Reaction-diffusion-branching models of stock price fluctuations
Tang, Lei-Han; Tian, Guang-Shan
Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ( H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.
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.
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.
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.
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.
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.
Generalized Markov branching models
Li, Junping
2005-01-01
In this thesis, we first considered a modified Markov branching process incorporating both state-independent immigration and resurrection. After establishing the criteria for regularity and uniqueness, explicit expressions for the extinction probability and mean extinction time are presented. The criteria for recurrence and ergodicity are also established. In addition, an explicit expression for the equilibrium distribution is presented.\\ud \\ud We then moved on to investigate the basic proper...
Generalized Markov branching models
Li, Junping
2005-01-01
In this thesis, we first considered a modified Markov branching process incorporating both state-independent immigration and resurrection. After establishing the criteria for regularity and uniqueness, explicit expressions for the extinction probability and mean extinction time are presented. The criteria for recurrence and ergodicity are also established. In addition, an explicit expression for the equilibrium distribution is presented. We then moved on to investigate the basic proper...
Mechanisms of side branching and tip splitting in a model of branching morphogenesis.
Directory of Open Access Journals (Sweden)
Yina Guo
Full Text Available Recent experimental work in lung morphogenesis has described an elegant pattern of branching phenomena. Two primary forms of branching have been identified: side branching and tip splitting. In our previous study of lung branching morphogenesis, we used a 4 variable partial differential equation (PDE, due to Meinhardt, as our mathematical model to describe the reaction and diffusion of morphogens creating those branched patterns. By altering key parameters in the model, we were able to reproduce all the branching styles and the switch between branching modes. Here, we attempt to explain the branching phenomena described above, as growing out of two fundamental instabilities, one in the longitudinal (growth direction and the other in the transverse direction. We begin by decoupling the original branching process into two semi-independent sub-processes, 1 a classic activator/inhibitor system along the growing stalk, and 2 the spatial growth of the stalk. We then reduced the full branching model into an activator/inhibitor model that embeds growth of the stalk as a controllable parameter, to explore the mechanisms that determine different branching patterns. We found that, in this model, 1 side branching results from a pattern-formation instability of the activator/inhibitor subsystem in the longitudinal direction. This instability is far from equilibrium, requiring a large inhomogeneity in the initial conditions. It successively creates periodic activator peaks along the growing stalk, each of which later on migrates out and forms a side branch; 2 tip splitting is due to a Turing-style instability along the transversal direction, that creates the spatial splitting of the activator peak into 2 simultaneously-formed peaks at the growing tip, the occurrence of which requires the widening of the growing stalk. Tip splitting is abolished when transversal stalk widening is prevented; 3 when both instabilities are satisfied, tip bifurcation occurs
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.
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.
Engländer, J.; Kyprianou, A.E.
2002-01-01
Consider a spatial branching particle process where the underlying motion is a conservative diffusion on D C Rd corresponding to the elliptic op- erator L on D, and the branching is strictly binary (dyadic), with spatially varying rate ß(x) => 0 (and ß <> 0) which is assumed to be bounded from above
Branching model for vegetation. [polarimetric remote sensing
Yueh, Simon H.; Kong, J. A.; Jao, Jen K.; Shin, Robert T.; Le Toan, Thuy
1992-01-01
In the present branching model for remote sensing of vegetation, the frequency and angular responses of a two-scale cylinder cluster are calculated to illustrate the importance of vegetation architecture. Attention is given to the implementation of a two-scale branching model for soybeans, where the relative location of soybean plants is described by a pair of distribution functions. Theoretical backscattering coefficients evaluated by means of hole-correction pair distribution are in agreement with extensive data collected from soybean fields. The hole-correction approximation is found to be the more realistic.
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.
Branching patterns emerge in a mathematical model of the dynamics of lung development.
Guo, Yina; Chen, Ting-Hsuan; Zeng, Xingjuan; Warburton, David; Boström, Kristina I; Ho, Chih-Ming; Zhao, Xin; Garfinkel, Alan
2014-01-15
Recent experimental work has described an elegant pattern of branching in the development of the lung. Multiple forms of branching have been identified, including side branching and tip bifurcation. A particularly interesting feature is the phenomenon of 'orthogonal rotation of the branching plane'. The lung must fill 3D space with the essentially 2D phenomenon of branching. It accomplishes this by rotating the branching plane by 90° with each generation. The mechanisms underlying this rotation are not understood. In general, the programmes that underlie branching have been hypothetically attributed to genetic 'subroutines' under the control of a 'global master routine' to invoke particular subroutines at the proper time and location, but the mechanisms of these routines are not known. Here, we demonstrate that fundamental mechanisms, the reaction and diffusion of biochemical morphogens, can create these patterns. We used a partial differential equation model that postulates three morphogens, which we identify with specific molecules in lung development. We found that cascades of branching events, including side branching, tip splitting and orthogonal rotation of the branching plane, all emerge immediately from the model, without further assumptions. In addition, we found that one branching mode can be easily switched to another, by increasing or decreasing the values of key parameters. This shows how a 'global master routine' could work by the alteration of a single parameter. Being able to simulate cascades of branching events is necessary to understand the critical features of branching, such as orthogonal rotation of the branching plane between successive generations, and branching mode switch during lung development. Thus, our model provides a paradigm for how genes could possibly act to produce these spatial structures. Our low-dimensional model gives a qualitative understanding of how generic physiological mechanisms can produce branching phenomena, and how
A branching model for hadronic air showers
Novotny, Vladimir; Ebr, Jan
2015-01-01
We introduce a simple branching model for the development of hadronic showers in the Earth's atmosphere. Based on this model, we show how the size of the pionic component followed by muons can be estimated. Several aspects of the subsequent muonic component are also discussed. We focus on the energy evolution of the muon production depth. We also estimate the impact of the primary particle mass on the size of the hadronic component. Even though a precise calculation of the development of air showers must be left to complex Monte Carlo simulations, the proposed model can reveal qualitative insight into the air shower physics.
Modeling branching pore structures in membrane filters
Sanaei, Pejman; Cummings, Linda J.
2016-11-01
Membrane filters are in widespread industrial use, and mathematical models to predict their efficacy are potentially very useful, as such models can suggest design modifications to improve filter performance and lifetime. Many models have been proposed to describe particle capture by membrane filters and the associated fluid dynamics, but most such models are based on a very simple structure in which the pores of the membrane are assumed to be simple circularly-cylindrical tubes spanning the depth of the membrane. Real membranes used in applications usually have much more complex geometry, with interconnected pores which may branch and bifurcate. Pores are also typically larger on the upstream side of the membrane than on the downstream side. We present an idealized mathematical model, in which a membrane consists of a series of bifurcating pores, which decrease in size as the membrane is traversed. Feed solution is forced through the membrane by applied pressure, and particles are removed from the feed either by sieving, or by particle adsorption within pores (which shrinks them). Thus the membrane's permeability decreases as the filtration progresses, ultimately falling to zero. We discuss how filtration efficiency depends on the characteristics of the branching structure. Partial support from NSF DMS 1261596 is gratefully acknowledged.
Simple statistical model for branched aggregates
DEFF Research Database (Denmark)
Lemarchand, Claire; Hansen, Jesper Schmidt
2015-01-01
, 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......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....... 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...
Markov branching in the vertex splitting model
Stefansson, Sigurdur Orn
2011-01-01
We study a special case of the vertex splitting model which is a recent model of randomly growing trees. For any finite maximum vertex degree $D$, we find a one parameter model, with parameter $\\alpha \\in [0,1]$ which has a so--called Markov branching property. When $D=\\infty$ we find a two parameter model with an additional parameter $\\gamma \\in [0,1]$ which also has this feature. In the case $D = 3$, the model bears resemblance to Ford's $\\alpha$--model of phylogenetic trees and when $D=\\infty$ it is similar to its generalization, the $\\alpha\\gamma$--model. For $\\alpha = 0$, the model reduces to the well known model of preferential attachment. In the case $\\alpha > 0$, we prove convergence of the finite volume probability measures, generated by the growth rules, to a measure on infinite trees which is concentrated on the set of trees with a single spine. We show that the annealed Hausdorff dimension with respect to the infinite volume measure is $1/\\alpha$. When $\\gamma = 0$ the model reduces to a model of ...
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...
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.
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.
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
Kim, D.M.; Iedema, P.D.
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
A branch-and-bound methodology within algebraic modelling systems
Bisschop, J.J.; Heerink, J.B.J.; Kloosterman, G.
1998-01-01
Through the use of application-specific branch-and-bound directives it is possible to find solutions to combinatorial models that would otherwise be difficult or impossible to find by just using generic branch-and-bound techniques within the framework of mathematical programming. {\\sc Minto} is an e
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.
Oak Ridge Gaseous Diffusion Plant Biological Monitoring and Abatement Program for Mitchell Branch
Energy Technology Data Exchange (ETDEWEB)
Loar, J.M.; Adams, S.M.; Kszos, L.A.; Ryon, M.G.; Smith, J.G.; Southworth, G.R.; Stewart, A.J.
1992-01-01
A proposed Biological Monitoring and Abatement Program (BMAP) for the Oak Ridge Gaseous Diffusion Plant (ORGDP; currently the Oak Ridge K-25 Site) was prepared in December 1986, as required by the modified National Pollutant Discharge Elimination System (NPDES) permit that was issued on September 11, 1986. The effluent discharges to Mitchell Branch are complex, consisting of trace elements, organic chemicals, and radionuclides in addition to various conventional pollutants. Moreover, the composition of these effluent streams will be changing over time as various pollution abatement measures are implemented over the next several years. Although contaminant inputs to the stream originate primarily as point sources from existing plant operations, area sources, such as the classified burial grounds and the K-1407-C holding pond, can not be eliminated as potential sources of contaminants. The proposed BMAP consists of four tasks. These tasks include (1) ambient toxicity testing, (2) bioaccumulation studies, (3) biological indicator studies, and (4) ecological surveys of the benthic invertebrate and fish communities. BMAP will determine whether the effluent limits established for ORGDP protect the designated use of the receiving stream (Mitchell Branch) for growth and propagation of fish and aquatic life. Another objective of the program is to document the ecological effects resulting from various pollution abatement projects, such as the Central Neutralization Facility.
Stability of earthquake clustering models: criticality and branching ratios.
Zhuang, Jiancang; Werner, Maximilian J; Harte, David S
2013-12-01
We study the stability conditions of a class of branching processes prominent in the analysis and modeling of seismicity. This class includes the epidemic-type aftershock sequence (ETAS) model as a special case, but more generally comprises models in which the magnitude distribution of direct offspring depends on the magnitude of the progenitor, such as the branching aftershock sequence (BASS) model and another recently proposed branching model based on a dynamic scaling hypothesis. These stability conditions are closely related to the concepts of the criticality parameter and the branching ratio. The criticality parameter summarizes the asymptotic behavior of the population after sufficiently many generations, determined by the maximum eigenvalue of the transition equations. The branching ratio is defined by the proportion of triggered events in all the events. Based on the results for the generalized case, we show that the branching ratio of the ETAS model is identical to its criticality parameter because its magnitude density is separable from the full intensity. More generally, however, these two values differ and thus place separate conditions on model stability. As an illustration of the difference and of the importance of the stability conditions, we employ a version of the BASS model, reformulated to ensure the possibility of stationarity. In addition, we analyze the magnitude distributions of successive generations of the BASS model via analytical and numerical methods, and find that the compound density differs substantially from a Gutenberg-Richter distribution, unless the process is essentially subcritical (branching ratio less than 1) or the magnitude dependence between the parent event and the direct offspring is weak.
Stability of earthquake clustering models: Criticality and branching ratios
Zhuang, Jiancang; Werner, Maximilian J.; Harte, David S.
2013-12-01
We study the stability conditions of a class of branching processes prominent in the analysis and modeling of seismicity. This class includes the epidemic-type aftershock sequence (ETAS) model as a special case, but more generally comprises models in which the magnitude distribution of direct offspring depends on the magnitude of the progenitor, such as the branching aftershock sequence (BASS) model and another recently proposed branching model based on a dynamic scaling hypothesis. These stability conditions are closely related to the concepts of the criticality parameter and the branching ratio. The criticality parameter summarizes the asymptotic behavior of the population after sufficiently many generations, determined by the maximum eigenvalue of the transition equations. The branching ratio is defined by the proportion of triggered events in all the events. Based on the results for the generalized case, we show that the branching ratio of the ETAS model is identical to its criticality parameter because its magnitude density is separable from the full intensity. More generally, however, these two values differ and thus place separate conditions on model stability. As an illustration of the difference and of the importance of the stability conditions, we employ a version of the BASS model, reformulated to ensure the possibility of stationarity. In addition, we analyze the magnitude distributions of successive generations of the BASS model via analytical and numerical methods, and find that the compound density differs substantially from a Gutenberg-Richter distribution, unless the process is essentially subcritical (branching ratio less than 1) or the magnitude dependence between the parent event and the direct offspring is weak.
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...
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 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.
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...
Kelbert, M. Ya.; Suhov, Yu. M.
1995-02-01
A general model of a branching random walk in R 1 is considered, with several types of particles, where the branching occurs with probabilities determined by the type of a parent particle. Each new particle starts moving from the place where it was born, independently of other particles. The distribution of the displacement of a particle, before it splits, depends on its type. A necessary and sufficient condition is given for the random variable 220_2005_Article_BF02101538_TeX2GIFE1.gif X^0 = mathop {sup max}limits_{ n ≥q 0 1 ≤q k ≤q N_n } X_{n,k} to be finite. Here, X n, k is the position of the k th particle in the n th generation, N n is the number of particles in the n th generation (regardless of their type). It turns out that the distribution of X 0 gives a minimal solution to a natural system of stochastic equations which has a linearly ordered continuum of other solutions. The last fact is used for proving the existence of a monotone travelling-wave solution to systems of coupled non-linear parabolic PDE's.
Modelling the Diffusion of Scientific Publications
Ph.H.B.F. Franses (Philip Hans); D. Fok (Dennis)
2007-01-01
textabstractThis paper illustrates that salient features of a panel of time series of annual citations can be captured by a Bass type diffusion model. We put forward an extended version of this diffusion model, where we consider the relation between key characteristics of the diffusion process and f
Modeling the diffusion of scientific publications
D. Fok (Dennis); Ph.H.B.F. Franses (Philip Hans)
2005-01-01
textabstractThis paper illustrates that salient features of a panel of time series of annual citations can be captured by a Bass type diffusion model. We put forward an extended version of this diffusion model, where we consider the relation between key characteristics of the diffusion process and f
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.
Countability of Planck Boxes in Quantum Branching Models
Berezin, Alexander A.
2002-04-01
Two popular paradigms of cosmological quantum branching are Many World (MW) model of parallel universes (Everett, Deutsch) and inflationary quantum foam (IQF) model (Guth, Linde). Taking Planck L,T units as physically smallest, our Big Bang miniverse with size 10E28 cm and duration 10E18 sec has some 10E244 (N) elementary 4D Planck Boxes (PB) in its entire spacetime history. Using combinatorics, N! (about 10E10E247) is upper estimate for number of all possible 4D states, i.e. scale of "eternal return" (ER; Nietzsche, Eliade) for such miniverses. To count all states in full Megaverse (all up and down branches of infinite tree of all MW and/or IQF miniverses) we recall that all countable infinities have same (aleph-naught) cardinality (Cantor). Using Godel-type numbering, count PB in our miniverse by primes. This uses first N primes. Both MW and IQF models presume splitting of miniverses as springing (potentially) from each PB, making each PB infinitely rich, inexhaustible and unique. Next branching level is counted by integers p1Ep2, third level by p1Ep2Ep3 integers, etc, ad infinitum. To count in up and down directions from "our" miniverse, different branching subsets of powers of primes can be used at all levels of tower exponentiation. Thus, all PB in all infinitude of MW and/or IQF branches can be uniquely counted by never repeating integers (tower exponents of primes), offering escape from grim ER scenarios.
Modeling Internet Diffusion in Developing Countries
Directory of Open Access Journals (Sweden)
Scott McCoy
2012-04-01
Full Text Available Despite the increasing importance of the Internet, there is little work that addresses the degree to which the models and theories of Internet diffusion in developed countries can be applied to Internet diffusion in developing countries. This paper presents the first attempt to address this issue through theory driven modeling of Internet diffusion. Consistent with previous research, our findings suggest that economic development and technology infrastructure are musts for Internet diffusion. Interestingly, users’ cognition and government policies can accelerate Internet diffusion only after a certain level of human rights has been reached in a developing country.
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.
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.
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.
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.
Computer models of complex multiloop branched pipeline systems
Kudinov, I. V.; Kolesnikov, S. V.; Eremin, A. V.; Branfileva, A. N.
2013-11-01
This paper describes the principal theoretical concepts of the method used for constructing computer models of complex multiloop branched pipeline networks, and this method is based on the theory of graphs and two Kirchhoff's laws applied to electrical circuits. The models make it possible to calculate velocities, flow rates, and pressures of a fluid medium in any section of pipeline networks, when the latter are considered as single hydraulic systems. On the basis of multivariant calculations the reasons for existing problems can be identified, the least costly methods of their elimination can be proposed, and recommendations for planning the modernization of pipeline systems and construction of their new sections can be made. The results obtained can be applied to complex pipeline systems intended for various purposes (water pipelines, petroleum pipelines, etc.). The operability of the model has been verified on an example of designing a unified computer model of the heat network for centralized heat supply of the city of Samara.
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.
Trait Characteristics of Diffusion Model Parameters
Directory of Open Access Journals (Sweden)
Anna-Lena Schubert
2016-07-01
Full Text Available Cognitive modeling of response time distributions has seen a huge rise in popularity in individual differences research. In particular, several studies have shown that individual differences in the drift rate parameter of the diffusion model, which reflects the speed of information uptake, are substantially related to individual differences in intelligence. However, if diffusion model parameters are to reflect trait-like properties of cognitive processes, they have to qualify as trait-like variables themselves, i.e., they have to be stable across time and consistent over different situations. To assess their trait characteristics, we conducted a latent state-trait analysis of diffusion model parameters estimated from three response time tasks that 114 participants completed at two laboratory sessions eight months apart. Drift rate, boundary separation, and non-decision time parameters showed a great temporal stability over a period of eight months. However, the coefficients of consistency and reliability were only low to moderate and highest for drift rate parameters. These results show that the consistent variance of diffusion model parameters across tasks can be regarded as temporally stable ability parameters. Moreover, they illustrate the need for using broader batteries of response time tasks in future studies on the relationship between diffusion model parameters and intelligence.
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.
[Branch growth of Korean pine plantation based on nonlinear mixed model].
Wang, Chun-Hong; Li, Feng-Ri; Jia, Wei-Wei; Dong, Li-Hu
2013-07-01
Based on the branch analysis data from 36 sample trees in a Korean pine plantation in Mengjiagang Forest Farm of Heilongjiang Province, Northeast China, and by using Mitcherlich and Richards equations as the models of branch diameter and branch length growth, respectively, the effects of sampling plot and sample tree were investigated, and the nonlinear mixed models of branch diameter and branch length growth were established by the PROC NLMIXED procedure of SAS software. The evaluation statistics such as Akaike information criterion (AIC), Bayesian information criterion (BIC), -2Log likelihood, and likelihood ratio test (LRT) were used to compare the prediction precisions of the models. When considering plot effect, and taking alpha1 and alpha3 and beta1 and beta3 as the random parameters, respectively, the models of branch diameter and branch length growth had the best performance. When considering tree effect, and taking alpha2 and alpha3 and beta2 and beta3 as the random parameters, respectively, the models of branch diameter and branch length growth had the best performance. The nonlinear mixed model could not only reflect the mean variation of branch growth, but also show the differences among the individual trees. No matter considering plot effect or tree effect, the fitting precision of the nonlinear mixed model was better than that of the ordinary regression analysis model. Moreover, the fitting precision of the nonlinear mixed model was better when considering tree effect than considering plot effect.
Stellar Models and Yields of Asymptotic Giant Branch Stars
Karakas, Amanda I
2007-01-01
We present stellar yields calculated from detailed models of low and intermediate-mass asymptotic giant branch (AGB) stars. We evolve models with a range of mass from 1 to 6Msun, and initial metallicities from solar to 1/200th of the solar metallicity. Each model was evolved from the zero age main sequence to near the end of the thermally-pulsing AGB phase, and through all intermediate phases including the core He-flash for stars initially less massive than 2.5Msun. For each mass and metallicity, we provide tables containing structural details of the stellar models during the TP-AGB phase, and tables of the stellar yields for 74 species from hydrogen through to sulphur, and for a small number of iron-group nuclei. All tables are available for download. Our results have many applications including use in population synthesis studies and the chemical evolution of galaxies and stellar systems, and for comparison to the composition of AGB and post-AGB stars and planetary nebulae.
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.
Agent-based modelling of cholera diffusion
Augustijn, Ellen-Wien; Doldersum, Tom; Useya, Juliana; Augustijn, Denie
2016-01-01
This paper introduces a spatially explicit agent-based simulation model for micro-scale cholera diffusion. The model simulates both an environmental reservoir of naturally occurring V. cholerae bacteria and hyperinfectious V. cholerae. Objective of the research is to test if runoff from open refuse
Agent-based modelling of cholera diffusion
Augustijn, Ellen-Wien; Doldersum, Tom; Useya, Juliana; Augustijn, Denie
2016-01-01
This paper introduces a spatially explicit agent-based simulation model for micro-scale cholera diffusion. The model simulates both an environmental reservoir of naturally occurring V.cholerae bacteria and hyperinfectious V. cholerae. Objective of the research is to test if runoff from open refuse d
An Information Access Model at a Distant Branch Library
Stratton, John M.
2004-01-01
Academic branch libraries located at a distance from the parent institution often face unique challenges in meeting users' needs for scholarly information. This is especially true for distant branch libraries that do not have a specialized function or collection, but who often face the challenge of meeting users' needs for scholarly materials…
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...
Numerical modeling of mantle plume diffusion
Krupsky, D.; Ismail-Zadeh, A.
2004-12-01
To clarify the influence of the heat diffusion on the mantle plume evolution, we develop a two-dimensional numerical model of the plume diffusion and relevant efficient numerical algorithm and code to compute the model. The numerical approach is based on the finite-difference method and modified splitting algorithm. We consider both von Neumann and Direchlet conditions at the model boundaries. The thermal diffusivity depends on pressure in the model. Our results show that the plume is disappearing from the bottom up - the plume tail at first and its head later - because of the mantle plume geometry (a thin tail and wide head) and higher heat conductivity in the lower mantle. We study also an effect of a lateral mantle flow associated with the plate motion on the distortion of the diffusing mantle plume. A number of mantle plumes recently identified by seismic tomography seem to disappear in the mid-mantle. We explain this disappearance as the effect of heat diffusion on the evolution of mantle plume.
Shear Modification of long-chain branched polymers : a theoretical approach using POM-POM model
Bourrigault, S.; Marin, Gérard; Poitou, Arnaud
2003-01-01
International audience; “Shear modification” is a strong modification of rheological properties which affects mainly long-chain branched polymers like LDPE. The aim of this work is to explain this effect using recent advances in molecular dynamics and especially the pom-pom model which was designed for branched polymers. The original model was slightly modified in order to take into account the change in molecular topology related to the branch point withdrawal mechanism without introducing a...
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.
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.
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.
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.
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.
A numerical model of stress driven grain boundary diffusion
Sethian, J. A.; Wilkening, Jon
2004-01-01
The stress driven grain boundary diffusion problem is a continuum model of mass transport phenomena in microelectronic circuits due to high current densities (electromigration) and gradients in normal stress along grain boundaries. The model involves coupling many different equations and phenomena, and difficulties such as non-locality, stiffness, complex geometry, and singularities in the stress tensor near corners and junctions make the problem difficult to analyze rigorously and simulate numerically. We present a new numerical approach to this problem using techniques from semigroup theory to represent the solution. The generator of this semigroup is the composition of a type of Dirichlet to Neumann map on the grain boundary network with the Laplace operator on the network. To compute the former, we solve the equations of linear elasticity several times, once for each basis function on the grain boundary. We resolve singularities in the stress field near corners and junctions by adjoining special singular basis functions to both finite element spaces (2d for elasticity, 1d for grain boundary functions). We develop data structures to handle jump discontinuities in displacement across grain boundaries, singularities in the stress field, complicated boundary conditions at junctions and interfaces, and the lack of a natural ordering for the nodes on a branching grain boundary network. The method is used to study grain boundary diffusion for several geometries.
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'.
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.
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.
A Specification Test of Stochastic Diffusion Models
Institute of Scientific and Technical Information of China (English)
Shu-lin ZHANG; Zheng-hong WEI; Qiu-xiang BI
2013-01-01
In this paper,we propose a hypothesis testing approach to checking model mis-specification in continuous-time stochastic diffusion model.The key idea behind the development of our test statistic is rooted in the generalized information equality in the context of martingale estimating equations.We propose a bootstrap resampling method to implement numerically the proposed diagnostic procedure.Through intensive simulation studies,we show that our approach is well performed in the aspects of type Ⅰ error control,power improvement as well as computational efficiency.
Creatinine Diffusion Modeling in Capacitive Sensors
Mohabbati-Kalejahi, Elham; Azimirad, Vahid; Bahrami, Manouchehr
2016-12-01
In this paper, creatinine diffusion in capacitive sensors is discussed. The factors influencing the response time of creatinine biosensors are mathematically formulated and then three novel approaches for decreasing the response time are presented. At first, a piezoelectric actuator is used to vibrate the microtube that contains the blood sample, in order to reduce the viscosity of blood, and thus to increase the coefficient of diffusion. Then, the blood sample is assumed to be pushed through a porous medium, and the relevant conditions are investigated. Finally, the effect of the dentate shape of dielectric on response time is studied. The algorithms and the mathematical models are presented and discussed, and the results of simulations are illustrated. The response times for the first, second and third method are 60, 0.036 and about 31 s, respectively. It is also found that pumping results in very fast responses.
NEW CAR DEMAND MODELING AND FORECASTING USING BASS DIFFUSION MODEL
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.
Diffusion through thin membranes: Modeling across scales
Aho, Vesa; Mattila, Keijo; Kühn, Thomas; Kekäläinen, Pekka; Pulkkinen, Otto; Minussi, Roberta Brondani; Vihinen-Ranta, Maija; Timonen, Jussi
2016-04-01
From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.
