a class of coalescents derived from a sampling procedure out of N i.i.d. Pareto(α) random variables, normalized by their sum, including β-size-biasing on total length effects (β < α). Depending on the range of α we derive the large N limit coalescents structure, leading either to a discrete-time Poisson-Dirichlet (α, -β) Ξ-coalescent (α ε[0, 1)), or to a family of continuous-time Beta (2 - α, α - β)Λ-coalescents (α ε[1, 2)), or to the Kingman coalescent (α ≥ 2). We indicate that this class of coalescent processes (and their scaling limits) may be viewed as the genealogical processes of some forward in time evolving branching population models including selection effects. In such constant-size population models, the reproduction step, which is based on a fitness-dependent Poisson Point Process with scaling power-law(α) intensity, is coupled to a selection step consisting of sorting out the N fittest individuals issued from the reproduction step.
Modeling competition between two pharmaceutical drugs using innovation diffusion models
Guseo, Renato; Mortarino, Cinzia
2016-01-01
The study of competition among brands in a common category is an interesting strategic issue for involved firms. Sales monitoring and prediction of competitors’ performance represent relevant tools for management. In the pharmaceutical market, the diffusion of product knowledge plays a special role, different from the role it plays in other competing fields. This latent feature naturally affects the evolution of drugs’ performances in terms of the number of packages sold. In this paper, we pr...
Chaotic map models of soot fluctuations in turbulent diffusion flames
Energy Technology Data Exchange (ETDEWEB)
Mukerji, S.; McDonough, J.M.; Menguec, M.P.; Manickavasagam, S. [Univ. of Kentucky, Lexington, KY (United States). Dept. of Mechanical Engineering; Chung, S. [Univ. of Illinois, Urbana, IL (United States). Dept. of Chemical Engineering
1998-10-01
In this paper, the authors introduce a methodology to characterize time-dependent soot volume fraction fluctuations in turbulent diffusion flames via chaotic maps. The approach is based on the hypothesis that fluctuations of properties in turbulent flames are deterministic in nature, rather than statistical. The objective is to develop models of these fluctuations to be used in comprehensive algorithms to study the nature of turbulent flames and the interaction of turbulence with radiation. To this end the authors measured the time series of soot scattering coefficient in an ethylene diffusion flame from light scattering experiments and fit these data to linear combinations of chaotic maps of the unit interval. Both time series and power spectra can be modeled with reasonable accuracy in this way.
Modeling and Analysis of New Products Diffusion on Heterogeneous Networks
Directory of Open Access Journals (Sweden)
Shuping Li
2014-01-01
Full Text Available We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.
Thermomechanics of damageable materials under diffusion: modelling and analysis
Roubíček, Tomáš; Tomassetti, Giuseppe
2015-12-01
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat generation/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation, water and heat transport in concrete, and if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type.
Energy Technology Data Exchange (ETDEWEB)
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)
Global Dynamics Analysis of Homogeneous New Products Diffusion Model
Shuping Li; Zhen Jin
2013-01-01
A mathematical model with stage structures is presented that incorporates the awareness stage and the decision-making stage; individuals exchange product information by two channels: mass media and interpersonal communication. When the persuasive advertisement is neglected in the decision-making stage, we find a threshold value about whether new products diffusion is successful or not. When the persuasive advertisement is considered, there must exist a positive equilibrium unde...
Spatio-Temporal Patterns for a Generalized Innovation Diffusion Model
Hashemi, Fariba; Hongler, Max-Olivier; Gallay, Olivier
2011-01-01
We construct a model of innovation diffusion that incorporates a spatial component into a classical imitation-innovation dynamics first introduced by F. Bass. Relevant for situations where the imitation process explicitly depends on the spatial proximity between agents, the resulting nonlinear field dynamics is exactly solvable. As expected for nonlinear collective dynamics, the imitation mechanism generates spatio-temporal patterns, possessing here the remarkable feature that they can be exp...
A Punctuated-Equilibrium Model of Technology Diffusion
Christoph H. Loch; Huberman, Bernardo A.
1999-01-01
We present an evolutionary model of technology diffusion in which an old and a new technology are available, both of which improve their performance incrementally over time. Technology adopters make repeated choices between the established and the new technology based on their perceived performance, which is subject to uncertainty. Both technologies exhibit positive externalities, or performance benefits from others using the same technology. We find that the superior technology will not nece...
Pricing turbo warrants under mixed-exponential jump diffusion model
Yu, Jianfeng; Xu, Weidong
2016-06-01
Turbo warrant is a special type of barrier options in which the rebate is calculated as another exotic option. In this paper, using Laplace transforms we obtain the valuation of turbo warrant under the mixed-exponential jump diffusion model, which is able to approximate any jump size distribution. The numerical Laplace inversion examples verify that the analytical solutions are accurate. The results of simulation confirm the argument that jump risk should not be ignored in the valuation of turbo warrants.
Numerical modelling and image reconstruction in diffuse optical tomography
Dehghani, Hamid; Srinivasan, Subhadra; Pogue, Brian W.; Gibson, Adam
2009-01-01
The development of diffuse optical tomography as a functional imaging modality has relied largely on the use of model-based image reconstruction. The recovery of optical parameters from boundary measurements of light propagation within tissue is inherently a difficult one, because the problem is nonlinear, ill-posed and ill-conditioned. Additionally, although the measured near-infrared signals of light transmission through tissue provide high imaging contrast, the reconstructed images suffer ...
Applications of advanced atmospheric diffusion models in complex terrain
International Nuclear Information System (INIS)
The recalculation of a single diffusion pattern experimentally determined in the field near an artificial hill in a brown coal mining area serves as an example to show the performance of the MOSES modular modelling system. The other example presented refers to the determination of the large-area, mean wind direction distribution in the large, orographically structured region of North-Rhine Westfalia. (DG)
A New Model of Interfacial Physical Contact in Diffusion Bonding
Institute of Scientific and Technical Information of China (English)
Peng HE; Jicai FENG; Yiyu QIAN
2004-01-01
Through eliminating voids not affecting the primary bonding process, and incorporating interlayer and flexible base material, the interface geometry character and brief mathematics process were put forth. Through analyzing contact process of diffusion bonding, contact area model was settled. It can interpret the phenomenon of different interface areas taking on different strengths. In the course of physical contact, shear stresses serve an important function for the plastic deformation and the cohesion of interface voids.
Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems
Karakaya, Emrah
2014-01-01
This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of phot...
DEFF Research Database (Denmark)
Vester, Steen
2015-01-01
We study the complexity of the model-checking problem for the branching-time logic CTL ∗ and the alternating-time temporal logics ATL/ATL ∗ in one-counter processes and one-counter games respectively. The complexity is determined for all three logics when integer weights are input in unary (non...
A flamelet model for turbulent diffusion combustion in supersonic flow
Institute of Scientific and Technical Information of China (English)
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.
Jun, K S; Kang, J W; Lee, K S
2007-01-01
Diffuse pollution sources along a stream reach are very difficult to both monitor and estimate. In this paper, a systematic method using an optimal estimation algorithm is presented for simultaneous estimation of diffuse pollution and model parameters in a stream water quality model. It was applied with the QUAL2E model to the South Han River in South Korea for optimal estimation of kinetic constants and diffuse loads along the river. Initial calibration results for kinetic constants selected from a sensitivity analysis reveal that diffuse source inputs for nitrogen and phosphorus are essential to satisfy the system mass balance. Diffuse loads for total nitrogen and total phosphorus were estimated by solving the expanded inverse problem. Comparison of kinetic constants estimated simultaneously with diffuse sources to those estimated without diffuse loads, suggests that diffuse sources must be included in the optimization not only for its own estimation but also for adequate estimation of the model parameters. Application of the optimization method to river water quality modeling is discussed in terms of the sensitivity coefficient matrix structure.
Hub and spoke: A community model for child branch students at the University of Southampton
Wigley, W.
2006-01-01
Whilst existing health care education provides a foundation in public health there is a need to enhance the knowledge and skills of practitioners expected to contribute to the new public health agenda. Child branch graduates will be important to delivering this agenda as most children are cared for in a community setting. Previously child health students would receive little community experience as part of their training and on qualifying child branch students applying to work in communi...
Body size and the small branch niche: using marsupial ontogeny to model primate locomotor evolution.
Shapiro, Liza J; Young, Jesse W; VandeBerg, John L
2014-03-01
Recently proposed ancestral locomotor and morphological 'stages' leading to the evolution of primates have emphasized small body size, and a transition from a clawed non-grasping stage, to a clawed, grasping stage with clawless opposable hallux, to a fully-nailed primate with grasping extremities. This evolutionary transition was presumably associated with frequent use of the small branch niche. To model elements of these evolutionary transitions, we investigate how body size, substrate size, substrate orientation and grasping morphology interact to influence quadrupedal kinematics within and between ontogenetic samples of two small-bodied marsupials, one arboreal (Petaurus breviceps) and the other mainly terrestrial (Monodelphis domestica). Longitudinal morphometric and kinematic data were collected from four juvenile P. breviceps (33-75 g) and two juvenile M. domestica (18-95 g) walking across poles of three diameters (2.5, 1.0, and 0.5 cm) and three orientations (horizontal, 30° incline, 30° decline). The two species responded similarly to some substrate conditions, but diverged in response to others. Kinematic divergence between the two species reflects Monodelphis' relatively shorter digits, reduced grasping ability and greater need for stabilizing mechanisms on narrow substrates. At a given relative body size or pole orientation, Monodelphis used higher limb duty factors, more limbs in support per stride, lower limb phases, and in some conditions, faster speeds compared with Petaurus. Interspecific differences were the least distinct on declined poles, highlighting the particular challenge of this substrate condition, even for arboreally adapted species. Small-bodied, arboreal primate ancestors would likely have employed the kinematic mechanisms common to our model taxa, but those with enhanced grasping adaptations would most likely not have required the increased level of stabilizing mechanisms exhibited by Monodelphis. Thus, using these two species
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.
Measurements and modeling of explosive vapor diffusion in snow
Albert, Mary R.; Cragin, James H.; Leggett, Daniel C.
2000-08-01
The detection of buried mines is important to both for humanitarian and military strategic de-mining both at home and abroad, and recent efforts in chemical detection show promise for definitive identification of buried miens. The impact of weather has a large effect on the fate and transport of the explosives vapor that these systems sense. In many areas of military conflict, and at Army military training grounds in cold regions, winter weather affects military operations for many months of the year. In cold regions, the presence of freezing ground or a snow cover may provide increased temporary storage of the explosive, potentially leading to opportunities for more optimal sensing conditions later. This paper discusses the result of a controlled laboratory experiment to investigate explosives diffusion through snow, quantitative microscopy measurements of snow microstructure including specific surface, and verifications of our transport model using this data. In experiments measuring 1,3-DNB, 2,4-DNT and 2,4,6-TNT we determined an effective diffusion coefficient of 1.5 X 10-6 cm2/s from measurements through isothermal sieved snow with equivalent sphere radius of 0.11 mm. Adsorption is a major factor in diffusive transport of these explosives through snow. The data was used to verify our finite element mole of explosives transport. Measurements and model results show close agreement.
Diffusion limited growth in laminar flows
R.M.H. Merks; A.G. Hoekstra; J.A. Kaandorp; P.M.A. Sloot
2003-01-01
In the diffusion-limited aggregation (DLA) model, pioneered by Witten and Sander (Phys. Rev. Lett.47, 1400 (1981)), diffusing particles irreversibly attach to a growing cluster which is initiated with a single solid seed. This process generates clusters with a branched morphology. Advectiondiffusion
Gurau, Razvan
2013-01-01
Melonic graphs constitute the family of graphs arising at leading order in the 1/N expansion of tensor models. They were shown to lead to a continuum phase, reminiscent of branched polymers. We show here that they are in fact precisely branched polymers, that is, they possess Hausdorff dimension 2 and spectral dimension 4/3.
Time Fractional Diffusion Equations and Analytical Solvable Models
Bakalis, Evangelos; Zerbetto, Francesco
2016-08-01
The anomalous diffusion of a particle that moves in complex environments is analytically studied by means of the time fractional diffusion equation. The influence on the dynamics of a random moving particle caused by a uniform external field is taken into account. We extract analytical solutions in terms either of the Mittag-Leffler functions or of the M- Wright function for the probability distribution, for the velocity autocorrelation function as well as for the mean and the mean square displacement. Discussion of the applicability of the model to real systems is made in order to provide new insight of the medium from the analysis of the motion of a particle embedded in it.
Modeling of Moisture Diffusion in Carbon Braided Composites
Directory of Open Access Journals (Sweden)
S. Laurenzi
2008-01-01
Full Text Available In this study, we develop a methodology based on finite element analysis to predict the weight gain of carbon braided composite materials exposed to moisture. The analysis was based on the analogy between thermal conduction and diffusion processes, which allowed for a commercial code for finite element analysis to be used. A detailed finite element model using a repetitive unit cell (RUC was developed both for bundle and carbon braided composites. Conditioning tests were performed to estimate the diffusivity of both the resin and composite. When comparing numerical and experimental results, it was observed that the procedure introduces an average error of 20% and a maximum error of 31% if the RUC is assumed to be isotropic. On the other hand, the average error does not exceed 10% and the maximum error is less than 20% when the material is considered as orthotropic. The procedure is independent of the particular fiber architecture and can be extended to other composites.
Diffusion of innovations in Axelrod’s model
Tilles, Paulo F. C.; Fontanari, José F.
2015-11-01
Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e., individuals interact preferentially with similar others). The strength of these social influences are controlled by two parameters: $F$, the number of features that characterizes the cultures and $q$, the common number of states each feature can assume. Here we assume that the innovation is a new state of a cultural feature of a single individual -- the innovator -- and study how the innovation spreads through the networks among the individuals. For infinite regular lattices in one (1D) and two dimensions (2D), we find that initially the successful innovation spreads linearly with the time $t$, but in the long-time limit it spreads diffusively ($\\sim t^{1/2}$) in 1D and sub-diffusively ($\\sim t/\\ln t$) in 2D. For finite lattices, the growth curves for the number of adopters are typically concave functions of $t$. For random graphs with a finite number of nodes $N$, we argue that the classical S-shaped growth curves result from a trade-off between the average connectivity $K$ of the graph and the per feature diversity $q$. A large $q$ is needed to reduce the pace of the initial spreading of the innovation and thus delimit the early-adopters stage, whereas a large $K$ is necessary to ensure the onset of the take-off stage at which the number of adopters grows superlinearly with $t$. In an infinite random graph we find that the number of adopters of a successful innovation scales with $t^\\gamma$ with $\\gamma =1$ for $K> 2$ and $1/2 diffusion of successful innovations in diverse scenarios.
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.
Modeling Simple Driving Tasks with a One-Boundary Diffusion Model
Ratcliff, Roger; Strayer, David
2014-01-01
A one-boundary diffusion model was applied to the data from two experiments in which subjects were performing a simple simulated driving task. In the first experiment, the same subjects were tested on two driving tasks using a PC-based driving simulator and the psychomotor vigilance test (PVT). The diffusion model fit the response time (RT) distributions for each task and individual subject well. Model parameters were found to correlate across tasks which suggests common component processes w...
Sound Field Modeling in Architectural Acoustics using a Diffusion Equation Based Model
Fortin, Nicolas; Picaut, Judicaël; Billon, Alexis; Valeau, Vincent; SAKOUT, Anas
2009-01-01
In this paper, an implementation of a model for room-acoustic predictions in COMSOL Multiphysics is presented. The model (called diffusion model) is based on the solving of diffusion equations instead of classical wave equations and allows simulating the sound propagation in complex geometries at high frequency. Instead of using COMSOL Multiplysics to solve directly the problem, a specific tool has been developed. It is composed of a user-friendly interface (I-Simpa) which manipulates all the...
Sound Field Modeling in Architectural Acoustics using a Diffusion Equation Based Model
Fortin, Nicolas; Picaut, Judicaël; Billon, Alexis; Valeau, Vincent; SAKOUT, Anas
2009-01-01
In this paper, an implementation of a model for room-acoustic predictions in COMSOL Multiphysics is presented. The model (called diffusion model) is based on the solving of diffusion equations instead of classical wave equations and allows simulating the sound propagation in complex geometries at high frequency. Instead of using COMSOL Multiplysics to solve directly the problem, a specific tool has been developed. It is composed of a user-friendly interface (I-Simpa) which manipulates a...
