Predictability of extreme events in a branching diffusion model
Gabrielov, Andrei; Olsen, Sayaka; Zaliapin, Ilya
2010-01-01
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with immigration. New elements -- observation space and observed events -- are introduced in order to formulate a prediction problem patterned after the geophysical and environmental applications. The problem consists of estimating the likelihood of occurrence of an extreme event given the observations of smaller events while the complete internal dynamics of the system is unknown. We look for premonitory patterns that emerge as an extreme event approaches; those patterns are deviations from the long-term system's averages. We have found a single control parameter that governs multiple spatio-temporal premonitory patterns. For that purpose, we derive i) complete analytic description of time- and space-dependent size distribution of particles generated by a single immigrant; ii) the...
Parra-Robles, Juan; Wild, Jim M
2014-02-01
Our extensive investigation of the cylinder model theory through numerical modelling and purpose-designed experiments has demonstrated that it does produce inaccurate estimates of airway dimensions at all diffusion times currently used. This is due to a variety of effects: incomplete treatment of non-Gaussian effects, finite airway size, branching geometry, background susceptibility gradients and diffusion time dependence of the (3)He MR diffusion behaviour in acinar airways. The cylinder model is a good starting point for the development of a lung morphometry technique from (3)He diffusion MR but its limitations need to be understood and documented in the interest of reliable clinical interpretation. PMID:24342570
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.
Residence times of branching diffusion processes
Dumonteil, E.; Mazzolo, A.
2016-07-01
The residence time of a branching Brownian process is the amount of time that the mother particle and all its descendants spend inside a domain. Using the Feynman-Kac formalism, we derive the residence-time equation as well as the equations for its moments for a branching diffusion process with an arbitrary number of descendants. This general approach is illustrated with simple examples in free space and in confined geometries where explicit formulas for the moments are obtained within the long time limit. In particular, we study in detail the influence of the branching mechanism on those moments. The present approach can also be applied to investigate other additive functionals of branching Brownian process.
The branching structure of diffusion-limited aggregates
Halsey, T C
1997-01-01
I analyze the topological structures generated by diffusion-limited aggregation (DLA), using the recently developed "branched growth model". The computed bifurcation number B for DLA in two dimensions is B ~ 4.9, in good agreement with the numerically obtained result of B ~ 5.2. In high dimensions, B -> 3.12; the bifurcation ratio is thus a decreasing function of dimensionality. This analysis also determines the scaling properties of the ramification matrix, which describes the hierarchy of branches.
Jochem B. Evers; Vos, Jan
2013-01-01
Cereals and grasses adapt their structural development to environmental conditions and the resources available. The primary adaptive response is a variable degree of branching, called tillering in cereals. Especially for heterogeneous plant configurations the degree of tillering varies per plant. Functional–structural plant modeling (FSPM) is a modeling approach allowing simulation of the architectural development of individual plants, culminating in the emergent behavior at the canopy level....
Mechanisms of side branching and tip splitting in a model of branching morphogenesis.
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
Mechanisms of Side Branching and Tip Splitting in a Model of Branching Morphogenesis
Guo, Yina; Sun, Mingzhu; Garfinkel, Alan; Zhao, Xin
2014-01-01
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 together with side
Some distance bounds of branching processes and their diffusion limits
Kammerer, Niels B
2010-01-01
We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitrary type of criticality). Implications for asymptotic distinguishability behaviour in terms of contiguity and entire separation of the involved GWI are given, too. Furthermore, we determine the corresponding limit quantities for the context in which the two GWI converge to Feller-type branching diffusion processes, as the time-lags between observations tend to zero. Some applications to (static random environment like) Bayesian decision making and Neyman-Pearson testing are presented as well.
Infinite-Scale Percolation in a New Type of Branching Diffusion Processes
Mezhlumian, A.; Molchanov, S. A.
1992-01-01
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes with diffusion on the space of parameters distinguishing the branching `particles' each other.
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.
Measuring neuronal branching patterns using model-based approach.
Luczak, Artur
2010-01-01
Neurons have complex branching systems which allow them to communicate with thousands of other neurons. Thus understanding neuronal geometry is clearly important for determining connectivity within the network and how this shapes neuronal function. One of the difficulties in uncovering relationships between neuronal shape and its function is the problem of quantifying complex neuronal geometry. Even by using multiple measures such as: dendritic length, distribution of segments, direction of branches, etc, a description of three dimensional neuronal embedding remains incomplete. To help alleviate this problem, here we propose a new measure, a shape diffusiveness index (SDI), to quantify spatial relations between branches at the local and global scale. It was shown that growth of neuronal trees can be modeled by using diffusion limited aggregation (DLA) process. By measuring "how easy" it is to reproduce the analyzed shape by using the DLA algorithm it can be measured how "diffusive" is that shape. Intuitively, "diffusiveness" measures how tree-like is a given shape. For example shapes like an oak tree will have high values of SDI. This measure is capturing an important feature of dendritic tree geometry, which is difficult to assess with other measures. This approach also presents a paradigm shift from well-defined deterministic measures to model-based measures, which estimate how well a model with specific properties can account for features of analyzed shape. PMID:21079752
Path integral formulation and Feynman rules for phylogenetic branching models
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance
Measuring neuronal branching patterns using model-based approach
Artur Luczak
2010-10-01
Full Text Available Neurons have complex branching systems which allow them to communicate with thousands of other neurons. Thus understanding neuronal geometry is clearly important for determining connectivity within the network and how this shapes neuronal function. One of the difficulties in uncovering relationships between neuronal shape and its function is the problem of quantifying complex neuronal geometry. Even by using multiple measures such as: dendritic length, topology, distribution of segments, direction of branches, etc, a description of three dimensional neuronal embedding remains incomplete. To help alleviate this problem, here we propose a new measure, a shape diffusiveness index (SDI, to quantify spatial relations between branches at the local and global scale. It was shown that growth of neuronal trees can be modeled by using Diffusion Limited Aggregation (DLA process. By measuring ‘how easy’ it is to reproduce the analyzed shape by using the DLA algorithm it can be measured how ‘diffusive’ is that shape. Intuitively, ‘diffusiveness’ measures how tree-like is a given shape. For example shapes like an oak tree will have high values of SDI. This measure is capturing an important feature of dendritic tree geometry, which is difficult to assess with other measures. This approach also presents a paradigm shift from well-defined deterministic measures to model-based measures, which estimate how well a model with specific properties can account for features of analyzed shape.