Elements of a Model State Education Agency Diffusion System.
Mojkowski, Charles
A study, presented to the National Dissemination Conference, provides a conceptualization of a model diffusion system as it might exist within a state education agency (SEA) and places this diffusion model within the context of the SEA's expanding role as an educational service. Five conclusions were reached regarding a model diffusion system.…
Model Checking Games for a Fair Branching-Time Temporal Epistemic Logic
Huang, Xiaowei; van der Meyden, Ron
Model checking games are instances of Hintikka's game semantics for logic used for purposes of debugging systems verification models. Previous work in the area has developed these games for branching time logic. The paper develops an extension to a logic that adds epistemic operators, and interprets the branching time operators with respect to fairness constraints. The implementation of the extended games in the epistemic model checker MCK is described.
Modeling of Reaction Processes Controlled by Diffusion
Revelli, J
2003-01-01
Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider differe...
ANALYSIS OF THE MECHANISM MODELS OF TECHNOLOGICAL INNOVATION DIFFUSION
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.
Ancestral process and diffusion model with selection
Mano, Shuhei
2008-01-01
The ancestral selection graph in population genetics introduced by Krone and Neuhauser (1997) is an analogue to the coalescent genealogy. The number of ancestral particles, backward in time, of a sample of genes is an ancestral process, which is a birth and death process with quadratic death and linear birth rate. In this paper an explicit form of the number of ancestral particle is obtained, by using the density of the allele frequency in the corresponding diffusion model obtained by Kimura (1955). It is shown that fixation is convergence of the ancestral process to the stationary measure. The time to fixation of an allele is studied in terms of the ancestral process.
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.
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy; Kurien, Susan
2016-11-01
A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
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.
Mathematical Modeling of the Process for Microbial Production of Branched Chained Amino Acids
Todorov K.; Georgiev T.; Ratkov A.
2009-01-01
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 rat...
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.
A computational model of dendrite elongation and branching based on MAP2 phosphorylation.
Hely, T A; Graham, B; Ooyen, A V
2001-06-07
We introduce a new computational model of dendritic development in neurons. In contrast to previous models, our model explicitly includes cellular mechanisms involved in dendritic development. It is based on recent experimental data which indicates that the phosphorylation state of microtubule-associated protein 2 (MAP2) may play a key role in controlling dendritic elongation and branching (Audesirk et al., 1997). Dephosphorylated MAP2 favours elongation by promoting microtubule polymerization and bundling, whilst branching is more likely to occur when MAP2 is phosphorylated and microtubules are spaced apart. In the model, the rate of elongation and branching is directly determined by the ratio of phosphorylated to dephosphorylated MAP2. This is regulated by calmodulin-dependent protein kinase II (CaMKII) and calcineurin, which are both dependent on the intracellular calcium concentration. Results from computer simulations of the model suggest that the wide variety of branching patterns observed among different cell types may be generated by the same underlying mechanisms and that elongation and branching are not necessarily independent processes. The model predicts how the branching pattern will change following manipulations with calcium, CaMKII and MAP2 phosphorylation.
Four-State Model for Three-Branch Molecule's Two-Photon Absorption Properties
Institute of Scientific and Technical Information of China (English)
SU Yan; WANG Pei-Ji; ZHAO Peng; RONG Zhen-Yu
2006-01-01
@@ We present a four-state model for calculating the two-photon absorption of multi-branched molecules by using the time-depended function method. The numerical results indicate that the two-photon absorption cross section has a strong enhancement for three-branch molecules compared to two-branch structures. The maximal two-photon-absorption cross section is 2.358 × 10-47 cm 4 s/photon. At the same time, the charge-transfer process for the charge-transfer states is visualized in order to explain mechanism about the maximal TPA cross section.
Recommendation based on trust diffusion model.
Yuan, Jinfeng; Li, Li
2014-01-01
Recommender system is emerging as a powerful and popular tool for online information relevant to a given user. The traditional recommendation system suffers from the cold start problem and the data sparsity problem. Many methods have been proposed to solve these problems, but few can achieve satisfactory efficiency. In this paper, we present a method which combines the trust diffusion (DiffTrust) algorithm and the probabilistic matrix factorization (PMF). DiffTrust is first used to study the possible diffusions of trust between various users. It is able to make use of the implicit relationship of the trust network, thus alleviating the data sparsity problem. The probabilistic matrix factorization (PMF) is then employed to combine the users' tastes with their trusted friends' interests. We evaluate the algorithm on Flixster, Moviedata, and Epinions datasets, respectively. The experimental results show that the recommendation based on our proposed DiffTrust + PMF model achieves high performance in terms of the root mean square error (RMSE), Recall, and F Measure.
Bass-SIR model for diffusion of new products
Fibich, Gadi
2016-01-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the SIR model, but rather by a novel model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from non-adopters to adopters is described by a non-standard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
Voter Model Perturbations and Reaction Diffusion Equations
Cox, J Theodore; Perkins, Edwin
2011-01-01
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins and the second confirms a conjecture of Ohtsuki et al in the ...
Mathematical model for radon diffusion in earthen materials
Energy Technology Data Exchange (ETDEWEB)
Nielson, K.K.; Rogers, V.C.
1982-10-01
Radon migration in porous, earthen materials is characterized by diffusion in both the air and water components of the system as well as by the interaction of the radon between the air and water. The size distribution and configuration of the pore spaces and their moisture distributions are key parameters in determining the radon diffusion coefficient for the bulk material. A mathematical model is developed and presented for calculating radon diffusion coefficients solely from the moisture content and pore size distribution of a soil, reducing the need for resorting to radon diffusion measurements. The resulting diffusion coefficients increase with the median pore diameter of the soil and decrease with increasing widths of the pore size distribution. The calculated diffusion coefficients are suitable for use in simple homogeneous-medium diffusion expressions for predicting radon transport and compare well with measured diffusion coefficients and with empirical diffusion coefficient correlations.
Wang, Shifang; Wu, Tao; Deng, Yongju; Zheng, Qiusha; Zheng, Qian
2016-08-01
Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging-diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging-diverging effect included is in good agreement with reported experimental data.
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
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.
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.
Some Problems in Using Diffusion Models for New Products
Bernhardt, Irwin; Mackenzie, Kenneth D.
1972-01-01
Analyzes some of the problems involved in using diffusion models to formulate marketing strategies for introducing new products. Six models, which remove some of the theoretical and methodological restrictions inherent in current models of the adoption and diffusion process, are presented. (Author/JH)
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
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
Modelling of non-equilibrium flow in the branched pipeline systems
Sumskoi, S. I.; Sverchkov, A. M.; Lisanov, M. V.; Egorov, A. F.
2016-09-01
This article presents a mathematical model and a numerical method for solving the task of water hammer in the branched pipeline system. The task is considered in the onedimensional non-stationary formulation taking into account the realities such as the change in the diameter of the pipeline and its branches. By comparison with the existing analytic solution it has been shown that the proposed method possesses good accuracy. With the help of the developed model and numerical method the task has been solved concerning the transmission of the compression waves complex in the branching pipeline system when several shut down valves operate. It should be noted that the offered model and method may be easily introduced to a number of other tasks, for example, to describe the flow of blood in the vessels.
Large eddy simulation of high frequency oscillating flow in an asymmetric branching airway model.
Nagels, Martin A; Cater, John E
2009-11-01
The implementation of artificial ventilation schemes is necessary when respiration fails. One approach involves the application of high frequency oscillatory ventilation (HFOV) to the respiratory system. Oscillatory airflow in the upper bronchial tree can be characterized by Reynolds numbers as high as 10(4), hence, the flow presents turbulent features. In this study, transitional and turbulent flow within an asymmetric bifurcating model of the upper airway during HFOV are studied using large eddy simulation (LES) methods. The flow, characterized by a peak Reynolds number of 8132, is analysed using a validated LES model of a three-dimensional branching geometry. The pressures, velocities, and vorticity within the flow are presented and compared with prior models for branching flow systems. The results demonstrate how pendelluft occurs at asymmetric branches within the respiratory system. These results may be useful in optimising treatments using HFOV methods.
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...
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.
Diffusive description of lattice gas models
DEFF Research Database (Denmark)
Fiig, T.; Jensen, H.J.
1993-01-01
in time. We have numerically investigated the power spectrum of the density fluctuations, the lifetime distribution, and the spatial correlation function. We discuss the appropriate Langevin-like diffusion equation which can reproduce our numerical findings. Our conclusion is that the deterministic...... lattice gases are described by a diffusion equation without any bulk noise. The open lattice gas exhibits a crossover behavior as the probability for introducing particles at the edge of the system becomes small. The power spectrum changes from a 1/f to a 1/f2 spectrum. The diffusive description, proven...
A variable-order fractal derivative model for anomalous diffusion
Directory of Open Access Journals (Sweden)
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
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 consistent transported PDF model for treating differential molecular diffusion
Wang, Haifeng; Zhang, Pei
2016-11-01
Differential molecular diffusion is a fundamentally significant phenomenon in all multi-component turbulent reacting or non-reacting flows caused by the different rates of molecular diffusion of energy and species concentrations. In the transported probability density function (PDF) method, the differential molecular diffusion can be treated by using a mean drift model developed by McDermott and Pope. This model correctly accounts for the differential molecular diffusion in the scalar mean transport and yields a correct DNS limit of the scalar variance production. The model, however, misses the molecular diffusion term in the scalar variance transport equation, which yields an inconsistent prediction of the scalar variance in the transported PDF method. In this work, a new model is introduced to remedy this problem that can yield a consistent scalar variance prediction. The model formulation along with its numerical implementation is discussed, and the model validation is conducted in a turbulent mixing layer problem.
Counting Tensor Model Observables and Branched Covers of the 2-Sphere
Geloun, Joseph Ben
2013-01-01
Lattice gauge theories of permutation groups with a simple topological action (henceforth permutation-TFTs) have recently found several applications in the combinatorics of quantum field theories (QFTs). They have been used to solve counting problems of Feynman graphs in QFTs and ribbon graphs of large $N$, often revealing inter-relations between different counting problems. In another recent development, tensor theories generalizing matrix theories have been actively developed as models of random geometry in three or more dimensions. Here, we apply permutation-TFT methods to count gauge invariants for tensor models (colored as well as non-colored), exhibiting a relationship with counting problems of branched covers of the 2-sphere, where the rank $d$ of the tensor gets related to a number of branch points. We give explicit generating functions for the relevant counting and describe algorithms for the enumeration of the invariants. As well as the classic count of Hurwitz equivalence classes of branched covers...
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.
Feller Property for a Special Hybrid Jump-Diffusion Model
Directory of Open Access Journals (Sweden)
Jinying Tong
2014-01-01
Full Text Available We consider the stochastic stability for a hybrid jump-diffusion model, where the switching here is a phase semi-Markovian process. We first transform the process into a corresponding jump-diffusion with Markovian switching by the supplementary variable technique. Then we prove the Feller and strong Feller properties of the model under some assumptions.
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.
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.
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…
Stochastic modeling 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 a physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficient D is strongly dependent on the w/c ratio and the temperature....... A deterministic relationship between the diffusion coefficient and the w/c ratio and the temperature is used for the stochastic modelling. The w/c ratio and the temperature are modelled by log-normally and normally distributed stochastic variables, respectively. It is then shown by Monte Carlo simulation...... that the diffusion coefficient D may be modelled by a normally distributed stochastic variable. The sensitivities of D with regard to the mean values and the standard deviations are evaluated....
Spatial Pattern of an Epidemic Model with Cross-diffusion
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.
Varakin, A I; Mazur, V V; Arkhipova, N V; Serianov, Iu V
2009-01-01
Mathematical models of the transfer of charged macromolecules have been constructed on the basis of the classical equations of electromigration diffusion of Helmholtz-Smolukhovskii, Goldman, and Goldman-Hodgkin-Katz. It was shown that ion transfer in placental (mimicking lipid-protein barriers) and muscle barriers occurs by different mechanisms. In placental barriers, the electromigration diffusion occurs along lipid-protein channels formed due to the conformational deformation of phospholipid and protein molecules with the coefficients of diffusion D = (2.6-3.6) x 10(-8) cm2/s. The transfer in muscle barriers is due to the migration across charged interfibrillar channels with the negative diffusion activation energy, which is explained by changes in the structure of muscle fibers and expenditures of thermal energy for the extrusion of Cl- from channel walls with the diffusion coefficient D = (6.0-10.0) x 10(-6) cm2/s.
A memory diffusion model for molecular anisotropic diffusion in siliceous β-zeolite.
Ji, Xiangfei; An, Zhuanzhuan; Yang, Xiaofeng
2016-01-01
A memory diffusion model of molecules on β-zeolite is proposed. In the model, molecular diffusion in β-zeolites is treated as jumping from one adsorption site to its neighbors and the jumping probability is a compound probability which includes that provided by the transitional state theory as well as that derived from the information about which direction the target molecule comes from. The proposed approach reveals that the diffusivities along two crystal axes on β-zeolite are correlated. The model is tested by molecular dynamics simulations on diffusion of benzene and other simple molecules in β-zeolites. The results show that the molecules with larger diameters fit the prediction much better and that the "memory effects" are important in all cases.
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
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.
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.
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 mo...
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...
"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
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.
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO
2012-12-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.
Pricing Participating Products under a Generalized Jump-Diffusion Model
Directory of Open Access Journals (Sweden)
Tak Kuen Siu
2008-01-01
Full Text Available We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.
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.
Cross-Diffusion-Driven Instability in a Reaction-Diffusion Harrison Predator-Prey Model
Directory of Open Access Journals (Sweden)
Xiaoqin Wang
2013-01-01
Full Text Available We present a theoretical analysis of processes of pattern formation that involves organisms distribution and their interaction of spatially distributed population with cross-diffusion in a Harrison-type predator-prey model. We analyze the global behaviour of the model by establishing a Lyapunov function. We carry out the analytical study in detail and find out the certain conditions for Turing’s instability induced by cross-diffusion. And the numerical results reveal that, on increasing the value of the half capturing saturation constant, the sequences “spots → spot-stripe mixtures → stripes → hole-stripe mixtures → holes” are observed. The results show that the model dynamics exhibits complex pattern replication controlled by the cross-diffusion.
New Symmetries for a Model of Fast Diffusion
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....
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.
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...
Theoretical model of blood flow measurement by diffuse correlation spectroscopy
Sakadžić, Sava; Boas, David A.; Carp, Stefan
2017-02-01
Diffuse correlation spectroscopy (DCS) is a noninvasive method to quantify tissue perfusion from measurements of the intensity temporal autocorrelation function of diffusely scattered light. However, DCS autocorrelation function measurements in tissue better match theoretical predictions based on the diffusive motion of the scatterers than those based on a model where the advective nature of blood flow dominates the stochastic properties of the scattered light. We have recently shown using Monte Carlo (MC) simulations and assuming a simplistic vascular geometry and laminar flow profile that the diffusive nature of the DCS autocorrelation function decay is likely a result of the shear-induced diffusion of the red blood cells. Here, we provide theoretical derivations supporting and generalizing the previous MC results. Based on the theory of diffusing-wave spectroscopy, we derive an expression for the autocorrelation function along the photon path through a vessel that takes into account both diffusive and advective scatterer motion, and we provide the solution for the DCS autocorrelation function in a semi-infinite geometry. We also derive the correlation diffusion and correlation transfer equation, which can be applied for an arbitrary sample geometry. Further, we propose a method to take into account realistic vascular morphology and flow profile.
Innovation Diffusion Model in Higher Education: Case Study of E-Learning Diffusion
Buc, Sanjana; Divjak, Blaženka
2015-01-01
The diffusion of innovation (DOI) is critical for any organization and especially nowadays for higher education institutions (HEIs) in the light of vast pressure of emerging educational technologies as well as of the demand of economy and society. DOI takes into account the initial and the implementation phase. The conceptual model of DOI in…
Toward Information Diffusion Model for Viral Marketing in Business
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.
Discrete random walk models for space-time fractional diffusion
Energy Technology Data Exchange (ETDEWEB)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation.
Diffuse Scattering Model of Indoor Wideband Propagation
DEFF Research Database (Denmark)
Franek, Ondrej; Andersen, Jørgen Bach; Pedersen, Gert Frølund
2011-01-01
This paper presents a discrete-time numerical algorithm for computing field distribution in indoor environment by diffuse scattering from walls. Calculations are performed for a rectangular room with semi-reflective walls. The walls are divided into 0.5 x 0.5 m segments, resulting in 2272 wall...... segments in total and approximately 2 min running time on average computer. Frequency independent power levels at the walls around the circumference of the room and at four receiver locations in the middle of the room are observed. It is demonstrated that after finite period of initial excitation the field...... intensity in all locations eventually follows exponential decay with the same slope and approximately the same level for given delay. These observations are shown to be in good agreement with theory and previous measurements—the slopes of the decay curves for measurement, simulation and theory are found...
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.
Update on Advection-Diffusion Purge Flow Model
Brieda, Lubos
2015-01-01
Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.
Modeling and Power Flow Analysis for Herringbone Gears Power Dual-Branching Transmission System
Yang, Xiaofang; Zhu, Yanxiang; Fang, Zongde; Gu, Jiangong
Based on power dual-branching transmission system of herringbone gears, the mechanical structural model was established. This study represented the simplified algorithm to obtain its power flow situations through formulating the deformation compatibility condition for the linear relationship between the torque and transverse deformation of tooth surface and the torque equilibrium condition. Besides, the effects on the power flow of system were calculated under all kinds of the installation error and processing error of gear pairs. Finally, the power flow situations of dual branches were solved via Programming. A numerical example that illustrated the developed theory was provided. The research results can be applied to analyze the actual application of herringbone gears power split-path transmission system.
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)
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.
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...
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.
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
Langevin equation with fluctuating diffusivity: A two-state model.
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
Modeling Copper Diffusion in Polycrystalline CdTe Solar Cells
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
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.
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.
A combinatorial model of malware diffusion via bluetooth connections.
Merler, Stefano; Jurman, Giuseppe
2013-01-01
We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression.
A combinatorial model of malware diffusion via bluetooth connections.
Directory of Open Access Journals (Sweden)
Stefano Merler
Full Text Available We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy and closed form (more complex but efficiently computable expression.
Relaxation and diffusion models with non-singular kernels
Sun, HongGuang; Hao, Xiaoxiao; Zhang, Yong; Baleanu, Dumitru
2017-02-01
Anomalous relaxation and diffusion processes have been widely quantified by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to its limitation in describing different kinds of non-exponential decays (e.g. stretched exponential decay). Meanwhile, many efforts by mathematicians and engineers have been made to overcome the singularity of power function kernel in its definition. This study first explores physical properties of relaxation and diffusion models where the temporal derivative was defined recently using an exponential kernel. Analytical analysis shows that the Caputo type derivative model with an exponential kernel cannot characterize non-exponential dynamics well-documented in anomalous relaxation and diffusion. A legitimate extension of the previous derivative is then proposed by replacing the exponential kernel with a stretched exponential kernel. Numerical tests show that the Caputo type derivative model with the stretched exponential kernel can describe a much wider range of anomalous diffusion than the exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes.
Weak diffusion limits of dynamic conditional correlation models
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 dif......The properties of dynamic conditional correlation (DCC) models are still not entirely understood. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized...... by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a non-degenerate diffusion limit can be obtained. Alternative sets of conditions are considered...... for the rate of convergence of the parameters, obtaining time-varying but deterministic variances and/or correlations. A Monte Carlo experiment confirms that the quasi approximate maximum likelihood (QAML) method to estimate the diffusion parameters is inconsistent for any fixed frequency, but that it may...
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.
Modelling on cavitation in a diffuser with vortex generator
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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.
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.
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.
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
Habitability of super-Earth planets around other suns: models including Red Giant Branch evolution.
von Bloh, W; Cuntz, M; Schröder, K-P; Bounama, C; Franck, S
2009-01-01
The unexpected diversity of exoplanets includes a growing number of super-Earth planets, i.e., exoplanets with masses of up to several Earth masses and a similar chemical and mineralogical composition as Earth. We present a thermal evolution model for a 10 Earth-mass planet orbiting a star like the Sun. Our model is based on the integrated system approach, which describes the photosynthetic biomass production and takes into account a variety of climatological, biogeochemical, and geodynamical processes. This allows us to identify a so-called photosynthesis-sustaining habitable zone (pHZ), as determined by the limits of biological productivity on the planetary surface. Our model considers solar evolution during the main-sequence stage and along the Red Giant Branch as described by the most recent solar model. We obtain a large set of solutions consistent with the principal possibility of life. The highest likelihood of habitability is found for "water worlds." Only mass-rich water worlds are able to realize pHZ-type habitability beyond the stellar main sequence on the Red Giant Branch.
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.
Bentley, Lisa Patrick; Stegen, James C; Savage, Van M; Smith, Duncan D; von Allmen, Erica I; Sperry, John S; Reich, Peter B; Enquist, Brian J
2013-08-01
Several theories predict whole-tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self-similar within trees. However, differences among scaling exponents calculated at node- and whole-tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.
Energy Technology Data Exchange (ETDEWEB)
Belucz, Bernadett; Forgács-Dajka, Emese [Eötvös University, Department of Astronomy, 1518 Budapest, Pf. 32 (Hungary); Dikpati, Mausumi, E-mail: bbelucz@astro.elte.hu, E-mail: dikpati@ucar.edu [High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Green, Boulder, CO 80307-3000 (United States)
2015-06-20
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 the presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in the butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of the butterfly wing to an antisolar type. A butterfly diagram constructed from the 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 latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow speed is strong enough, of similar order of magnitude as the surface flow speed.
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.
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.
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
Directory of Open Access Journals (Sweden)
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.
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_...
Cellular Automata Models for Diffusion of Innovations
Fuks, H; Fuks, Henryk; Boccara, Nino
1997-01-01
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the rule increases, the takeover time for innovation increases and converges toward its mean-field value, which is almost inversely proportional to R when R is large. Exact solutions for R=1 and $R=\\infty$ (mean-field) are presented, as well as simulation results for other values of R. The average local density is found to converge to a certain stationary value, which allows us to obtain a semi-phenomenological solution valid in the vicinity of the fixed point n=1 (for large t).
Background Error Correlation Modeling with Diffusion Operators
2013-01-01
functions defined on the orthogonal curvilin- ear grid of the Navy Coastal Ocean Model (NCOM) [28] set up in the Monterrey Bay (Fig. 4). The number N...H2 = [1 1; 1−1], the HMs with order N = 2n, n= 1,2... can be easily constructed. HMs with N = 12,20 were constructed ” manually ” more than a century
[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.
THE SEPARATION OF URANIUM ISOTOPES BY GASEOUS DIFFUSION: A LINEAR PROGRAMMING MODEL,
URANIUM, ISOTOPE SEPARATION), (*GASEOUS DIFFUSION SEPARATION, LINEAR PROGRAMMING ), (* LINEAR PROGRAMMING , GASEOUS DIFFUSION SEPARATION), MATHEMATICAL MODELS, GAS FLOW, NUCLEAR REACTORS, OPERATIONS RESEARCH
A stellar model with diffusion in general relativity
Alho, Artur
2016-01-01
We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self-similar solution.
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.
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.
Reaction-diffusion models of decontamination
DEFF Research Database (Denmark)
Hjorth, Poul G.
A contaminant, which also contains a polymer is in the form of droplets on a solid surface. It is to be removed by the action of a decontaminant, which is applied in aqueous solution. The contaminant is only sparingly soluble in water, so the reaction mechanism is that it slowly dissolves...... in the aqueous solution and then is oxidized by the decontaminant. The polymer is insoluble in water, and so builds up near the interface, where its presence can impede the transport of contaminant. In these circumstances, Dstl wish to have mathematical models that give an understanding of the process, and can...
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.
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 ...
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.
A Simple Model of the Warm-water Branch of Meridional Overturning
Samelson, R. M.
2008-12-01
A reduced-gravity model is presented of the warm-water branch of the mid-depth meridional overturning circulation in a rectangular basin with a circumpolar connection. The model describes the balance between production of warm water by Ekman advection across the circumpolar current, dissipation of water water by eddy fluxes southward across the current, and the net production or dissipation of warm water by diabatic processes north of the current. Analytical solutions are obtained for weak friction and diabatic forcing. The results emphasize the role of the eastern boundary condition in setting the thermocline structure north of the current, and the nonlinear interactions between wind forcing, eddy fluxes, and diabatic mixing, which together control the structure and amplitude of the model meridional overturning circulation.
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.
Yaghini, N.; Iedema, P.D.
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
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.
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
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.
Modeling intragranular diffusion in low-connectivity granular media
Ewing, Robert P.; Liu, Chongxuan; Hu, Qinhong
2012-03-01
Characterizing the diffusive exchange of solutes between bulk water in an aquifer and water in the intragranular pores of the solid phase is still challenging despite decades of study. Many disparities between observation and theory could be attributed to low connectivity of the intragranular pores. The presence of low connectivity indicates that a useful conceptual framework is percolation theory. The present study was initiated to develop a percolation-based finite difference (FD) model, and to test it rigorously against both random walk (RW) simulations of diffusion starting from nonequilibrium, and data on Borden sand published by Ball and Roberts (1991a,b) and subsequently reanalyzed by Haggerty and Gorelick (1995) using a multirate mass transfer (MRMT) approach. The percolation-theoretical model is simple and readily incorporated into existing FD models. The FD model closely matches the RW results using only a single fitting parameter, across a wide range of pore connectivities. Simulation of the Borden sand experiment without pore connectivity effects reproduced the MRMT analysis, but including low pore connectivity effects improved the fit. Overall, the theory and simulation results show that low intragranular pore connectivity can produce diffusive behavior that appears as if the solute had undergone slow sorption, despite the absence of any sorption process, thereby explaining some hitherto confusing aspects of intragranular diffusion.
Modeling the diffusion of phosphorus in silicon in 3-D
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.
Diffusion models in experimental psychology: a practical introduction.