Directory of Open Access Journals (Sweden)
Lee Shaish
Full Text Available Phenotypic plasticity enables multicellular organisms to adjust morphologies and various life history traits to variable environmental challenges. Here, we elucidate fixed and plastic architectural rules for colony astogeny in multiple types of colonial ramets, propagated by cutting from genets of the branching coral Stylophora pistillata from Eilat, the Red Sea. We examined 16 morphometric parameters on 136 one-year old S. pistillata colonies (of seven genotypes, originating from small fragments belonging, each, to one of three single-branch types (single tips, start-up, and advanced bifurcating tips or to structural preparative manipulations (representing a single or two growth axes. Experiments were guided by the rationale that in colonial forms, complexity of evolving phenotypic plasticity can be associated with a degree of structural modularity, where shapes are approached by erecting iterative growth patterns at different levels of coral-colony organization. Analyses revealed plastic morphometric characters at branch level, and predetermined morphometric traits at colony level (only single trait exhibited plasticity under extreme manipulation state. Therefore, under the experimental manipulations of this study, phenotypic plasticity in S. pistillata appears to be related to branch level of organization, whereas colony traits are controlled by predetermined genetic architectural rules. Each level of organization undergoes its own mode of astogeny. However, depending on the original ramet structure, the spherical 3-D colonial architecture in this species is orchestrated and assembled by both developmental trajectories at the branch level, and traits at the colony level of organization. In nature, branching colonial forms are often subjected to harsh environmental conditions that cause fragmentation of colony into ramets of different sizes and structures. Developmental traits that are plastic, responding to fragment structure and are not
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
Subgrid models for mass and thermal diffusion in turbulent mixing
International Nuclear Information System (INIS)
We propose a new method for the large eddy simulation (LES) of turbulent mixing flows. The method yields convergent probability distribution functions (PDFs) for temperature and concentration and a chemical reaction rate when applied to reshocked Richtmyer-Meshkov (RM) unstable flows. Because such a mesh convergence is an unusual and perhaps original capability for LES of RM flows, we review previous validation studies of the principal components of the algorithm. The components are (i) a front tracking code, FronTier, to control numerical mass diffusion and (ii) dynamic subgrid scale (SGS) models to compensate for unresolved scales in the LES. We also review the relevant code comparison studies. We compare our results to a simple model based on 1D diffusion, taking place in the geometry defined statistically by the interface (the 50% isoconcentration surface between the two fluids). Several conclusions important to physics could be drawn from our study. We model chemical reactions with no closure approximations beyond those in the LES of the fluid variables itself, and as with dynamic SGS models, these closures contain no adjustable parameters. The chemical reaction rate is specified by the joint PDF for temperature and concentration. We observe a bimodal distribution for the PDF and we observe significant dependence on fluid transport parameters.
Reaction-Diffusion Modeling ERK- and STAT-Interaction Dynamics
Directory of Open Access Journals (Sweden)
Georgiev Nikola
2006-01-01
Full Text Available The modeling of the dynamics of interaction between ERK and STAT signaling pathways in the cell needs to establish the biochemical diagram of the corresponding proteins interactions as well as the corresponding reaction-diffusion scheme. Starting from the verbal description available in the literature of the cross talk between the two pathways, a simple diagram of interaction between ERK and STAT5a proteins is chosen to write corresponding kinetic equations. The dynamics of interaction is modeled in a form of two-dimensional nonlinear dynamical system for ERK—and STAT5a —protein concentrations. Then the spatial modeling of the interaction is accomplished by introducing an appropriate diffusion-reaction scheme. The obtained system of partial differential equations is analyzed and it is argued that the possibility of Turing bifurcation is presented by loss of stability of the homogeneous steady state and forms dissipative structures in the ERK and STAT interaction process. In these terms, a possible scaffolding effect in the protein interaction is related to the process of stabilization and destabilization of the dissipative structures (pattern formation inherent to the model of ERK and STAT cross talk.
Study of Pre-equilibrium Fission Based on Diffusion Model
Institute of Scientific and Technical Information of China (English)
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.
Modeling Diffusion Induced Stresses for Lithium-Ion Battery Materials
Chiu Huang, Cheng-Kai
Advancing lithium-ion battery technology is of paramount importance for satisfying the energy storage needs in the U.S., especially for the application in the electric vehicle industry. To provide a better acceleration for electric vehicles, a fast and repeatable discharging rate is required. However, particle fractures and capacity loss have been reported under high current rate (C-rate) during charging/discharging and after a period of cycling. During charging and discharging, lithium ions extract from and intercalate into electrode materials accompanied with the volume change and phase transition between Li-rich phase and Li-poor phase. It is suggested that the diffusion-induced-stress is one of the main reasons causing capacity loss due to the mechanical degradation of electrode particles. Therefore, there is a fundamental need to provide a mechanistic understanding by considering the structure-mechanics-property interactions in lithium-ion battery materials. Among many cathode materials, the olivine-based lithium-iron-phosphate (LiFePO4) with an orthorhombic crystal structure is one of the promising cathode materials for the application in electric vehicles. In this research we first use a multiphysic approach to investigate the stress evolution, especially on the phase boundary during lithiation in single LiFePO4 particles. A diffusion-controlled finite element model accompanied with the experimentally observed phase boundary propagation is developed via a finite element package, ANSYS, in which lithium ion concentration-dependent anisotropic material properties and volume misfits are incorporated. The stress components on the phase boundary are used to explain the Mode I, Mode II, and Mode III fracture propensities in LiFePO4 particles. The elastic strain energy evolution is also discussed to explain why a layer-by-layer lithium insertion mechanism (i.e. first-order phase transformation) is energetically preferred. Another importation issue is how current
The Effectiveness Analysis of Waiting Processes in the Different Branches of a Bank by Queue Model
Directory of Open Access Journals (Sweden)
Abdullah ÖZÇİL
2015-06-01
Full Text Available Despite the appreciable increase in the number of bank branches every year, nowadays queues for services don’t decrease and even become parts of our daily lives. By minimizing waiting processes the least, increasing customer satisfaction should be one of branch managers’ main goals. A quick and also customer oriented service with high quality is the most important factor for customer loyalty. In this study, Queueing theory, one of Operation Research techniques, is handled and in application, the data are obtained related to waiting in queue of customer in six different branches of two banks operating in Denizli and then they are analyzed by Queueing theory and also calculated the average effectiveness of the system. The study’s data are obtained by six branches of two banks called as A1, A2, A3, B1, B2 and B3. At the end of study it is presented to the company some advices that can bring benefits to the staff and customers. In this study, Queueing theory, one of Operation Research techniques, is handled and in application, the data are obtained related to waiting in queue of customer in three different branches of a bank operating in Denizli and then they are analyzed by Queueing theory and also calculated the average effectiveness of the system. The study’s data are obtained by three branches of the bank called A1, A2 and A3. At last it is presented to the company some advices that can bring more benefits to the staff and clients.
Dun, Elizabeth A.; Hanan, Jim; Beveridge, Christine A.
2009-01-01
Bud outgrowth is regulated by the interplay of multiple hormones, including auxin, cytokinin, strigolactones, and an unidentified long-distance feedback signal that moves from shoot to root. The model of bud outgrowth regulation in pea (Pisum sativum) includes these signals and a network of five RAMOSUS (RMS) genes that operate in a shoot-root-shoot loop to regulate the synthesis of, and response to, strigolactones. The number of components in this network renders the integration of new and existing hypotheses both complex and cumbersome. A hypothesis-driven computational model was therefore developed to help understand regulation of shoot branching. The model evolved in parallel with stepwise laboratory research, helping to define and test key hypotheses. The computational model was used to verify new mechanisms involved in the regulation of shoot branching by confirming that the new hypotheses captured all relevant biological data sets. Based on cytokinin and RMS1 expression analyses, this model is extended to include subtle but important differences in the function of RMS3 and RMS4 genes in the shoot and rootstock. Additionally, this research indicates that a branch-derived signal upregulates RMS1 expression independent of the other feedback signal. Furthermore, we propose xylem-sap cytokinin promotes sustained bud outgrowth, rather than acting at the earlier stage of bud release. PMID:19948786
Efficient hedging for a complete jump-diffusion model
Kirch, Michael; Krutchenko, R. N.; Melnikov, Aleksandr V.
2002-01-01
This paper is devoted to the problem of hedging contingent claims in the framework of a complete two-factor jump-diffusion model. In this context, it is well understood that every contingent claim can be hedged perfectly if one invests the unique arbitrage-free price. Based on the results of H. Föllmer and P. Leukert [4][ 5] in a general semimartingale setting, we determine the unique hedging strategies which minimize a suitably defined shortfall risk under a given cost constraint. We derive ...
Parametric pattern selection in a reaction-diffusion model.
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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.
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.
Diffusion-based leaching models for glassy waste forms
International Nuclear Information System (INIS)
Most scenarios for the disposal of high-level nuclear wastes assume burial under conditions in which only a limited quantity of groundwater will contact the waste form. In order to model these conditions, it is necessary to describe the release of species from a waste form matrix in contact with a limited volume of leachant in which the concentration of released species is not zero and is itself a function of release rate. Eight leaching models are presented that include the cases of a dissolving and a nondissolving matrix, finite, infinite, and replenished leachant volumes, and a matrix covered by a surface layer with different properties. The equations that describe these models assume a linear concentration profile of the diffusing species within the waste form and apply Fick's first law to obtain the leach rate. In three cases a direct comparison is possible between the solutions of these equations and solutions obtained by use of the diffusion equation derived from Fick's second law. Good agreement is found. The equations given are convenient for use with programmable calculators
Energy Technology Data Exchange (ETDEWEB)
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
Energy Technology Data Exchange (ETDEWEB)
Pivovarov, M.A.; Zhang, H.; Ramakev, D.E.; Tatem, P.A.; Williams, F.W. (George Washington Univ., Washington, DC (United States). Dept. of Chemistry)
1993-02-01
This paper considers the applicability of different versions of the k-[epsilon] hypothesis of turbulence for flame modeling. Utilizing similarity solutions, the authors find that the k-[epsilon] hypothesis gives a finite radius for a weak axisymmetric plume above the heat source. The radius of this plume is defined as an eigenvalue of the boundary value problem with unknown boundary. Solving this problem with an adjusted set of parameters from the standard version of the k-[epsilon] hypothesis gives excellent agreement with experimental data for center line and radial profiles of the mean and turbulent quantities, and also for the radius of the plume and entrainment level. In contrast, the standard set of parameters, widely utilized in flame modeling, gives inaccurate predictions. Specifically, this set of parameters yields underestimates of the radius of the plume and the entrainment level. Since this same trend has been extensively observed in flame modeling, the authors conclude that the standard set of parameters for the k-[epsilon] hypothesis is inadequate, and that this is the main reason for the shortcomings of previous numerical models.
A polarizable continuum model for molecules at spherical diffuse interfaces.
Di Remigio, Roberto; Mozgawa, Krzysztof; Cao, Hui; Weijo, Ville; Frediani, Luca
2016-03-28
We present an extension of the Polarizable Continuum Model (PCM) to simulate solvent effects at diffuse interfaces with spherical symmetry, such as nanodroplets and micelles. We derive the form of the Green's function for a spatially varying dielectric permittivity with spherical symmetry and exploit the integral equation formalism of the PCM for general dielectric environments to recast the solvation problem into a continuum solvation framework. This allows the investigation of the solvation of ions and molecules in nonuniform dielectric environments, such as liquid droplets, micelles or membranes, while maintaining the computationally appealing characteristics of continuum solvation models. We describe in detail our implementation, both for the calculation of the Green's function and for its subsequent use in the PCM electrostatic problem. The model is then applied on a few test systems, mainly to analyze the effect of interface curvature on solvation energetics. PMID:27036423
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.
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.
Digital Repository Service at National Institute of Oceanography (India)
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...
Dorval, Eric
2016-01-01
Neutron transport calculations by Monte Carlo methods are finding increased application in nuclear reactor simulations. In particular, a versatile approach entails the use of a 2-step pro-cedure, with Monte Carlo as a few-group cross section data generator at lattice level, followed by deterministic multi-group diffusion calculations at core level. In this thesis, the Serpent 2 Monte Carlo reactor physics burnup calculation code is used in order to test a set of diffusion coefficient model...
Modeling viscosity and diffusion of plasma mixtures across coupling regimes
Arnault, Philippe
2014-10-01
Viscosity and diffusion of plasma for pure elements and multicomponent mixtures are modeled from the high-temperature low-density weakly coupled regime to the low-temperature high-density strongly coupled regime. Thanks to an atom in jellium modeling, the effect of electron screening on the ion-ion interaction is incorporated through a self-consistent definition of the ionization. This defines an effective One Component Plasma, or an effective Binary Ionic Mixture, that is representative of the strength of the interaction. For the viscosity and the interdiffusion of mixtures, approximate kinetic expressions are supplemented by mixing laws applied to the excess viscosity and self-diffusion of pure elements. The comparisons with classical and quantum molecular dynamics results reveal deviations in the range 20--40% on average with almost no predictions further than a factor of 2 over many decades of variation. Applications in the inertial confinement fusion context could help in predicting the growth of hydrodynamic instabilities.
Diffusion dynamics in the disordered Bose Hubbard model
Wadleigh, Laura; Russ, Philip; Demarco, Brian
2016-05-01
We explore the dynamics of diffusion for out-of-equilibrium superfluid, Mott insulator, and Bose glass states using an atomic realization of the disordered Bose Hubbard (DBH) model. Dynamics in strongly correlated systems, especially far from equilibrium, are not well understood. The introduction of disorder further complicates these systems. We realize the DBH model--which has been central to our understanding of quantum phase transitions in disordered systems--using ultracold Rubidium-87 atoms trapped in a cubic disordered optical lattice. By tightly focusing a beam into the center of the gas, we create a hole in the atomic density profile. We achieve Mott insulator, superfluid, or Bose glass states by varying the interaction and disorder strength, and measure the time evolution of the density profile after removing the central barrier. This allows us to infer diffusion rates from the velocities at the edge of the hole and to look for signatures of superfluid puddles in the Bose glass state. We acknowledge funding from NSF Grant PHY 15-05468, NSF Grant DGE-1144245, and ARO Grant W911NF-12-1-0462.
Modelling thermal radiation and soot formation in buoyant diffusion flames
International Nuclear Information System (INIS)
The radiative heat transfer plays an important role in fire problems since it is the dominant mode of heat transfer between flames and surroundings. It controls the pyrolysis, and therefore the heat release rate, and the growth rate of the fire. In the present work a numerical study of buoyant diffusion flames is carried out, with the main objective of modelling the thermal radiative transfer and the soot formation/destruction processes. In a first step, different radiative property models were tested in benchmark configurations. It was found that the FSCK coupled with the Modest and Riazzi mixing scheme was the best compromise in terms of accuracy and computational requirements, and was a good candidate to be implemented in CFD codes dealing with fire problems. In a second step, a semi-empirical soot model, considering acetylene and benzene as precursor species for soot nucleation, was validated in laminar co flow diffusion flames over a wide range of hydrocarbons (C1-C3) and conditions. In addition, the optically-thin approximation was found to produce large discrepancies in the upper part of these small laminar flames. Reliable predictions of soot volume fractions require the use of an advanced radiation model. Then the FSCK and the semi-empirical soot model were applied to simulate laboratory-scale and intermediate-scale pool fires of methane and propane. Predicted flame structures as well as the radiant heat flux transferred to the surroundings were found to be in good agreement with the available experimental data. Finally, the interaction between radiation and turbulence was quantified. (author)
Pre-Clinical Models of Diffuse Intrinsic Pontine Glioma
Directory of Open Access Journals (Sweden)
Oren J Becher
2015-07-01
Full Text Available Diffuse Intrinsic Pontine Glioma (DIPG is a rare and incurable brain tumor that arises in the brainstem of children predominantly between the ages of six and eight. Its intricate morphology and involvement of normal pons tissue precludes surgical resection, and the standard of care today remains fractionated radiation alone. In the past 30 years, there have been no significant advances made in the treatment of DIPG. This is largely because we lack good models of DIPG and therefore have little biological basis for treatment. In recent years however, due to increased biopsy and acquisition of autopsy specimens, research is beginning to unravel the genetic and epigenetic drivers of DIPG. Insight gleaned from these studies has led to improvements in approaches to both model these tumors in the lab, as well as to potentially treat them in the clinic. This review will detail the initial strides towards modeling DIPG in animals, which included allograft and xenograft rodent models using non-DIPG glioma cells. Important advances in the field came with the development of in vitro cell and in vivo xenograft models derived directly from autopsy material of DIPG patients or from human embryonic stem cells. Lastly, we will summarize the progress made in the development of genetically engineered mouse models of DIPG. Cooperation of studies incorporating all of these modeling systems to both investigate the unique mechanisms of gliomagenesis in the brainstem and to test potential novel therapeutic agents in a preclinical setting will result in improvement in treatments for DIPG patients.