Voss, Andreas; Nagler, Markus; Lerche, Veronika
2013-01-01
Stochastic diffusion models (Ratcliff, 1978) can be used to analyze response time data from binary decision tasks. They provide detailed information about cognitive processes underlying the performance in such tasks. Most importantly, different parameters are estimated from the response time distributions of correct responses and errors that map (1) the speed of information uptake, (2) the amount of information used to make a decision, (3) possible decision biases, and (4) the duration of nondecisional processes. Although this kind of model can be applied to many experimental paradigms and provides much more insight than the analysis of mean response times can, it is still rarely used in cognitive psychology. In the present paper, we provide comprehensive information on the theory of the diffusion model, as well as on practical issues that have to be considered for implementing the model.
Bayesian Model Selection with Network Based Diffusion Analysis.
Whalen, Andrew; Hoppitt, William J E
2016-01-01
A number of recent studies have used Network Based Diffusion Analysis (NBDA) to detect the role of social transmission in the spread of a novel behavior through a population. In this paper we present a unified framework for performing NBDA in a Bayesian setting, and demonstrate how the Watanabe Akaike Information Criteria (WAIC) can be used for model selection. We present a specific example of applying this method to Time to Acquisition Diffusion Analysis (TADA). To examine the robustness of this technique, we performed a large scale simulation study and found that NBDA using WAIC could recover the correct model of social transmission under a wide range of cases, including under the presence of random effects, individual level variables, and alternative models of social transmission. This work suggests that NBDA is an effective and widely applicable tool for uncovering whether social transmission underpins the spread of a novel behavior, and may still provide accurate results even when key model assumptions are relaxed.
Transport Corrections in Nodal Diffusion Codes for HTR Modeling
Energy Technology Data Exchange (ETDEWEB)
Abderrafi M. Ougouag; Frederick N. Gleicher
2010-08-01
The cores and reflectors of High Temperature Reactors (HTRs) of the Next Generation Nuclear Plant (NGNP) type are dominantly diffusive media from the point of view of behavior of the neutrons and their migration between the various structures of the reactor. This means that neutron diffusion theory is sufficient for modeling most features of such reactors and transport theory may not be needed for most applications. Of course, the above statement assumes the availability of homogenized diffusion theory data. The statement is true for most situations but not all. Two features of NGNP-type HTRs require that the diffusion theory-based solution be corrected for local transport effects. These two cases are the treatment of burnable poisons (BP) in the case of the prismatic block reactors and, for both pebble bed reactor (PBR) and prismatic block reactor (PMR) designs, that of control rods (CR) embedded in non-multiplying regions near the interface between fueled zones and said non-multiplying zones. The need for transport correction arises because diffusion theory-based solutions appear not to provide sufficient fidelity in these situations.
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.)
Solutions to a nonlinear drift-diffusion model for semiconductors
Directory of Open Access Journals (Sweden)
Weifu Fang
1999-05-01
Full Text Available A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
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.
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.
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: .
Mechanical reaction-diffusion model for bacterial population dynamics
Ngamsaad, Waipot
2015-01-01
The effect of mechanical interaction between cells on the spreading of bacterial population was investigated in one-dimensional space. A nonlinear reaction-diffusion equation has been formulated as a model for this dynamics. In this model, the bacterial cells are treated as the rod-like particles that interact, when contacting each other, through the hard-core repulsion. The repulsion introduces the exclusion process that causes the fast diffusion in bacterial population at high density. The propagation of the bacterial density as the traveling wave front in long time behavior has been analyzed. The analytical result reveals that the front speed is enhanced by the exclusion process---and its value depends on the packing fraction of cell. The numerical solutions of the model have been solved to confirm this prediction.
Fractional Heat Conduction Models and Thermal Diffusivity Determination
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.
Antiproton Flux in Cosmic Ray Propagation Models with Anisotropic Diffusion
Grajek, Phillip
2010-01-01
Recently a cosmic ray propagation model has been introduced, where anisotropic diffusion is used as a mechanism to allow for $\\mathcal{O}(100)$ km/s galactic winds. This model predicts a reduced antiproton background flux, suggesting an excess is being observed. We implement this model in GALPROP v50.1 and perform a $\\chi^2$ analysis for B/C, $^{10}$Be/$^{9}$Be, and the recent PAMELA $\\bar{p}/p$ datasets. By introducing a power-index parameter $\\alpha$ that dictates the dependence of the diffusion coefficient $D_{xx}$ on height $|z|$ away from the galactic plane, we confirm that isotropic diffusion models with $\\alpha=0$ cannot accommodate high velocity convective winds suggested by ROSAT, while models with $\\alpha=1$ ($D_{xx}\\propto |z|$) can give a very good fit. A fit to B/C and $^{10}$Be/$^{9}$Be data predicts a lower $\\bar{p}/p$ flux ratio than the PAMELA measurement at energies between approximately 2 GeV to 20 GeV. A combined fit including in addition the $\\bar{p}/p$ data is marginal, suggesting only a...
Characterization and modeling of thermal diffusion and aggregation in nanofluids.
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.
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
Directory of Open Access Journals (Sweden)
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.
Performance of turbulence models for transonic flows in a diffuser
Liu, Yangwei; Wu, Jianuo; Lu, Lipeng
2016-09-01
Eight turbulence models frequently used in aerodynamics have been employed in the detailed numerical investigations for transonic flows in the Sajben diffuser, to assess the predictive capabilities of the turbulence models for shock wave/turbulent boundary layer interactions (SWTBLI) in internal flows. The eight turbulence models include: the Spalart-Allmaras model, the standard k - 𝜀 model, the RNG k - 𝜀 model, the realizable k - 𝜀 model, the standard k - ω model, the SST k - ω model, the v2¯ - f model and the Reynolds stress model. The performance of the different turbulence models adopted has been systematically assessed by comparing the numerical results with the available experimental data. The comparisons show that the predictive performance becomes worse as the shock wave becomes stronger. The v2¯ - f model and the SST k - ω model perform much better than other models, and the SST k - ω model predicts a little better than the v2¯ - f model for pressure on walls and velocity profile, whereas the v2¯ - f model predicts a little better than the SST k - ω model for separation location, reattachment location and separation length for strong shock case.
Water diffusion in bicelles and the mixed bicelle model.
Soong, Ronald; Macdonald, Peter M
2009-01-06
To test a prediction of the mixed bicelle model, stimulated echo (STE) pulsed field gradient (PFG) (1)H nuclear magnetic resonance (NMR) measurements of water diffusion between and across bicellar lamellae were performed in positively and negatively magnetically aligned bicelles, composed of mixtures of DHPC (1,2-dihexanoyl-sn-glycero-3-phosphocholine) and DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine), as a function of temperature and of the proportion of added short-chain lipid DHPC. (31)P NMR spectra obtained for each situation confirmed that the DHPC undergoes fast exchange between curved and planar regions as per the mixed bicelle model and permitted an estimate of the proportion of the two DHPC populations. Water diffusion across the bicellar lamellae was shown to scale directly with q*, the fraction of edge versus planar phospholipid, rather than simply the ratio q, the global fraction of long-chain to short-chain phospholipid. Geometric modeling of the dependence of water diffusion on q* suggested an upper limit of 400 A for the size of DHPC-rich toroidal perforations within the bicelle lamellae. These findings constitute an independent confirmation of the mixed bicelle model in which DHPC is not confined to edge regions but enjoys, instead, a finite miscibility with DMPC.
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)
Experimental exploration of diffusion panel labyrinth in scale model
Vance, Mandi M.
Small rehearsal and performance venues often lack the rich reverberation found in larger spaces. Higini Arau-Puchades has designed and implemented a system of diffusion panels in the Orchestra Rehearsal Room at the Great Theatre Liceu and the Tonhalle St. Gallen that lengthen the reverberation time. These panels defy traditional room acoustics theory which holds that adding material to a room will shorten the reverberation time. This work explores several versions of Arau-Puchades' panels and room characteristics in scale model. Reverberation times are taken from room impulse response measurements in order to better understand the unusual phenomenon. Scale modeling enables many tests but has limitations in its accuracy due to the higher frequency range involved. Further investigations are necessary to establish how the sound energy interacts with the diffusion panels and confirm their validity in a range of applications.
Modeling and Analysis of New Products Diffusion on Heterogeneous Networks
Directory of Open Access Journals (Sweden)
Shuping Li
2014-01-01
Full Text Available We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.
Modelling of diffusion and conductivity relaxation of oxide ceramics
Preis, Wolfgang
2016-12-01
A two-dimensional square grain model has been applied to simulate simultaneously the diffusion process and relaxation of the dc conduction of polycrystalline oxide materials due to a sudden change of the oxygen partial pressure of the surrounding gas phase. The numerical calculations are performed by employing the finite element approach. The grains are squares of equal side length (average grain size) and the grain boundaries may consist of thin slabs of uniform thickness. An additional (space charge) layer adjacent to the grain boundary cores (thin slabs) either blocking (depletion layer) or highly conductive for electronic charge carriers may surround the grains. The electronic transport number of the mixed ionic-electronic conducting oxide ceramics may be close to unity (predominant electronic conduction). If the chemical diffusion coefficient of the neutral mobile component (oxygen) of the grain boundary core regions is assumed to be higher by many orders of magnitude than that in the bulk, the simulated relaxation curves for mass transport (diffusion) and dc conduction can deviate remarkably from each other. Deviations between the relaxation of mass transport and dc conduction are found in the case of considerably different electronic conductivities of grain boundary core regions, space charge layers, and bulk. On the contrary, the relaxation curves of mass transport and electronic conductivity are in perfect coincidence, when either effective medium diffusion occurs or the effective conductivity is unaffected by the individual conductivities of core regions and possible space charge layers, i.e. the grain boundary resistivity is negligible.
Modeling geomagnetic storms on prompt and diffusive time scales
Li, Zhao
The discovery of the Van Allen radiation belts in the 1958 was the first major discovery of the Space Age. There are two belts of energetic particles. The inner belt is very stable, but the outer belt is extremely variable, especially during geomagnetic storms. As the energetic particles are hazardous to spacecraft, understanding the source of these particles and their dynamic behavior driven by solar activity has great practical importance. In this thesis, the effects of magnetic storms on the evolution of the electron radiation belts, in particular the outer zone, is studied using two types of numerical simulation: radial diffusion and magnetohydrodynamics (MHD) test-particle simulation. A radial diffusion code has been developed at Dartmouth, applying satellite measurements to model flux as an outer boundary condition, exploring several options for the diffusion coefficient and electron loss time. Electron phase space density is analyzed for July 2004 coronal mass ejection (CME) driven storms and March-April 2008 co-rotating interaction region (CIR) driven storms, and compared with Global Positioning System (GPS) satellite measurements within 5 degrees of the magnetic equator at L=4.16. A case study of a month-long interval in the Van Allen Probes satellite era, March 2013, confirms that electron phase space density is well described by radial diffusion for the whole month at low first invariant 0.6 MeV by an order of magnitude over 24 hours as observed.
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...
Percival, Susan M
2010-01-01
The presence of an extended blue horizontal branch (HB) in a stellar population is known to affect the age inferred from spectral fitting to stellar population synthesis models. However, most population synthesis models still rely on theoretical isochrones which do not include realistic modelling of extended HBs. In this work, we create detailed models for a range of old simple stellar populations (SSPs), to create a variety of realistic HB morphologies, from extended red clumps, to extreme blue HBs. We achieve this by utilising stellar tracks from the BaSTI database and implementing a different mass loss prescription for each SSP created, resulting in different HB morphologies. We find that, for each metallicity, there is some HB morphology which maximises Hbeta, making an underlying 14Gyr population look ~5-6Gyr old for the low and intermediate metallicity cases, and as young as 2Gyr for a solar metallicity SSP. We explore whether there are any spectral indices capable of breaking the degeneracy between an ...
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.
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.
THE LOS ALAMOS NATIONAL LABORATORY ATMOSPHERIC TRANSPORT AND DIFFUSION MODELS
Energy Technology Data Exchange (ETDEWEB)
M. WILLIAMS [and others
1999-08-01
The LANL atmospheric transport and diffusion models are composed of two state-of-the-art computer codes. The first is an atmospheric wind model called HOThlAC, Higher Order Turbulence Model for Atmospheric circulations. HOTMAC generates wind and turbulence fields by solving a set of atmospheric dynamic equations. The second is an atmospheric diffusion model called RAPTAD, Random Particle Transport And Diffusion. RAPTAD uses the wind and turbulence output from HOTMAC to compute particle trajectories and concentration at any location downwind from a source. Both of these models, originally developed as research codes on supercomputers, have been modified to run on microcomputers. Because the capability of microcomputers is advancing so rapidly, the expectation is that they will eventually become as good as today's supercomputers. Now both models are run on desktop or deskside computers, such as an IBM PC/AT with an Opus Pm 350-32 bit coprocessor board and a SUN workstation. Codes have also been modified so that high level graphics, NCAR Graphics, of the output from both models are displayed on the desktop computer monitors and plotted on a laser printer. Two programs, HOTPLT and RAPLOT, produce wind vector plots of the output from HOTMAC and particle trajectory plots of the output from RAPTAD, respectively. A third CONPLT provides concentration contour plots. Section II describes step-by-step operational procedures, specifically for a SUN-4 desk side computer, on how to run main programs HOTMAC and RAPTAD, and graphics programs to display the results. Governing equations, boundary conditions and initial values of HOTMAC and RAPTAD are discussed in Section III. Finite-difference representations of the governing equations, numerical solution procedures, and a grid system are given in Section IV.
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.
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...
Gentsch, Lydia; Hammerle, Albin; Sturm, Patrick; Ogée, Jérôme; Wingate, Lisa; Siegwolf, Rolf; Plüss, Peter; Baur, Thomas; Buchmann, Nina; Knohl, Alexander
2014-07-01
Field measurements of photosynthetic carbon isotope discrimination ((13)Δ) of Fagus sylvatica, conducted with branch bags and laser spectrometry, revealed a high variability of (13)Δ, both on diurnal and day-to-day timescales. We tested the prediction capability of three versions of a commonly used model for (13)Δ [called here comprehensive ((13)(Δcomp)), simplified ((13) Δsimple) and revised ((13)(Δrevised)) versions]. A Bayesian approach was used to calibrate major model parameters. Constrained estimates were found for the fractionation during CO(2) fixation in (13)(Δcomp), but not in (13)(Δsimple), and partially for the mesophyll conductance for CO(2)(gi). No constrained estimates were found for fractionations during mitochondrial and photorespiration, and for a diurnally variable apparent fractionation between current assimilates and mitochondrial respiration, specific to (13)(Δrevised). A quantification of parameter estimation uncertainties and interdependencies further helped explore model structure and behaviour. We found that (13)(Δcomp) usually outperformed (13)(Δsimple) because of the explicit consideration of gi and the photorespiratory fractionation in (13)(Δcomp) that enabled a better description of the large observed diurnal variation (≈9‰) of (13)Δ. Flux-weighted daily means of (13)Δ were also better predicted with (13)(Δcomp) than with (13)(Δsimple).
Two-phase flow with surfactants: Diffuse interface models and their analysis
Abels, Helmut; Lam, Kei Fong; Weber, Josef
2016-01-01
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a particular diffuse interface model.
[Diffusion factor calculation for TIP4P model of water].
Zlenko, D V
2012-01-01
A molecular dynamics study has been undertaken for a model of liquid TIP4P water. Thermal dependencies of water density and radial distribution functions were calculated for model verification. Three methods have been used for calculation of diffusion factor thermal dependencies. Their sensitivity to molecular system size and length of used trajectory has been analyzed. It has been shown that Green-Kubo formula-based approach which associates diffusion factor with speed autocorrelation function integral is preferred in case of short MD simulations. The second approach based on Einstein equation which associates mean square displacement of molecule with time is preferred in case of long simulations. It has been also demonstrated that it is possible to modify the second approach to make it more stable and reliable. This modification is to use a slope of the graph of the mean square displacement on time as the estimation of the diffusion factor instead of the ratio of molecule mean square displacement and time.
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.
Partial Differential Equations of an Epidemic Model with Spatial Diffusion
Directory of Open Access Journals (Sweden)
El Mehdi Lotfi
2014-01-01
Full Text Available The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the eradication of disease from population. When the basic reproduction number is greater than unity, then disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable; in this case the disease persists in the population. Numerical simulations are presented to illustrate our theoretical results.
Jones, A. P.
2016-12-01
The origin of the diffuse interstellar bands (DIBs), one of the longest-standing mysteries of the interstellar medium (ISM), is explored within the framework of The Heterogeneous dust Evolution Model for Interstellar Solids (THEMIS). The likely nature of the DIB carriers and their evolution is here explored within the framework of the structures and sub-structures inherent to doped hydrogenated amorphous carbon grains in the ISM. Based on the natural aromatic-rich moieties (asphaltenes) recovered from coal and oil, the likely structure of their interstellar analogues is investigated within the context of the diffuse band problem. It is here proposed that the top-down evolution of interstellar carbonaceous grains, and, in particular, a-C(:H) nanoparticles, is at the heart of the formation and evolution of the DIB carriers and their associations with small molecules and radicals, such as C2, C3, CH and CN. It is most probable that the DIBs are carried by dehydrogenated, ionized, hetero-cyclic, olefinic and aromatic-rich moieties that form an integral part of the contiguous structure of hetero-atom-doped hydrogenated amorphous carbon nanoparticles and their daughter fragmentation products. Within this framework, it is proposed that polyene structures in all their variants could be viable DIB carrier candidates.
Diffusion Based Modeling of Human Brain Response to External Stimuli
Namazi, Hamidreza
2012-01-01
Human brain response is the overall ability of the brain in analyzing internal and external stimuli in the form of transferred energy to the mind/brain phase-space and thus, making the proper decisions. During the last decade scientists discovered about this phenomenon and proposed some models based on computational, biological, or neuropsychological methods. Despite some advances in studies related to this area of the brain research there was less effort which have been done on the mathematical modeling of the human brain response to external stimuli. This research is devoted to the modeling of human EEG signal, as an alert state of overall human brain activity monitoring, due to receiving external stimuli, based on fractional diffusion equation. The results of this modeling show very good agreement with the real human EEG signal and thus, this model can be used as a strong representative of the human brain activity.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
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
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
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.
Clima, Lilia; Ursu, Elena L; Cojocaru, Corneliu; Rotaru, Alexandru; Barboiu, Mihail; Pinteala, Mariana
2015-09-28
The complexes formed by DNA and polycations have received great attention owing to their potential application in gene therapy. In this study, the binding efficiency between double-stranded oligonucleotides (dsDNA) and branched polyethylenimine (B-PEI) has been quantified by processing of the images captured from the gel electrophoresis assays. The central composite experimental design has been employed to investigate the effects of controllable factors on the binding efficiency. On the basis of experimental data and the response surface methodology, a multivariate regression model has been constructed and statistically validated. The model has enabled us to predict the binding efficiency depending on experimental factors, such as concentrations of dsDNA and B-PEI as well as the initial pH of solution. The optimization of the binding process has been performed using simplex and gradient methods. The optimal conditions determined for polyplex formation have yielded a maximal binding efficiency close to 100%. In order to reveal the mechanism of complex formation at the atomic-scale, a molecular dynamic simulation has been carried out. According to the computation results, B-PEI amine hydrogen atoms have interacted with oxygen atoms from dsDNA phosphate groups. These interactions have led to the formation of hydrogen bonds between macromolecules, stabilizing the polyplex structure.
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 of 1D Anomalous Diffusion in Fractured Nanoporous Media
Directory of Open Access Journals (Sweden)
Albinali Ali
2016-07-01
Full Text Available Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy’s law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.
Hot Bottom Burning in Asymptotic Giant Branch Stars and the Turbulent Convection Model
D'Antona, Francesca; Mazzitelli, Italo
1996-10-01
We investigate the effect of two different local turbulent convection models on the structure of intermediate-mass stars (IMSs, 3.5 Msun ≤ M ≤7 Msun) in the asymptotic giant branch (AGB) phase where, according to observations, they should experience hot bottom burning (HBB). Evolutionary models adopting either the mixing length theory (MLT) or the Canuto & Mazzitelli (CM) description of stellar convection are discussed. It is found that, while the MLT structures require some degree of tuning to achieve, at the bottom of the convective envelope, the large temperatures required for HBB, the CM structures spontaneously achieve these conditions. Since the observational evidence for HBB (existence of a class of very luminous, lithium-rich AGB stars in the Magellanic Clouds showing low 12C/13C ratios) is quite compelling, the above result provides a further, successful test for the CM convective model, in stellar conditions far from solar. With the aid of the CM model, we then explore a number of problems related to the late evolution of this class of objects, and give first results for (1) the luminosity evolution of IMSs in the AGB phase (core mass-luminosity relation and luminosity range in which HBB occurs) for Population I and Population II structures, (2) the minimum core mass for semidegenerate carbon ignition (˜1.05 Msun), (3) the relation between initial mass and final white dwarf (WD) mass (also based on some observational evidences about the upper AGB stars), and (4) the expected mass function of massive WDs. Confirmation of the theoretical framework could arise from an observational test: the luminosity function of AGB stars is expected to show a gap at Mbol ˜ -6, which would distinguish between the low-luminosity regime, in which AGBs become carbon stars, and the upper luminosities, at which they undergo HBB, have very low 12C/13C ratios, and become lithium rich.
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...
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...... 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...
Parametric pattern selection in a reaction-diffusion model.
Directory of Open Access Journals (Sweden)
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.
Global dynamics and diffusion in triaxial galactic models
Papaphilippou, Y.
We apply the Frequency Map Analysis method to the 3--dimensional logarithmic galactic potential in order to clarify the dynamical behaviour of triaxial power--law galactic models. All the fine dynamical details are displayed in the complete frequency map, a direct representation of the system's Arnol'd web. The influence of resonant lines and the extent of the chaotic zones are directly associated with the physical space of the system. Some new results related with the diffusion of galactic orbits are also discussed. This approach reveals many unknown dynamical features of triaxial galactic potentials and provides strong indications that chaos should be an innate characteristic of triaxial configurations.
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
Water Diffusion Modelling of CFB Fly Ash Thermoset Composite
Directory of Open Access Journals (Sweden)
Villa Ralph P.
2016-01-01
Full Text Available The shift in coal-fired power plants from pulverized coal (PC boiler technology into the greener circulating fluidized bed (CFB boiler technology resulted into a major deviation in the properties of the waste fly ash generated making it less suitable for its previous application as additives for construction materials. A new market for CFB fly ash had to be found for it not to end up as a zero value by-product. Using CFB fly ash as filler for thermoset composites is a new and remarkable application. Only a few studies, however, have been done to characterize the properties of this new material. Further experimentation and analysis may be costly and time-consuming since common procedures are material destructive. A computer-aided modeling of the composite’s water sorption behavior was done. The effect of particle loading, size and shape were considered. These properties were varied and the resulting overall diffusivities were compared to previous experimental studies. The comparison of the model and experimental diffusivity values showed satisfactory results. This model may then provide a cheaper and more time-efficient method for the characterization of the water sorption properties of CFB fly ash thermoset composites. In the future, this may lead to further studies on its application as a green material.
A chaotic model for advertising diffusion problem with competition
Ip, W. H.; Yung, K. L.; Wang, Dingwei
2012-08-01
In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win-Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win-Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy.
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.
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
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...
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.
Modeling the Determinants Influencing the Diffusion of Mobile Internet
Alwahaishi, Saleh; Snášel, Václav
2013-04-01
Understanding individual acceptance and use of Information and Communication Technology (ICT) is one of the most mature streams of information systems research. In Information Technology and Information System research, numerous theories are used to understand users' adoption of new technologies. Various models were developed including the Innovation Diffusion Theory, Theory of Reasoned Action, Theory of Planned Behavior, Technology Acceptance Model, and recently, the Unified Theory of Acceptance and Use of Technology. This research composes a new hybrid theoretical framework to identify the factors affecting the acceptance and use of Mobile Internet -as an ICT application- in a consumer context. The proposed model incorporates eight constructs: Performance Expectancy (PE), Effort Expectancy (EE), Facilitating Conditions (FC), Social Influences (SI), Perceived Value (PV), Perceived Playfulness (PP), Attention Focus (AF), and Behavioral intention (BI). Individual differences-namely, age, gender, education, income, and experience are moderating the effects of these constructs on behavioral intention and technology use.
Agent-based multi-optional model of innovations diffusion
Laciana, Carlos E
2013-01-01
We propose a formalism that allows the study of the process of diffusion of several products competing in a common market. It is based on the generalization of the statistics Ising model (Potts model). For the implementation, agent based modeling is used, applied to a problem of three options; to adopt a product A, a product B, or non-adoption. A launching strategy is analyzed for one of the two products, which delays its launching with the objective of competing with improvements. The proportion reached by one and another product is calculated at market saturation. The simulations are produced varying the social network topology, the uncertainty in the decision, and the population's homogeneity.
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...
Percival, Susan M.; Salaris, Maurizio
2011-04-01
The presence of an extended blue horizontal branch (HB) in a stellar population is known to affect the age inferred from spectral fitting to stellar population synthesis models. This is due to the hot blue component which increases the strength of the Balmer lines and can make an old population look spuriously young. However, most population synthesis models still rely on theoretical isochrones, which do not include realistic modelling of extended HBs. In this work, we create detailed models for a range of old simple stellar populations (SSPs), with metallicities ranging from [Fe/H]=-1.3 to solar, to create a variety of realistic HB morphologies, from extended red clumps, to extreme blue HBs. We achieve this by utilizing stellar tracks from the BaSTI data base and implementing a different mass-loss prescription for each SSP created. This includes setting an average mass and a Gaussian spread in masses of individual stars coming on to the zero-age HB for each model, and hence resulting in different HB morphologies. We find that, for each metallicity, there is some HB morphology which maximizes Hβ, making an underlying 14-Gyr population look ˜5-6 Gyr old for the low- and intermediate-metallicity cases, and as young as 2 Gyr in the case of the solar metallicity SSP. We explore whether there are any spectral indices capable of breaking the degeneracy between an old SSP with extended blue HB and a truly young or intermediate-age SSP, and find that the Ca II index of Rose and the strength of the Mg II doublet at 2800 Å are promising candidates, in combination with Hβ and other metallicity indicators, such as Mgb and Fe5406. We also run Monte Carlo simulations to investigate the level of statistical fluctuations in the spectra of typical stellar clusters. We find that fluctuations in spectral indices are significant even for average to large globular clusters and that various spectral indices are affected in different ways, which has implications for full
A NEW MODEL FOR THE DETERMINATION OF GRAIN BOUNDARY DIFFUSIVITIES
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R LOUAHDI
2001-12-01
Full Text Available A new model, based on a surface saturation technique, is suggested to determine grain boundary diffusivity of impurities. The model is applied to the Ni-S system that is of great practical interest. The initial saturation of nickel grain boundaries with sulphur is obtained by annealing at a temperature which satisfies the thermodynamics criterion for surface saturation. In order to reduce the annealing time, dynamic (non-equilibrium segregation is induced by carrying out the anneal on cold worked nickel (e = 0.2 true strain. Both the grain boundaries and the surface were saturated after only 24 hours of annealing at a temperature as low as 450°C. The heat treatment of the cold rolled material was carried out inside the vacuum chamber of an Auger Electron Spectrometer (AES. The diffusivity, as obtained from the slope of the linear parts of the kinetics curves recorded by the AES, is found to be given by the relationship D = 2.7×10-9exp(-58.700/RT m2s-1 in the temperature range 450 to 700°C.