Liang, L. Z. J.; Lemmens, D.; Tempere, J.
2010-06-01
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.
Introducing atmospheric attenuation within a diffusion model for room-acoustic predictions (L)
Billon, Alexis; Picaut, Judicaël; FOY, Cédric; Valeau, Vincent; SAKOUT, Anas
2008-01-01
This paper presents an extension of a diffusion model for room acoustics to handle the atmospheric attenuation. This phenomenon is critical at high frequencies and in large rooms to obtain correct acoustic predictions. An additional term is introduced in the diffusion equation as well as in the diffusion constant, in order to take the atmospheric attenuation into account. The modified diffusion model is then compared with the statistical theory and a cone-tracing software. Three typical room-...
Impact of Social Network and Business Model on Innovation Diffusion of Electric Vehicles in China
D. Y. Kong; X. H. Bi
2014-01-01
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 ...
A mirror-diffusion model of options pricing
Levin, Pavel
2008-01-01
In Black-Scholes delta-hedging method generalization, a "mirror-diffusion" inverse stochastic process is introduced with condition determined by the underlying price variance and payoff function. The process reduces an expected option value at maturity under equivalent martingale measure back to the current time. The normalized ksi-returns, correspondent to the kernel function in the found general solution and not dependent explicitly on time, were used for verification of the one-parameter model inherent efficiency, i.e. self-calibration using only historical volatility data. The model minimizes implied volatility bias (for 2004-2007 S&P100 index options) and theoretically yields skews correspondent to practical term structure for interest rate derivatives. It allows increasing the number of stock price distribution parameters.
Modeling realistic breast lesions using diffusion limited aggregation
Rashidnasab, Alaleh; Elangovan, Premkumar; Dance, David R.; Young, Kenneth C.; Diaz, Oliver; Wells, Kevin
2012-03-01
Synthesizing the appearance of malignant masses and inserting these into digital mammograms can be used as part of a wider framework for investigating the radiological detection task in X-ray mammography. However, the randomness associated with cell division within cancerous masses and the associated complex morphology challenges the realism of the modeling process. In this paper, Diffusion Limited Aggregation (DLA), a type of fractal growth process is proposed and utilized for modeling breast lesions. Masses of different sizes, shapes and densities were grown by controlling DLA growth parameters either prior to growth, or dynamically updating these during growth. A validation study was conducted by presenting 30 real and 30 simulated masses in a random order to a team of radiologists. The results from the validation study suggest that the observers found it difficult to differentiate between the real and simulated lesions.
A Jump Diffusion Model for Volatility and Duration
DEFF Research Database (Denmark)
Wei, Wei; Pelletier, Denis
by the market microstructure theory. Traditional measures of volatility do not utilize durations. I adopt a jump diffusion process to model the persistence of intraday volatility and conditional duration, and their interdependence. The jump component is disentangled from the continuous part of the price......, volatility and conditional duration process. I develop a MCMC algorithm for the inference of irregularly spaced multivariate process with jumps. The algorithm provides smoothed estimates of the latent variables such as spot volatility, jump times and jump sizes. I apply this model to IBM data and I find...... meaningful relationship between volatility and conditional duration. Also, jumps play an important role in the total variation, but the jump variation is smaller than traditional measures that use returns sampled at lower frequency....
Physical modeling of contaminant diffusion from a cementious waste form
International Nuclear Information System (INIS)
Cementitious materials can be used to immobilize waste materials for disposal. The Westinghouse Hanford Company is pursuing approval of disposal technologies by which hazardous and radioactive wastes are blended or packaged with cementitious materials for disposal. Of significant concern is the mobility of the waste contaminants both from the waste form and in the arid soils of the Hanford Site. A physical model has been developed to study the diffusion of waste contaminants from simulated cementitious waste forms in unsaturated Hanford Site soils. The model can be used to predict cementitious waste form performance in a representative environment, support design of waste management facilities and technologies, and provide data for environmental permitting of proposed treatment and disposal facilities
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.
Rule-based spatial modeling with diffusing, geometrically constrained molecules
Directory of Open Access Journals (Sweden)
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
Magnetic field diffusion modeling of a small enclosed firing system
Energy Technology Data Exchange (ETDEWEB)
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.
Modelling interactions between soil evolution and diffusive surface processes
Kirkby, Mike; Johnson, Michelle; Gloor, Emanual
2014-05-01
Bioturbation, combined with settlement under gravity, generates profiles of bulk density, porosity and hydraulic conductivity (Ksat). Rates of bioturbation are linked to rates of diffusive downslope sediment transport (creep) and rates can be compared via the increase in OSL ages of soil aggregate grains with depth. Some primary porosity is also produced by weathering of rock to saprolite, often with little reduction in bulk density but some dilation of joints. Downward percolation of rain water near the surface is controlled by the diffusion-induced decrease in porosity and Ksat, driving lateral subsurface flow in the zone of fluctuating water table, and leaving progressively less water for downward percolation. As the depth to the weathering front is varied, progressively less water is therefore available for weathering, producing the observed decrease in weathering rate with increasing soil depth. These processes are modelled by repeatedly applying a stochastic realisation of daily rainfalls for an area until the annual hydrological cycle stabilises, providing the average partition of rainfall into its components of evapotranspiration, lateral flow and downward percolation, with depth in the soil. The average hydrology is then applied to drive evolution of the weathering profile over longer time spans.
Nait-Ali, K.L; Bergeret, A.; Ferry, L.; Colin, Xavier
2012-01-01
International audience; The detection of branched chains in thermally degraded thermoplastic polymers is far from simple, especially at a low conversion ratio, mainly because of the low sensitivity of commonly used laboratory analytical techniques. The objective of this article is to present an approach able to demonstrate the formation of such macromolecular structures during thermal degradation of molten PET at low oxygen partial pressures (typically for pressures lower than 9% of atmospher...
BF3 PIII modeling: Implantation, amorphisation and diffusion
International Nuclear Information System (INIS)
In the race for highly doped ultra-shallow junctions (USJs) in complementary metal oxide semi-conductor (CMOS) technologies, plasma immersion ion implantation (PIII) is a promising alternative to traditional beamline implantation. Currently, no commercial technology computer aided design (TCAD) process simulator allows modeling the complete USJ fabrication process by PIII, including as-implanted dopant profiles, damage formation, dopant diffusion and activation. In this work, a full simulation of a p-type BF3 PIII USJ has been carried out. In order to investigate the various physical phenomena mentioned above, process conditions included a high energy/high dose case (10 kV, 5×1015 cm−2), specifically designed to increase damage formation, as well as more technology relevant implant conditions (0.5 kV) for comparison. All implanted samples were annealed at different temperatures and times. As implanted profiles for both boron and fluorine in BF3 implants were modeled and compared to Secondary Ion Mass Spectrometry (SIMS) measurements. Amorphous/crystalline (a/c) interface depths were measured by transmission electron microscopy (TEM) and successfully simulated. Diffused profiles simulations agreed with SIMS data at low thermal budgets. A boron peak behind the a/c interface was observed in all annealed SIMS profiles for the 10 kV case, indicating boron trapping from EOR defects in this region even after high thermal budgets. TEM measurements on the annealed samples showed an end of range (EOR) defects survival behind the a/c interface, including large dislocation loops (DLs) lying on (001) plane parallel to the surface. In the last part of this work, activation simulations were compared to Hall measurements and confirmed the need to develop a (001) large BICs model.
A cladding oxidation model based on diffusion equations
International Nuclear Information System (INIS)
During severe accident in PWRs, the cladding oxidation with steam in the core is very important to the accident process. When oxidation time is long, or oxidation occurs in steam starvation conditions, the parabolic rate correlations based on experiments are restricted, which impacts the prediction of cladding failure, hydrogen production, and temperature. According to Fick's laws, a cladding oxidation model in a wide temperature range based on diffusion equations is developed. The developed oxidation model has a wider applicability than those parabolic rate correlations, and can simulate long-term experiments well. The restricted assumptions of short term oxidation time and enough steam environment in the core implemented by those parabolic rate correlations are removed in the model, therefore this model perfectly fit for long-term and steam starvation conditions which are more realistic during a severe accident. This model also can obtain detailed oxygen distribution in the cladding, which is helpful to simulate the cladding failure in detail and develop advanced cladding failure criteria. (authors)
A reaction-diffusion model of human brain development.
Directory of Open Access Journals (Sweden)
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.
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.
Matsui, Yoshihiko; Nakao, Soichi; Taniguchi, Takuma; Matsushita, Taku
2013-05-15
2-Methylisoborneol (MIB) and geosmin are naturally occurring compounds responsible for musty-earthy taste and odor in public drinking-water supplies, a severe problem faced by many utilities throughout the world. In this study, we investigated adsorptive removal of these compounds by superfine powdered activation carbon (SPAC, particle size powdered activated carbon; we also discuss the optimization of carbon particle size to efficiently enhance the adsorptive removal. After grinding, the absorptive capacity remained unchanged for a 2007 carbon sample and was increased for a 2010 carbon sample; the capacity increase was quantitatively described by the shell adsorption model, in which MIB and geosmin adsorbed more in the exterior of a carbon particle than in the center. The extremely high uptake rates of MIB and geosmin by SPAC were simulated well by a combination of the branched-pore kinetic model and the shell adsorption model, in which intraparticle diffusion through macropores was followed by diffusion from macropore to micropore. Simulations suggested that D40 was on the whole the best characteristic diameter to represent a size-disperse group of adsorbent particles; D40 is the diameter through which 40% of the particles by volume pass. Therefore, D40 can be used as an index for evaluating the improvement of adsorptive removal that resulted from pulverization. The dose required for a certain percentage removal of MIB or geosmin decreased linearly with carbon particle size (D40), but the dose reduction became less effective as the activated carbon was ground down to smaller sizes around a critical value of D40. For a 60-min contact time, critical D40 was 2-2.5 μm for MIB and 0.4-0.5 μm for geosmin. The smaller critical D40 was when the shorter the carbon-water contact time was or the slower the intraparticle mass transfer rate of an adsorbate was. PMID:23528781
A radiative diffusion model for laser-compression simulations
International Nuclear Information System (INIS)
A radiation diffusion package is described which can handle the transport of continuum radiation arising from free-free and free-bound transitions in a laser-compressed plasma. This model has been incorporated into MEDUSA, a two temperature, 1-D Lagrangian computer code, and numerous computer runs have been carried out to study the effect of radiative preheat on target compression. The calculations show that in compression of a 10-μg solid carbon microsphere the radiation effects reduce the final target density by up to a factor of 6. In the case of a neon filled thin glass microballoon, the radiative preheat reduces maximum neon density by a factor of 3 while the maximum shell density drops from 105 Kg/m3 to 1.8 x 104 Kg/m3. (author)
Technology diffusion in energy-economy models: The case of Danish vintage models
DEFF Research Database (Denmark)
Klinge Jacobsen, Henrik
2000-01-01
the costs of greenhouse gas mitigation. This paper examines the effect on aggregate energy efficiency of using technological vintage models to describe technology diffusion. The focus is on short- to medium-term issues. Three different models of Danish energy supply and demand are used to illustrate...... 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...
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...
Erickson, Richard A.; Eager, Eric A.; Stanton, Jessica C.; Beston, Julie A.; Diffendorfer, James E.; Thogmartin, Wayne E.
2015-01-01
Quantifying the impact of anthropogenic development on local populations is important for conservation biology and wildlife management. However, these local populations are often subject to demographic stochasticity because of their small population size. Traditional modeling efforts such as population projection matrices do not consider this source of variation whereas individual-based models, which include demographic stochasticity, are computationally intense and lack analytical tractability. One compromise between approaches is branching process models because they accommodate demographic stochasticity and are easily calculated. These models are known within some sub-fields of probability and mathematical ecology but are not often applied in conservation biology and applied ecology. We applied branching process models to quantitatively compare and prioritize species locally vulnerable to the development of wind energy facilities. Specifically, we examined species vulnerability using branching process models for four representative species: A cave bat (a long-lived, low fecundity species), a tree bat (short-lived, moderate fecundity species), a grassland songbird (a short-lived, high fecundity species), and an eagle (a long-lived, slow maturation species). Wind turbine-induced mortality has been observed for all of these species types, raising conservation concerns. We simulated different mortality rates from wind farms while calculating local extinction probabilities. The longer-lived species types (e.g., cave bats and eagles) had much more pronounced transitions from low extinction risk to high extinction risk than short-lived species types (e.g., tree bats and grassland songbirds). High-offspring-producing species types had a much greater variability in baseline risk of extinction than the lower-offspring-producing species types. Long-lived species types may appear stable until a critical level of incidental mortality occurs. After this threshold, the risk of
On applicability of permanent coefficient model to diffusion description in solid state
International Nuclear Information System (INIS)
A mathematical method is assessed using the model of the constant diffusion coefficients for the solution of diffusion equations in bynary and multicomponent systems. Consideration is given to the solution of a direct problem, viz., determination of element concentration from available diffusion coefficients, and a inverse problem, viz., determination of the diffusion coefficients from known concentration curves. Errors due to using this method are estimated (particularly, in the case of the Fe-Cr-Ni ternary system)
National Space Development Agency; 宇宙開発事業団
2001-01-01
The following topics were discussed: hard sphere model of liquid metal, refined theory of liquid, molecular dynamics simulation of liquid lithium, self-diffusion of hard sphere fluids, isotope effect of liquid lithium, microgravity diffusion of highly reactive liquid metals, diffusion of Ag-Cu alloys, structure of liquid tin, effective pair potential of liquid tin and germanium, shear cell method for diffusion measurement, wettability and reaction of liquid silicon, solidification effects on ...
Saichev, A
2005-01-01
Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Bath's law. Our theory shows that Bath's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +- 0.1 for Bath's constant value around 1.2, our exact analytical treatment of Bath's law provides new constraints on the productivity exponent alpha and the branching ratio n: $0.9 <= alpha <= 1$ and 0.8 <= n <= 1. We propose a novel method for measuring alpha based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the ``second Bath's law for foreshocks: the pro...
Kushner, Joseph; Deen, William; Blankschtein, Daniel; Langer, Robert
2007-12-01
To account for the effect of branched, parallel transport pathways in the intercellular domain of the stratum corneum (SC) on the passive transdermal transport of hydrophobic permeants, we have developed, from first-principles, a new theoretical model-the Two-Tortuosity Model. This new model requires two tortuosity factors to account for: (1) the effective diffusion path length, and (2) the total volume of the branched, parallel transport pathways present in the SC intercellular domain, both of which may be evaluated from known values of the SC structure. After validating the Two-Tortuosity model with simulated SC diffusion experiments in FEMLAB (a finite element software package), the vehicle-bilayer partition coefficient, K(b), and the lipid bilayer diffusion coefficient, D(b), in untreated human SC were evaluated using this new model for two hydrophobic permeants, naphthol (K(b) = 225 +/- 42, D(b) = 1.7 x 10(-7) +/- 0.3 x 10(-7) cm(2)/s) and testosterone (K(b) = 92 +/- 29, D(b) = 1.9 x 10(-8) +/- 0.5 x 10(-8) cm(2)/s). The results presented in this paper demonstrate that this new method to evaluate K(b) and D(b) is comparable to, and simpler than, previous methods, in which SC permeation experiments were combined with octanol-water partition experiments, or with SC solute release experiments, to evaluate K(b) and D(b). PMID:17887175
Matsui, Yoshihiko; Nakao, Soichi; Taniguchi, Takuma; Matsushita, Taku
2013-05-15
2-Methylisoborneol (MIB) and geosmin are naturally occurring compounds responsible for musty-earthy taste and odor in public drinking-water supplies, a severe problem faced by many utilities throughout the world. In this study, we investigated adsorptive removal of these compounds by superfine powdered activation carbon (SPAC, particle size geosmin adsorbed more in the exterior of a carbon particle than in the center. The extremely high uptake rates of MIB and geosmin by SPAC were simulated well by a combination of the branched-pore kinetic model and the shell adsorption model, in which intraparticle diffusion through macropores was followed by diffusion from macropore to micropore. Simulations suggested that D40 was on the whole the best characteristic diameter to represent a size-disperse group of adsorbent particles; D40 is the diameter through which 40% of the particles by volume pass. Therefore, D40 can be used as an index for evaluating the improvement of adsorptive removal that resulted from pulverization. The dose required for a certain percentage removal of MIB or geosmin decreased linearly with carbon particle size (D40), but the dose reduction became less effective as the activated carbon was ground down to smaller sizes around a critical value of D40. For a 60-min contact time, critical D40 was 2-2.5 μm for MIB and 0.4-0.5 μm for geosmin. The smaller critical D40 was when the shorter the carbon-water contact time was or the slower the intraparticle mass transfer rate of an adsorbate was.