Analysis of a diffuse interface model of multispecies tumor growth
Dai, Mimi; Feireisl, Eduard; Rocca, Elisabetta; Schimperna, Giulio; Schonbek, Maria E.
2017-04-01
We consider a diffuse interface model for tumor growth recently proposed in Chen et al (2014 Int. J. Numer. Methods Biomed. Eng. 30 726–54). In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn–Hilliard type equation for the tumor cells (which include proliferating and dead cells), a Darcy law for the tissue velocity field, whose divergence may be different from 0 and depend on the other variables, a transport equation for the proliferating (viable) tumor cells, and a quasi-static reaction diffusion equation for the nutrient concentration. We establish existence of weak solutions for the PDE system coupled with suitable initial and boundary conditions. In particular, the proliferation function at the boundary is supposed to be nonnegative on the set where the velocity \\mathbf{u} satisfies \\mathbf{u}\\centerdot ν >0 , where ν is the outer normal to the boundary of the domain.
Pharmacokinetic modeling of ascorbate diffusion through normal and tumor tissue.
Kuiper, Caroline; Vissers, Margreet C M; Hicks, Kevin O
2014-12-01
Ascorbate is delivered to cells via the vasculature, but its ability to penetrate into tissues remote from blood vessels is unknown. This is particularly relevant to solid tumors, which often contain regions with dysfunctional vasculature, with impaired oxygen and nutrient delivery, resulting in upregulation of the hypoxic response and also the likely depletion of essential plasma-derived biomolecules, such as ascorbate. In this study, we have utilized a well-established multicell-layered, three-dimensional pharmacokinetic model to measure ascorbate diffusion and transport parameters through dense tissue in vitro. Ascorbate was found to penetrate the tissue at a slightly lower rate than mannitol and to travel via the paracellular route. Uptake parameters into the cells were also determined. These data were fitted to the diffusion model, and simulations of ascorbate pharmacokinetics in normal tissue and in hypoxic tumor tissue were performed with varying input concentrations, ranging from normal dietary plasma levels (10-100 μM) to pharmacological levels (>1 mM) as seen with intravenous infusion. The data and simulations demonstrate heterogeneous distribution of ascorbate in tumor tissue at physiological blood levels and provide insight into the range of plasma ascorbate concentrations and exposure times needed to saturate all regions of a tumor. The predictions suggest that supraphysiological plasma ascorbate concentrations (>100 μM) are required to achieve effective delivery of ascorbate to poorly vascularized tumor tissue.
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
Directory of Open Access Journals (Sweden)
Timo Friedrich
2012-03-01
Analysis of zebrafish mutants that demonstrate abnormal locomotive behavior can elucidate the molecular requirements for neural network function and provide new models of human disease. Here, we show that zebrafish quetschkommode (que mutant larvae exhibit a progressive locomotor defect that culminates in unusual nose-to-tail compressions and an inability to swim. Correspondingly, extracellular peripheral nerve recordings show that que mutants demonstrate abnormal locomotor output to the axial muscles used for swimming. Using positional cloning and candidate gene analysis, we reveal that a point mutation disrupts the gene encoding dihydrolipoamide branched-chain transacylase E2 (Dbt, a component of a mitochondrial enzyme complex, to generate the que phenotype. In humans, mutation of the DBT gene causes maple syrup urine disease (MSUD, a disorder of branched-chain amino acid metabolism that can result in mental retardation, severe dystonia, profound neurological damage and death. que mutants harbor abnormal amino acid levels, similar to MSUD patients and consistent with an error in branched-chain amino acid metabolism. que mutants also contain markedly reduced levels of the neurotransmitter glutamate within the brain and spinal cord, which probably contributes to their abnormal spinal cord locomotor output and aberrant motility behavior, a trait that probably represents severe dystonia in larval zebrafish. Taken together, these data illustrate how defects in branched-chain amino acid metabolism can disrupt nervous system development and/or function, and establish zebrafish que mutants as a model to better understand MSUD.
Pre-Clinical Models of Diffuse Intrinsic Pontine Glioma
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Oren J Becher
2015-07-01
Full Text Available Diffuse Intrinsic Pontine Glioma (DIPG is a rare and incurable brain tumor that arises in the brainstem of children predominantly between the ages of six and eight. Its intricate morphology and involvement of normal pons tissue precludes surgical resection, and the standard of care today remains fractionated radiation alone. In the past 30 years, there have been no significant advances made in the treatment of DIPG. This is largely because we lack good models of DIPG and therefore have little biological basis for treatment. In recent years however, due to increased biopsy and acquisition of autopsy specimens, research is beginning to unravel the genetic and epigenetic drivers of DIPG. Insight gleaned from these studies has led to improvements in approaches to both model these tumors in the lab, as well as to potentially treat them in the clinic. This review will detail the initial strides towards modeling DIPG in animals, which included allograft and xenograft rodent models using non-DIPG glioma cells. Important advances in the field came with the development of in vitro cell and in vivo xenograft models derived directly from autopsy material of DIPG patients or from human embryonic stem cells. Lastly, we will summarize the progress made in the development of genetically engineered mouse models of DIPG. Cooperation of studies incorporating all of these modeling systems to both investigate the unique mechanisms of gliomagenesis in the brainstem and to test potential novel therapeutic agents in a preclinical setting will result in improvement in treatments for DIPG patients.
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas
2016-12-17
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
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.
An HBV model with diffusion and time delay.
Xu, Rui; Ma, Zhien
2009-04-07
In this paper, a hepatitis B virus (HBV) model with spatial diffusion and saturation response of the infection rate is investigated, in which the intracellular incubation period is modelled by a discrete time delay. By analyzing the corresponding characteristic equations, the local stability of an infected steady state and an uninfected steady state is discussed. By comparison arguments, it is proved that if the basic reproductive number is less than unity, the uninfected steady state is globally asymptotically stable. If the basic reproductive number is greater than unity, by successively modifying the coupled lower-upper solution pairs, sufficient conditions are obtained for the global stability of the infected steady state. Numerical simulations are carried out to illustrate the main results.
Rule-based spatial modeling with diffusing, geometrically constrained molecules
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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
Review of Integrated Modeling and Optimization Software for Advance Concepts Branch Models
2013-04-01
ignore any feature of a model that allows for parametric and Monte Carlo runs since this will be controlled by the analysis phase of the IMO...TECHNICAL (PDF) INFORMATION CTR DTIC OCA 8725 JOHN J KINGMAN RD STE 0944 FORT BELVOIR VA 22060-6218 1 DIRECTOR (PDF) US ARMY RESEARCH LAB
The Effectiveness Analysis of Waiting Processes in the Different Branches of a Bank by Queue Model
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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.
Analytical model of diffuse reflectance spectrum of skin tissue
Energy Technology Data Exchange (ETDEWEB)
Lisenko, S A; Kugeiko, M M; Firago, V A [Belarusian State University, Minsk (Belarus); Sobchuk, A N [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus)
2014-01-31
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.
2014-01-01
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.
Postural control model interpretation of stabilogram diffusion analysis
Peterka, R. J.
2000-01-01
Collins and De Luca [Collins JJ. De Luca CJ (1993) Exp Brain Res 95: 308-318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.
A policy model for diffusion of electricity saving technologies
Energy Technology Data Exchange (ETDEWEB)
Heimdal, Sverre Inge; Bjoernstad, Even (Even Enova SF (Norway))
2009-07-01
This paper discusses an integrated model for information and marketing tools combined with various subsidy elements developed for achieving electricity savings and improved energy efficiency in the Norwegian residential sector. The model represents the framework within which current Norwegian policies within this field are based. A central element of the model is the way marketing and subsidy elements are combined in different phases of the market diffusion process of the relevant technologies, and how market distortions are sought minimized through criteria for entry and exit to the scheme. The paper further gives examples of applications of the model. In 2003 Norwegian parliament launched a one-shot Household Subsidy Programme for heating and efficiency technologies in the residential sector. The evaluation report of the subsidy scheme as well as the IEA national report on Norway in 2005 concluded that the subsidy scheme had been a great success. This programme was reinstated on a permanent basis in 2006, and the paper uses data from these programmes as illustrations to the theoretical model.
A reaction-diffusion model of human brain development.
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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.
Hébert, M.; Becker, J.-M.
2008-01-01
This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelka's layering model describes the multiple reflections and transmissions of light taking place between various superposed diffusing layers (disc...
Technology diffusion in energy-economy models: The case of Danish vintage models
DEFF Research Database (Denmark)
Klinge Jacobsen, Henrik
2000-01-01
the consequences of the vintage modelling approach. The fluctuating utilization rates for power capacity in Denmark are found to have a significant impact on average fuel efficiencies. Diffusion of electric appliances is linked to economic activity and saturation levels for each appliance. In the sector......Technological progress is an important issue in long-term energy demand projections and in environmental analyses. Different assumptions on technological progress and diffusion of new technologies are among the reasons for diverging results obtained using bottom-up and top-down models for analyzing...... the costs of greenhouse gas mitigation. This paper examines the effect on aggregate energy efficiency of using technological vintage models to describe technology diffusion. The focus is on short- to medium-term issues. Three different models of Danish energy supply and demand are used to illustrate...
Acoustic Predictions in Industrial Spaces Using a Diffusion Model
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Alexis Billon
2012-01-01
Full Text Available Industrial spaces are known to be very noisy working environment. This noise exposure can be uncomfortable, tiring, or even harmful, at worst. Industrial spaces have several characteristics: they are often huge flat volumes fitted with many obstacles and sound sources. Moreover, they are usually surrounded by rooms where low noise levels are required. The existing prediction tools can seldom model all these phenomena accurately. In this paper, a prediction model based on a diffusion equation is presented. The successive developments carried out to deal with the various propagating phenomena met in industrial spaces are shown. For each phenomenon, numerical or experimental examples are given to highlight the validity of this model. It is also shown that its computation load is very little in comparison to ray-tracing-based methods. In addition, this model can be used as a reliable and flexible tool to study the physics of the coupling between rooms. Finally, an application to a virtual factory is presented.
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...
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Tudor Barbu
2014-06-01
Full Text Available A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explaining the mathematical reasons behind it. Also, we perform a rigorous mathematical investigation on of the existence and uniqueness of the solution of our nonlinear diffusion equation. This PDE-based noise removal approach outperforms most diffusion-based methods, producing considerably better smoothing results and providing a much better edge preservation.
The dynamics of multimodal integration: The averaging diffusion model.
Turner, Brandon M; Gao, Juan; Koenig, Scott; Palfy, Dylan; L McClelland, James
2017-03-08
We combine extant theories of evidence accumulation and multi-modal integration to develop an integrated framework for modeling multimodal integration as a process that unfolds in real time. Many studies have formulated sensory processing as a dynamic process where noisy samples of evidence are accumulated until a decision is made. However, these studies are often limited to a single sensory modality. Studies of multimodal stimulus integration have focused on how best to combine different sources of information to elicit a judgment. These studies are often limited to a single time point, typically after the integration process has occurred. We address these limitations by combining the two approaches. Experimentally, we present data that allow us to study the time course of evidence accumulation within each of the visual and auditory domains as well as in a bimodal condition. Theoretically, we develop a new Averaging Diffusion Model in which the decision variable is the mean rather than the sum of evidence samples and use it as a base for comparing three alternative models of multimodal integration, allowing us to assess the optimality of this integration. The outcome reveals rich individual differences in multimodal integration: while some subjects' data are consistent with adaptive optimal integration, reweighting sources of evidence as their relative reliability changes during evidence integration, others exhibit patterns inconsistent with optimality.
Distributed-order diffusion equations and multifractality: Models and solutions
Sandev, Trifce; Chechkin, Aleksei V.; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M.; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Diffusion in Liquids: Equilibrium Molecular Simulations and Predictive Engineering Models
Liu, X.
2013-01-01
The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations. From a practical point of view, systems consisting more than two components are more interesting. However, experimental and simulation data on transport diffusion for such systems are scarce. There...
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...
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.
Diffusion in Liquids: Equilibrium Molecular Simulations and Predictive Engineering Models
Liu, X.
2013-01-01
The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations.
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.
Perceptual decision making: Drift-diffusion model is equivalent to a Bayesian model
Directory of Open Access Journals (Sweden)
Sebastian eBitzer
2014-02-01
Full Text Available Behavioural data obtained with perceptual decision making experiments are typically analysed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence towards a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses.
Synchronized stability in a reaction–diffusion neural network model
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.
Simulating Radiotherapy Effect in High-Grade Glioma by Using Diffusive Modeling and Brain Atlases
Directory of Open Access Journals (Sweden)
Alexandros Roniotis
2012-01-01
Full Text Available Applying diffusive models for simulating the spatiotemporal change of concentration of tumour cells is a modern application of predictive oncology. Diffusive models are used for modelling glioblastoma, the most aggressive type of glioma. This paper presents the results of applying a linear quadratic model for simulating the effects of radiotherapy on an advanced diffusive glioma model. This diffusive model takes into consideration the heterogeneous velocity of glioma in gray and white matter and the anisotropic migration of tumor cells, which is facilitated along white fibers. This work uses normal brain atlases for extracting the proportions of white and gray matter and the diffusion tensors used for anisotropy. The paper also presents the results of applying this glioma model on real clinical datasets.
Empirically Grounded Agent-Based Models of Innovation Diffusion: A Critical Review
Zhang, Haifeng
2016-01-01
Innovation diffusion has been studied extensively in a variety of disciplines, including sociology, economics, marketing, ecology, and computer science. Traditional literature on innovation diffusion has been dominated by models of aggregate behavior and trends. However, the agent-based modeling (ABM) paradigm is gaining popularity as it captures agent heterogeneity and enables fine-grained modeling of interactions mediated by social and geographic networks. While most ABM work on innovation diffusion is theoretical, empirically grounded models are increasingly important, particularly in guiding policy decisions. We present a critical review of empirically grounded agent-based models of innovation diffusion, developing a categorization of this research based on types of agent models as well as applications. By connecting the modeling methodologies in the fields of information and innovation diffusion, we suggest that the maximum likelihood estimation framework widely used in the former is a promising paradigm...
A simple model for diffusion-induced dislocations during the lithiation of crystalline materials
Directory of Open Access Journals (Sweden)
Fuqian Yang
2014-01-01
Full Text Available Assuming that the lithiation reaction occurs randomly in individual small particles in the vicinity of the reaction front, a simple model of diffusion-induced dislocations was developed. The diffusion-induced dislocations are controlled by the misfit strain created by the diffusion of solute atoms or the phase transformation in the vicinity of the reaction front. The dislocation density is proportional to the total surface area of the “lithiated particle” and inversely proportional to the particle volume. The diffusion-induced dislocations relieve the diffusion-induced stresses.
Borovkov, Konstantin; Rice, Timothy
2011-01-01
We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. Instead of using a single virulence characteristic which is typical of most mathematical models for infectious diseases, our model uses a combination of two characteristics: lethality and transmissibility. This makes the model capable of reproducing the empirically observed fact that the increase in the host density can lead to the prevalence of the more virulent pathogen type. We provide some numerical illustrations and discuss the effects of the size of the enclosure containing the host population on the encounter rate in our model that plays the key role in determining what pathogen type will eventually prevail. We also present a multistage extension of the model to situations where there are several populations and parasites can be transmitted from one of them to another.
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
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
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...
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.
An electrodynamics-based model for ion diffusion in microbial polysaccharides.
Liu, Chongxuan; Zachara, John M; Felmy, Andrew; Gorby, Yuri
2004-10-10
An electrodynamics-based model was formulated for simulation of ion diffusion in microbial polysaccharides. The fixed charges and electrostatic double layers that may associate with microbial polysaccharides and their effects on ion diffusion were explicitly built into the model. The model extends a common multicomponent ion diffusion formulation that is based on irreversible thermodynamics under a zero ionic charge flux condition, which is only applicable to the regions without fixed charges and electrostatic double layers. An efficient numerical procedure was presented to solve the differential equations in the model. The model well described key features of experimental observations of ion diffusion in negatively charged microbial polysaccharides including accelerated diffusive transport of cations, exclusion of anions, and increased rate of cation transport with increasing negative charge density. The simulated diffusive fluxes of cations and anions were consistent with a cation exchange diffusion concept in negatively charged polysaccharides at the interface of plant roots and soils; and the developed model allows to mathematically study such diffusion phenomena. An illustrative example was also provided to simulate dynamic behavior of ionic current during ion diffusion within a charged bacterial cell wall polysaccharide and the effects of the ionic current on the compression or expansion of the bacterial electrostatic double layer at the interface of the cell wall and bulk solution.
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.
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.
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...
Osei, Frank B.; Duker, Alfred A.; Stein, Alfred
2011-01-01
This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint
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...
Nonlocal-response diffusion model of holographic recording in photopolymer
Sheridan, John T.; Lawrence, Justin R.
2000-01-01
The standard one-dimensional diffusion equation is extended to include nonlocal temporal and spatial medium responses. How such nonlocal effects arise in a photopolymer is discussed. It is argued that assuming rapid polymer chain growth, any nonlocal temporal response can be dealt with so that the response can be completely understood in terms of a steady-state nonlocal spatial response. The resulting nonlocal diffusion equation is then solved numerically, in low-harmonic approximation, to de...
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.
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
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.
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.
Spatiotemporal Pattern in a Self- and Cross-Diffusive Predation Model with the Allee Effect
Directory of Open Access Journals (Sweden)
Feng Rao
2013-01-01
Full Text Available This paper proposes and analyzes a mathematical model for a predator-prey interaction with the Allee effect on prey species and with self- and cross-diffusion. The effect of diffusion which can drive the model with zero-flux boundary conditions to Turing instability is investigated. We present numerical evidence of time evolution of patterns controlled by self- and cross-diffusion in the model and find that the model dynamics exhibits a cross-diffusion controlled formation growth to spotted and striped-like coexisting and spotted pattern replication. Moreover, we discuss the effect of cross-diffusivity on the stability of the nontrivial equilibrium of the model, which depends upon the magnitudes of the self- and cross-diffusion coefficients. The obtained results show that cross-diffusion plays an important role in the pattern formation of the predator-prey model. It is also useful to apply the reaction-diffusion model to reveal the spatial predation in the real world.
Stalled-Flow and Head-Loss Model for Diffuser Pumps
Meng, S. Y.
1984-01-01
Modeling procedure approximates inlet transition zone (blade leading edge to blade throat) of diffuser pump as two-dimensional cascade, properties of which are well known. Model applied to stators as well as rotors. Procedure much faster than previous methods.
Bass-SIR model for diffusion of new products in social networks.
Fibich, Gadi
2016-09-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
Bass-SIR model for diffusion of new products in social networks
Fibich, Gadi
2016-09-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
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.
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
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Boli Xie
2014-01-01
Full Text Available A predator-prey model with both cross diffusion and time delay is considered. We give the conditions for emerging Turing instability in detail. Furthermore, we illustrate the spatial patterns via numerical simulations, which show that the model dynamics exhibits a delay and diffusion controlled formation growth not only of spots and stripe-like patterns, but also of the two coexist. The obtained results show that this system has rich dynamics; these patterns show that it is useful for the diffusive predation model with a delay effect to reveal the spatial dynamics in the real model.
A Fractional Fokker-Planck Model for Anomalous Diffusion
anderson, Johan; Moradi, Sara
2014-01-01
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the transition from a Gaussian distribution to a L\\'evy distribution. The statistical properties of the distribution functions are assessed by a generalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
Energy Technology Data Exchange (ETDEWEB)
Ho, C.K.; Webb, S.W.
1996-05-01
A review of mechanisms, models, and data relevant to the postulated phenomenon of enhanced vapor-phase diffusion in porous media is presented. Information is obtained from literature spanning two different disciplines (soil science and engineering) to gain a diverse perspective on this topic. Findings indicate that while enhanced vapor diffusion tends to correct the discrepancies observed between past theory and experiments, no direct evidence exists to support the postulated processes causing enhanced vapor diffusion. Numerical modeling analyses of experiments representative of the two disciplines are presented in this paper to assess the sensitivity of different systems to enhanced vapor diffusion. Pore-scale modeling is also performed to evaluate the relative significance of enhanced vapor diffusion mechanisms when compared to Fickian diffusion. The results demonstrate the need for additional experiments so that more discerning analyses can be performed.
Kee, Kerk F; Sparks, Lisa; Struppa, Daniele C; Mannucci, Mirco A; Damiano, Alberto
2016-01-01
By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that coexist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data.
Wu, Hao; Noé, Frank
2011-03-01
Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.
Simulation of levulinic acid adsorption in packed beds using parallel pore/surface diffusion model
Energy Technology Data Exchange (ETDEWEB)
Zeng, L.; Mao, J. [Zhejiang Provincial Key Laboratory for Chemical and Biological Processing Technology of Farm Products, Zhejiang University of Science and Technology, Hangzhou (China); Ren, Q. [National Laboratory of Secondary Resources Chemical Engineering, Zhejiang University, Hangzhou (China); Liu, B.
2010-07-15
The adsorption of levulinic acid in fixed beds of basic polymeric adsorbents at 22 C was studied under various operating conditions. A general rate model which considers pore diffusion and parallel pore/surface diffusion was solved numerically by orthogonal collocation on finite elements to describe the experimental breakthrough data. The adsorption isotherms, and the pore and surface diffusion coefficients were determined independently in batch adsorption studies. The external film resistance and the axial dispersion coefficient were estimated by the Wilson-Geankoplis equation and the Chung-Wen equation, respectively. Simulation elucidated that the model which considers parallel diffusion successfully describes the breakthrough behavior and gave a much better prediction than the model which considers pore diffusion. The results obtained in this work are applicable to design and optimizes the separation process. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
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.
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.
Stochastic modelling and diffusion modes for POD models and small-scale flow analysis
Resseguier, Valentin; Heitz, Dominique; Chapron, Bertrand
2016-01-01
We introduce a stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a decomposition of the velocity in terms of a smooth large-scale velocity component and a rough, highly oscillating, component gives rise, without any supplementary assumption, to a large-scale flow dynamics that includes a modified advection term together with an inhomogeneous diffusion term. Both of those terms, related respectively to turbophoresis and mixing effects, depend on the variance of the unre-solved small-scale velocity component. They bring to the reduced system an explicit subgrid term enabling to take into account the action of the truncated modes. Besides, a decomposition of the variance tensor in terms of diffusion modes provides a meaningful statistical representation of the stationary or nonstationary structuration of the small-scale velocity and of its action on the reso...
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
in 1954, by Dougherty and Drickamer in 1955, by Haase in 1969, by Kempers in 1989 and 2002, and by Shucla and Firoozabadi in 1998. The calculated values of thermal diffusion factors were compared with a few sets of experimental data for hydrocarbon mixtures. For calculation of the partial molar properties...
A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Walker, Christoph
2011-01-01
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
Two-dimensional MHD model of the reconnection diffusion region
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N. V. Erkaev
2002-01-01
Full Text Available Magnetic reconnection is an important process providing a fast conversion of magnetic energy into thermal and kinetic plasma energy. In this concern, a key problem is that of the resistive diffusion region where the reconnection process is initiated. In this paper, the diffusion region is associated with a nonuniform conductivity localized to a small region. The nonsteady resistive incompressible MHD equations are solved numerically for the case of symmetric reconnection of antiparallel magnetic fields. A Petschek type steady-state solution is obtained as a result of time relaxation of the reconnection layer structure from an arbitrary initial stage. The structure of the diffusion region is studied for various ratios of maximum and minimum values of the plasma resistivity. The effective length of the diffusion region and the reconnection rate are determined as functions of the length scale and the maximum of the resistivity. For sufficiently small length scale of the resistivity, the reconnection rate is shown to be consistent with Petschek's formula. By increasing the resistivity length scale and decreasing the resistivity maximum, the reconnection layer tends to be wider, and correspondingly, the reconnection rate tends to be more consistent with that of the Parker-Sweet regime.
Anomalous chain diffusion in unentangled model polymer nanocomposites
Schneider, G.; Nusser, K.; Neueder, S.; Brodeck, M.; Willner, L.; Farago, B.; Holderer, O.; Briels, W.J.; Richter, D.
2013-01-01
We studied unentangled poly(ethylene-alt-propylene) (PEP) in a composite with hydrophobic silica particles as a function of the filler concentration. Our neutron spin echo (NSE) experiments cover both the internal dynamics as well as the center of mass diffusion beyond the Rouse time. The key experi
A 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
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...
Martin, Elliot; Shreim, Amer; Paczuski, Maya
2010-01-01
We define an activity-dependent branching ratio that allows comparison of different time series X(t). The branching ratio b(x) is defined as b(x)=E[xi(x)/x]. The random variable xi(x) is the value of the next signal given that the previous one is equal to x, so xi(x)=[X(t+1) | X(t)=x]. If b(x)>1, the process is on average supercritical when the signal is equal to x, while if b(x)market hypothesis." For stock volumes, solar x-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, b(x) 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 b(x) approximately equal 1, which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for X(t) and for xi(x). For the BTW model the distribution of xi(x) 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 b(x) is close to one disappears once bulk dissipation is introduced in the BTW model-supporting our hypothesis that it is an indicator of criticality.
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
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...
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.
Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion
Directory of Open Access Journals (Sweden)
Xinze Lian
2013-01-01
Full Text Available We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.
Modeling 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.
Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates
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Marcus C. Christiansen
2013-10-01
Full Text Available In the actuarial literature, it has become common practice to model future capital returns and mortality rates stochastically in order to capture market risk and forecasting risk. Although interest rates often should and mortality rates always have to be non-negative, many authors use stochastic diffusion models with an affine drift term and additive noise. As a result, the diffusion process is Gaussian and, thus, analytically tractable, but negative values occur with positive probability. The argument is that the class of Gaussian diffusions would be a good approximation of the real future development. We challenge that reasoning and study the asymptotics of diffusion processes with affine drift and a general noise term with corresponding diffusion processes with an affine drift term and an affine noise term or additive noise. Our study helps to quantify the error that is made by approximating diffusive interest and mortality rate models with Gaussian diffusions and affine diffusions. In particular, we discuss forward interest and forward mortality rates and the error that approximations cause on the valuation of life insurance claims.
Branching geometry induced by lung self-regulated growth
Clément, Raphaël; Douady, Stéphane; Mauroy, Benjamin
2012-12-01
Branching morphogenesis is a widely spread phenomenon in nature. In organogenesis, it results from the inhomogeneous growth of the epithelial sheet, leading to its repeated branching into surrounding mesoderm. Lung morphogenesis is an emblematic example of tree-like organogenesis common to most mammals. The core signalling network is well identified, notably the Fgf10/Shh couple, required to initiate and maintain branching. In a previous study, we showed that the restriction by SHH of Fgf10 expression domain to distal mesenchyme spontaneously induces differential epithelial proliferation leading to branching. A simple Laplacian model qualitatively reproduced FGF10 dynamics in the mesenchyme and the spontaneous self-avoiding branching morphogenesis. However, early lung geometry has several striking features that remain to be addressed. In this paper, we investigate, through simulations and data analysis, if the FGF10-diffusion scenario accounts for the following aspects of lung morphology: size dispersion, asymmetry of branching events, and distal epithelium-mesothelium equilibrium. We report that they emerge spontaneously in the model, and that most of the underlying mechanisms can be understood as dynamical interactions between gradients and shape. This suggests that specific regulation may not be required for the emergence of these striking geometrical features.
Hierarchical Bass model: a product diffusion model considering a diversity of sensitivity to fashion
Tashiro, Tohru
2016-11-01
We propose a new product diffusion model including the number of how many adopters or advertisements a non-adopter met until he/she adopts the product, where (non-)adopters mean people (not) possessing it. By this effect not considered in the Bass model, we can depict a diversity of sensitivity to fashion. As an application, we utilize the model to fit the iPod and the iPhone unit sales data, and so the better agreement is obtained than the Bass model for the iPod data. We also present a new method to estimate the number of advertisements in a society from fitting parameters of the Bass model and this new model.
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)
The Water-Induced Linear Reduction Gas Diffusivity Model Extended to Three Pore Regions
DEFF Research Database (Denmark)
Chamindu, T. K. K. Deepagoda; de Jonge, Lis Wollesen; Kawamoto, Ken
2015-01-01
. Characterization of soil functional pore structure is an essential prerequisite to understand key gas transport processes in variably saturated soils in relation to soil ecosystems, climate, and environmental services. In this study, the water-induced linear reduction (WLR) soil gas diffusivity model originally......An existing gas diffusivity model developed originally for sieved, repacked soils was extended to characterize gas diffusion in differently structured soils and functional pore networks. A gas diffusivity-derived pore connectivity index was used as a measure of soil structure development...... developed for sieved, repacked soil was extended to two simple, linear regions to characterize gas diffusion and functional pore-network structure also in intact, structured soil systems. Based on the measurements in soils with markedly different pore regions, we showed that the two linear regions can...
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.
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...
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.
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.
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.
A Functional Model for Teaching Osmosis-Diffusion to Biology Students
Olsen, Richard W.; Petry, Douglas E.
1976-01-01
Described is a maternal-fetal model, operated by the student, to teach osmosis-diffusion to biology students. Included are materials needed, assembly instructions, and student operating procedures. (SL)
Woo, Jiyoung; Chen, Hsinchun
2016-01-01
As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums.
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.
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.
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.
A Mathematic Model of Gas-diffusion Electrodes in Contact with Liquid Electrolytes
Institute of Scientific and Technical Information of China (English)
LI Jun; XI Dan-li; SHI Yong; WU Xi-hui
2008-01-01
A mathematic model is developed which is applied to analyze the main factors that affect electrode performance and to account for the process of reaction and mass transfer in gas-diffusion electrodes in contact with liquid electrolytes. Electrochemical Thiele modulus φ2 and electrochemical effectiveness factor ηD are introduced to elucidate the effects of diffusion on electrochemical reaction and utilization of the gas-diffusion electrode.Profile of the reactant along axial direction is discussed,dependence of electrode potential V on current density J.are predicated by means of the newly developed mathematical model.
Many-server queues with customer abandonment: Numerical analysis of their diffusion model
Directory of Open Access Journals (Sweden)
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 Solution of Fractional Diffusion Equation Model for Freezing in Finite Media
Directory of Open Access Journals (Sweden)
R. S. Damor
2013-01-01
Full Text Available Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.
A model of modulated diffusion. II. Numerical results on statistical properties
Energy Technology Data Exchange (ETDEWEB)
Bazzani, A.; Siboni, S.; Turchetti, G. [dell`Universita Bologna (Italy)] [and others
1994-08-01
We investigate numerically the statistical properties of a model of modulated diffusion for which we have already computed analytically the diffusion coefficient D. Our model is constructed by adding a deterministic or random noise to the frequency of an integrable isochronous system. We consider in particular the central limit theorem and the invariance principle and we show that they follow whenever D is positive and for any magnitude of the noise; we also investigate the asymptotic distribution in a case when D=0.
AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL
Institute of Scientific and Technical Information of China (English)
闫振亚; 张鸿庆
2001-01-01
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known.Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine- cosine method, more exact solutions are found which contain soliton solutions.
Sakashita, Tetsuya; Hamada, Nobuyuki; Kawaguchi, Isao; Hara, Takamitsu; Kobayashi, Yasuhiko; Saito, Kimiaki
2014-05-01
A single cell can form a colony, and ionizing irradiation has long been known to reduce such a cellular clonogenic potential. Analysis of abortive colonies unable to continue to grow should provide important information on the reproductive cell death (RCD) following irradiation. Our previous analysis with a branching process model showed that the RCD in normal human fibroblasts can persist over 16 generations following irradiation with low linear energy transfer (LET) γ-rays. Here we further set out to evaluate the RCD persistency in abortive colonies arising from normal human fibroblasts exposed to high-LET carbon ions (18.3 MeV/u, 108 keV/µm). We found that the abortive colony size distribution determined by biological experiments follows a linear relationship on the log-log plot, and that the Monte Carlo simulation using the RCD probability estimated from such a linear relationship well simulates the experimentally determined surviving fraction and the relative biological effectiveness (RBE). We identified the short-term phase and long-term phase for the persistent RCD following carbon-ion irradiation, which were similar to those previously identified following γ-irradiation. Taken together, our results suggest that subsequent secondary or tertiary colony formation would be invaluable for understanding the long-lasting RCD. All together, our framework for analysis with a branching process model and a colony formation assay is applicable to determination of cellular responses to low- and high-LET radiation, and suggests that the long-lasting RCD is a pivotal determinant of the surviving fraction and the RBE.
Karakas, Amanda I; Nataf, David M
2014-01-01
We investigate the effect of helium enrichment on the evolution and nucleosynthesis of low-mass asymptotic giant branch (AGB) stars of 1.7Msun and 2.36Msun with a metallicity of Z=0.0006 ([Fe/H] = -1.4). We calculate evolutionary sequences with the primordial helium abundance (Y = 0.24) and with helium-enriched compositions (Y = 0.30, 0.35, 0.40). For comparison we calculate models of the same mass but at a lower metallicity Z=0.0003 ([Fe/H] = -1.8) with Y=0.24. Post-processing nucleosynthesis calculations are performed on each of the evolutionary sequences to determine the production of elements from hydrogen through to bismuth. Elemental surface abundance predictions and stellar yields are presented for each model. The models with enriched helium have shorter main sequence and AGB lifetimes, and enter the AGB with a more massive hydrogen exhausted core than the primordial helium model. The main consequences are 1) low-mass AGB models with enhanced helium will evolve more than twice as fast, giving them the ...
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 pres...
Self-diffusion in liquid gallium and hard sphere model
Directory of Open Access Journals (Sweden)
Blagoveshchenskii Nikolay
2015-01-01
Full Text Available Incoherent and coherent components of quasielastic neutron scattering have been studied in the temperature range of T = 313 K – 793 K aiming to explore the applicability limits of the hard-sphere approach for the microscopic dynamics of liquid gallium, which is usually considered as a non-hard-sphere system. It was found that the non-hard-sphere effects come into play at the distances shorter than the average interatomic distance. The longer range diffusive dynamics of liquid Ga is dominated by the repulsive forces between the atoms.
Comparison of two stochastic models of scalar diffusion in turbulent flow
Rodean, H. C.; Lange, R.; Nasstrom, J. S.; Gavrilov, V. P.
1992-07-01
This report describes and compares two Lagrangian stochastic models for turbulent diffusion: (1) the random velocity increment model based on the Langevin equation; and (2) the random displacement model. We apply both models to identical test problems for one-dimensional (vertical) diffusion, using identical parameterizations of turbulence statistics as inputs. We compare the results and discuss the advantages and disadvantages of each model. This work is part of an effort to improve the ADPIC dispersion model which is based on the eddy diffusivity model. It is also part of a cooperative research effort on the transport and dispersion of hazardous materials in the atmosphere by the Lawrence Livermore National Laboratory and the Institute of Experimental Meteorology (USSR).
Comparison and analysis of theoretical models for diffusion-controlled dissolution.
Wang, Yanxing; Abrahamsson, Bertil; Lindfors, Lennart; Brasseur, James G
2012-05-07
Dissolution models require, at their core, an accurate diffusion model. The accuracy of the model for diffusion-dominated dissolution is particularly important with the trend toward micro- and nanoscale drug particles. Often such models are based on the concept of a "diffusion layer." Here a framework is developed for diffusion-dominated dissolution models, and we discuss the inadequacy of classical models that are based on an unphysical constant diffusion layer thickness assumption, or do not correctly modify dissolution rate due to "confinement effects": (1) the increase in bulk concentration from confinement of the dissolution process, (2) the modification of the flux model (the Sherwood number) by confinement. We derive the exact mathematical solution for a spherical particle in a confined fluid with impermeable boundaries. Using this solution, we analyze the accuracy of a time-dependent "infinite domain model" (IDM) and "quasi steady-state model" (QSM), both formally derived for infinite domains but which can be applied in approximate fashion to confined dissolution with proper adjustment of a concentration parameter. We show that dissolution rate is sensitive to the degree of confinement or, equivalently, to the total concentration C(tot). The most practical model, the QSM, is shown to be very accurate for most applications and, consequently, can be used with confidence in design-level dissolution models so long as confinement is accurately treated. The QSM predicts the ratio of diffusion layer thickness to particle radius (the Sherwood number) as a constant plus a correction that depends on the degree of confinement. The QSM also predicts that the time required for complete saturation or dissolution in diffusion-controlled dissolution experiments is singular (i.e., infinite) when total concentration equals the solubility. Using the QSM, we show that measured differences in dissolution rate in a diffusion-controlled dissolution experiment are a result of
Garrido-Baserba, Manel; Sobhani, Reza; Asvapathanagul, Pitiporn; McCarthy, Graham W; Olson, Betty H; Odize, Victory; Al-Omari, Ahmed; Murthy, Sudhir; Nifong, Andrea; Godwin, Johnnie; Bott, Charles B; Stenstrom, Michael K; Shaw, Andrew R; Rosso, Diego
2017-03-15
This research systematically studied the behavior of aeration diffuser efficiency over time, and its relation to the energy usage per diffuser. Twelve diffusers were selected for a one year fouling study. Comprehensive aeration efficiency projections were carried out in two WRRFs with different influent rates, and the influence of operating conditions on aeration diffusers' performance was demonstrated. This study showed that the initial energy use, during the first year of operation, of those aeration diffusers located in high rate systems (with solids retention time - SRT-less than 2 days) increased more than 20% in comparison to the conventional systems (2 > SRT). Diffusers operating for three years in conventional systems presented the same fouling characteristics as those deployed in high rate processes for less than 15 months. A new procedure was developed to accurately project energy consumption on aeration diffusers; including the impacts of operation conditions, such SRT and organic loading rate, on specific aeration diffusers materials (i.e. silicone, polyurethane, EPDM, ceramic). Furthermore, it considers the microbial colonization dynamics, which successfully correlated with the increase of energy consumption (r(2):0.82 ± 7). The presented energy model projected the energy costs and the potential savings for the diffusers after three years in operation in different operating conditions. Whereas the most efficient diffusers provided potential costs spanning from 4900 USD/Month for a small plant (20 MGD, or 74,500 m(3)/d) up to 24,500 USD/Month for a large plant (100 MGD, or 375,000 m(3)/d), other diffusers presenting less efficiency provided spans from 18,000USD/Month for a small plant to 90,000 USD/Month for large plants. The aim of this methodology is to help utilities gain more insight into process mechanisms and design better energy efficiency strategies at existing facilities to reduce energy consumption.
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)
Preliminary Hybrid Modeling of the Panama Canal: Operations and Salinity Diffusion
Directory of Open Access Journals (Sweden)
Luis Rabelo
2012-01-01
Full Text Available This paper deals with the initial modeling of water salinity and its diffusion into the lakes during lock operation on the Panama Canal. A hybrid operational model was implemented using the AnyLogic software simulation environment. This was accomplished by generating an operational discrete-event simulation model and a continuous simulation model based on differential equations, which modeled the salinity diffusion in the lakes. This paper presents that unique application and includes the effective integration of lock operations and its impact on the environment.
Perpendicular Diffusion of Solar Energetic Particles: Model Results and Implications for Electrons
Strauss, R. Du Toit; Dresing, Nina; Engelbrecht, N. Eugene
2017-03-01
The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model that includes perpendicular diffusion. By implementing, as far as possible, the most reasonable estimates of the transport (diffusion) coefficients, we compare our results, in a qualitative manner, to recent observations at energies of 55–105 keV, focusing on the longitudinal distribution of the peak intensity, the maximum anisotropy, and the onset time. By using transport coefficients that are derived from first principles, we limit the number of free parameters in the model to (i) the probability of SEPs following diffusing magnetic field lines, quantified by a\\in [0,1], and (ii) the broadness of the Gaussian injection function. It is found that the model solutions are extremely sensitive to the magnitude of the perpendicular diffusion coefficient and relatively insensitive to the form of the injection function as long as a reasonable value of a = 0.2 is used. We illustrate the effects of perpendicular diffusion on the model solutions and discuss the viability of this process as a dominant mechanism by which SEPs are transported in longitude. Lastly, we try to quantity the effectiveness of perpendicular diffusion as an interplay between the magnitude of the relevant diffusion coefficient and the SEP intensity gradient driving the diffusion process. It follows that perpendicular diffusion is extremely effective early in an SEP event when large intensity gradients are present, while the effectiveness quickly decreases with time thereafter.
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...
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.
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...
Modeling cation diffusion in compacted water-saturatedNa-bentonite at low ionic strength
Energy Technology Data Exchange (ETDEWEB)
Bourg, Ian C.; Sposito, Garrison; Bourg, Alain C.M.
2007-08-28
Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the 'macropore/nanopore' model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the 'surface diffusion' model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm{sup -3} (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.2 kg dm{sup -3}.
Directory of Open Access Journals (Sweden)
Ying Liu
2015-01-01
Full Text Available Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.
A Bayesian hierarchical diffusion model decomposition of performance in Approach-Avoidance Tasks.
Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan
2015-01-01
Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach-Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest.
A simple branching model that reproduces language family and language population distributions
Schwämmle, Veit; de Oliveira, Paulo Murilo Castro
2009-07-01
Human history leaves fingerprints in human languages. Little is known about language evolution and its study is of great importance. Here we construct a simple stochastic model and compare its results to statistical data of real languages. The model is based on the recent finding that language changes occur independently of the population size. We find agreement with the data additionally assuming that languages may be distinguished by having at least one among a finite, small number of different features. This finite set is also used in order to define the distance between two languages, similarly to linguistics tradition since Swadesh.
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.
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.
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.
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...
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
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.
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.
A kinetic model for molecular diffusion through pores.
D'Agostino, Tommaso; Salis, Samuele; Ceccarelli, Matteo
2016-07-01
The number of pathogens developing multiple drug resistance is ever increasing. The impact on healthcare systems is huge and the need for novel antibiotics as well a new way to develop them is urgent, especially against Gram-negative bacteria. The first defense of these bacteria is the outer membrane, where unspecific protein channels (porins) modulate nutrients passive diffusion. Also polar antibiotics enter through this path and down-regulation and/or mutation of porins are very common in drug resistant strains. Our inability to come up with novel effective antibiotics mostly relies upon the insufficient comprehension of the key molecular features enabling better penetration through porins. Molecular dynamics simulations offer an extraordinary tool in the study of the dynamics of biological systems; however, one of the major drawbacks of this method is that its use is currently restricted to study time scales of the order of microsecond. Enhanced sampling methods like Metadynamics have been recently used to investigate the diffusion of antibiotics through bacterial porins. The main limitation is that dynamical properties cannot be estimated because of the different potential that the systems under study are experiencing. Recently, the scope of Metadynamics has been extended. By applying an a posteriori analysis one can obtain rates of transitions and rate-limiting steps of the process under study, directly comparable with kinetic data extracted from electrophysiology experiments. In this work, we apply this method to the study of the permeability of Escherichia coli's OmpF with respect to Meropenem, finding good agreement with the residence time obtained analyzing experimental current noise. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.
A hybrid transport-diffusion model for radiative transfer in absorbing and scattering media
Energy Technology Data Exchange (ETDEWEB)
Roger, M., E-mail: maxime.roger@insa-lyon.fr [Université de Lyon, CNRS, INSA-Lyon, CETHIL, UMR5008, F-69621 Villeurbanne (France); Caliot, C. [PROMES-UPR CNRS 6144, 7 rue du Four Solaire, 66120 Font Romeu Odeillo (France); Crouseilles, N. [INRIA-Rennes Bretagne-Atlantique (IPSO Project) and Université de Rennes 1 (IRMAR), Campus de Beaulieu, 35042 Rennes Cedex (France); Coelho, P.J. [Mechanical Engineering Department, LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001, Lisboa (Portugal)
2014-10-15
A new multi-scale hybrid transport-diffusion model for radiative transfer is proposed in order to improve the efficiency of the calculations close to the diffusive regime, in absorbing and strongly scattering media. In this model, the radiative intensity is decomposed into a macroscopic component calculated by the diffusion equation, and a mesoscopic component. The transport equation for the mesoscopic component allows to correct the estimation of the diffusion equation, and then to obtain the solution of the linear radiative transfer equation. In this work, results are presented for stationary and transient radiative transfer cases, in examples which concern solar concentrated and optical tomography applications. The Monte Carlo and the discrete-ordinate methods are used to solve the mesoscopic equation. It is shown that the multi-scale model allows to improve the efficiency of the calculations when the medium is close to the diffusive regime. The proposed model is a good alternative for radiative transfer at the intermediate regime where the macroscopic diffusion equation is not accurate enough and the radiative transfer equation requires too much computational effort.
Cross-diffusion induced Turing patterns in a sex-structured predator-prey model
DEFF Research Database (Denmark)
Liu, J.; Zhou, H.; Zhang, Lai
2012-01-01
In this paper, we consider a sex-structured predator-prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray-Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate...... that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions...
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.
Assessing Cognitive Processes with Diffusion Model Analyses: A Tutorial based on fast-dm-30
Directory of Open Access Journals (Sweden)
Andreas eVoss
2015-03-01
Full Text Available Diffusion models can be used to infer cognitive processes involved in fast binary decision tasks. The model assumes that information is accumulated continuously until one of two thresholds is hit. In the analysis, response time distributions from numerous trials of the decision task are used to estimate a set of parameters mapping distinct cognitive processes. In recent years, diffusion model analyses have become more and more popular in different fields of psychology. This increased popularity is based on the recent development of several software solutions for the parameter estimation. Although these programs make the application of the model relatively easy, there is a shortage of knowledge about different steps of a state-of-the-art diffusion model study. In this paper, we give a concise tutorial on diffusion modelling, and we present fast-dm-30, a thoroughly revised and extended version of the fast-dm software (Voss & Voss, 2007 for diffusion model data analysis. The most important improvement of the fast-dm version is the possibility to choose between different optimization criteria (i.e., Maximum Likelihood, Chi-Square, and Kolmogorov-Smirnov, which differ in applicability for different data sets.
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.
Generalized Density-Corrected Model for Gas Diffusivity in Variably Saturated Soils
DEFF Research Database (Denmark)
Chamindu, Deepagoda; Møldrup, Per; Schjønning, Per
2011-01-01
Accurate predictions of the soil-gas diffusivity (Dp/Do, where Dp is the soil-gas diffusion coefficient and Do is the diffusion coefficient in free air) from easily measureable parameters like air-filled porosity (ε) and soil total porosity (φ) are valuable when predicting soil aeration...... and the emission of greenhouse gases and gaseous-phase contaminants from soils. Soil type (texture) and soil density (compaction) are two key factors controlling gas diffusivity in soils. We extended a recently presented density-corrected Dp(ε)/Do model by letting both model parameters (α and β) be interdependent...... and also functions of φ. The extension was based on literature measurements on Dutch and Danish soils ranging from sand to peat. The parameter α showed a promising linear relation to total porosity, while β also varied with α following a weak linear relation. The thus generalized density-corrected (GDC...
Modelling the impact of an invasive insect via reaction-diffusion.
Roques, Lionel; Auger-Rozenberg, Marie-Anne; Roques, Alain
2008-11-01
An exotic, specialist seed chalcid, Megastigmus schimitscheki, has been introduced along with its cedar host seeds from Turkey to southeastern France during the early 1990s. It is now expanding in plantations of Atlas Cedar (Cedrus atlantica). We propose a model to predict the expansion and impact of this insect. This model couples a time-discrete equation for the ovo-larval stage with a two-dimensional reaction-diffusion equation for the adult stage, through a formula linking the solution of the reaction-diffusion equation to a seed attack rate. Two main diffusion operators, of Fokker-Planck and Fickian types, are tested. We show that taking account of the dependence of the insect mobility with respect to spatial heterogeneity, and choosing the appropriate diffusion operator, are critical factors for obtaining good predictions.
Critical branching neural networks.
Kello, Christopher T
2013-01-01
It is now well-established that intrinsic variations in human neural and behavioral activity tend to exhibit scaling laws in their fluctuations and distributions. The meaning of these scaling laws is an ongoing matter of debate between isolable causes versus pervasive causes. A spiking neural network model is presented that self-tunes to critical branching and, in doing so, simulates observed scaling laws as pervasive to neural and behavioral activity. These scaling laws are related to neural and cognitive functions, in that critical branching is shown to yield spiking activity with maximal memory and encoding capacities when analyzed using reservoir computing techniques. The model is also shown to account for findings of pervasive 1/f scaling in speech and cued response behaviors that are difficult to explain by isolable causes. Issues and questions raised by the model and its results are discussed from the perspectives of physics, neuroscience, computer and information sciences, and psychological and cognitive sciences.
Directory of Open Access Journals (Sweden)
M. M. Becker
2013-01-01
Full Text Available Common fluid models used for the description of electron transport in nonthermal discharge plasmas are subject to substantial restrictions if the electron energy transport significantly influences the discharge behaviour. A drift-diffusion approach is presented which is based on a multiterm approximation of the electron velocity distribution function and overcomes some of these restrictions. It is validated using a benchmark model and applied for the analysis of argon discharge plasmas at low and atmospheric pressure. The results are compared to those of common drift-diffusion models as well as to experimental data. It is pointed out that fluid models are able to describe nonlocal phenomena caused by electron energy transport, if the energy transport is consistently described. Numerical difficulties that frequently occur when the conventional drift-diffusion model is consistently applied are avoided by the proposed method.
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
Qualitative Analysis on a Reaction-Diffusion Prey Predator Model and the Corresponding Steady-States
Institute of Scientific and Technical Information of China (English)
Qunyi BIE; Rui PENG
2009-01-01
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem.The local and global stability of the positive constant steady-state are discussed,and then some results for nonexistence of positive non-constant steady-states are derived.
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.
Porth, O.; Vorster, M. J.; Lyutikov, M.; Engelbrecht, N. E.
2016-08-01
We study the transport of high-energy particles in pulsar wind nebulae (PWN) using three-dimensional magnetohydrodynamic (MHD) and test-particle simulations, as well as a Fokker-Planck particle transport model. The latter includes radiative and adiabatic losses, diffusion, and advection on the background flow of the simulated MHD nebula. By combining the models, the spatial evolution of flux and photon index of the X-ray synchrotron emission is modelled for the three nebulae G21.5-0.9, the inner regions of Vela, and 3C 58, thereby allowing us to derive governing parameters: the magnetic field strength, average flow velocity, and spatial diffusion coefficient. For comparison, the nebulae are also modelled with the semi-analytic Kennel & Coroniti model but the Porth et al. model generally yields better fits to the observational data. We find that high velocity fluctuations in the turbulent nebula (downstream of the termination shock) give rise to efficient diffusive transport of particles, with average Péclet number close to unity, indicating that both advection and diffusion play an important role in particle transport. We find that the diffusive transport coefficient of the order of ˜ 2 × 1027(Ls/0.42 Ly) cm2 s- 1 (Ls is the size of the termination shock) is independent of energy up to extreme particle Lorentz factors of γp ˜ 1010.
Distribution of branch lengths and phylogenetic diversity under homogeneous speciation models
Stadler, Tanja
2011-01-01
The constant rate birth--death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces `reconstructed trees' which describe the relationship between extant lineages. We derive the probability density of the length of a randomly chosen pendant edge in a reconstructed tree. For the special case of a pure-birth process with complete sampling, we also provide the probability density of the length of an interior edge, of the length of an edge descending from the root, and of the diversity (which is the sum of all edge lengths). We show that the results depend on whether the reconstructed trees are conditioned on the number of leaves, the age, or both.