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 of a collaborative care model in primary care: a longitudinal qualitative study
Vedel Isabelle; Ghadi Veronique; De Stampa Matthieu; Routelous Christelle; Bergman Howard; Ankri Joel; Lapointe Liette
2013-01-01
Background Although collaborative team models (CTM) improve care processes and health outcomes, their diffusion poses challenges related to difficulties in securing their adoption by primary care clinicians (PCPs). The objectives of this study are to understand: (1) how the perceived characteristics of a CTM influenced clinicians' decision to adopt -or not- the model; and (2) the model's diffusion process. Methods We conducted a longitudinal case study based on the Diffusion of Innovations Th...
Grain-boundary diffusion: structural effects, models and mechanisms
Energy Technology Data Exchange (ETDEWEB)
Peterson, N L
1979-01-01
Grain boundary diffusion phenomena were considered including: anisotropy, effect of orientation, crystallographic transformation, boundary type, dislocation dissociation, pressure, and isotope effects. Diffusivity is different for various boundaries. Dissociated dislocations and stacking faults are not efficient paths for grain boundary diffusion. Results suggest a vacancy mechanism along the dislocation core, and involves atomic jumps away from the back towards the dislocation as well as jumps along the core. Measurements were made on nickel and silver. (FS)
Stochastic Modeling and Simulation of Reaction-Diffusion Biochemical Systems
LI Fei
2016-01-01
Reaction Diffusion Master Equation (RDME) framework, characterized by the discretization of the spatial domain, is one of the most widely used methods in the stochastic simulation of reaction-diffusion systems. Discretization sizes for RDME have to be appropriately chosen such that each discrete compartment is "well-stirred" and the computational cost is not too expensive. An efficient discretization size based on the reaction-diffusion dynamics of each species is derived in this disserta...
Toward Information Diffusion Model for Viral Marketing in Business
Lulwah AlSuwaidan; Mourad Ykhlef
2016-01-01
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 t...
Branching processes in biology
Kimmel, Marek
2015-01-01
This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition. This second ex...
DEFF Research Database (Denmark)
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...... fraction of 0.19 in accordance with the accepted value from histology. The absolute apparent diffusion coefficient obtained from the model was similar to that of experiments. The model and the experimental results indicate significant differences in diffusion and transverse relaxation between the tissue...... 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...
Martin, Elliot; Shreim, Amer; Paczuski, Maya
2010-01-01
We define an activity-dependent branching ratio that allows comparison of different time series Xt . The branching ratio bx is defined as bx=E[ξx/x] . The random variable ξx is the value of the next signal given that the previous one is equal to x , so ξx={Xt+1∣Xt=x} . If bx>1 , the process is on average supercritical when the signal is equal to x , while if bxefficient market hypothesis.” For stock volumes, solar x-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, bx is supercritical for small values of activity and subcritical for the largest ones, indicating a tendency to return to a typical value. For stock volumes this tendency has an approximate power-law behavior. For solar x-ray flux and the BTW model, there is a broad regime of activity where bx≃1 , which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for Xt and for ξx . For the BTW model the distribution of ξx is Gaussian, for x sufficiently larger than 1, and its variance grows linearly with x . Hence, the activity in the BTW model obeys a central limit theorem when sampling over past histories. The broad region of activity where bx is close to one disappears once bulk dissipation is introduced in the BTW model—supporting our hypothesis that it is an indicator of criticality.
Kim, W G; Park, J J; Oh, S I
2001-01-01
We report a reliable chronic heart failure model in sheep using sequential ligation of the homonymous artery and its diagonal branch. After a left anterior thoracotomy in Corridale sheep, the homonymous artery was ligated at a point approximately 40% of the distance from the apex to the base of the heart, and after 1 hour, the diagonal vessel was ligated at a point at the same level. Hemodynamic measurements were done preligation, 30 minutes after the homonymous artery ligation, and 1 hour after diagonal branch ligation. The electrocardiograms were obtained as needed, and cardiac function was also evaluated with ultrasonography. After a predetermined interval (2 months for five animals and 3 months for two animals), the animals were reevaluated in the same way as before, and were killed for postmortem examination of their hearts. All seven animals survived the experimental procedures. Statistically significant decreases in systemic arterial blood pressure and cardiac output and increases in pulmonary artery capillary wedge pressure were observed 1 hour after sequential ligation of the homonymous artery and its diagonal branch. Untrasonographic analyses demonstrated variable degrees of anteroseptal dyskinesia and akinesia in all animals. The data from animals at 2 months after coronary artery ligation showed significant increases in central venous pressure, pulmonary artery pressure, and pulmonary artery capillary wedge pressure. Left ventricular enddiastolic dimension and left ventricular end-systolic dimension on ultrasonographic studies were also increased. Electrocardiography showed severe ST elevation immediately after the ligation and pathologic Q waves were found at 2 months after ligation. The thin walled infarcted areas with chamber enlargement were clearly seen in the hearts removed at 2 and 3 months after ligation. In conclusion, we could achieve a reliable ovine model of chronic heart failure using a simple concept of sequential ligation of the
Quasineutral limit of a standard drift diffusion model for semiconductors
Institute of Scientific and Technical Information of China (English)
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.
Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system
Energy Technology Data Exchange (ETDEWEB)
Abdusalam, H.A E-mail: hosny@operamail.com; Fahmy, E.S
2003-10-01
It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional.
Cohen, Roger E; Mauro, Francesco; Geisler, Douglas; Alonso-Garcia, Javier; Kinemuchi, Karen
2015-01-01
We present wide field near-infrared photometry of 12 Galactic globular clusters, typically extending from the tip of the cluster red giant branch (RGB) to the main sequence turnoff. Using recent homogenous values of cluster distance, reddening and metallicity, the resulting photometry is directly compared to the predictions of several recent libraries of stellar evolutionary models. Of the sets of models investigated, Dartmouth and Victoria-Regina models best reproduce the observed RGB morphology, albeit with offsets in J-Ks color which vary in their significance in light of all sources of observational uncertainty. Therefore, we also present newly recalibrated relations between near-IR photometric indices describing the upper RGB versus cluster iron abundance as well as global metallicity. The influence of enhancements in alpha elements and helium are analyzed, finding that the former affect the morphology of the upper RGB in accord with model predictions. Meanwhile, the empirical relations we derive are in ...
Bounds for perpetual American option prices in a jump diffusion model
Ekström, Erik
2006-01-01
We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black-Scholes model. We also investigate the dependence of the bounds on different parameters of the model.
Synchronized stability in a reaction–diffusion neural network model
Energy Technology Data Exchange (ETDEWEB)
Wang, Ling; Zhao, Hongyong, E-mail: hongyongz@126.com
2014-11-14
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability.
Regularized lattice Boltzmann model for a class of convection-diffusion equations.
Wang, Lei; Shi, Baochang; Chai, Zhenhua
2015-10-01
In this paper, a regularized lattice Boltzmann model for a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations. PMID:26565368
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...
Developing A Laser Shockwave Model For Characterizing Diffusion Bonded Interfaces
Energy Technology Data Exchange (ETDEWEB)
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
Fuzzy branching temporal logic.
Moon, Seong-ick; Lee, Kwang H; Lee, Doheon
2004-04-01
Intelligent systems require a systematic way to represent and handle temporal information containing uncertainty. In particular, a logical framework is needed that can represent uncertain temporal information and its relationships with logical formulae. Fuzzy linear temporal logic (FLTL), a generalization of propositional linear temporal logic (PLTL) with fuzzy temporal events and fuzzy temporal states defined on a linear time model, was previously proposed for this purpose. However, many systems are best represented by branching time models in which each state can have more than one possible future path. In this paper, fuzzy branching temporal logic (FBTL) is proposed to address this problem. FBTL adopts and generalizes concurrent tree logic (CTL*), which is a classical branching temporal logic. The temporal model of FBTL is capable of representing fuzzy temporal events and fuzzy temporal states, and the order relation among them is represented as a directed graph. The utility of FBTL is demonstrated using a fuzzy job shop scheduling problem as an example. PMID:15376850
Poupon, Cyril; Rieul, Bernard; Kezele, Irina; Perrin, Muriel; Poupon, Fabrice; Mangin, Jean-François
2008-12-01
We present new diffusion phantoms dedicated to the study and validation of high-angular-resolution diffusion imaging (HARDI) models. The phantom design permits the application of imaging parameters that are typically employed in studies of the human brain. The phantoms were made of small-diameter acrylic fibers, chosen for their high hydrophobicity and flexibility that ensured good control of the phantom geometry. The polyurethane medium was filled under vacuum with an aqueous solution that was previously degassed, doped with gadolinium-tetraazacyclododecanetetraacetic acid (Gd-DOTA), and treated by ultrasonic waves. Two versions of such phantoms were manufactured and tested. The phantom's applicability was demonstrated on an analytical Q-ball model. Numerical simulations were performed to assess the accuracy of the phantom. The phantom data will be made accessible to the community with the objective of analyzing various HARDI models. PMID:19030160
An entropic Quantum Drift-Diffusion model for electron transport in resonant tunneling diodes
Degond, Pierre; Gallego, Samy; Méhats, Florian
2007-01-01
International audience We present an entropic Quantum Drift Diffusion model (eQDD) and show how it can be derived on a bounded domain as the diffusive approximation of the Quantum Liouville equation with a quantum BGK operator. Some links between this model and other existing models are exhibited, especially with the Density Gradient (DG) model and the Schrödinger-Poisson Drift Diffusion model (SPDD). Then a finite difference scheme is proposed to discretize the eQDD model coupled to the P...
Institute of Scientific and Technical Information of China (English)
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.
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-01
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch-Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients.
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-01
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. PMID:27385441
Neuroprotective effect of minocycline in a rat model of branch retinal vein occlusion.
Sun, Chuan; Li, Xiao-Xin; He, Xiang-Jun; Zhang, Qi; Tao, Yong
2013-08-01
Branch retinal vein occlusion (BRVO) is the second most frequent retinal vascular disorder. Currently the first-line therapies for BRVO include anti-VEGF and dexamethasone implant treatment, however, with direct or indirect damage on retinal neurons, it has limited effect in improving patients visual acuity. Therefore, novel treatments with neuroprotective effect for BRVO retina were expected. Minocycline is a semisynthetic, broad spectrum tetracycline antibiotic with high penetration through the blood brain barrier. The neuroprotective effects of minocycline have been shown in various central nervous system (CNS) disease. Since both CNS and retina were composed of neurons and glials, it is reasonable to expect a neuroprotective effect by minocycline for BRVO retina. Therefore, the aim of the present study was to study whether minocycline has neuroprotective effect in branch retinal vein occlusion (BRVO) and the possible underlying molecular basis. We created BRVO in rats using laser photocoagulation. The animals were then randomly divided into 4 groups to evaluate the effect of minocycline: group A: minocycline 45 mg/kg intraperitoneal injection (i.p.), group B: minocycline 90 mg/kg i.p., group C: normal saline i.p., group D: sham injection. Fundus photography and fluorescein angiography (FA) were conducted. The changes in thickness of retinal layers were measured with optical coherence tomography (OCT) in vivo. We found that retinal edema occurred predominantly in the inner retinal layers. Intraperitoneal administration of minocycline significantly ameliorated retinal edema in the early stage of BRVO. We performed Full field Electroretinography (ffERG) to evaluate retinal function and found that the reduction of b wave amplitude decreased in the combined maximal response. The expressional levels of apoptosis related genes (Bax, Bcl-2) and inflammation related genes (IL-1 β, TNF α, MCP-1 and CCR2) were measured by real-time PCR, the results showed that
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.
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...
Application of the Sea-Level Affecting Marshes Model (SLAMM 6) to Big Branch Marsh NWR
US Fish and Wildlife Service, Department of the Interior — Model SummaryChanges in tidal marsh area and habitat type in response to sea-level rise were modeled using the Sea Level Affecting Marshes Model (SLAMM 6) that...
Comparison of homogenized and enhanced diffusion solutions of model PWR problems
International Nuclear Information System (INIS)
Model problem comparisons in slab geometry are made between two forms of homogenized diffusion theory and enhanced diffusion theory. The pin-cell discontinuity factors for homogenized diffusion calculations are derived from homogenized variational nodal P1 response matrices and from standard finite differencing. Enhanced diffusion theory consists of applying quasi-reflected interface conditions to reduce variational nodal Pn response matrices to one degree of freedom per interface, without homogenization within the cell. As expected both homogenized diffusion methods preserve reaction rates exactly if the discontinuity factors are derived from the P 11 reference solutions. If no reference lattice solution is available, discontinuity factors may be approximated from single cells with reflected boundary conditions; the computational effort is then comparable to calculating the enhanced diffusion response matrices. In this situation enhanced diffusion theory gives the most accurate results and finite difference discontinuity factors the least accurate. (authors)
Comparison of kinetic and dynamical models of DNA-protein interaction and facilitated diffusion
Florescu, Ana-Maria; 10.1021/jp101151a
2010-01-01
It has long been asserted that proteins like transcription factors may locate their target in DNA sequences at rates that surpass by several orders of magnitude the three-dimensional diffusion limit thank to facilitated diffusion, that is the combination of one-dimensional (sliding along the DNA) and three-dimensional diffusion. This claim has been supported along the years by several mass action kinetic models, while the dynamical model we proposed recently (J. Chem. Phys. 130, 015103 (2009)) suggests that acceleration of targeting due to facilitated diffusion cannot be large. In order to solve this apparent contradiction, we performed additional simulations to compare the results obtained with our model to those obtained with the kinetic model of Klenin et al (Phys. Rev. Letters 96, 018104 (2006)). We show in this paper that the two models actually support each other and agree in predicting a low efficiency for facilitated diffusion. Extrapolation of these results to real systems even indicates that facilit...
A reaction diffusion model of pattern formation in clustering of adatoms on silicon surfaces
Directory of Open Access Journals (Sweden)
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.
Pattern Formation in a Cross-Diffusive Ratio-Dependent Predator-Prey Model
Directory of Open Access Journals (Sweden)
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 computer simulation model for room sound field considering diffuse reflection
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
A multiple random ray-tracing model was developed for predicting the distribution of sound pressure levels in an enclosed space of any shape. This model considered two diffuse factors of a room-diffuse reflection due to room surfaces and scattering due to objects. The surface diffusion was treated by two different methods on the basis of probability analysis, and the scattering was simulated by a multiple random ray-tracing process. Thus the sound pressure level distribution in a diffuse sound filed can be calculate more precisely.
Energy Technology Data Exchange (ETDEWEB)
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.
Models for the estimation of diffuse solar radiation for typical cities in Turkey
International Nuclear Information System (INIS)
In solar energy applications, diffuse solar radiation component is required. Solar radiation data particularly in terms of diffuse component are not readily affordable, because of high price of measurements as well as difficulties in their maintenance and calibration. In this study, new empirical models for predicting the monthly mean diffuse solar radiation on a horizontal surface for typical cities in Turkey are established. Therefore, fifteen empirical models from studies in the literature are used. Also, eighteen diffuse solar radiation models are developed using long term sunshine duration and global solar radiation data. The accuracy of the developed models is evaluated in terms of different statistical indicators. It is found that the best performance is achieved for the third-order polynomial model based on sunshine duration and clearness index. - Highlights: • Diffuse radiation is given as a function of clearness index and sunshine fraction. • The diffuse radiation is an important parameter in solar energy applications. • The diffuse radiation measurement is for limited periods and it is very rare. • The new models can be used to estimate monthly average diffuse solar radiation. • The accuracy of the models is evaluated on the basis of statistical indicators
Side-Branching Statistics of Plant Root Networks
Pollen, N.; Malamud, B.
2001-12-01
Many studies exist that characterise plant root architecture by calculating the fractal dimension of the root network, but few studies quantify the branching characteristics of the root network. This paper examines the Tokunaga side-branching statistics for the root systems of four plants--Sugar Beet (Beta vulgaris), Lucern (Medicago sativa), Common Wheat (Triticum aestivum) and White Clover (Trifolium michelianum)--and compares the resulting statistics to those calculated by similar means (by other authors) for the Kentucky and Powder River drainage basins and several Diffusion Limited Aggregation (DLA) models. The plant root networks studied all contained similar numbers of different order roots, but the side-branching statistics differed, offering one explanation for the differing visual appearance of the branching root networks. The White Clover plant had similar Tokunaga branching statistics to the drainage networks and DLA models. This may be due to the dichotomous root structure of the White Clover plant, which produces a network that is much more similar in appearance to the two drainage networks and DLA models than the other three plants, which had herringbone root. All of the root networks, drainage basins, and DLA models had branching networks that could be quantified well to very well by Tokunaga side-branching statistics. For many years, engineers have avoided implementation of stabilisation schemes involving vegetation, due to the inherent problems involved in the quantification of their dynamic and complex root structures. The use of Tokunaga statistics as a simplifying measure of root branching characteristics, may aid in this aspect, as well as others, such as the modelling of nutrient or water uptake.