Chemical kinetic modeling of a methane opposed flow diffusion flame and comparison to experiments
Energy Technology Data Exchange (ETDEWEB)
Marinov, N.M., Pitz, W.J.; Westbrook, C.K. [Lawrence Livermore National Lab., CA (United States); Vincitore, A.M.; Senka, S.M. [Univ. of California, Los Angeles, CA (United States); Lutz, A.E. [Sandia National Labs., Livermore, CA (United States)
1998-01-01
The chemical structure of an opposed flow, methane diffusion flame is studied using a chemical kinetic model and the results are compared to experimental measurements. The chemical kinetic paths leading to aromatics and polycyclic aromatics hydrocarbons (PAHs) in the diffusion flame are identified. These paths all involve resonantly stabilized radicals which include propargyl, allyl, cyclopentadienyl, and benzyl radicals. The modeling results show reasonable agreement with the experimental measurements for the large hydrocarbon aliphatic compounds, aromatics, and PAHs. the benzene was predicted to be formed primarily by the reaction sequence of Allyl plus Propargyl equals Fulvene plus H plus H followed by fulvene isomerization to benzene. Naphthalene was modeled using the reaction of benzyl with propargyl, while the combination of cyclopentadienyl radicals were shown to be a minor contributor in the diffusion flame. The agreement between the model and experiment for the four-ring PAHs was poor.
Density-Corrected Models for Gas Diffusivity and Air Permeability in Unsaturated Soil
DEFF Research Database (Denmark)
Chamindu, Deepagoda; Møldrup, Per; Schjønning, Per
2011-01-01
Accurate prediction of gas diffusivity (Dp/Do) and air permeability (ka) and their variations with air-filled porosity (e) in soil is critical for simulating subsurface migration and emission of climate gases and organic vapors. Gas diffusivity and air permeability measurements from Danish soil...... in subsurface soil. The data were regrouped into four categories based on compaction (total porosity F 0.4 m3 m-3) and soil texture (volume-based content of clay, silt, and organic matter 15%). The results suggested that soil compaction more than soil type was the major control on gas...... diffusivity and to some extent also on air permeability. We developed a density-corrected (D-C) Dp(e)/Do model as a generalized form of a previous model for Dp/ Do at -100 cm H2O of matric potential (Dp,100/Do). The D-C model performed well across soil types and density levels compared with existing models...
A comparison between the fission matrix method, the diffusion model and the transport model
Energy Technology Data Exchange (ETDEWEB)
Dehaye, B.; Hugot, F. X.; Diop, C. M. [Commissariat a l' Energie Atomique et aux Energies Alternatives, Direction de l' Energie Nucleaire, Departement de Modelisation des Systemes et Structures, CEA DEN/DM2S, PC 57, F-91191 Gif-sur-Yvette cedex (France)
2013-07-01
The fission matrix method may be used to solve the critical eigenvalue problem in a Monte Carlo simulation. This method gives us access to the different eigenvalues and eigenvectors of the transport or fission operator. We propose to compare the results obtained via the fission matrix method with those of the diffusion model, and an approximated transport model. To do so, we choose to analyse the mono-kinetic and continuous energy cases for a Godiva-inspired critical sphere. The first five eigenvalues are computed with TRIPOLI-4{sup R} and compared to the theoretical ones. An extension of the notion of the extrapolation distance is proposed for the modes other than the fundamental one. (authors)
Quasi-Brittle Fracture Modeling of Preflawed Bitumen Using a Diffuse Interface Model
Directory of Open Access Journals (Sweden)
Yue Hou
2016-01-01
Full Text Available Fundamental understandings on the bitumen fracture mechanism are vital to improve the mixture design of asphalt concrete. In this paper, a diffuse interface model, namely, phase-field method is used for modeling the quasi-brittle fracture in bitumen. This method describes the microstructure using a phase-field variable which assumes one in the intact solid and negative one in the crack region. Only the elastic energy will directly contribute to cracking. To account for the growth of cracks, a nonconserved Allen-Cahn equation is adopted to evolve the phase-field variable. Numerical simulations of fracture are performed in bituminous materials with the consideration of quasi-brittle properties. It is found that the simulation results agree well with classic fracture mechanics.
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.
Awan, Iftikhar A; Burgess, Donald R; Manion, Jeffrey A
2012-03-22
The decomposition and intramolecular H-transfer isomerization reactions of the 1-pentyl radical have been studied at temperatures of 880 to 1055 K and pressures of 80 to 680 kPa using the single pulse shock tube technique and additionally investigated with quantum chemical methods. The 1-pentyl radical was generated by shock heating dilute mixtures of 1-iodopentane and the stable products of its decomposition have been observed by postshock gas chromatographic analysis. Ethene and propene are the main olefin products and account for >97% of the carbon balance from 1-pentyl. Also produced are very small amounts of (E)-2-pentene, (Z)-2-pentene, and 1-butene. The ethene/propene product ratio is pressure dependent and varies from about 3 to 5 over the range of temperatures and pressures studied. Formation of ethene and propene can be related to the concentrations of 1-pentyl and 2-pentyl radicals in the system and the relative rates of five-center intramolecular H-transfer reactions and β C-C bond scissions. The 3-pentyl radical, formed via a four-center intramolecular H transfer, leads to 1-butene and plays only a very minor role in the system. The observed (E/Z)-2-pentenes can arise from a small amount of beta C-H bond scission in the 2-pentyl radical. The current experimental and computational results are considered in conjunction with relevant literature data from lower temperatures to develop a consistent kinetics model that reproduces the observed branching ratios and pressure effects. The present experimental results provide the first available data on the pressure dependence of the olefin product branching ratio for alkyl radical decomposition at high temperatures and require a value of = (675 ± 100) cm(-1) for the average energy transferred in deactivating collisions in an argon bath gas when an exponential-down model is employed. High pressure rate expressions for the relevant H-transfer reactions and β bond scissions are derived and a Rice Ramsberger
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.
Pattern selection in a predation model with self and cross diffusion
Institute of Scientific and Technical Information of China (English)
Wang Wei-Ming; Wang Wen-Juan; Lin Ye-Zhi; Tan Yong-Ji
2011-01-01
In this paper, we present the amplitude equations for the excited modes in a cross-diffusive predator-prey model with zero-flux boundary conditions. From these equations, the stability of patterns towards uniform and inhomogenous perturbations is determined. Furthermore, we present novel numerical evidence of six typical turing patterns, and find that the model dynamics exhibits complex pattern replications: for μ1 μ4, the stripe pattern emerges. This may enrich the pattern formation in the cross-diffusive predator-prey model.
Submodels of model of nonlinear diffusion in the inhomogeneous medium involving absorption
Energy Technology Data Exchange (ETDEWEB)
Chirkunov, Yu. A., E-mail: chr101@mail.ru [Novosibirsk State Technical University, Marks Avenue 20, Novosibirsk 630073 (Russian Federation)
2015-10-15
We study the five-parameter model, describing the process of nonlinear diffusion in an inhomogeneous medium in the presence of absorption, for which the differential equation of the model admits a continuous Lie group of transformations, acting on the set of its solutions. We found six submodels of the original model of nonlinear diffusion, with different symmetry properties. Of these six submodels, the five submodels with transient absorption, for which the absorption coefficient depends on time according to a power law, represent the greatest interest with a mathematical point of view and with the point of view of physical applications. For each of these nonlinear submodels, we obtained formulas for producing new solutions that contain arbitrary constants, and we found all invariant submodels. All essentially distinct invariant solutions describing these invariant submodels are found in an explicit form or are reduced to finding the solution of nonlinear integral equations. The presence of the arbitrary constants in the integral equations that determine these solutions provide new opportunities for analytical and numerical study of boundary value problems for the received submodels and, thus, for the original model of nonlinear diffusion. For the received invariant submodels, we studied diffusion processes for which at the initial moment of the time at a fixed point is specified as a concentration and its gradient or as a concentration and its velocity. Solving of boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. The obtained results can be used to study the diffusion of substances, diffusion of conduction electrons and other particles, diffusion of physical fields and propagation of heat in inhomogeneous medium, and also to study a turbulence (Leith model, differential
Forecasting turbulent modes with nonparametric diffusion models: Learning from noisy data
Berry, Tyrus; Harlim, John
2016-04-01
In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the availability of a noise-free training data set observing the full state space of the dynamics, in real applications we often have only partial observations which are corrupted by noise. To alleviate these practical issues, following the theory of embedology, the diffusion model is built using the delay-embedding coordinates of the data. We show that this delay embedding biases the geometry of the data in a way which extracts the most stable component of the dynamics and reduces the influence of independent additive observation noise. The resulting diffusion forecast model approximates the semigroup solutions of the generator of the underlying dynamics in the limit of large data and when the observation noise vanishes. As in any standard forecasting problem, the forecasting skill depends crucially on the accuracy of the initial conditions. We introduce a novel Bayesian method for filtering the discrete-time noisy observations which works with the diffusion forecast to determine the forecast initial densities. Numerically, we compare this nonparametric approach with standard stochastic parametric models on a wide-range of well-studied turbulent modes, including the Lorenz-96 model in weakly chaotic to fully turbulent regimes and the barotropic modes of a quasi-geostrophic model with baroclinic instabilities. We show that when the only available data is the low-dimensional set of noisy modes that are being modeled, the diffusion forecast is indeed competitive to the perfect model.
Jump diffusion models and the evolution of financial prices
Energy Technology Data Exchange (ETDEWEB)
Figueiredo, Annibal; Castro, Marcio T. de [Institute of Physics, University of Brasilia (Brazil); Silva, Sergio da [Department of Economics, Federal University of Santa Catarina (Brazil); Gleria, Iram, E-mail: iram@pq.cnpq.br [Institute of Physics, Federal University of Alagoas (Brazil)
2011-08-08
We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior. -- Highlights: → We analyze a stochastic model to describe the evolution of financial prices. → The stochastic term is considered as a sum of the Wiener noise and a jump process. → The process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. → We extend the De Finetti functions to a generalized nonlinear model.
Akimoto, Takuma; Yamamoto, Eiji
2016-12-01
Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the time-averaged diffusion coefficients are intrinsically random (irreproducible) even in the long-time measurements in non-equilibrium situations. Furthermore, the distribution of the time-averaged diffusion coefficients converges to a universal distribution in the sense that it does not depend on initial conditions. Our findings pave the way for a theoretical understanding of distributional behavior of the time-averaged diffusion coefficients in disordered systems.
Directory of Open Access Journals (Sweden)
Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
Memory Effects and Coverage Dependence of Surface Diffusion in a Model Adsorption System
DEFF Research Database (Denmark)
Vattulainen, Ilpo Tapio; Ying, S. C.; Ala-Nissila, T.
1999-01-01
diffusion is found to decay following a power law after an initial transient period. This behavior persists until the hydrodynamic regime is reached, after which the memory effect decays exponentially. The time required to reach the hydrodynamical regime and the related exponential decay is strongly......We study the coverage dependence of surface diffusion coefficients for a strongly interacting adsorption system O/W(110) via Monte Carlo simulations of a lattice-gas model. In particular, we consider the nature and emergence of memory effects as contained in the corresponding correlation factors...... influenced by both the critical effects related to long-wavelength fluctuations and the local order in the overlayer. We also analyze the influence of the memory effects on the effective diffusion barriers extracted from the Arrhenius analysis. For tracer diffusion, we find that the contribution from memory...
Rare events and their impact on velocity diffusion in a stochastic Fermi-Ulam model.
Karlis, A K; Diakonos, F K; Constantoudis, V; Schmelcher, P
2008-10-01
A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards.
Desvillettes, Laurent
2010-01-01
We study a continuous coagulation-fragmentation model with constant kernels for reacting polymers (see [M. Aizenman and T. Bak, Comm. Math. Phys., 65 (1979), pp. 203-230]). The polymers are set to diffuse within a smooth bounded one-dimensional domain with no-flux boundary conditions. In particular, we consider size-dependent diffusion coefficients, which may degenerate for small and large cluster-sizes. We prove that the entropy-entropy dissipation method applies directly in this inhomogeneous setting. We first show the necessary basic a priori estimates in dimension one, and second we show faster-than-polynomial convergence toward global equilibria for diffusion coefficients which vanish not faster than linearly for large sizes. This extends the previous results of [J.A. Carrillo, L. Desvillettes, and K. Fellner, Comm. Math. Phys., 278 (2008), pp. 433-451], which assumes that the diffusion coefficients are bounded below. © 2009 Society for Industrial and Applied Mathematics.
DSOM: a novel self-organizing model based on NO dynamic diffusing mechanism
Institute of Scientific and Technical Information of China (English)
YIN Junsong; HU Dewen; CHEN Shuang; ZHOU Zongtan
2005-01-01
In this paper the four-dimensional dynamic diffusing mechanism and the enhancement in Long-Term Potentiation (LTP) of intrinsic nitric oxide (NO) in nervous system are studied computationally. A novel unsupervised Diffusing Self-Organizing Maps (DSOM) model is presented on the union of SOM with NO diffusing mechanism. Based on the spatial prototype mapping, temporal enhancement is introduced in DSOM and the fine-tuning manner is improved by the simplified NO diffusing mechanism. Furthermore, the quantization error of optimal weights is valuated and the detailed noise analysis of DSOM is presented. Finally some typical stimulation experiments are presented to illustrate how DSOM gracefully handles time warping and multiple patterns with overlapping reference vectors.
Modelling Of Eco-innovation Diffusion: The EU Eco-label
Directory of Open Access Journals (Sweden)
KIJEK TOMASZ
2015-03-01
Full Text Available The aim of this article is to carry out a theoretical and empirical analysis of the process of eco-label diffusion. Eco-labels allow consumers to identify products and services that have a reduced environmental impact during their life cycle. Thus, they are aimed at diminishing the information gap between sellers and buyers. The results of the estimation using the Bass model indicate that the diffusion of the EU eco-label has been most dynamic in countries such as Hungary, Poland, Denmark, Germany and France. In turn, the scope of diffusion (absolute saturation level reached the highest value for companies in France and Italy. In addition, the results of the study confirm the stimulating impact of the scope of eco-label diffusion on consumer awareness of environmental issues. This finding points to the need for environmental education among consumers, which could in turn encourage firms to undertake pro-environmental actions.
Proposing an Educational Scaling-and-Diffusion Model for Inquiry-Based Learning Designs
Hung, David; Lee, Shu-Shing
2015-01-01
Education cannot adopt the linear model of scaling used by the medical sciences. "Gold standards" cannot be replicated without considering process-in-learning, diversity, and student-variedness in classrooms. This article proposes a nuanced model of educational scaling-and-diffusion, describing the scaling (top-down supports) and…
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Wagenmakers, E.-J.
2009-01-01
The Ratcliff diffusion model for simple two-choice decisions (e.g., Ratcliff, 1978; Ratcliff & McKoon, 2008) has two outstanding advantages. First, the model generally provides an excellent fit to the observed data (i.e., response accuracy and the shape of RT distributions, both for correct and erro
Spreading Speed for a Periodic Reaction-diffusion Model with Nonmonotone Birth Function
Institute of Scientific and Technical Information of China (English)
HUANG Ye-hui; WENG Pei-xuan
2012-01-01
A reaction-diffusion model for a single spccies with age structure and nonlocal reaction for periodic time t is derived.Some results about the model with monotone birth function are firstly introduced,and then by constructing two auxiliary equations and squeezing method,the spreading speed for the system with nonmonotone birth function is obtained.
A time-periodic reaction-diffusion epidemic model with infection period
Zhang, Liang; Wang, Zhi-Cheng
2016-10-01
In this paper, we propose a time-periodic and diffusive SIR epidemic model with constant infection period. By introducing the basic reproduction number R_0 via a next generation operator for this model, we show that the disease goes extinction if R_0 1.
On the well posedness and further regularity of a diffusive three species aquatic model
Parshad, R.D.
2012-01-01
We consider Upadhay\\'s three species aquatic food chain model, with the inclusion of spatial spread. This is a well established food chain model for the interaction of three given aquatic species. It exhibits rich dynamical behavior, including chaos. We prove the existence of a global weak solution to the diffusive system, followed by existence of local mild and strong solution.
Energy Technology Data Exchange (ETDEWEB)
Barbante, Paolo [Dipartimento di Matematica, Politecnico di Milano - Piazza Leonardo da Vinci 32 - 20133 Milano (Italy); Frezzotti, Aldo; Gibelli, Livio [Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano - Via La Masa 34 - 20156 Milano (Italy)
2014-12-09
The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviations of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.
Weak localization as a definitive test of diffusive models in the Casimir effect
Allocca, Andrew; Wilson, Justin; Galitski, Victor
2015-03-01
Results from many measurements of the Casimir effect suggest that the metallic plates in these experiments should be modeled with the plasma model of free electrons as opposed to the naive diffusive Drude model, while other experiments seem to indicate the exact opposite, with results more in line with a diffusive model. We study the Casimir effect at low temperatures between a thick disordered plate and purely two-dimensional disordered system where the Drude conductivity decreases logarithmically at low temperatures due to weak localization. This effect can be tuned with either temperature or applied magnetic field leading to a measurable change in the Casimir force. On the other hand, a ballistic model cannot experience such an effect and is only weakly dependent on temperature and magnetic field. As a result, we propose that an experiment would unambiguously differentiate between diffusive and ballistic models by measuring the effect at low temperatures with an applied magnetic field. Additionally, we calculate the impact that fluctuations in the disorder distribution have on the Casimir effect. Assuming the validity of a diffusive model, we find that the Drude model is a good approximation of a more exact treatment of disorder. This work was supported by the DOE-BES (Grant No. DESC0001911) (A.A. and V.G.), the JQI-PFC (J.W.), and the Simons Foundation.
Improvement of the One-dimensional Vertical Advection-diffusion Model in Seawater
Institute of Scientific and Technical Information of China (English)
王保栋; 单宝田; 战闰; 王修林
2003-01-01
The classical 1-D vertical advection-diffusion model was improved in this work. Themain advantages of the improved model over the previous one are: 1 ) The applicable condition ofthe 1-D model is made clear in the improved model, in that it is substantively applicable only to avertical domain on which two end-member water masses are mixing. 2) The substitution of parame-ter f(z) in the equation of the classical 1-D model with end-member fraction f1 makes the modelmore precisely and easily solved. 3 ) All the terms in the improved model equation have specificphysical meanings, which makes the model easily understood. Practical application of the improvedmodel to predict the vertical profiles of dissolved oxygen and micronutrients in abyssal ocean waterof the North Pacific proved that the improvement of the 1-D advection-diffusion model is successfuland practicable.
Jump diffusion models and the evolution of financial prices
Figueiredo, Annibal; de Castro, Marcio T.; da Silva, Sergio; Gleria, Iram
2011-08-01
We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior.
The effect of a realistic thermal diffusivity on numerical model of a subducting slab
Maierova, P.; Steinle-Neumann, G.; Cadek, O.
2010-12-01
A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the
Effects of spatial diffusion on nonequilibrium steady states in a model for prebiotic evolution
Intoy, B. F.; Wynveen, A.; Halley, J. W.
2016-10-01
Effects of spatial diffusion in a Kauffman-like model for prebiotic evolution previously studied in a "well-mixed" limit are reported. The previous model was parametrized by a parameter p defined as the probability that a possible reaction in a network of reactions characterizing the artificial chemistry actually appears in the chemical network. In the model reported here, we numerically study a grid of such well-mixed reactors on a two-dimensional spatial lattice in which the model chemical constituents can hop between neighboring reactors at a rate controlled by a second parameter η . We report the frequency of appearance of three distinct types of nonequilibrium steady states, characterized as "diffusively alive locally dead" (DALD), "diffusively dead locally alive" (DDLA) and "diffusively alive locally alive" (DALA). The types are defined according to whether they are chemically equilibrated at each site, diffusively equilibrated between sites, or neither, respectively. With our parametrization of the definitions of these nonequilibrium states, many of the DALA states are growing rapidly in population due to the explosive population growth of a few sites, while their entropy remains well below its equilibrium value. Sharp temporal transitions occur as exploding sites appear. DALD states occur less commonly than the other types and also usually harbor a few explosively growing sites but transitions are less sharp than in DALA systems.
Mathematical model of diffusion-limited evolution of multiple gas bubbles in tissue.
Srinivasan, R Srini; Gerth, Wayne A; Powell, Michael R
2003-04-01
Models of gas bubble dynamics employed in probabilistic analyses of decompression sickness incidence in man must be theoretically consistent and simple, if they are to yield useful results without requiring excessive computations. They are generally formulated in terms of ordinary differential equations that describe diffusion-limited gas exchange between a gas bubble and the extravascular tissue surrounding it. In our previous model (Ann. Biomed. Eng. 30: 232-246, 2002), we showed that with appropriate representation of sink pressures to account for gas loss or gain due to heterogeneous blood perfusion in the unstirred diffusion region around the bubble, diffusion-limited bubble growth in a tissue of finite volume can be simulated without postulating a boundary layer across which gas flux is discontinuous. However, interactions between two or more bubbles caused by competition for available gas cannot be considered in this model, because the diffusion region has a fixed volume with zero gas flux at its outer boundary. The present work extends the previous model to accommodate interactions among multiple bubbles by allowing the diffusion region volume of each bubble to vary during bubble evolution. For given decompression and tissue volume, bubble growth is sustained only if the bubble number density is below a certain maximum.
Wang, Junjian; Kang, Qinjun; Rahman, Sheik S
2016-01-01
Gas flow in shale is associated with both organic matter (OM) and inorganic matter (IOM) which contain nanopores ranging in size from a few to hundreds of nanometers. In addition to the noncontinuum effect which leads to an apparent permeability of gas higher than the intrinsic permeability, the surface diffusion of adsorbed gas in organic pores also can influence the apparent permeability through its own transport mechanism. In this study, a generalized lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed shale matrix consisting of OM and IOM. The Expectation-Maximization (EM) algorithm is used to assign the pore size distribution to each component, and the dusty gas model (DGM) and generalized Maxwell-Stefan model (GMS) are adopted to calculate the apparent permeability accounting for multiple transport mechanisms including viscous flow, Knudsen diffusion and surface diffusion. Effects of pore radius and pressure on permeability of both IOM and OM as well as effects of Langmuir ...
On strongly degenerate convection-diffusion Problems Modeling sedimentation-consolidation Processes
Energy Technology Data Exchange (ETDEWEB)
Buerger, R.; Evje, S.; Karlsen, S. Hvistendahl
1999-10-01
This report investigates initial-boundary value problems for a quasilinear strongly degenerate convection-diffusion equation with a discontinuous diffusion coefficient. These problems come from the mathematical modelling of certain sedimentation-consolidation processes. Existence of entropy solutions belonging to BV is shown by the vanishing viscosity method. The existence proof for one of the models includes a new regularity result for the integrated diffusion coefficient. New uniqueness proofs for entropy solutions are also presented. These proofs rely on a recent extension to second order equations of Kruzkov`s method of `doubling of the variables`. The application to a sedimentation-consolidation model is illustrated by two numerical examples. 25 refs., 2 figs.
Mutual diffusion coefficient models for polymer-solvent systems based on the Chapman-Enskog theory
Directory of Open Access Journals (Sweden)
R. A. Reis
2004-12-01
Full Text Available There are numerous examples of the importance of small molecule migration in polymeric materials, such as in drying polymeric packing, controlled drug delivery, formation of films, and membrane separation, etc. The Chapman-Enskog kinetic theory of hard-sphere fluids with the Weeks-Chandler-Andersen effective hard-sphere diameter (Enskog-WCA has been the most fruitful in diffusion studies of simple fluids and mixtures. In this work, the ability of the Enskog-WCA model to describe the temperature and concentration dependence of the mutual diffusion coefficient, D, for a polystyrene-toluene system was evaluated. Using experimental diffusion data, two polymer model approaches and three mixing rules for the effective hard-sphere diameter were tested. Some procedures tested resulted in models that are capable of correlating the experimental data with the refereed system well for a solvent mass fraction greater than 0.3.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Natural gas diffusion through the cap rock is mainly by means ofdissolving in water, so its concentration can be replaced by solubility, which varies with temperature, pressure and salinity in strata. Under certain geological conditions the maximal solubility is definite, so the diffusion com-putation can be handled approximately by stable state equation. Furthermore, on the basis of the restoration of the paleo-buried history, the diffusion is calculated with the dynamic method, and the result is very close to the real diffusion value in the geological history.
Directory of Open Access Journals (Sweden)
JAIR RODRIGUES GARCIA-JÃŠNIOR
2009-07-01
Full Text Available
The influence of supplementary-branched chain amino acids (BCAA on 65Zn metabolism in rats was investigated in this study. Nutritional indicators of Zn, as absorption, body retention and secretion, were estimated using a multicompartment model. Two groups of eight male rats were force-fed a zinc-adequate diet (control group and a zinc-adequate diet plus 0.52 9 BCAA/kg diet during 15 days. There was no significant difference for intake of Zn, absorption (34%, intestinal transit (tso and the leveI of Zn in the intravascular compartment (plasma. On the other hand the extravascular compartment (organs and specific concentration of Zn per 9 of tissue decreased after experimental period (p < 0.05 The rats supplememted with BCAA secreted Zn by urine twice faster than controls, but the secrotion of zinc by endogen feces were not decreased in this group. Thus, BCAA supplement changed the kinetic of Zn, increasing the urinary secretion and the loss of Zn from the body.
Jacquemet, Vincent
2010-09-01
Microscale electrical propagation in the heart can be modeled by a reaction-diffusion system, describing cell and tissue electrophysiology. Macroscale features of wavefront propagation can be reproduced by an eikonal model, a reduced formulation involving only wavefront shape. In this paper, these two approaches are combined to incorporate global information about reentrant pathways into a reaction-diffusion model. The eikonal-diffusion formulation is generalized to handle reentrant activation patterns and wavefront collisions. Boundary conditions are used to specify pathways of reentry. Finite-element-based numerical methods are presented to solve this nonlinear equation on a coarse triangular mesh. The macroscale eikonal model serves to construct an initial condition for the microscale reaction-diffusion model. Electrical propagation simulated from this initial condition is then compared to the isochrones predicted by the eikonal model. Results in 2-D and thin 3-D test-case geometries demonstrate the ability of this technique to initiate anatomical and functional reentries along prescribed pathways, thus facilitating the development of dedicated models aimed at better understanding clinical case reports.