Computer modeling of Earthshine contamination on the VIIRS solar diffuser
Mills, Stephen P.; Agravante, Hiroshi; Hauss, Bruce; Klein, James E.; Weiss, Stephanie C.
2005-10-01
The Visible/Infrared Imager Radiometer Suite (VIIRS), built by Raytheon Santa Barbara Remote Sensing (SBRS) will be one of the primary earth-observing remote-sensing instruments on the National Polar-Orbiting Operational Environmental Satellite System (NPOESS). It will also be installed on the NPOESS Preparatory Project (NPP). These satellite systems fly in near-circular, sun-synchronous low-earth orbits at altitudes of approximately 830 km. VIIRS has 15 bands designed to measure reflectance with wavelengths between 412 nm and 2250 nm, and an additional 7 bands measuring primarily emissive radiance between 3700nm and 11450 nm. The calibration source for the reflective bands is a solar diffuser (SD) that is illuminated once per orbit as the satellite passes from the dark side to the light side of the earth near the poles. Sunlight enters VIIRS through an opening in the front of the instrument. An attenuation screen covers the opening, but other than this there are no other optical elements between the SD and the sun. The BRDF of the SD and the transmittance of the attenuation screen is measured pre-flight, and so with knowledge of the angles of incidence, the radiance of the sun can be computed and is used as a reference to produce calibrated reflectances and radiances. Unfortunately, the opening also allows a significant amount of reflected earthshine to illuminate part of the SD, and this component introduces radiometric error to the calibration process, referred to as earthshine contamination (ESC). The VIIRS radiometric error budget allocated a 0.3% error based on modeling of the ESC done by SBRS during the design phase. This model assumes that the earth has Lambertian BRDF with a maximum top-of-atmosphere albedo of 1. The Moderate Resolution Imaging Spectroradiometer (MODIS) has an SD with a design similar to VIIRS, and in 2003 the MODIS Science Team reported to Northrop Grumman Space Technology (NGST), the prime contractor for NPOESS, their suspicion that ESC
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.
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.
In-situ diffusion experiments at Mont Terri: modeling aspects
International Nuclear Information System (INIS)
Full text of publication follows: Clay-rich formations, such as the Opalinus Clay (Switzerland), are currently being considered as potential host rocks for the deep geological disposal of radioactive waste. Diffusion is the main transport mechanism for radionuclides in these impermeable rocks. Besides, sorption provides additional retardation for cationic species. The objective of the DI-A in-situ diffusion experiment at the Mont Terri Underground Rock Laboratory (URL) was to confirm the expected diffusion-controlled transport and to compare the results of the experiment with those from small-scale (cm) through-diffusion experiments. The experimental setup at Mont Terri consisted of a borehole drilled in the rock, with a 1-meter-long injection interval at its bottom. Synthetic pore-water containing an initial pulse of tracers (HTO, I-, 22Na+, Cs+) was circulated through the borehole, and the evolution of tracer concentration was monitored. After about 10 months, a volume of rock around the injection borehole was excavated and tracer distribution profiles in the rock were measured. Reactive transport simulations allowed the fitting of (a) the temporal evolution of the concentrations of the tracers in the injection system and (b) the tracer profiles in the rock, which provided unique sets of effective diffusion coefficients (De) and accessible porosities (sorption parameters for sorbing tracers). The results for HTO, I- and 22Na+ were in excellent agreement with those from through-diffusion experiments, confirming the important effects of anionic exclusion (I-) and sorption (22Na+). There were no previous experimental values of De for Cs+, although batch sorption data were available. The results of DI-A indicated less sorption (by a factor of about 2) in the intact rock than in batch. Also, De for Cs+ was about 5 times larger than for water (HTO). These results are now being confirmed by through-diffusion experiments. A second experiment (DI-A2) is currently under
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
4 new model, phase equilibrium-kinetics model (PEKM), for estimation of diffusioncoefficient was proposed in this paper. Kinetic experiments of phenol desorption on NKAII resin inthe presence and the absence of ultrasound were separately conducted, and diffusion coefficients ofphenol within an adsorbent particle were estimated by means of proposed PEKM and classicsimplified model. Results show that the use of ultrasound not only changes the phase equilibriumstate of NKAll resin/phenol/water system which had been equilibrium at normal condition, but alsoenhances diffusion of phenol within the resin. The diffusion coefficient of phenol in the resin in thefield of ultrasound increases in an order of magnitude in comparison with the diffusion coefficientdetermined under no ultrasound Experimental results also indicated that the diffusion coefficientsestimated by PEKM were more accurate than that estimated by the classic simplified model.
A STUDY ON NEW PRODUCT DEMAND FORECASTING BASED ON BASS DIFFUSION MODEL
Zuhaimy Ismail; Noratikah Abu
2013-01-01
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 lev...
Prediction model for the diffusion length in silicon-based solar cells
Energy Technology Data Exchange (ETDEWEB)
Cheknane, A [Laboratoire d' Etude et Developpement des Materiaux Semiconducteurs et Dielectrques, Universite Amar Telidji de Laghouat, BP 37G, Laghouat 03000 (Algeria); Benouaz, T, E-mail: cheknanali@yahoo.co [Laboratoire de Modelisation, Universite Abou BakarBelkaid de Tlemcen Algerie (Algeria)
2009-07-15
A novel approach to compute diffusion lengths in solar cells is presented. Thus, a simulation is done; it aims to give computational support to the general development of a neural networks (NNs), which is a very powerful predictive modelling technique used to predict the diffusion length in mono-crystalline silicon solar cells. Furthermore, the computation of the diffusion length and the comparison with measurement data, using the infrared injection method, are presented and discussed.
Pegoretti, Giovanni; Rentocchini,Francesco; Vittucci Marzetti, Giuseppe
2012-01-01
The paper analyzes how the structure of social networks affects innovation diffusion and competition under different information regimes. Diffusion is modeled as the result of idiosyncratic adoption thresholds, local network effects and information diffusion (broadcasting and demonstration effect from previous adopters). A high social cohesion decreases the probability of one innovation cornering the market. Nonetheless, with imperfect information, in small-world networks the higher speed of ...
Numerical Modeling of the Flow in a Vaneless Diffuser of Centrifugal Compressor Stage
Mykola Kalinkevych; Oleg Shcherbakov
2013-01-01
This paper presents the results of numerical investigation of the flow in a vaneless diffuser of centrifugal compressor stage. Simulations were performed using both a commercial CFD package ANSYS CFX and the own-designed computer program. Steady conditions involving SST turbulence model were used for the calculations using CFX. To consider the interaction between impeller and diffuser, not just a diffuser but the whole stage was calculated. The own-designed methodology is based on solving of ...
National Oceanic and Atmospheric Administration, Department of Commerce — This dataset represents depth predictions from a bathymetric model developed for the New York offshore spatial planning area. The model also includes...
National Oceanic and Atmospheric Administration, Department of Commerce — This dataset represents sediment size predictions from a sediment spatial model developed for the New York offshore spatial planning area. The model also includes...
Belucz, Bernadett; Forgacs-Dajka, Emese
2015-01-01
Babcock-Leighton type solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock-Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of butterfly wing to an anti-solar type. A butterfly diagram constructed from middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in...
Pattern Formation in a Predator-Prey Model with Both Cross Diffusion and Time Delay
Directory of Open Access Journals (Sweden)
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.
Aryee, Samuel; Walumbwa, Fred O; Seidu, Emmanuel Y M; Otaye, Lilian E
2012-03-01
We proposed and tested a multilevel model, underpinned by empowerment theory, that examines the processes linking high-performance work systems (HPWS) and performance outcomes at the individual and organizational levels of analyses. Data were obtained from 37 branches of 2 banking institutions in Ghana. Results of hierarchical regression analysis revealed that branch-level HPWS relates to empowerment climate. Additionally, results of hierarchical linear modeling that examined the hypothesized cross-level relationships revealed 3 salient findings. First, experienced HPWS and empowerment climate partially mediate the influence of branch-level HPWS on psychological empowerment. Second, psychological empowerment partially mediates the influence of empowerment climate and experienced HPWS on service performance. Third, service orientation moderates the psychological empowerment-service performance relationship such that the relationship is stronger for those high rather than low in service orientation. Last, ordinary least squares regression results revealed that branch-level HPWS influences branch-level market performance through cross-level and individual-level influences on service performance that emerges at the branch level as aggregated service performance. PMID:21967297
A fractional Fokker-Planck model for anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
2014-12-15
In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
A microscopic model of ballistic-diffusive crossover
International Nuclear Information System (INIS)
Several low-dimensional systems show a crossover from diffusive to ballistic heat transport when system size is decreased. Although there is some phenomenological understanding of this crossover phenomenon at the coarse-grained level, a microscopic picture that consistently describes both the ballistic and the diffusive transport regimes has been lacking. In this work we derive a scaling form for the thermal current in a class of one dimensional systems attached to heat baths at boundaries and rigorously show that the crossover occurs when the characteristic length scale of the system competes with the system size. (paper)
Osada, Noriyuki; Takeda, Hiroshi
2003-01-01
To investigate crown development patterns, branch architecture, branch-level light interception, and leaf and branch dynamics were studied in saplings of a plagiotropically branching tree species, Polyalthia jenkinsii Hk. f. & Thoms. (Annonaceae) in a Malaysian rain forest. Lengths of branches and parts of the branches lacking leaves ('bare' branches) were smaller in upper branches than in lower branches within crowns, whereas lengths of 'leafy' parts and the number of leaves per branch were larger in intermediate than in upper and lower branches. Maximum diffuse light absorption (DLA) of individual leaves was not related to sapling height or branch position within crowns, whereas minimum DLA was lower in tall saplings. Accordingly, branch-level light interception was higher in intermediate than in upper and lower branches. The leaf production rate was higher and leaf loss rate was smaller in upper than in intermediate and lower branches. Moreover, the branch production rate of new first-order branches was larger in the upper crowns. Thus, leaf and branch dynamics do not correspond to branch-level light interception in the different canopy zones. As a result of architectural constraints, branches at different vertical positions experience predictable light microenvironments in plagiotropic species. Accordingly, this pattern of carbon allocation among branches might be particularly important for growth and crown development in plagiotropic species. PMID:12495920
Li, Feng; Stolarski, Richard S.; Pawson, Steven; Newman, Paul A.; Waugh, Darryn
2010-01-01
Changes in the width of the upwelling branch of the Brewer-Dobson circulation and Hadley cell in the 21st Century are investigated using simulations from a coupled chemistry-climate model. In these model simulations the tropical upwelling region narrows in the troposphere and lower stratosphere. The narrowing of the Brewer-Dobson circulation is caused by an equatorward shift of Rossby wave critical latitudes and Eliassen-Palm flux convergence in the subtropical lower stratosphere. In the troposphere, the model projects an expansion of the Hadley cell's poleward boundary, but a narrowing of the Hadley cell's rising branch. Model results suggest that eddy forcing may also play a part in the narrowing of the rising branch of the Hadley cell.
International Nuclear Information System (INIS)
The mesoscopic description of a system with chemical reactions predicts that if the detailed balance condition is not satisfied then nonequilibrium spatial correlations between concentrations of reactants may appear. The present work is concerned with the dynamics of their growth in a system which initially is well mixed. The discrepancy between the theory based on the master equation, in which Fick's law was assumed for the diffusive flow, and molecular dynamics simulations performed for a model system of ''reacting'' hard spheres was found in our previous work. Molecular dynamics indicates front-like expansion of correlations towards their stationary form, whereas the theory supports more uniform growth at all distances. In this paper, we introduce the relaxation of the diffusive flow towards Fick's law based on the Langevin approach in order to explain the front-like expansion of the spatial correlations. (author)
An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes
International Nuclear Information System (INIS)
We present an entropic quantum drift-diffusion model (eQDD) and show how it can be derived on a bounded domain as the diffusive approximation of the Quantum Liouville equation with a quantum BGK operator. Some links between this model and other existing models are exhibited, especially with the density gradient (DG) model and the Schroedinger-Poisson drift-diffusion model (SPDD). Then a finite difference scheme is proposed to discretize the eQDD model coupled to the Poisson equation and we show how this scheme can be slightly modified to discretize the other models. Numerical results show that the properties listed for the eQDD model are checked, as well as the model captures important features concerning the modeling of a resonant tunneling diode. To finish, some comparisons between the models stated above are realized
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.
Diffusion of PAH in potato and carrot slices and application for a potato model
DEFF Research Database (Denmark)
Trapp, Stefan; Cammarano, A.; Capri, E.;
2007-01-01
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...
Branching dynamics of viral information spreading
Iribarren, José Luis; Moro, Esteban
2011-10-01
Despite its importance for rumors or innovations propagation, peer-to-peer collaboration, social networking, or marketing, the dynamics of information spreading is not well understood. Since the diffusion depends on the heterogeneous patterns of human behavior and is driven by the participants’ decisions, its propagation dynamics shows surprising properties not explained by traditional epidemic or contagion models. Here we present a detailed analysis of our study of real viral marketing campaigns where tracking the propagation of a controlled message allowed us to analyze the structure and dynamics of a diffusion graph involving over 31 000 individuals. We found that information spreading displays a non-Markovian branching dynamics that can be modeled by a two-step Bellman-Harris branching process that generalizes the static models known in the literature and incorporates the high variability of human behavior. It explains accurately all the features of information propagation under the “tipping point” and can be used for prediction and management of viral information spreading processes.
Directory of Open Access Journals (Sweden)
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
Abels, H; Grün, G
2011-01-01
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is frame indifferent. Moreover, it is generalized to situations with a soluble species. Using the method of matched asymptotic expansions we derive various sharp interface models in the limit when the interfacial thickness tends to zero. Depending on the scaling of the mobility in the diffusion equation we either derive classical sharp interface models or models where bulk or surface diffusion is possible in the limit. In the latter case a new term resulting from surface diffusion appears in the momentum balance at the interface. Finally, we show that all sharp interface models fulfill natural energy inequalities.
Diffusion versus network models as descriptions for the spread of prion diseases in the brain.
Matthäus, Franziska
2006-05-01
In this paper we will discuss different modeling approaches for the spread of prion diseases in the brain. Firstly, we will compare reaction-diffusion models with models of epidemic diseases on networks. The solutions of the resulting reaction-diffusion equations exhibit traveling wave behavior on a one-dimensional domain, and the wave speed can be estimated. The models can be tested for diffusion-driven (Turing) instability, which could present a possible mechanism for the formation of plaques. We also show that the reaction-diffusion systems are capable of reproducing experimental data on prion spread in the mouse visual system. Secondly, we study classical epidemic models on networks, and use these models to study the influence of the network topology on the disease progression. PMID:16219329
Employing a Modified Diffuser Momentum Model to Simulate Ventilation of the Orion CEV
Straus, John; Lewis, John F.
2011-01-01
The Ansys CFX CFD modeling tool was used to support the design efforts of the ventilation system for the Orion CEV. CFD modeling was used to establish the flow field within the cabin for several supply configurations. A mesh and turbulence model sensitivity study was performed before the design studies. Results were post-processed for comparison with performance requirements. Most configurations employed straight vaned diffusers to direct and throw the flow. To manage the size of the models, the diffuser vanes were not resolved. Instead, a momentum model was employed to account for the effect of the diffusers. The momentum model was tested against a separate, vane-resolved side study. Results are presented for a single diffuser configuration for a low supply flow case.
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. PMID:26362453
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.
The calculation of gas diffusion from grains in fuel modelling
International Nuclear Information System (INIS)
Further tests have been made on the variational method of calculating gas diffusion from a spherical fuel grain. The effect of varying the junction positions for two trial functions is examined and an improved correction function given. The resultant method is suitable for gas releases of 10-7 to 1.0, with estimated relative errors of < 2%. (author)
A hierarchy of diffusion models for partially ionized plasmas.
Choquet, Isabelle; Degond, Pierre; Lucquin-Desreux, Brigitte
2007-01-01
Partially ionized plasmas corresponding to different ionization degrees are derived and connected one with each other by the diffusion approximation methodology. These plasmas are the following electrical discharges: a thermal arc discharge, glow discharges in local thermodynamic equilibrium -LTE- and in non-LTE, and a non-LTE glow discharge interacting with an electron beam (or flow).