A diffusion-precipitation model for gaseous nitriding of Fe-2 wt.% V alloy
Energy Technology Data Exchange (ETDEWEB)
Kouba, R., E-mail: r_kouba11@yahoo.fr [Departement SDM, Laboratoire de Technologie des Materiaux, Faculte de Genie Mecanique et Genie des Procedes, USTHB, BP 32 El-Alia, 16111 Alger (Algeria); Keddam, M. [Departement SDM, Laboratoire de Technologie des Materiaux, Faculte de Genie Mecanique et Genie des Procedes, USTHB, BP 32 El-Alia, 16111 Alger (Algeria); Djeghlal, M.E. [Laboratoire LSGM, Departement de Metallurgie, Ecole Nationale Polytechnique, 10 Avenue Hassen Badi, BP 182-16200 El Harrach (Algeria)
2012-09-25
Highlights: Black-Right-Pointing-Pointer Simulation of binary Fe-V nitriding was realized on the diffusion zone. Black-Right-Pointing-Pointer The model takes into account nitrogen diffusion in ferrite and VN precipitation. Black-Right-Pointing-Pointer VN precipitation was considered via thermodynamic equilibrium calculation. Black-Right-Pointing-Pointer The model predicts nitrogen profile and highlights nitrogen excess phenomenon. Black-Right-Pointing-Pointer The model was validated by using experimental data available on literature. - Abstract: A diffusion-precipitation model for gaseous nitriding of a Fe-2 wt.% V binary alloy has been presented. The nitriding treatment is assumed to be completely realized in the ferritic zone. The model takes into account both nitrogen diffusion and vanadium nitride precipitation. The VN precipitation was obtained with the assumption that it exists a local thermodynamic equilibrium between the matrix phase and the precipitate. The thermodynamic equilibrium calculations are based on Gibbs energies minimization, which were performed by the Thermocalc software. The suggested model allowed the prediction of the nitrogen profiles, and also takes into account the nitrogen excess phenomenon. This nitrogen excess has been explained by the presence of iron atoms within the precipitate. The theoretical results of the model have been compared to the experimental data given in the literature. A good agreement was then noticed between the experimental data and the numerical results.
American Society for Testing and Materials. Philadelphia
2008-01-01
1.1 This test method provides procedures for measuring the leach rates of elements from a solidified matrix material, determining if the releases are controlled by mass diffusion, computing values of diffusion constants based on models, and verifying projected long-term diffusive releases. This test method is applicable to any material that does not degrade or deform during the test. 1.1.1 If mass diffusion is the dominant step in the leaching mechanism, then the results of this test can be used to calculate diffusion coefficients using mathematical diffusion models. A computer program developed for that purpose is available as a companion to this test method (Note 1). 1.1.2 It should be verified that leaching is controlled by diffusion by a means other than analysis of the leach test solution data. Analysis of concentration profiles of species of interest near the surface of the solid waste form after the test is recommended for this purpose. 1.1.3 Potential effects of partitioning on the test results can...
Modeling photovoltaic diffusion: an analysis of geospatial datasets
Davidson, Carolyn; Drury, Easan; Lopez, Anthony; Elmore, Ryan; Margolis, Robert
2014-07-01
This study combines address-level residential photovoltaic (PV) adoption trends in California with several types of geospatial information—population demographics, housing characteristics, foreclosure rates, solar irradiance, vehicle ownership preferences, and others—to identify which subsets of geospatial information are the best predictors of historical PV adoption. Number of rooms, heating source and house age were key variables that had not been previously explored in the literature, but are consistent with the expected profile of a PV adopter. The strong relationship provided by foreclosure indicators and mortgage status have less of an intuitive connection to PV adoption, but may be highly correlated with characteristics inherent in PV adopters. Next, we explore how these predictive factors and model performance varies between different Investor Owned Utility (IOU) regions in California, and at different spatial scales. Results suggest that models trained with small subsets of geospatial information (five to eight variables) may provide similar explanatory power as models using hundreds of geospatial variables. Further, the predictive performance of models generally decreases at higher resolution, i.e., below ZIP code level since several geospatial variables with coarse native resolution become less useful for representing high resolution variations in PV adoption trends. However, for California we find that model performance improves if parameters are trained at the regional IOU level rather than the state-wide level. We also find that models trained within one IOU region are generally representative for other IOU regions in CA, suggesting that a model trained with data from one state may be applicable in another state.
Konukoglu, Ender; Clatz, Olivier; Menze, Bjoern H; Stieltjes, Bram; Weber, Marc-André; Mandonnet, Emmanuel; Delingette, Hervé; Ayache, Nicholas
2010-01-01
Reaction-diffusion based tumor growth models have been widely used in the literature for modeling the growth of brain gliomas. Lately, recent models have started integrating medical images in their formulation. Including different tissue types, geometry of the brain and the directions of white matter fiber tracts improved the spatial accuracy of reaction-diffusion models. The adaptation of the general model to the specific patient cases on the other hand has not been studied thoroughly yet. In this paper, we address this adaptation. We propose a parameter estimation method for reaction-diffusion tumor growth models using time series of medical images. This method estimates the patient specific parameters of the model using the images of the patient taken at successive time instances. The proposed method formulates the evolution of the tumor delineation visible in the images based on the reaction-diffusion dynamics; therefore, it remains consistent with the information available. We perform thorough analysis of the method using synthetic tumors and show important couplings between parameters of the reaction-diffusion model. We show that several parameters can be uniquely identified in the case of fixing one parameter, namely the proliferation rate of tumor cells. Moreover, regardless of the value the proliferation rate is fixed to, the speed of growth of the tumor can be estimated in terms of the model parameters with accuracy. We also show that using the model-based speed, we can simulate the evolution of the tumor for the specific patient case. Finally, we apply our method to two real cases and show promising preliminary results.
Lin, Guoxing
2017-02-01
Pulsed field gradient (PFG) technique is a noninvasive tool, and has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is much more complicated than normal diffusion. In this paper, a fractal derivative model based modified Gaussian phase distribution method is proposed to describe PFG anomalous diffusion. By using the phase distribution obtained from the effective phase shift diffusion method based on fractal derivatives, and employing some of the traditional Gaussian phase distribution approximation techniques, a general signal attenuation expression for free fractional diffusion is derived. This expression describes a stretched exponential function based attenuation, which is distinct from both the exponential attenuation for normal diffusion obtained from conventional Gaussian phase distribution approximation, and the Mittag-Leffler function based attenuation for anomalous diffusion obtained from fractional derivative. The obtained signal attenuation expression can analyze the finite gradient pulse width (FGPW) effect. Additionally, it can generally be applied to all three types of PFG fractional diffusions classified based on time derivative order α and space derivative order β. These three types of fractional diffusions include time-fractional diffusion with { 0 reported results based on effective phase shift diffusion equation method and instantaneous signal attenuation method. This method provides a new, convenient approximation formalism for analyzing PFG anomalous diffusion experiments. The expression that can simultaneously interpret general fractional diffusion and FGPW effect could be especially important in PFG MRI, where the narrow gradient pulse limit cannot be satisfied.
A Jump-Diffusion Model with Stochastic Volatility and Durations
DEFF Research Database (Denmark)
Wei, Wei; Pelletier, Denis
Market microstructure theories suggest that the durations between transactions carry information about volatility. This paper puts forward a model featuring stochastic volatility, stochastic conditional duration, and jumps to analyze high frequency returns and durations. Durations affect price...... jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate Ornstein-Ulenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps....... The algorithm provides smoothed estimates of the latent variables such as spot volatility, conditional duration, jump times, and jump sizes. We apply this model to IBM data and find that volatility and conditional duration are interdependent. We also find that jumps play an important role in return variation...
Diffusive dynamics and stochastic models of turbulent axisymmetric wakes
Rigas, G; Brackston, R D; Morrison, J F
2015-01-01
A modelling methodology to reproduce the experimental measurements of a turbulent flow under the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake- flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries which occur at the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.
Fitting the CDO correlation skew: a tractable structural jump-diffusion model
DEFF Research Database (Denmark)
Willemann, Søren
2007-01-01
We extend a well-known structural jump-diffusion model for credit risk to handle both correlations through diffusion of asset values and common jumps in asset value. Through a simplifying assumption on the default timing and efficient numerical techniques, we develop a semi-analytic framework...... allowing for instantaneous calibration to heterogeneous CDS curves and fast computation of CDO tranche spreads. We calibrate the model to CDX and iTraxx data from February 2007 and achieve a satisfactory fit. To price the senior tranches for both indices, we require a risk-neutral probability of a market...
Parameters estimation using the first passage times method in a jump-diffusion model
Khaldi, K.; Meddahi, S.
2016-06-01
The main purposes of this paper are two contributions: (1) it presents a new method, which is the first passage time (FPT method) generalized for all passage times (GPT method), in order to estimate the parameters of stochastic Jump-Diffusion process. (2) it compares in a time series model, share price of gold, the empirical results of the estimation and forecasts obtained with the GPT method and those obtained by the moments method and the FPT method applied to the Merton Jump-Diffusion (MJD) model.
Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric
2003-03-01
We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.
Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
Li, Shanbing; Wu, Jianhua; Dong, Yaying
2015-09-01
In this paper, we consider a reaction-diffusion model with Degn-Harrison reaction scheme. Some fundamental analytic properties of nonconstant positive solutions are first investigated. We next study the stability of constant steady-state solution to both ODE and PDE models. Our result also indicates that if either the size of the reactor or the effective diffusion rate is large enough, then the system does not admit nonconstant positive solutions. Finally, we establish the global structure of steady-state bifurcations from simple eigenvalues by bifurcation theory and the local structure of the steady-state bifurcations from double eigenvalues by the techniques of space decomposition and implicit function theorem.
Inhomogeneous diffusion model for recent data on high-energy cosmic rays
Tomassetti, Nicola
2015-01-01
The AMS Collaboration has recently released precision data on cosmic ray (CR) leptons and protons at high energies. Interesting progresses have also been made on the measurement of CR nuclei, such as the boron-to-carbon ratio or the lithium spectrum, up to TeV/nucleon energies. In order to provide a description these data, I consider a diffusion model of CR propagation which allows for latitudinal variations of the CR diffusion properties in the Galactic halo. I discuss the role of high-precision data on light CR nuclei in resolutely testing this model and the key propagation parameters.
High-Resolution Numerical Model for Shallow Water Flows and Pollutant Diffusions
Institute of Scientific and Technical Information of China (English)
王嘉松; 何友声
2002-01-01
A finite-volume high-resolution numerical model for coupling the shallow water flows and pollutant diffusions was presented based on using a hybrid TVD scheme in space discretization and a Runge-Kutta method in time discretization. Numerical simulations for modelling dam- break, enlarging open channel flow and pollutant dispersion were implemented and compared with experimental data or other published computations. The validation of this method shows that it can not only deal with the problem involving discontinuities and unsteady flows, but also solve the general shallow water flows and pollutant diffusions.
Density of capillaries and the oxygen diffusion model in the porous silk fibroin film
Institute of Scientific and Technical Information of China (English)
BAI Lun; XU Jianmei; SUN Qilong; DI Chuanxia; ZUO Baoqi; GUAN Guoping; WU Zhenyu
2007-01-01
In order to obtain porous silk fibroin films(PSFFs)fit for the repair of different tissues and organs and design the configuration of the PSFFs more rationally,a model of the oxygen diffusing system of the capillary was built,and also the equations of the model were solved.Moreover,the relationships between the distribution of the oxygen concentration and each affecting factors were discussed,a method was developed to estimate the density of the capillaries in the tissue,and hereby discussed the characteristics of the oxygen diffusion in the tissues around the open capillaries.
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
Diffusion of active particles with stochastic torques modeled as α-stable noise
Nötel, Jörg; Sokolov, Igor M.; Schimansky-Geier, Lutz
2017-01-01
We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a Lévy-stable noise. Two situations are investigated. First, we study white Lévy noise where the constant speed and the angular noise generate a persistent motion characterized by the persistence time {τ }D. At this time scale the crossover from ballistic to normal diffusive behavior is observed. The corresponding diffusion coefficient can be obtained analytically for the whole class of symmetric α-stable noises. As typical for models with noise-driven angular dynamics, the diffusion coefficient depends non-monotonously on the angular noise intensity. As second example, we study angular noise as described by an Ornstein–Uhlenbeck process with correlation time {τ }c driven by the Cauchy white noise. We discuss the asymptotic diffusive properties of this model and obtain the same analytical expression for the diffusion coefficient as in the first case which is thus independent on {τ }c. Remarkably, for {τ }c\\gt {τ }D the crossover from a non-Gaussian to a Gaussian distribution of displacements takes place at a time {τ }G which can be considerably larger than the persistence time {τ }D.
Yao, Yi; Berkowitz, Max L; Kanai, Yosuke
2015-12-28
The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na(+) and K(+) ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.
Social Content Recommendation Based on Spatial-Temporal Aware Diffusion Modeling in Social Networks
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Farman Ullah
2016-09-01
Full Text Available User interactions in online social networks (OSNs enable the spread of information and enhance the information dissemination process, but at the same time they exacerbate the information overload problem. In this paper, we propose a social content recommendation method based on spatial-temporal aware controlled information diffusion modeling in OSNs. Users interact more frequently when they are close to each other geographically, have similar behaviors, and fall into similar demographic categories. Considering these facts, we propose multicriteria-based social ties relationship and temporal-aware probabilistic information diffusion modeling for controlled information spread maximization in OSNs. The proposed social ties relationship modeling takes into account user spatial information, content trust, opinion similarity, and demographics. We suggest a ranking algorithm that considers the user ties strength with friends and friends-of-friends to rank users in OSNs and select highly influential injection nodes. These nodes are able to improve social content recommendations, minimize information diffusion time, and maximize information spread. Furthermore, the proposed temporal-aware probabilistic diffusion process categorizes the nodes and diffuses the recommended content to only those users who are highly influential and can enhance information dissemination. The experimental results show the effectiveness of the proposed scheme.
Directory of Open Access Journals (Sweden)
J. Y. Tang
2014-01-01
Full Text Available Representation of gaseous diffusion in variably saturated near-surface soils is becoming more common in land biogeochemical models, yet the formulations and numerical solution algorithms applied vary widely. We present three different but equivalent formulations of the dual-phase (gaseous and aqueous tracer diffusion transport problem that is relevant to a wide class of volatile tracers in land biogeochemical models. Of these three formulations (i.e., the gas-primary, aqueous-primary, and bulk tracer based formulations, we contend the gas-primary formulation is the most convenient for modeling tracer dynamics in biogeochemical models. We then provide finite volume approximation to the gas-primary equation and evaluate its accuracy against three analytical models: one for steady-state soil CO2 dynamics, one for steady-state soil CO2 dynamics, and one for transient tracer diffusion from a constant point source into two different sequentially aligned medias. All evaluations demonstrated good accuracy of the numerical approximation. We expect our result will standardize an efficient mechanistic numerical method for solving relatively simple, multi-phase, one-dimensional diffusion problems in land models.
Hood, L. L.
1983-01-01
A modeling analysis is carried out of six experimental phase space density profiles for nearly equatorially mirroring protons using methods based on the approach of Thomsen et al. (1977). The form of the time-averaged radial diffusion coefficient D(L) that gives an optimal fit to the experimental profiles is determined under the assumption that simple satellite plus Ring E absorption of inwardly diffusing particles and steady-state radial diffusion are the dominant physical processes affecting the proton data in the L range that is modeled. An extension of the single-satellite model employed by Thomsen et al. to a model that includes multisatellite and ring absorption is described, and the procedures adopted for estimating characteristic satellite and ring absorption times are defined. The results obtained in applying three representative solid-body absorption models to evaluate D(L) in the range where L is between 4 and 16 are reported, and a study is made of the sensitivity of the preferred amplitude and L dependence for D(L) to the assumed model parameters. The inferred form of D(L) is then compared with that which would be predicted if various proposed physical mechanisms for driving magnetospheric radial diffusion are operative at Saturn.
The Reactive-Diffusive Length of OH and Ozone in Model Organic Aerosols.
Lee, Lance; Wilson, Kevin
2016-09-01
A key step in the heterogeneous oxidation of atmospheric aerosols is the reaction of ozone (O3) and hydroxyl radicals (OH) at the gas-particle interface. The formation of reaction products and free radical intermediates and their spatial distribution inside the particle is a sensitive function of the length over which these oxidants diffuse prior to reaction. The reactive-diffusive length of OH and ozone at organic aerosol interfaces is determined by observing the change in the effective uptake coefficient for size-selected model aerosols comprising a reactive core and a thin nanometer-sized (0-12 nm) organic shell. The core and shell materials are selected so that they are immiscible and adopt an assumed core-shell configuration. The results indicate a reactive-diffusive length of 1.4 nm for hydroxyl (OH) radicals in squalane and 1.0 nm for ozone in squalene. Measurements for a purely diffusive system allow for an estimate for diffusion constant (1.6 × 10(-6) cm(2)/s) of ozone in squalane to be determined. The reactive-diffusive length offers a simple first order estimate of how shielding of aerosols by immiscible layers can alter estimates of oxidative lifetimes of aerosols in the atmosphere.
Uniform asymptotic approximation of diffusion to a small target: Generalized reaction models
Isaacson, Samuel A.; Mauro, Ava J.; Newby, Jay
2016-10-01
The diffusion of a reactant to a binding target plays a key role in many biological processes. The reaction radius at which the reactant and target may interact is often a small parameter relative to the diameter of the domain in which the reactant diffuses. We develop uniform in time asymptotic expansions in the reaction radius of the full solution to the corresponding diffusion equations for two separate reactant-target interaction mechanisms: the Doi or volume reactivity model and the Smoluchowski-Collins-Kimball partial-absorption surface reactivity model. In the former, the reactant and target react with a fixed probability per unit time when within a specified separation. In the latter, upon reaching a fixed separation, they probabilistically react or the reactant reflects away from the target. Expansions of the solution to each model are constructed by projecting out the contribution of the first eigenvalue and eigenfunction to the solution of the diffusion equation and then developing matched asymptotic expansions in Laplace-transform space. Our approach offers an equivalent, but alternative, method to the pseudopotential approach we previously employed [Isaacson and Newby, Phys. Rev. E 88, 012820 (2013), 10.1103/PhysRevE.88.012820] for the simpler Smoluchowski pure-absorption reaction mechanism. We find that the resulting asymptotic expansions of the diffusion equation solutions are identical with the exception of one parameter: the diffusion-limited reaction rates of the Doi and partial-absorption models. This demonstrates that for biological systems in which the reaction radius is a small parameter, properly calibrated Doi and partial-absorption models may be functionally equivalent.
An analytical model for estimating water exchange rate in white matter using diffusion MRI.
Davoodi-Bojd, Esmaeil; Chopp, Michael; Soltanian-Zadeh, Hamid; Wang, Shiyang; Ding, Guangliang; Jiang, Quan
2014-01-01
Substantial effort is being expended on using micro-structural modeling of the white matter, with the goal of relating diffusion weighted magnetic resonance imaging (DWMRI) to the underlying structure of the tissue, such as axonal density. However, one of the important parameters affecting diffusion is the water exchange rate between the intra- and extra-axonal space, which has not been fully investigated and is a crucial marker of brain injury such as multiple sclerosis (MS), stroke, and traumatic brain injury (TBI). To our knowledge, there is no diffusion analytical model which includes the Water eXchange Rate (WXR) without the requirement of short gradient pulse (SGP) approximation. We therefore propose a new analytical model by deriving the diffusion signal for a permeable cylinder, assuming a clinically feasible pulse gradient spin echo (PGSE) sequence. Simulations based on Markov Random Walk confirm that the exchange parameter included in our model has a linear correlation (R2>0.88) with the actual WXR. Moreover, increasing WXR causes the estimated values of diameter and volume fraction of the cylinders to increase and decrease, respectively, which is consistent with our findings from histology measurements in tissues near TBI regions. This model was also applied to the diffusion signal acquired from ex vivo brains of 14 male (10 TBI and 4 normal) rats using hybrid diffusion imaging. The estimated values of axon diameter and axonal volume fraction are in agreement with their corresponding histological measurements in normal brains, with 0.96 intra-class correlation coefficient value resulting from consistency analysis. Moreover, a significant increase (p = 0.001) in WXR and diameter and decrease in axonal volume fraction in the TBI boundary were detected in the TBI rats compared with the normal rats.
STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies
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Hepburn Iain
2012-05-01
Full Text Available Abstract Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins, conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates
Fluid particle diffusion in a semidilute suspension of model micro-organisms.
Ishikawa, Takuji; Locsei, J T; Pedley, T J
2010-08-01
We calculate non-Brownian fluid particle diffusion in a semidilute suspension of swimming micro-organisms. Each micro-organism is modeled as a spherical squirmer, and their motions in an infinite suspension otherwise at rest are computed by the Stokesian-dynamics method. In calculating the fluid particle motions, we propose a numerical method based on a combination of the boundary element technique and Stokesian dynamics. We present details of the numerical method and examine its accuracy. The limitation of semidiluteness is required to ensure accuracy of the fluid particle velocity calculation. In the case of a suspension of non-bottom-heavy squirmers the spreading of fluid particles becomes diffusive in a shorter time than that of the squirmers, and the diffusivity of fluid particles is smaller than that of squirmers. It is confirmed that the probability density distribution of fluid particles also shows diffusive properties. The effect of tracer particle size is investigated by inserting some inert spheres of the same radius as the squirmers, instead of fluid particles, into the suspension. The diffusivity for inert spheres is not less than one tenth of that for fluid particles, even though the particle size is totally different. Scaling analysis indicates that the diffusivity of fluid particles and inert spheres becomes proportional to the volume fraction of squirmers in the semidilute regime provided that there is no more than a small recirculation region around a squirmer, which is confirmed numerically. In the case of a suspension of bottom-heavy squirmers, horizontal diffusivity decreases considerably even with small values of the bottom heaviness, which indicates the importance of bottom heaviness in the diffusion phenomena. We believe that these fundamental findings will enhance our understanding of the basic mechanics of a suspension of swimming micro-organisms.
Minimal model for short-time diffusion in periodic potentials.
Emary, Clive; Gernert, Robert; Klapp, Sabine H L
2012-12-01
We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the density field, that is, average position and the mean-squared displacement, show nontrivial (nondiffusive) short-time behavior characterized by the appearance of plateaus. We demonstrate that this "cage-like" dynamics can be well described by a discretized master equation model involving two states (related to two positions) within each potential valley. Nontrivial predictions of our approach include analytic expressions for the plateau heights and an estimate of the "de-caging time" obtained from the study of deviations from Gaussian behavior. The simplicity of our approach means that it offers a minimal model to describe the short-time behavior of systems with hindered dynamics.
Rule-based spatial modeling with diffusing, geometrically constrained molecules
Lohel Maiko; Lenser Thorsten; Ibrahim Bashar; Gruenert Gerd; Hinze Thomas; Dittrich Peter
2010-01-01
Abstract Background We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction net...
Basan, Markus; Lenz, Martin; Joanny, Jean-François; Risler, Thomas
2015-01-01
Contact inhibition is the process by which cells switch from a motile growing state to a passive and stabilized state upon touching their neighbors. When two cells touch, an adhesion link is created between them by means of transmembrane E-cadherin proteins. Simultaneously, their actin filaments stop polymerizing in the direction perpendicular to the membrane and reorganize to create an apical belt that colocalizes with the adhesion links. Here, we propose a detailed quantitative model of the role of the cytoplasmic $\\beta$-catenin and $\\alpha$-catenin proteins in this process, treated as a reaction-diffusion system. Upon cell-cell contact, the concentration in $\\alpha$-catenin dimers increases, inhibiting actin branching and thereby reducing cellular motility and expansion pressure. This model provides a mechanism for contact inhibition that could explain previously unrelated experimental findings on the role played by E-cadherin, $\\beta$-catenin and $\\alpha$-catenin in the cellular phenotype and in tumorige...
Longtime Behavior for Mutually Catalytic Branching with Negative Correlations
Doering, Leif
2011-01-01
In several examples, dualities for interacting diffusion and particle systems permit the study of the longtime behavior of solutions. A particularly difficult model in which many techniques collapse is a two-type model with mutually catalytic interaction introduced by Dawson/Perkins for which they proved under some assumptions a dichotomy between extinction and coexistence directly from the defining equations. In the present article we show how to prove a precise dichotomy for a related model with negatively correlated noises. The proof combines a self-duality to ensure uniform integrability via moment bounds on exit-times of correlated Brownian motions from the first quadrant and explicit second moment calculations. Since the uniform integrability bound is independent of the branching rate our proof can be extended to infinite branching rate processes.
The Illumination Model of the Valley Based on the Diffuse Reflect of Forest
Directory of Open Access Journals (Sweden)
He Guoliang
2016-01-01
Full Text Available In this paper, models are build to evaluate the impact of the forest on the valley’s illumination. Based on the assumes that all the light reach the ground comes from the diffuse reflection which comes from the sun directly and from the diffuse reflection of other points, One model is build to consider the impact of time and latitude on the direction of the sunlight. So we can get the direction of the sunlight at different time and latitude through the model. Besides, this paper develops a illumination model to evaluate the intensity of illumination of the ground. Combining the models above, this paper get a complete model which can not only evaluate the overall light intensity of the valley but also convert the light intensity to the intensity of illumination. Simulation of the intensity illumination of some basic terrains and finally gives a comprehensive results which is practical and close to the common sense.
A Model of Sequence Dependent Rna-Polymerase Diffusion Along Dna
Barbi, M; Popkov, V; Salerno, M; Barbi, Maria; Place, Christophe; Popkov, Vladislav; Salerno, Mario
2001-01-01
We introduce a probabilistic model for the RNA-polymerase sliding motion along DNA during the promoter search. The model accounts for possible effects due to sequence-dependent interactions between the nonspecific DNA and the enzyme. We focus on T7 RNA-polymerase and exploit the available information about its interaction at the promoter site in order to investigate the influence of bacteriophage T7 DNA sequence on the dynamics of the sliding process. Hydrogen bonds in the major groove are used as the main sequence-dependent interaction between the RNA-polymerase and the DNA. The resulting dynamical properties and the possibility of an experimental validation are discussed in details. We show that, while at large times the process reaches a pure diffusive regime, it initially displays a sub-diffusive behavior. The crossover from anomalous to normal diffusion may occur at times large enough to be of biological interest.
MODELING OF SUPERCRITICAL FLUID EXTRACTION KINETIC OF FLAXSEED OIL BY DIFFUSION CONTROL METHOD
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Emir Zafer HOŞGÜN
2013-06-01
Full Text Available In this study, Flaxseed oil was extracted by Supercritical Carbondioxide Extraction, and extractionkinetics was modelled using diffusion controlled method.The effect of process parameters, such as pressure (20, 35, 55 MPa, temperature (323 and 343 K, and CO2 flow rate (1 and 3 L CO2 /min on the extraction yield and effective diffusivity (De was investigated. The effective diffusion coefficient varied between 2.4 x10-12 and 10.8 x10-12 m2s-1 for the entire range of experiments and increased with the pressure and flow rate. The model fitted well theexperimental data (ADD varied between 2.35 and 7.48%.
DePalma, Glen; Turnidge, John; Craig, Bruce A
2017-02-01
The determination of diffusion test breakpoints has become a challenging issue due to the increasing resistance of microorganisms to antibiotics. Currently, the most commonly-used method for determining these breakpoints is the modified error-rate bounded method. Its use has remained widespread despite the introduction of several model-based methods that have been shown superior in terms of precision and accuracy. However, the computational complexities associated with these new approaches has been a significant barrier for clinicians. To remedy this, we developed and examine the utility of a free online software package designed for the determination of diffusion test breakpoints: dBETS (diffusion Breakpoint Estimation Testing Software). This software package allows clinicians to easily analyze data from susceptibility experiments through visualization, error-rate bounded, and model-based approaches. We analyze four publicly available data sets from the Clinical and Laboratory Standards Institute using dBETS.
A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model
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L. Päivärinta
2011-12-01
Full Text Available In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM. Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT is applied to enlarge the convergence region and rate of solution series given by the HAM.
Hwang, Hyoun-Tae; Jeen, Sung-Wook; Sudicky, Edward A.; Illman, Walter A.
2015-06-01
The applicability of a newly-developed chain-decay multispecies model (CMM) was validated by obtaining kinetic rate constants and branching ratios along the reaction pathways of trichloroethene (TCE) reduction by zero-valent iron (ZVI) from column experiments. Changes in rate constants and branching ratios for individual reactions for degradation products over time for two columns under different geochemical conditions were examined to provide ranges of those parameters expected over the long-term. As compared to the column receiving deionized water, the column receiving dissolved CaCO3 showed higher mean degradation rates for TCE and all of its degradation products. However, the column experienced faster reactivity loss toward TCE degradation due to precipitation of secondary carbonate minerals, as indicated by a higher value for the ratio of maximum to minimum TCE degradation rate observed over time. From the calculated branching ratios, it was found that TCE and cis-dichloroethene (cis-DCE) were dominantly dechlorinated to chloroacetylene and acetylene, respectively, through reductive elimination for both columns. The CMM model, validated by the column test data in this study, provides a convenient tool to determine simultaneously the critical design parameters for permeable reactive barriers and natural attenuation such as rate constants and branching ratios.
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
Baudron, Anne-Marie A -M; Maday, Yvon; Riahi, Mohamed Kamel; Salomon, Julien
2014-01-01
We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for the space discretization, our implementation provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner (LMW) benchmark [1].
Spatially explicit control of invasive species using a reaction-diffusion model
Bonneau, Mathieu; Johnson, Fred A.; Romagosa, Christina M.
2016-01-01
Invasive species, which can be responsible for severe economic and environmental damages, must often be managed over a wide area with limited resources, and the optimal allocation of effort in space and time can be challenging. If the spatial range of the invasive species is large, control actions might be applied only on some parcels of land, for example because of property type, accessibility, or limited human resources. Selecting the locations for control is critical and can significantly impact management efficiency. To help make decisions concerning the spatial allocation of control actions, we propose a simulation based approach, where the spatial distribution of the invader is approximated by a reaction–diffusion model. We extend the classic Fisher equation to incorporate the effect of control both in the diffusion and local growth of the invader. The modified reaction–diffusion model that we propose accounts for the effect of control, not only on the controlled locations, but on neighboring locations, which are based on the theoretical speed of the invasion front. Based on simulated examples, we show the superiority of our model compared to the state-of-the-art approach. We illustrate the use of this model for the management of Burmese pythons in the Everglades (Florida, USA). Thanks to the generality of the modified reaction–diffusion model, this framework is potentially suitable for a wide class of management problems and provides a tool for managers to predict the effects of different management strategies.
Turbulence modelling of the aerodynamic interaction ofOGV wakes and diffuser flow
Institute of Scientific and Technical Information of China (English)
LI Jing-hua; Page Gary; McGuirk Jim
2011-01-01
Different turbulence closures were used to predict the flow interaction between the wakes created by compressor outlet guide vanes（OGVs） and a downstream annular pre-diffuser.Two statistical turbulence models were tested based on the classical Reynolds-averaged Navier-Stokes（RANS） approach.Both high-Re and low-Re（Launder-Sharma） versions of the k-ε model were applied to a selected test problem for OGV wake/diffuser flows.The test problem was specifically chosen because experimentally determined inlet conditions and both profile and performance data were available to validate predictions.A preliminary study was also reported of the more advanced large eddy simulation（LES） approach.The LES sub-grid-scale（SGS） model was the basic Smagorinsky eddy viscosity assumption,with a Van-Driest damping function for improved capture of near-wall viscous behaviour.Comparison between the two RANS models showed little difference in terms of velocity contours at OGV trailing edge and diffuser exit.In terms of overall diffuser performance（static pressure recovery and total pressure loss coefficients）,the high-Re model was shown to agree well with experimental data.The preliminary LES study indicates the highly unsteady character of the OGV wake flow,but requires improved treatment of inlet conditions.
An Application of Epidemiological Modeling to Information Diffusion
McCormack, Robert; Salter, William
Messages often spread within a population through unofficial - particularly web-based - media. Such ideas have been termed "memes." To impede the flow of terrorist messages and to promote counter messages within a population, intelligence analysts must understand how messages spread. We used statistical language processing technologies to operationalize "memes" as latent topics in electronic text and applied epidemiological techniques to describe and analyze patterns of message propagation. We developed our methods and applied them to English-language newspapers and blogs in the Arab world. We found that a relatively simple epidemiological model can reproduce some dynamics of observed empirical relationships.
Diffusion and wave behaviour in linear Voigt model
De Angelis, Monica
2012-01-01
A boundary value problem related to a third- order parabolic equation with a small parameter is analized. This equation models the one-dimensional evolution of many dissipative media as viscoelastic fluids or solids, viscous gases, superconducting materials, incompressible and electrically conducting fluids. Moreover, the third-order parabolic operator regularizes various non linear second order wave equations. In this paper, the hyperbolic and parabolic behaviour of the solution is estimated by means of slow time and fast time. As consequence, a rigorous asymptotic approximation for the solution is established.
Muñoz-Jaramillo, Andrés; Martens, Petrus C H
2010-01-01
The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main featur...
Approximation of epidemic models by diffusion processes and their statistical inference.
Guy, Romain; Larédo, Catherine; Vergu, Elisabeta
2015-02-01
Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an
Diffuse-Interface Modelling of Flow in Porous Media
Addy, Doug; Pradas, Marc; Schmuck, Marcus; Kalliadasis, Serafim
2016-11-01
Multiphase flows are ubiquitous in a wide spectrum of scientific and engineering applications, and their computational modelling often poses many challenges associated with the presence of free boundaries and interfaces. Interfacial flows in porous media encounter additional challenges and complexities due to their inherently multiscale behaviour. Here we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard (CH) equation recently developed in from a Stokes-CH equation for microscopic heterogeneous domains by means of a homogenization methodology, where the microscopic details are taken into account as effective tensor coefficients which are given by a Poisson equation. The equations are decoupled under appropriate assumptions and solved in series using a classic finite-element formulation with the open-source software FEniCS. We investigate the effects of different microscopic geometries, including periodic and non-periodic, at the bulk fluid flow, and find that our model is able to describe the effective macroscopic behaviour without the need to resolve the microscopic details.
A GPU Reaction Diffusion Soil-Microbial Model
Falconer, Ruth; Houston, Alasdair; Schmidt, Sonja; Otten, Wilfred
2014-05-01
Parallelised algorithms are frequent in bioinformatics as a consequence of the close link to informatics - however in the field of soil science and ecology they are less prevalent. A current challenge in soil ecology is to link habitat structure to microbial dynamics. Soil science is therefore entering the 'big data' paradigm as a consequence of integrating data pertinent to the physical soil environment obtained via imaging and theoretical models describing growth and development of microbial dynamics permitting accurate analyses of spatio-temporal properties of different soil microenvironments. The microenvironment is often captured by 3D imaging (CT tomography) which yields large datasets and when used in computational studies the physical sizes of the samples that are amenable to computation are less than 1 cm3. Today's commodity graphics cards are programmable and possess a data parallel architecture that in many cases is capable of out-performing the CPU in terms of computational rates. The programmable aspect is achieved via a low-level parallel programming language (CUDA, OpenCL and DirectX). We ported a Soil-Microbial Model onto the GPU using the DirectX Compute API. We noted a significant computational speed up as well as an increase in the physical size that can be simulated. Some of the drawbacks of such an approach were concerned with numerical precision and the steep learning curve associated with GPGPU technologies.
Developing a laser shockwave model for characterizing diffusion bonded interfaces
Lacy, Jeffrey M.; Smith, James A.; Rabin, Barry H.
2015-03-01
The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) with the goal of reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU in high-power research reactors. The new LEU fuel is a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to support the fuel qualification process, the Laser Shockwave Technique (LST) is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However, because the deposition of laser energy into the containment layer on a specimen's surface is intractably complex, the shock wave energy is inferred from the surface velocity measured on the backside of the fuel plate and the depth of the impression left on the surface by the high pressure plasma pulse created by the shock laser. To help quantify the stresses generated at the interfaces, a finite element method (FEM) model is being utilized. This paper will report on initial efforts to develop and validate the model by comparing numerical and experimental results for back surface velocities and front surface depressions in a single aluminum plate representative of the fuel cladding.
Modeling diffusion of electrical appliances in the residential sector
Energy Technology Data Exchange (ETDEWEB)
McNeil, Michael A.; Letschert, Virginie E.
2009-11-22
This paper presents a methodology for modeling residential appliance uptake as a function of root macroeconomic drivers. The analysis concentrates on four major energy end uses in the residential sector: refrigerators, washing machines, televisions and air conditioners. The model employs linear regression analysis to parameterize appliance ownership in terms of household income, urbanization and electrification rates according to a standard binary choice (logistic) function. The underlying household appliance ownership data are gathered from a variety of sources including energy consumption and more general standard of living surveys. These data span a wide range of countries, including many developing countries for which appliance ownership is currently low, but likely to grow significantly over the next decades as a result of economic development. The result is a 'global' parameterization of appliance ownership rates as a function of widely available macroeconomic variables for the four appliances studied, which provides a reliable basis for interpolation where data are not available, and forecasting of ownership rates on a global scale. The main value of this method is to form the foundation of bottom-up energy demand forecasts, project energy-related greenhouse gas emissions, and allow for the construction of detailed emissions mitigation scenarios.
Theoretical model estimation of guest diffusion in Metal-Organic Frameworks (MOFs)
Zheng, Bin
2015-08-11
Characterizing molecule diffusion in nanoporous matrices is critical to understanding the novel chemical and physical properties of metal-organic frameworks (MOFs). In this paper, we developed a theoretical model to fastly and accurately compute the diffusion rate of guest molecules in a zeolitic imidazolate framework-8 (ZIF-8). The ideal gas or equilibrium solution diffusion model was modified to contain the effect of periodical media via introducing the possibility of guests passing through the framework gate. The only input in our model is the energy barrier of guests passing through the MOF’s gate. Molecular dynamics (MD) methods were employed to gather the guest density profile, which then was used to deduce the energy barrier values. This produced reliable results that require a simulation time of 5 picoseconds, which is much shorter when using pure MD methods (in the billisecond scale) . Also, we used density functional theory (DFT) methods to obtain the energy profile of guests passing through gates, as this does not require specification of a force field for the MOF degrees of freedom. In the DFT calculation, we only considered one gate of MOFs each time; as this greatly reduced the computational cost. Based on the obtained energy barrier values we computed the diffusion rate of alkane and alcohol in ZIF-8 using our model, which was in good agreement with experimental test results and the calculation values from standard MD model. Our model shows the advantage of obtaining accurate diffusion rates for guests in MOFs for a lower computational cost and shorter calculation time. Thus, our analytic model calculation is especially attractive for high-throughput computational screening of the dynamic performance of guests in a framework.
Maxwell's Law Based Models for Liquid and Gas Phase Diffusivities in Variably-Saturated Soil
DEFF Research Database (Denmark)
Mamamoto, Shoichiro; Møldrup, Per; Kawamoto, Ken
2012-01-01
The gas diffusion coefficient (D-s,D-g) and solute diffusion coefficient (D-s,D-l) and their dependencies on fluid content (kappa) (equal to soil-air content theta for D-s,D-g and soil-water content epsilon for D-s,D-l) are controlling factors for gas and solute transport in variably saturated...... soils. In this study, we propose unified, predictive models for D-s,D-g(epsilon) and D-s,D-l(theta) based on modifying and extending the classical Maxwell model at fluid saturation with a fluid-induced reduction term including a percolation threshold (epsilon(th) for D-s,D-g and theta(th) for D......-s,D-l). Different percolation threshold terms adopted from recent studies for gas (D-s,D-g) and solute (D-s,D-l) diffusion were applied. For gas diffusion, epsilon(th) was a function of bulk density (total porosity), while for solute diffusion theta(th) was best described by volumetric content of finer soil...
A multiscale theoretical model for diffusive mass transfer in cellular biological media.
Kapellos, George E; Alexiou, Terpsichori S; Payatakes, Alkiviades C
2007-11-01
An integrated methodology is developed for the theoretical analysis of solute transport and reaction in cellular biological media, such as tissues, microbial flocs, and biofilms. First, the method of local spatial averaging with a weight function is used to establish the equation which describes solute conservation at the cellular biological medium scale, starting with a continuum-based formulation of solute transport at finer spatial scales. Second, an effective-medium model is developed for the self-consistent calculation of the local diffusion coefficient in the cellular biological medium, including the effects of the structural heterogeneity of the extra-cellular space and the reversible adsorption to extra-cellular polymers. The final expression for the local effective diffusion coefficient is: D(Abeta)=lambda(beta)D(Aupsilon), where D(Aupsilon) is the diffusion coefficient in water, and lambda(beta) is a function of the composition and fundamental geometric and physicochemical system properties, including the size of solute molecules, the size of extra-cellular polymer fibers, and the mass permeability of the cell membrane. Furthermore, the analysis sheds some light on the function of the extra-cellular hydrogel as a diffusive barrier to solute molecules approaching the cell membrane, and its implications on the transport of chemotherapeutic agents within a cellular biological medium. Finally, the model predicts the qualitative trend as well as the quantitative variability of a large number of published experimental data on the diffusion coefficient of oxygen in cell-entrapping gels, microbial flocs, biofilms, and mammalian tissues.
Numerical modeling of a complex diffuser in a room with displacement ventilation
Energy Technology Data Exchange (ETDEWEB)
Cehlin, M. [Division of Energy and Mechanical Engineering, Department of Technology and Built Environment, University of Gaevle, Kungsbacksvagen 47, 801 76 Gavle (Sweden); Moshfegh, B. [Division of Energy and Mechanical Engineering, Department of Technology and Built Environment, University of Gaevle, Kungsbacksvagen 47, 801 76 Gavle (Sweden); Division of Energy Systems, Department of Management and Engineering, Linkoeping University (Sweden)
2010-10-15
A micro/macro-level approach (MMLA) has been proposed which makes it possible for HVAC engineers to easily study the effect of diffuser characteristics and diffuser placement on thermal comfort and indoor air quality. In this article the MMLA has been used to predict the flow and thermal behavior of the air in the near-zone of a complex low-velocity diffuser. A series of experiment has been carried out to validate the numerical predictions in order to ensure that simulations can be used with confidence to predict indoor airflow. The predictions have been performed by means of steady Reynolds Stress Model (RSM) and the results have good agreement both qualitatively and quantitatively with measurements. However, measurements indicated that the diffusion of the velocity and temperature was to some extent under-predicted by the RSM, which might be related to high instability of the airflow close to the diffuser. This effect might be captured by employing unsteady RSM. The present study also shows the importance of detailed inlet supply modeling in the accuracy of indoor air prediction. (author)
An evaluation of the role of eddy diffusion in stratospheric interactive two-dimensional models
Schneider, Hans R.; Ko, Malcolm K. W.; Sze, Nien Dak; Shi, Guang-Yu; Wang, Wei-Chyung
1989-01-01
An interactive two-dimensional model of the stratosphere, consisting of a primitive equation dynamics module, a simplified HO(x) ozone model, and a full radiative transfer scheme, is used to study the effect of eddy diffusion in the model. Consideration is given to the effects of nonlocal forcing from dissipation in the model troposphere and frictional drag at mesospheric levels, mechanical damping in the stratosphere itself, and potential vorticity flux due to large scale waves. It is found that the ozone distributions generated with the model are very sensitive to the choice of values for the friction and the eddy diffusion coefficients. It is shown that reasonable latitudinal gradients of ozone may be obtained by using small values for the mechanical damping for the mid- and high-latitude stratopsphere.
Lee, Shiu-Hang; Ellison, Donald C
2008-01-01
We present a 3-dimensional model of supernova remnants (SNRs) where the hydrodynamical evolution of the remnant is modeled consistently with nonlinear diffusive shock acceleration occuring at the outer blast wave. The model includes particle escape and diffusion outside of the forward shock, and particle interactions with arbitrary distributions of external ambient material, such as molecular clouds. We include synchrotron emission and cooling, bremsstrahlung radiation, neutral pion production, inverse-Compton (IC), and Coulomb energy-loss. Boardband spectra have been calculated for typical parameters including dense regions of gas external to a 1000 year old SNR. In this paper, we describe the details of our model but do not attempt a detailed fit to any specific remnant. We also do not include magnetic field amplification (MFA), even though this effect may be important in some young remnants. In this first presentation of the model we don't attempt a detailed fit to any specific remnant. Our aim is to devel...
Comparison study of fast responses in confined plasmas with diffusivity models
Energy Technology Data Exchange (ETDEWEB)
Iwasaki, Takuya [Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka (Japan); Itoh, Sanae-I.; Yagi, Masatoshi [Kyushu Univ., Fukuoka (Japan). Research Inst. for Applied Mechanics; Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2000-03-01
An equation which includes the non-local effect in the heat flux is introduced to study the transient transport phenomena. A non-local heat flux, which is expressed in terms of the integral equation, is superimposed on the conventional form of the heat flux. This model is applied to describe the fast responses in the transition from Low confinement mode (L-mode) to High confinement mode (H-mode) and in the heating power switching. Examples of diffusivity models are chosen, i.e., constant, Bohm and Rebut-Lallia-Watkins (RLW) model and the comparison study is done. A small reaction of non-local component in the heat flux is found to be very effective in reducing the response time. Independent of the diffusivity models, the fast transient transport in the heat pulse propagation is reproduced based on this non-local model. (author)
Mechanical properties of branched actin filaments
Razbin, Mohammadhosein; Benetatos, Panayotis; Zippelius, Annette
2015-01-01
Cells moving on a two dimensional substrate generate motion by polymerizing actin filament networks inside a flat membrane protrusion. New filaments are generated by branching off existing ones, giving rise to branched network structures. We investigate the force-extension relation of branched filaments, grafted on an elastic structure at one end and pushing with the free ends against the leading edge cell membrane. Single filaments are modeled as worm-like chains, whose thermal bending fluctuations are restricted by the leading edge cell membrane, resulting in an effective force. Branching can increase the stiffness considerably; however the effect depends on branch point position and filament orientation, being most pronounced for intermediate tilt angles and intermediate branch point positions. We describe filament networks without cross-linkers to focus on the effect of branching. We use randomly positioned branch points, as generated in the process of treadmilling, and orientation distributions as measur...
Energy Technology Data Exchange (ETDEWEB)
Weber, Adam
2010-03-05
A macroscopic-modeling methodology to account for the chemical and structural properties of fuel-cell diffusion media is developed. A previous model is updated to include for the first time the use of experimentally measured capillary pressure -- saturation relationships through the introduction of a Gaussian contact-angle distribution into the property equations. The updated model is used to simulate various limiting-case scenarios of water and gas transport in fuel-cell diffusion media. Analysis of these results demonstrate that interfacial conditions are more important than bulk transport in these layers, where the associated mass-transfer resistance is the result of higher capillary pressures at the boundaries and the steepness of the capillary pressure -- saturation relationship. The model is also used to examine the impact of a microporous layer, showing that it dominates the response of the overall diffusion medium. In addition, its primary mass-transfer-related effect is suggested to be limiting the water-injection sites into the more porous gas-diffusion layer.
$L^\\infty$ solutions for a model of polytropic gas flow with diffusive entropy
Frid, Hermano; Karlsen, Kenneth H
2010-01-01
We establish the global existence of $L^\\infty$ solutions for a model of polytropic gas flow with diffusive entropy. The result is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax-Friedrichs and Godunov schemes. Such convergence is achieved by proving the estimates required for the application of the compensated compactness theory.
Directory of Open Access Journals (Sweden)
Xiaohong Tian
2014-01-01
Full Text Available A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper-lower solutions and using Schauder's fixed point theorem, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
Numerical modeling of turbulent jet diffusion flames in the atmospheric surface layer
Hernández, J.; Crespo, A.; Duijm, N.J.
1995-01-01
The evolution of turbulent jet diffusion flames of natural gas in air is predicted using a finite-volume procedure for solving the flow equations. The model is three dimensional, elliptic and based on the conserved-scalar approach and the laminar flamelet concept. A laminar flamelet prescription for
A Simple Diffusion-Controled Model of Mixing Across a Stable Density Interface
Kranenburg, C.
1979-01-01
Mixing across a stable density interface caused by a shear stress externally acting on a two-layer fluid initially at rest is modelled using the turbulent-diffusion concept. The influence of a (relatively weak) longitudinal pressure gradient is also considered. The central point of view developed is
Rotational diffusion model of orientational enhancement in AC field biased photorefractive polymers
DEFF Research Database (Denmark)
Pedersen, T.G.; Jespersen, K.G.; Johansen, P.M.
2001-01-01
The response of photorefractive (PR) polymers subject to AC field biasing is analyzed within the space-charge field formalism. The frequency dependence of orientational enhancement is taken into account using a rotational diffusion model for the angular distribution of chromophores. The possibility...
Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane
Energy Technology Data Exchange (ETDEWEB)
Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V., E-mail: aneimark@rutgers.edu [Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854-8058 (United States)
2016-01-07
Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. The DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.
A MATHEMATICAL ANALYSIS FOR A DIFFUSIVE EPIDEMIC MODEL WITH CRISS-CROSS DYNAMICS
Institute of Scientific and Technical Information of China (English)
LiZhenayuan; Taoliyuan; YeQixiao
1999-01-01
Abstract. In this paper, an initial boundary value problem with homogeneous Neumann bound-ary condition is studied for a reaction diffusion system which models the spread of infectious dis-eases within two population groups by means of serf and criss-cross infection mechanism, Exis-tence, uniqueness and houndedness of the nonnegative global solution
Coarse-grained model of water diffusion and proton conductivity in hydrated polyelectrolyte membrane
Lee, Ming-Tsung; Vishnyakov, Aleksey; Neimark, Alexander V.
2016-01-01
Using dissipative particle dynamics (DPD), we simulate nanoscale segregation, water diffusion, and proton conductivity in hydrated sulfonated polystyrene (sPS). We employ a novel model [Lee et al. J. Chem. Theory Comput. 11(9), 4395-4403 (2015)] that incorporates protonation/deprotonation equilibria into DPD simulations. The polymer and water are modeled by coarse-grained beads interacting via short-range soft repulsion and smeared charge electrostatic potentials. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with the base beads representing water and sulfonate anions. Morse bond formation and breakup artificially mimics the Grotthuss mechanism of proton hopping between the bases. The DPD model is parameterized by matching the proton mobility in bulk water, dissociation constant of benzenesulfonic acid, and liquid-liquid equilibrium of water-ethylbenzene solutions. The DPD simulations semi-quantitatively predict nanoscale segregation in the hydrated sPS into hydrophobic and hydrophilic subphases, water self-diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from isolated water clusters to a 3D network. The analysis of hydrophilic subphase connectivity and water diffusion demonstrates the importance of the dynamic percolation effect of formation and breakup of temporary junctions between water clusters. The proposed DPD model qualitatively predicts the ratio of proton to water self-diffusion and its dependence on the hydration level that is in reasonable agreement with experiments.
Stability and Hopf Bifurcation Analysis of a Gene Expression Model with Diffusion and Time Delay
Directory of Open Access Journals (Sweden)
Yahong Peng
2014-01-01
Full Text Available We consider a model for gene expression with one or two time delays and diffusion. The local stability and delay-induced Hopf bifurcation are investigated. We also derive the formulas determining the direction and the stability of Hopf bifurcations by calculating the normal form on the center manifold.
Mathematical model of diffusion-limited gas bubble dynamics in unstirred tissue with finite volume.
Srinivasan, R Srini; Gerth, Wayne A; Powell, Michael R
2002-02-01
Models of gas bubble dynamics for studying decompression sickness have been developed by considering the bubble to be immersed in an extravascular tissue with diffusion-limited gas exchange between the bubble and the surrounding unstirred tissue. In previous versions of this two-region model, the tissue volume must be theoretically infinite, which renders the model inapplicable to analysis of bubble growth in a finite-sized tissue. We herein present a new two-region model that is applicable to problems involving finite tissue volumes. By introducing radial deviations to gas tension in the diffusion region surrounding the bubble, the concentration gradient can be zero at a finite distance from the bubble, thus limiting the tissue volume that participates in bubble-tissue gas exchange. It is shown that these deviations account for the effects of heterogeneous perfusion on gas bubble dynamics, and are required for the tissue volume to be finite. The bubble growth results from a difference between the bubble gas pressure and an average gas tension in the surrounding diffusion region that explicitly depends on gas uptake and release by the bubble. For any given decompression, the diffusion region volume must stay above a certain minimum in order to sustain bubble growth.