DEFF Research Database (Denmark)
Andersen, Karsten Brandt; Levinsen, Simon; Svendsen, Winnie Edith;
2009-01-01
In this article we present a generalized theoretical model for the continuous separation of particles using the pinched flow fractionation method. So far the theoretical models have not been able to predict the separation of particles without the use of correction factors. In this article we...
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
International Nuclear Information System (INIS)
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
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
Maximum Likelihood Estimation for an Innovation Diffusion Model of New Product Acceptance
David C Schmittlein; Vijay Mahajan
1982-01-01
A maximum likelihood approach is proposed for estimating an innovation diffusion model of new product acceptance originally considered by Bass (Bass, F. M. 1969. A new product growth model for consumer durables. (January) 215–227.). The suggested approach allows: (1) computation of approximate standard errors for the diffusion model parameters, and (2) determination of the required sample size for forecasting the adoption level to any desired degree of accuracy. Using histograms from eight di...
Weber, Adam
2010-01-01
A macroscopic-modeling methodology to account for the chemical and structural properties of fuel-cell diffusion media is developed. A previous model is updated to include for the first time the use of experimentally measured capillary pressure -- saturation relationships through the introduction of a Gaussian contact-angle distribution into the property equations. The updated model is used to simulate various limiting-case scenarios of water and gas transport in fuel-cell diffusion media. ...
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...
Engelbert Dockner; Steffen Jørgensen
1988-01-01
This paper deals with the determination of optimal advertising strategies for new product diffusion models. We consider the introduction of a new consumer durable in a monopolistic market and the evolution of sales is modelled by a flexible diffusion model. Repeat sales and possible entry of rivals are disregarded but we allow for discounting of future revenue streams and cost learning curve. Using standard methods of optimal control theory we characterize qualitatively the structure of an op...
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.
Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane.
Li, He; Zhang, Yihao; Ha, Vi; Lykotrafitis, George
2016-04-13
We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer
Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion
Directory of Open Access Journals (Sweden)
Xinze Lian
2013-01-01
Full Text Available We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.
Territorial and branch associations of the oil and gas complex and the trends in their modeling
Energy Technology Data Exchange (ETDEWEB)
Chudnovskaya, S.N.
1983-01-01
Tendencies in the development of the Western Siberian region are studied on the basis of economic and mathematical modeling. The basic interrelations for an expanded system of the oil and gas complex are examined.
A mixed integer bi-level DEA model for bank branch performance evaluation by Stackelberg approach
Shafiee, Morteza; Lotfi, Farhad Hosseinzadeh; Saleh, Hilda; Ghaderi, Mehdi
2016-11-01
One of the most complicated decision making problems for managers is the evaluation of bank performance, which involves various criteria. There are many studies about bank efficiency evaluation by network DEA in the literature review. These studies do not focus on multi-level network. Wu (Eur J Oper Res 207:856-864, 2010) proposed a bi-level structure for cost efficiency at the first time. In this model, multi-level programming and cost efficiency were used. He used a nonlinear programming to solve the model. In this paper, we have focused on multi-level structure and proposed a bi-level DEA model. We then used a liner programming to solve our model. In other hand, we significantly improved the way to achieve the optimum solution in comparison with the work by Wu (2010) by converting the NP-hard nonlinear programing into a mixed integer linear programming. This study uses a bi-level programming data envelopment analysis model that embodies internal structure with Stackelberg-game relationships to evaluate the performance of banking chain. The perspective of decentralized decisions is taken in this paper to cope with complex interactions in banking chain. The results derived from bi-level programming DEA can provide valuable insights and detailed information for managers to help them evaluate the performance of the banking chain as a whole using Stackelberg-game relationships. Finally, this model was applied in the Iranian bank to evaluate cost efficiency.
Modeling and Analysis of Epidemic Diffusion within Small-World Network
Directory of Open Access Journals (Sweden)
Ming Liu
2012-01-01
Full Text Available To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.
Bertolami, Marcelo M Miller
2015-01-01
The Post Asymptotic Giant Branch (AGB) phase is arguably one of the least understood phases of the evolution of low- and intermediate- mass stars. The two grids of models presently available are based on outdated micro- and macro-physics and do not agree with each other. We study the timescales of post-AGB and CSPNe in the context of our present understanding of the micro- and macro-physics of stars. We want to assess whether new post-AGB models, based on the latter improvements in TP-AGB modeling, can help to understand the discrepancies between observation and theory and within theory itself. We compute a grid of post-AGB full evolutionary sequences that include all previous evolutionary stages from the Zero Age Main Sequence to the White Dwarf phase. Models are computed for initial masses between 0.8 and 4 $M_\\odot$ and for a wide range of initial metallicities ($Z_0=$0.02, 0.01, 0.001, 0.0001), this allow us to provide post-AGB timescales and properties for H-burning post-AGB objects with masses in the re...
Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates
Directory of Open Access Journals (Sweden)
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.
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. PMID:26219250
The water-induced linear reduction gas diffusivity model extended to three pore regions
DEFF Research Database (Denmark)
Chamindu, Deepagoda; De Jonge, Lis Wollesen; Kawamoto, Ken;
2015-01-01
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....... 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...... 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...
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.
Modelling Gas Diffusion from Breaking Coal Samples with the Discrete Element Method
Directory of Open Access Journals (Sweden)
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)
Global Existence of the Equilibrium Diffusion Model in Radiative Hydrodynamics
Institute of Scientific and Technical Information of China (English)
Chunjin LIN; Thierry GOUDON
2011-01-01
This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the wellposedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.
A STUDY ON NEW PRODUCT DEMAND FORECASTING BASED ON BASS DIFFUSION MODEL
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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.
Modeling the Impacts of Diffuse Pollution on Receiving Water Quality
Shanahan, P.; Somlyody, L.
1995-01-01
Nonpoint or diffuse pollutants represent a major cause of water-quality degradation of rivers, estuaries, lakes, and reservoirs and have become increasingly significant in countries where point sources of pollution are largely controlled. Nonpoint sources cause eutrophication, oxygen depletion, sedimentation, acidification, and salinization in receiving water bodies, introduce pathogenic organisms and other pollutants, and through shock loads of pollutants, cause mortality and morbidity of aq...
A Fractional Fokker-Planck Model for Anomalous Diffusion
Anderson, Johan; Kim, Eun-Jin; 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 ge...
A Viral Branching Model for Predicting the Spread of Electronic Word-of-Mouth
R.J.A. van der Lans (Ralf); G.H. van Bruggen (Gerrit); J. Eliashberg (Jehoshua); B. Wierenga (Berend)
2009-01-01
textabstractIn a viral marketing campaign an organization develops a marketing message, and stimulates customers to forward this message to their contacts. Despite its increasing popularity, there are no models yet that help marketers to predict how many customers a viral marketing campaign will rea
Efficient model checking for duration calculus based on branching-time approximations
DEFF Research Database (Denmark)
Fränzle, Martin; Hansen, Michael Reichhardt
2008-01-01
Duration Calculus (abbreviated to DC) is an interval-based, metric-time temporal logic designed for reasoning about embedded real-time systems at a high level of abstraction. But the complexity of model checking any decidable fragment featuring both negation and chop, DC's only modality, is non...
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.
Martinez, R.; Slavtchova-Bojkova, M.
2005-01-01
2000 Mathematics Subject Classification: primary: 60J80, 60J85, secondary: 62M09, 92D40 This work aims to provide and to compare numerical computation and simulation method to estimate the distribution of some relevant variables related to an age-dependent model allowing immigration at state zero. Specifically, we analyze the behaviour of the following variables: the extinction time and the waiting time for the beginning of the survival of population forever. They are strongly related to t...
Pattern Formation in a Cross-Diffusive Holling-Tanner Model
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Weiming Wang
2012-01-01
Full Text Available We present a theoretical analysis of the processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with self- as well as cross-diffusion in a Holling-Tanner predator-prey model; the sufficient conditions for the Turing instability with zero-flux boundary conditions are obtained; Hopf and Turing bifurcation in a spatial domain is presented, too. Furthermore, we present novel numerical evidence of time evolution of patterns controlled by self- as well as cross-diffusion in the model, and find that the model dynamics exhibits a cross-diffusion controlled formation growth not only to spots, but also to strips, holes, and stripes-spots replication. And the methods and results in the present paper may be useful for the research of the pattern formation in the cross-diffusive model.
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.
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. PMID:26839759
Directory of Open Access Journals (Sweden)
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.
Grey Box Modelling of Flow in Sewer Systems with State Dependent Diffusion
DEFF Research Database (Denmark)
Breinholt, Anders; Thordarson, Fannar Örn; Møller, Jan Kloppenborg;
2011-01-01
Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both forecast......Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both...... hypotheses for the diffusion term are investigated and compared: one that assumes additive diffusion; one that assumes state proportional diffusion; and one that assumes state exponentiated diffusion. To implement the state dependent diffusion terms Itô's formula and the Lamperti transform are applied....... It is shown that an additive diffusion noise term description leads to a violation of the physical constraints of the system, whereas a state dependent diffusion noise avoids this problem and should be favoured. It is also shown that a logarithmic transformation of the flow measurements secures positive lower...
A novel tensor distribution model for the diffusion-weighted MR signal.
Jian, Bing; Vemuri, Baba C; Ozarslan, Evren; Carney, Paul R; Mareci, Thomas H
2007-08-01
Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo. The directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications. In this paper, we present a novel statistical model for diffusion-weighted MR signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors. An interesting observation is that this continuous mixture and the MR signal attenuation are related through the Laplace transform of a probability distribution over symmetric positive definite matrices. We then show that when the mixing distribution is a Wishart distribution, the resulting closed form of the Laplace transform leads to a Rigaut-type asymptotic fractal expression, which has been phenomenologically used in the past to explain the MR signal decay but never with a rigorous mathematical justification until now. Our model not only includes the traditional diffusion tensor model as a special instance in the limiting case, but also can be adjusted to describe complex tissue structure involving multiple fiber populations. Using this new model in conjunction with a spherical deconvolution approach, we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel-by-voxel basis. Experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms. PMID:17570683
Institute of Scientific and Technical Information of China (English)
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.
Numerical Solution of Fractional Diffusion Equation Model for Freezing in Finite Media
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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.
New dynamic model for non-Fickian diffusion of calcium spark in cardiac myocytes
Institute of Scientific and Technical Information of China (English)
TAN Wenchang; LIU Shiqiang; GUO Jingjing; WANG Shiqiang; CHENG Heping; T. Masuoka
2003-01-01
A new dynamic model for non-Fickian diffusion of calcium spark in cardiac myocytes was developed by introducing time lags on the basis of the microscale mass transport theory. Numerical simulation showed that the size of the calcium spark produced by the new dynamic model was larger than that of Fick diffusion and was in more agreement with experimental results. In addition, the time lags of the calcium spark in cardiac myocytes were about 0.1-0.8 ms. These results can be used to understand the mechanism of calcium spark diffusion in cardiac myocytes.
Many-server queues with customer abandonment: Numerical analysis of their diffusion model
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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.
Numerical Simulation of Water Jet Flow Using Diffusion Flux Mixture Model
Zhi Shang; Jing Lou; Hongying Li
2014-01-01
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 t...
Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models
Lods, Bertrand; Mouhot, Clément; Toscani, Giuseppe
2008-01-01
We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely the diffusivity. Then for the physical model of hard spheres we use a suitable entropy functional fo...
A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model
Jian Huang; Zhongdi Cen; Anbo Le
2013-01-01
We present a stable finite difference scheme on a piecewise uniform mesh along with a penalty method for pricing American put options under Kou's jump-diffusion model. By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodiffere...
An Adoption Diffusion Model of RFID-Based Livestock Management System in Australia
Hossain, Mohammad Alamgir; Quaddus, Mohammed
2010-01-01
International audience Many countries, like Australia, have introduced a radio frequency identifi cation (RFID) based livestock identification and management system,which can be used for condition monitoring and fault prognosis during an outbreak situation. This paper examines the adoption process and its subsequent diffusion and extended usage of RFID in Australian livestock management practices, and proposes a research model. The model is primarily built on Rogers' innovation-diffusion t...
Implementation of a generalized diffusion layer model for condensation into MELCOR
Energy Technology Data Exchange (ETDEWEB)
Hogan, Kevin [Texas A and M University Department of Nuclear Engineering, 3133 TAMU, College Station, TX 77843 (United States); Liao Yehong [Paul Scherrer Institut, 5232 Villigen PSI (Switzerland); Beeny, Bradley [Texas A and M University Department of Nuclear Engineering, 3133 TAMU, College Station, TX 77843 (United States); Vierow, Karen, E-mail: vierow@ne.tamu.ed [Texas A and M University Department of Nuclear Engineering, 3133 TAMU, College Station, TX 77843 (United States); Cole, Randall; Humphries, Larry; Gauntt, Randall [Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0739 (United States)
2010-10-15
Condensation of co-current steam-noncondensable gas mixtures in vertical tubes is an important, yet difficult to model, component of many passive nuclear reactor cooling systems. The stagnant film model, which is used by the severe accident code MELCOR, gains its name by assuming that the gas-vapor film formed along the condensation surface is stagnant. Liao developed a generalized diffusion layer model that removes limitations of the stagnant film model and considers additional phenomena to improve predictive capabilities for condensation heat transfer with noncondensable gases. Similarities between the formulations of the stagnant film model and generalized diffusion layer model allow for the generalized diffusion layer model to be implemented into MELCOR. Input decks representing experimental facilities that produced co-current condensation data have been created to analyze and validate the generalized diffusion layer model implemented in MELCOR. The experimental data span a wide range of noncondensable gas mass fractions and include condensation mass transfer both on a vertical flat plate and in vertical tubes. MELCOR predictions of the condensation mass flux are seen to improve when using the generalized diffusion layer model instead of the stagnant film model.
Modification of TOUGH2 to Include the Dusty Gas Model for Gas Diffusion; TOPICAL
International Nuclear Information System (INIS)
The GEO-SEQ Project is investigating methods for geological sequestration of CO(sub 2). This project, which is directed by LBNL and includes a number of other industrial, university, and national laboratory partners, is evaluating computer simulation methods including TOUGH2 for this problem. The TOUGH2 code, which is a widely used code for flow and transport in porous and fractured media, includes simplified methods for gas diffusion based on a direct application of Fick's law. As shown by Webb (1998) and others, the Dusty Gas Model (DGM) is better than Fick's Law for modeling gas-phase diffusion in porous media. In order to improve gas-phase diffusion modeling for the GEO-SEQ Project, the EOS7R module in the TOUGH2 code has been modified to include the Dusty Gas Model as documented in this report. In addition, the liquid diffusion model has been changed from a mass-based formulation to a mole-based model. Modifications for separate and coupled diffusion in the gas and liquid phases have also been completed. The results from the DGM are compared to the Fick's law behavior for TCE and PCE diffusion across a capillary fringe. The differences are small due to the relatively high permeability (k= 10(sup -11) m(sup 2)) of the problem and the small mole fraction of the gases. Additional comparisons for lower permeabilities and higher mole fractions may be useful
A hierarchy of models related to nanoflows and surface diffusion
Aoki, Kazuo; Charrier, Pierre; Degond, Pierre
2010-01-01
In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to analyze the mechanisms that determine mobility of molecules in nanoscale channels. This approach proved to be remarkably useful to give new insight on these issues, such as density dependence of the d...
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.
Comparative Biosorption Studies of Hexavalent Chromium Ion onto Raw and Modified Palm Branches
Directory of Open Access Journals (Sweden)
Mona A. Shouman
2013-01-01
Full Text Available The waste of palm branches (PB was tested for its ability to remove chromium (VI from aqueous solution by batch and column experiments. Palm branches chemically modified with an oxidizing agent (sulphuric acid then coated with chitosan and surfactant (hexadecyl trimethyl ammonium bromide surfactant, HDTMA, respectively, were carried out to improve the removal performance of PB. The results of their Cr (VI removal performances are pH dependent. The adsorption data could be well interpreted by the Langmuir, Freundlich, and Flory-Huggins isotherm models. The maximum adsorption capacity obtained from the Langmuir model for the chitosan coated oxidized palm branches is 55 mg/mg. The adsorption process could be described by pseudo-second-order kinetic model. The intraparticle diffusion study revealed that film diffusion might be involved. The biosorbents were successfully regenerated using 1 M HCL solution.
Directory of Open Access Journals (Sweden)
Wallace Agyei
2015-07-01
Full Text Available Abstract Queues are common sight of many banks in Ghana. The obvious implication of customers waiting in long and winding queues could result to prolonged discomfort and economic cost to them however increasing the service rate will require additional number of tellers which implies extra cost to management. This study therefore attempts to find the trade-off between minimizing the total economic cost waiting cost and service cost and the provision of a satisfactory and reasonably shortest possible time of service to customers in order to assist management of the bank in deciding the optimal number of tellers needed. Data for this study was collected at the Ghana Commercial Bank Ltd Kumasi Main Branch for one month through observations interviews and by administering of questionnaire and was formulated as multi-server single line queuing model. The data was analyzed using TORA optimization Software as well as using descriptive method of analysis. The performance measures of different queuing systems were evaluated and analyzed. The results of the analysis showed using a five teller system was better than a four or a six-teller system in terms of average waiting time and thetotal economic cost hence the study recommends that the management should adopt a five teller model to reduce total economic costs and increase customer satisfaction.
Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks
Rätz, Andreas; Röger, Matthias
2014-08-01
Signalling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term in the membrane equations. A specific model of this form was recently proposed by the authors for the GTPase cycle in cells. We investigate here a putative role of diffusive instabilities in cell polarization. By a linearized stability analysis, we identify two different mechanisms. The first resembles a classical Turing instability for the membrane subsystem and requires (unrealistically) large differences in the lateral diffusion of activator and substrate. On the other hand, the second possibility is induced by the difference in cytosolic and lateral diffusion and appears much more realistic. We complement our theoretical analysis by numerical simulations that confirm the new stability mechanism and allow us to investigate the evolution beyond the regime where the linearization applies.
Bellassai, Debora; Spinazzola, Antonio; Silvestri, Stefano
2015-01-01
In absence of results of environmental monitoring to proceed with the assessment of occupational exposure, it was developed a model that retraces the one of Pasquill and Gifford, currently used for the estimation of concentrations of pollutants at certain distances from the source in outdoor environment. Purpose of the study is the quantitative estimate of the diffusion of airborne asbestos fibers in function of the distance from the source in an factory where railway carriages were produced during the period when asbestos was sprayed as insulator of the body. The treatment was carried out in a large shed without separation from other operations. The application of the model, given the characteristics of the emitting source, has allowed us to estimate the diffusion of particles inside the shed with an expected decrease in concentration inversely proportional to the distance from the source. By appropriate calculations the concentration by weight has been converted into number offibers by volume, the unit of measure currently used for the definition of asbestos pollution. PMID:26193738
Random variability in mesoscale wind observations and implications for diffusion models
Energy Technology Data Exchange (ETDEWEB)
Hanna, S.R. [Sigma Research Corp., Concord, MA (United States)
1994-12-31
The investigation reported in this paper grew out of a preliminary analysis of methods by which regional air quality models such as the Regional Oxidant Model account for horizontal transport and diffusion. It was discovered that there is a variety of often inconsistent methods used to parameterize horizontal diffusion at meso- and regional scales, and the time seemed ripe to review and compare and contrast these schemes. This paper provides a brief overview of the major issues that were uncovered and lists a few specific examples of the technical approaches that are used. Subsequent sections cover the basic physics of horizontal diffusion, the characteristics of observed wind fields, and methods of parameterizing horizontal diffusion in air quality models.
A capacity fade model for lithium-ion batteries including diffusion and kinetics
International Nuclear Information System (INIS)
A one dimensional model incorporating solvent diffusion and kinetics of solid electrolyte interphase (SEI) formation is developed to study capacity fade in lithium ion batteries. The model assumes that solvent diffuses through the SEI (solid electrolyte interphase) and undergoes a two electron reduction at the carbon SEI interface. The kinetics of the reduction reaction at the SEI–electrolyte interface and the solvent diffusivity are seen to be the most important parameters governing SEI formation. The capacity loss is seen to be a function of the thickness of the SEI layer and is seen to vary linearly over time. The rate constant governing SEI formation and solvent diffusivity are seen to follow Arrhenius type relationships. The model results are compared with and are found to be in good agreement with experimental data.
International Nuclear Information System (INIS)
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)
Energy Technology Data Exchange (ETDEWEB)
Jakob, A
2004-07-01
In this report a comprehensive overview on the matrix diffusion of solutes in fractured crystalline rocks is presented. Some examples from observations in crystalline bedrock are used to illustrate that matrix diffusion indeed acts on various length scales. Fickian diffusion is discussed in detail followed by some considerations on rock porosity. Due to the fact that the dual-porosity medium model is a very common and versatile method for describing solute transport in fractured porous media, the transport equations and the fundamental assumptions, approximations and simplifications are discussed in detail. There is a variety of geometrical aspects, processes and events which could influence matrix diffusion. The most important of these, such as, e.g., the effect of the flow-wetted fracture surface, channelling and the limited extent of the porous rock for matrix diffusion etc., are addressed. In a further section open issues and unresolved problems related to matrix diffusion are mentioned. Since matrix diffusion is one of the key retarding processes in geosphere transport of dissolved radionuclide species, matrix diffusion was consequently taken into account in past performance assessments of radioactive waste repositories in crystalline host rocks. Some issues regarding matrix diffusion are site-specific while others are independent of the specific situation of a planned repository for radioactive wastes. Eight different performance assessments from Finland, Sweden and Switzerland were considered with the aim of finding out how matrix diffusion was addressed, and whether a consistent picture emerges regarding the varying methodology of the different radioactive waste organisations. In the final section of the report some conclusions are drawn and an outlook is given. An extensive bibliography provides the reader with the key papers and reports related to matrix diffusion. (author)
On fast and slow times in models with diffusion
De Angelis, M; Renno, P
2012-01-01
The linear Kelvin{Voigt operator L_\\epsilon is a typical example of wave operator L_0 perturbed by higher-order viscous terms as \\epsilonu_xxt. If P\\epsilon is a prefixed boundary value problem for L_\\epsilon, when \\epsilon = 0, L_\\epsilon turns into L_0 and P_\\epsilon into a problem P_0 with the same initial{boundary conditions of P\\epsilon. Boundary layers are missing and the related control terms depending on the fast time are negligible. In a small time interval, the wave behavior is a realistic approximation of u_\\epsilon when \\epsilon \\rightarrow 0. On the contrary, when t is large, diffusion effects should prevail and the behavior of u_\\epsilon for \\epsilon \\rightarrow 0 and t \\rightarrow 1 should be analyzed. For this, a suitable functional correspondence between the Green functions G_\\epsilon and G_0 of P_epsilon and P_0 is derived and its asymptotic behavior is rigorously examined. As a consequence, the interaction between diffusion effects and pure waves is evaluated by means of the slow time \\epsi...
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...
Modeling cation diffusion in compacted water-saturated Na-bentonite at low ionic strength
International Nuclear Information System (INIS)
Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the 'macropore/nanopore' model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the 'surface diffusion' model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm-3 (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.2 kg dm-3
Energy Technology Data Exchange (ETDEWEB)
Jacovides, C.P.; Asimakopoulos, D.N.; Kaltsounides, N.A. [Department of Environmental Physics and Meteorology, Athens University Campus, Builds PHYS-V, Athens 157 84 (Greece); Boland, J. [School of Mathematics and Statistics and Institute for Sustainable Systems and Technologies, University of South Australia (Australia)
2010-08-15
In the photosynthesis process, solar radiation energy is converted to chemical energy by using atmospheric CO{sub 2}. That is, almost all living species depend on energy produced through photosynthesis for their nourishing components thus making photosynthesis vital to the earth's life. Nevertheless, the knowledge of photosynthetic photon flux density Q{sub P} (PAR, 400-700 nm) is important in several applications dealing with plants physiology, biomass production, natural illumination in greenhouses and agricultural research. This study aiming to explore the applicability of several diffuse radiation empirical models, hourly measurements of diffuse PAR and global PAR irradiation collected at Athens (37 N, 23 E, 250 m above MSL) from 1 January 2000 to 31 December 2002, are employed. These data were used to establish an empirical model relating the spectral diffuse fraction, k{sub dP} (ratio of the diffuse-to-global PAR) with the fractional transmission of global PAR k{sub tP} (ratio of the global PAR-to-extraterrestrial solar PAR). The performance of the proposed empirical model was further compared with those of twelve other diffuse-global correlation models available in the literature in terms of the widely used statistical indicators mbe, rmse and t-test. From the overall analysis, it can be concluded that the proposed model predicts diffuse PAR values accurately, whereas most of the candidate empirical models examined here appear to be location-independent for the diffuse PAR predictions. (author)
Abels, Helmut; Grün, Günther
2010-01-01
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also generalized to situations with a soluble species. Using the method of matched asymptotic expansions we derive various sharp interface models in the limit when the interfacial thickness tends to zero. Depending on the scaling of the mobility in the diffusion equation we either derive classical sharp interface models or models where bulk or surface diffusion is possible in the limit. In the two latter cases the classical Gibbs-Thomson equation has to be modified to include kinetic terms. Finally, we show that all sharp interface models fulfill natural energy inequalities.
Directory of Open Access Journals (Sweden)
Ying Liu
2015-01-01
Full Text Available Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.
Diffusive to quasi-ballistic random laser: incoherent and coherent models
Guerin, W.; Chong, Y. D.; Baudouin, Q.; Liertzer, M.; Rotter, S.; Kaiser, R.
2016-09-01
We study the crossover between the diffusive and quasi-ballistic regimes of random lasers. In particular, we compare incoherent models based on the diffusion equation and the radiative transfer equation (RTE), which neglect all wave effects, with a coherent wave model for the random laser threshold. We show that both the incoherent and the coherent models predict qualitatively similar thresholds, with a smooth transition from a diffuse to a quasi-ballistic regime. The shape of the intensity distribution in the sample as predicted by the RTE model at threshold is also in good agreement with the coherent model. The approximate incoherent models thus provide useful analytical predictions for the threshold of random lasers as well as the shape of the random laser modes at threshold.
Diffusive to quasi-ballistic random laser: incoherent and coherent models
Guerin, William; Baudouin, Quentin; Liertzer, Matthias; Rotter, Stefan; Kaiser, Robin
2016-01-01
We study the crossover between the diffusive and quasi-ballistic regimes of random lasers. In particular, we compare incoherent models based on the diffusion equation and the radiative transfer equation (RTE), which neglect all wave effects, with a coherent wave model for the random laser threshold. We show that both the incoherent and the coherent models predict qualitatively similar thresholds, with a smooth transition from a diffuse to a quasi-ballistic regime. The shape of the intensity distribution in the sample as predicted by the RTE model at threshold is also in good agreement with the coherent model. The approximate incoherent models thus provide useful analytical predictions for the threshold of random lasers as well as the shape of the random laser modes at threshold.
King, M.D.; Burkardt, N.; Clark, B.T.
2006-01-01
Recent literature on the diffusion of innovations concentrates either specifically on public adoption of policy, where social or environmental conditions are the dependent variables for adoption, or on private adoption of an innovation, where emphasis is placed on the characteristics of the innovation itself. This article uses both the policy diffusion literature and the diffusion of innovation literature to assess watershed management councils' decisions to adopt, or not adopt, scientific models. Watershed management councils are a relevant case study because they possess both public and private attributes. We report on a survey of councils in the United States that was conducted to determine the criteria used when selecting scientific models for studying watershed conditions. We found that specific variables from each body of literature play a role in explaining the choice to adopt scientific models by these quasi-public organizations. The diffusion of innovation literature contributes to an understanding of how organizations select models by confirming the importance of a model's ability to provide better data. Variables from the policy diffusion literature showed that watershed management councils that employ consultants are more likely to use scientific models. We found a gap between those who create scientific models and those who use these models. We recommend shrinking this gap through more communication between these actors and advancing the need for developers to provide more technical assistance.
N. Yaghini; P.D. Iedema
2015-01-01
A full extensive 2-dimensional (2D) model of low-density Polyethylene chain length/branching distribution is provided in this paper. 2D Population Balance Equations are solved by the Galerkinfinite element method to obtain the distributions, accounting for 2D 'topological scission'; a manner to appr
Modelling of silica diffusion experiments with 32Si in Boom Clay.
Aertsens, Marc; De Cannière, Pierre; Moors, Hugo
2003-03-01
A mathematical model describing the dissolution of nuclear glass directly disposed in clay combines a first-order dissolution rate law with the diffusion of dissolved silica in clay. According to this model, the main parameters describing the long-term dissolution of the glass are etaR, the product of the diffusion accessible porosity eta and the retardation factor R, and the apparent diffusion coefficient D(app) of dissolved silica in clay. For determining the migration parameters needed for long-term predictions, four Through-Diffusion (T-D) experiments and one percolation test have been performed on undisturbed clay cores. In the Through-Diffusion experiments, the concentration decrease after injection of 32Si (radioactive labelled silica) was measured in the inlet compartment. At the end of the T-D experiments, the clay cores were cut in thin slices and the activity of labelled silica in each slice was determined. The measured activity profiles for these four clay cores are well reproducible. Since no labelled silica could be detected in the outlet compartments, the Through-Diffusion experiments are fitted by two In-Diffusion models: one model assuming linear and reversible sorption equilibrium and a second model taking into account sorption kinetics. Although the kinetic model provides better fits, due to the sufficiently long duration of the experiments, both models give approximately similar values for the fit parameters. The single percolation test leads to an apparent diffusion coefficient value about two to three times lower than those of the Through-Diffusion tests. Therefore, dissolved silica appears to be strongly retarded in Boom Clay. A retardation factor R between 100 and 300 was determined. The corresponding in situ distribution coefficient K(d) is in the range 25-75 cm(3) g(-1). The apparent diffusion coefficient of dissolved silica in Boom Clay is estimated between 2 x 10(-13) and 7 x 10(-13) m(2) s(-1). The pore diffusion coefficient is in the
Diffusion of a collaborative care model in primary care: a longitudinal qualitative study
Directory of Open Access Journals (Sweden)
Vedel Isabelle
2013-01-01
Full Text Available Background Although collaborative team models (CTM improve care processes and health outcomes, their diffusion poses challenges related to difficulties in securing their adoption by primary care clinicians (PCPs. The objectives of this study are to understand: (1 how the perceived characteristics of a CTM influenced clinicians' decision to adopt -or not- the model; and (2 the model's diffusion process. Methods We conducted a longitudinal case study based on the Diffusion of Innovations Theory. First, diffusion curves were developed for all 175 PCPs and 59 nurses practicing in one borough of Paris. Second, semi-structured interviews were conducted with a representative sample of 40 PCPs and 15 nurses to better understand the implementation dynamics. Results Diffusion curves showed that 3.5 years after the start of the implementation, 100% of nurses and over 80% of PCPs had adopted the CTM. The dynamics of the CTM's diffusion were different between the PCPs and the nurses. The slopes of the two curves are also distinctly different. Among the nurses, the critical mass of adopters was attained faster, since they adopted the CTM earlier and more quickly than the PCPs. Results of the semi-structured interviews showed that these differences in diffusion dynamics were mostly founded in differences between the PCPs' and the nurses' perceptions of the CTM's compatibility with norms, values and practices and its relative advantage (impact on patient management and work practices. Opinion leaders played a key role in the diffusion of the CTM among PCPs. Conclusion CTM diffusion is a social phenomenon that requires a major commitment by clinicians and a willingness to take risks; the role of opinion leaders is key. Paying attention to the notion of a critical mass of adopters is essential to developing implementation strategies that will accelerate the adoption process by clinicians.
Energy Technology Data Exchange (ETDEWEB)
Wang, Jing [Iowa State Univ., Ames, IA (United States)
2013-01-11
We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.
Morrison, M. D.; Cunningham, A. J.
1983-01-01
Branching ratios are presented of singly and doubly ionized sulfur EUV emissions. They are determined by measuring the relative photon intensities of each of the branching components. For several transitions in S II for which mean lifetimes have been measured with fast-beam spectroscopy, the data presented here are used to determine transition probabilities. The S II transitions originate from the 2P, 4s-prime 2D, and 4s 2P terms and terminate on the metastable states of the ion. The S III transitions originate from the 3d 3D0, 4s 3P0, 3p3 3S0, 4s 1P0, and 3s3p3 1P0 terms and terminate on the metastable and ground ionic states. The results for S III include branching ratios involving intercombination transitions that affect ongoing modeling of the energy budget of the Io plasma torus.
Directory of Open Access Journals (Sweden)
O. H. Kapitonov
2010-05-01
Full Text Available A mathematical model of coulostatic relaxation of the potential for solid metallic electrode was presented. The solution in the case of limiting diffusion current was obtained. On the basis of this model the technique of concentration measurements for heavy metal ions in diluted solutions was suggested. The model adequacy was proved by experimental data.
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.
Attractor for a Reaction-Diffusion System Modeling Cancer Network
Directory of Open Access Journals (Sweden)
Xueyong Chen
2014-01-01
Full Text Available A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in L2(Ω×L2(Ω and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.
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.
A model of space-fractional-order diffusion in the glial scar.
Prodanov, Dimiter; Delbeke, Jean
2016-08-21
Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, which is thought to be detrimental for the neurons surrounding the electrode. Mechanisms of this type of neuroinflammation are still poorly understood. Recent experimental and theoretical results point to a possible role of the diffusing species in this process. The paper considers a model of anomalous diffusion occurring in the glial scar around a chronic implant in two simple geometries - a separable rectilinear electrode and a cylindrical electrode, which are solvable exactly. We describe a hypothetical extended source of diffusing species and study its concentration profile in steady-state conditions. Diffusion transport is assumed to obey a fractional-order Fick law, derivable from physically realistic assumptions using a fractional calculus approach. Presented fractional-order distribution morphs into integer-order diffusion in the case of integral fractional exponents. The model demonstrates that accumulation of diffusing species can occur and the scar properties (i.e. tortuosity, fractional order, scar thickness) and boundary conditions can influence such accumulation. The observed shape of the concentration profile corresponds qualitatively with GFAP profiles reported in the literature. The main difference with respect to the previous studies is the explicit incorporation of the apparatus of fractional calculus without assumption of an ad hoc tortuosity parameter. The approach can be adapted to other studies of diffusion in biological tissues, for example of biomolecules or small drug molecules. PMID:27179458
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...
Numerical Simulation of Water Jet Flow Using Diffusion Flux Mixture Model
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Bernard Wong
2009-01-01
martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.
Does the diffusion DM-DE interaction model solve cosmological puzzles?
Szydlowski, Marek; Stachowski, Aleksander
2016-01-01
We study dynamics of cosmological models with diffusion effects modeling dark matter and dark energy interactions. We show the simple model with diffusion between the cosmological constant sector and dark matter, where the canonical scaling law of dark matter $(\\rho_{dm,0}a^{-3}(t))$ is modified by an additive $\\epsilon(t)=\\gamma t a^{-3}(t)$ to the form $\\rho_{dm}=\\rho_{dm,0}a^{-3}(t)+\\epsilon(t)$. We reduced this model to the autonomous dynamical system and investigate it using dynamical sy...
Qualitative analysis on a diffusive prey-predator model with ratio-dependent functional response
Institute of Scientific and Technical Information of China (English)
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
Energy Technology Data Exchange (ETDEWEB)
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.
Modeling and Uncertainty Quantification of Vapor Sorption and Diffusion in Heterogeneous Polymers
Energy Technology Data Exchange (ETDEWEB)
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 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
Guoping Xu; Harry Zheng
2010-01-01
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is...
A permeation-diffusion-reaction model of gas transport in cellular tissue of plant materials
Ho, Quang Tri; Verlinden, Bert; Verboven, Pieter; Vandewalle, Stefan; Nicolai, Bart
2006-01-01
Gas transport in fruit tissue is governed by both diffusion and permeation. The latter phenomenon is caused by overall pressure gradients which may develop due to the large difference in O-2 and CO2 diffusivity during controlled atmosphere storage of the fruit. A measurement set-up for tissue permeation based on unsteady-state gas exchange was developed. The gas permeability of pear tissue was determined based on an analytical gas transport model. The overall gas transport in pear tissue samp...
Xuefeng Zhang; Dong Li; Chu, Peter C.; Lianxin Zhang; Wei Li
2015-01-01
Sequential, adaptive, and gradient diffusion filters are implemented into spatial multiscale three-dimensional variational data assimilation (3DVAR) as alternative schemes to model background error covariance matrix for the commonly used correction scale method, recursive filter method, and sequential 3DVAR. The gradient diffusion filter (GDF) is verified by a two-dimensional sea surface temperature (SST) assimilation experiment. Compared to the existing DF, the new GDF scheme shows a superio...
Yuste, S B; Abad, E; Baumgaertner, A
2016-07-01
We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ,P(ℓ)∼ℓ^{-(1+α)} (α>0). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems. PMID:27575088
Miller Bertolami, Marcelo Miguel
2016-04-01
Context. The post-asymptotic giant branch (AGB) phase is arguably one of the least understood phases of the evolution of low- and intermediate- mass stars. The two grids of models presently available are based on outdated micro- and macrophysics and do not agree with each other. Studies of the central stars of planetary nebulae (CSPNe) and post-AGB stars in different stellar populations point to significant discrepancies with the theoretical predictions of post-AGB models. Aims: We study the timescales of post-AGB and CSPNe in the context of our present understanding of the micro- and macrophysics of stars. We want to assess whether new post-AGB models, based on the latter improvements in TP-AGB modeling, can help us to understand the discrepancies between observation and theory and within theory itself. In addition, we aim to understand the impact of the previous AGB evolution for post-AGB phases. Methods: We computed a grid of post-AGB full evolutionary sequences that include all previous evolutionary stages from the zero age main sequence to the white dwarf phase. We computed models for initial masses between 0.8 and 4 M⊙ and for a wide range of initial metallicities (Z0 = 0.02, 0.01, 0.001, 0.0001). This allowed us to provide post-AGB timescales and properties for H-burning post-AGB objects with masses in the relevant range for the formation of planetary nebulae (~0.5-0.8 M⊙). We included an updated treatment of the constitutive microphysics and included an updated description of the mixing processes and winds that play a key role during the thermal pulses (TP) on the AGB phase. Results: We present a new grid of models for post-AGB stars that take into account the improvements in the modeling of AGB stars in recent decades. These new models are particularly suited to be inputs in studies of the formation of planetary nebulae and for the determination of the properties of CSPNe from their observational parameters. We find post-AGB timescales that are at
Notes on the Langevin model for turbulent diffusion of ``marked`` particles
Energy Technology Data Exchange (ETDEWEB)
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.
Onset to First Alcohol Use in Early Adolescence: A Network Diffusion Model
Light, John M.; Greenan, Charlotte C.; Rusby, Julie C.; Nies, Kimberley M.; Snijders, Tom A.B.
2013-01-01
A novel version of Snijders’s stochastic actor-based modeling (SABM) framework is applied to model the diffusion of first alcohol use through middle school-wide longitudinal networks of early adolescents, aged approximately 11–14 years. Models couple a standard SABM for friendship network evolution with a proportional hazard model for first alcohol use. Meta-analysis of individual models for 12 schools found significant effects for friendship selection based on the same alco...
Option Pricing Model Based on the Stochastic Volatility and Jump Diffusion Process
Liu, Xudong
2014-01-01
Although the Black and Scholes (1973) model achieved great success in option pricing theory, the two obvious phenomena have received much attention in past decades (Kou, 2002). One is the asymmetric leptokurtic features; the other is the volatility “smiles”. To modify the Black and Scholes (1973) model, we introduce the Kou (2002) double exponential jump-diffusion model. It is more consistent with the price process than the Black and Scholes (1973) model. The Kou (2002) model not only contain...
DNA Looping Kinetics Analyzed Using Diffusive Hidden Markov Model
Beausang, J F; Finzi, L; Manzo, C; Nelson, P C; Zurla, C; Beausang, John F.; Dunlap, David; Finzi, Laura; Manzo, Carlo; Nelson, Philip C.; Zurla, Chiara
2007-01-01
Tethered particle experiments use light microscopy to measure the position of a micrometer-sized bead tethered to a microscope slide via a ~micrometer length polymer, in order to infer the behavior of the invisible polymer. Currently, this method is used to measure rate constants of DNA loop formation and breakdown mediated by repressor protein that binds to the DNA. We report a new technique for measuring these rates using a modified hidden Markov analysis that directly incorporates the diffusive motion of the bead, which is an inherent complication of tethered particle motion because it occurs on a time scale between the sampling frequency and the looping time. We compare looping lifetimes found with our method, which are consistent over a range of sampling frequencies, to those obtained via the traditional threshold-crossing analysis, which vary depending on how the raw data are filtered in the time domain. Our method does not involve such filtering, and so can detect short-lived looping events and sudden ...
A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick’s law
International Nuclear Information System (INIS)
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive stochastic drift term with diffusion coefficient obeying a Stokes–Einstein relation, in addition to the expected advection by a random velocity. The overdamped limit correctly reproduces both the enhanced diffusion in the ensemble-averaged mean and the long-range correlated giant fluctuations in individual realizations of the mixing process, and is amenable to efficient numerical solution. Through a combination of Eulerian and Lagrangian numerical methods we demonstrate that diffusion in liquids is not most fundamentally described by Fick’s irreversible law; rather, diffusion is better modeled as reversible random advection by thermal velocity fluctuations. We find that the diffusion coefficient is effectively renormalized to a value that depends on the scale of observation. Our work reveals somewhat unexpected connections between flows at small scales, dominated by thermal fluctuations, and flows at large scales, dominated by turbulent fluctuations. (paper)
A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick’s law
Donev, Aleksandar; Fai, Thomas G.; Vanden-Eijnden, Eric
2014-04-01
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive stochastic drift term with diffusion coefficient obeying a Stokes-Einstein relation, in addition to the expected advection by a random velocity. The overdamped limit correctly reproduces both the enhanced diffusion in the ensemble-averaged mean and the long-range correlated giant fluctuations in individual realizations of the mixing process, and is amenable to efficient numerical solution. Through a combination of Eulerian and Lagrangian numerical methods we demonstrate that diffusion in liquids is not most fundamentally described by Fick’s irreversible law; rather, diffusion is better modeled as reversible random advection by thermal velocity fluctuations. We find that the diffusion coefficient is effectively renormalized to a value that depends on the scale of observation. Our work reveals somewhat unexpected connections between flows at small scales, dominated by thermal fluctuations, and flows at large scales, dominated by turbulent fluctuations.
Modeling of Diffusive Convective and Electromechanical Processes in PEM fuel cells
DEFF Research Database (Denmark)
Bang, Mads
of their impact on the operational performance of the fuel cell. In the modelling work presented, the commercial CFD package CFX4.4 is used as the foundation to generate a model of a PEM fuel cell. The CFX4.4 platform provides the framework of solving the three-dimensional transport equations for mass, momentum...... 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...... of the gaseous phase in the fuel cell and allows prediction of the concentration of the species present. A special feature of the approach developed is a method that allows detailed modelling and prediction of electrode kinetics. The transport of electrons in the gas diffusion layer and catalyst layer, as well...
Effects of imperfect noise correlations on decoherence-free subsystems: SU(2) diffusion model
International Nuclear Information System (INIS)
We present a model of an N-qubit channel where consecutive qubits experience correlated random rotations. Our model is an extension to the standard decoherence-free subsystems approach which assumes that all qubits experience the same disturbance. The variation of rotations acting on consecutive qubits is modeled as diffusion on the SU(2) group. The model may be applied to spins traveling in a varying magnetic field or to photons passing through a fiber whose birefringence fluctuates over the time separation between photons. We derive an explicit formula describing the action of the channel on an arbitrary N-qubit state. For N=3 we investigate the effects of diffusion on both the classical and quantum capacities of the channel. We observe that nonorthogonal states are necessary to achieve optimal classical capacity. Furthermore, we find the threshold for the diffusion parameter above which coherent information of the channel vanishes
Diffusive model of pore shrinkage in final-stage sintering under hydrostatic pressure
Energy Technology Data Exchange (ETDEWEB)
Kim, B.-N., E-mail: kim.byung-nam@nims.go.jp [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Hiraga, K.; Morita, K.; Yoshida, H.; Zhang, H. [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan)
2011-06-15
A grain-boundary-diffusion model is developed to understand the densification behavior of pores in the final stage of sintering under compressive hydrostatic pressure. From analysis of the diffusive model, the bulk viscosity, densification rate and shrinkage rate of pores are predicted for a dense matrix polycrystal containing spherical pores, and compared with the existing experimental results and models. A transition in the sintering mechanism is predicted from the different pore-size dependence of the shrinkage rate between the diffusive and the viscous flow models. The transition effect is experimentally confirmed by the appearance of a downward inflection in the size distribution of pores during sintering. The upward inflection observed experimentally in the cavity-size distribution after superplastic deformation is also explained by the transition of the mechanism.
Inclusion of the diffuseness in the schematic model of heavy ion collisions
International Nuclear Information System (INIS)
The schematic model of central heavy ion collisions developed by Swiatecki includes the Coulomb and surface contributions to the potential energy of the system and one-body dissipation. This model is extended by considering the diffuseness of the nuclear surface; this has the implication that we must consider the proximity forces in the dynamics of the collisions. For the sake of simplicity we work with symmetrical systems. The results of the model studied are compared with experimental data and with other theoretical calculations. We conclude that the detailed consideration of the diffuseness of the nuclear surfaces does not substantially change the results of the schematic model for sharp surfaces in which the diffuseness is considered only through the parameters. (author)
Modified Diffusion Flux Model for Analysis of Turbulent Gas-Particle Two-Phase Flows
Institute of Scientific and Technical Information of China (English)
YANG Ruichang; ZHOU Weiduo; FUKUDA Kenji; JU Zejian; SHANG Zhi
2005-01-01
A modified diffusion flux model (DFM) was developed to analyze turbulent multi-dimensional gas-particle two-phase flows. In the model, the solid particles move in a modified acceleration field, , which includes the effects of various forces on the particles as if all the forces have the same effect on the particles as the gravity. The accelerations due to various forces are then taken into account in the calculation of the diffusion velocities of the solid particles in the gas-particle two-phase flow. The DFM was used to numerically simulate the gas-solid two-phase flow behind a vertical backward-facing step. The numerical simulation compared well with experimental data and numerical results using both the k-ε-Ap and k-ε-kp two-fluid models available in the literature. The comparison shows that the modified diffusion flux model correctly simulates the turbulent gas-particle two-phase flow.
International Nuclear Information System (INIS)
The interaction of hydrogen with tungsten is investigated by means of the Density Functional Theory (DFT) and statistical methods based on the transition-state theory and thermodynamics. This model yields temperature-dependent data that can help understanding macro-scale experimental results. Within this model, the concentrations of trapped hydrogen atoms at thermodynamic equilibrium are established. Taking into account the configurational entropy, hydrogen is shown to induce vacancy formation below 1000 K. Based on this model, TDS spectra are simulated with a basic kinetic model to provide some better insight into the desorption process of hydrogen. Finally, revised mechanisms for hydrogen diffusion in tungsten are proposed; we conclude that the discrepancy existing between the experimental diffusion coefficient measured by Frauenfelder (1969) and the one calculated by DFT would be reconciled provided one uses two different diffusion regimes that would depend on temperature and vacancies concentration
Measuring and modeling oxygen diffusion in niobium-vanadium and niobium-palladium alloys
Hennessey, Theresa P.
Niobium alloys are under consideration for high-temperature aerospace applications, but they have poor oxidation resistance and need high-temperature coatings for protection in severe environments. Our approach to creating an oxidation-resistant Nb alloy is to identify substitutional solute elements that lower the diffusivity of oxygen in Nb. In theory, this will induce a transition from internal to external oxidation and promote the formation of a desirable, protective oxide scale. The objective of this particular project is to compare the oxygen diffusivity in Nb alloys that contain either trap or repulsive sites. In Nb, oxygen atoms diffuse via an interstitial mechanism, and they can interact with substitutional solute atoms in different ways. The interstitial sites adjacent to a substitutional atom constitute a "zone of influence". If the sites in this zone have a lower energy than the normal sites, they are called "trap" sites. If these sites have a higher energy, they are called "repulsive" sites. Oxygen diffusion is inhibited in both cases: trap sites hold the oxygen and keep it from diffusing further, while repulsive sites block the path of the oxygen. Two new mathematical models for interstitial diffusion in these systems were derived from probability and statistical thermodynamic theory. The models were verified using a new random-walk computer simulation of oxygen diffusion through Nb alloys. These models were also tested experimentally by measuring oxygen diffusivity in Nb-V and Nb-Pd alloys. These results showed that V atoms create trap sites for oxygen atoms, confirming previous work. However, there was not enough data to prove definitively that Pd atoms create repulsive sites, as expected by theory.
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.
A diffuse interface model for two-phase ferrofluid flows
Nochetto, Ricardo H.; Salgado, Abner J.; Tomas, Ignacio
2016-01-01
We develop a model describing the behavior of two-phase ferrofluid flows using phase field-techniques and present an energy-stable numerical scheme for it. For a simplified, yet physically realistic, version of this model and the corresponding numerical scheme we prove, in addition to stability, convergence and as by-product existence of solutions. With a series of numerical experiments we illustrate the potential of these simple models and their ability to capture basic phenomenological feat...
On modeling and simulation of surfactants in diffuse interface flow
Engblom, Stefan; Amberg, Gustav; Tornberg, Anna-Karin
2011-01-01
An existing phase-field model of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and show that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.
Institute of Scientific and Technical Information of China (English)
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.