Wilkinson, P; Dimbylow, P J
1985-10-01
A mathematical model has been developed that examines the ingress of radon into houses, through a vertical crack in an otherwise impervious concrete floor. Initially, the model considered the diffusive flow of radon from its soil source and this simulation has highlighted the dependency of the flux of radon into the house on the magnitude of various parameters, such as the diffusion coefficient of radon in soil. A preliminary investigation of the modelling of pressure-driven flow into a building is presented, and the potential of this type of analysis is discussed. PMID:4081719
Modelling an observer's branch of extremal consciousness
Polley, L.
2012-01-01
Extreme-order statistics is applied to the branches of an observer in a many-worlds framework. A unitary evolution operator for a step of time is constructed, generating pseudostochastic behaviour with a power-law distribution when applied repeatedly to a particular initial state. The operator models the generation of records, their dating, the splitting of the wavefunction at quantum events, and the recalling of records by the observer. Due to the huge ensemble near an observer's end, the br...
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.
Model of information diffusion
Lande, D V
2008-01-01
The system of cellular automata, which expresses the process of dissemination and publication of the news among separate information resources, has been described. A bell-shaped dependence of news diffusion on internet-sources (web-sites) coheres well with a real behavior of thematic data flows, and at local time spans - with noted models, e.g., exponential and logistic ones.
Simple statistical model for branched aggregates
Lemarchand, Claire; Hansen, Jesper Schmidt
2015-01-01
We propose a statistical model that can reproduce the size distribution of any branched aggregate, including amylopectin, dendrimers, molecular clusters of monoalcohols, and asphaltene nanoaggregates. It is based on the conditional probability for one molecule to form a new bond with a molecule......, given that it already has bonds with others. The model is applied here to asphaltene nanoaggregates observed in molecular dynamics simulations of Cooee bitumen. The variation with temperature of the probabilities deduced from this model is discussed in terms of statistical mechanics arguments. The...... relevance of the statistical model in the case of asphaltene nanoaggregates is checked by comparing the predicted value of the probability for one molecule to have exactly i bonds with the same probability directly measured in the molecular dynamics simulations. The agreement is satisfactory...
Markov branching in the vertex splitting model
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 α element of [0,1] which has a so-called Markov branching property. When D=∞ we find a two parameter model with an additional parameter γ element of [0,1] which also has this feature. In the case D = 3, the model bears resemblance to Ford's α-model of phylogenetic trees and when D=∞ it is similar to its generalization, the αγ-model. For α = 0, the model reduces to the well known model of preferential attachment. In the case α > 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/α. When γ = 0 the model reduces to a model of growing caterpillar graphs in which case we prove that the Hausdorff dimension is almost surely 1/α and that the spectral dimension is almost surely 2/(1 + α). We comment briefly on the distribution of vertex degrees and correlations between degrees of neighbouring vertices
Branching process in a stochastic extremal model
Manna, S. S.
2009-08-01
We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the number M of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion. The critical behavior of the SBSM is found to be the same as the BS model in dimensions d=1 and 2. However on the scale-free graphs the critical fitness value is nonzero even in the thermodynamic limit but the critical behavior is mean-field like. Finally ⟨M⟩ has been made even smaller than two by probabilistically updating the mutation zone, which also shows the original BS model behavior. We conjecture that a SBSM on any arbitrary graph with any small branching factor greater than unity will lead to a self-organized critical state.
3D modelling of branching in plants
Evers, J.B.
2011-01-01
Shoot branching is a key determinant of overall aboveground plant form. During plant development, the number of branches formed strongly influences the amount of light absorbed by the plant, and thus the plant’s competitive strength in terms of light capture in relation to neighbouring plants. Branching is regulated by multiple internal factors which are modulated by different environmental signals. A key environmental signal in the context of a plant population is a low red / far-red intensi...
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.
Econometric Advances in Diffusion Models
Peers, Yuri
2011-01-01
textabstractThis thesis gives new and important insights in modeling diffusion data in marketing. It addresses modeling multiple series instead of just one series such that one can learn from the differences and similarities across products and countries. Additionally, this thesis addresses the current availability of higher frequency diffusion data. The two issues provide challenges for modeling of diffusion processes. In this thesis we provide solutions to these challenges, and we also sugg...
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 example of a system which offers the possibility to incorporate user-provided directives (written in {\\sc C}) to guide the branch-and-bound search. Its main focus, however, remains on mathematical p...
Multispecies diffusion models: A study of uranyl species diffusion
Rigorous numerical description of multi-species diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication for imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multi-species diffusion in groundwater. Diffusion of uranyl (U(VI)) species was used as an example in demonstrating the effectiveness of the models in describing multi-species diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multi-species U(VI) diffusion under steady-state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that a fully coupled diffusion model can be well approximated by a component-based diffusion model, which considers difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be rigorously enforced, if necessary, by adding an artificial kinetic reaction term induced by the charge separation. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from US Department of Energy's Hanford 300A where intragrain diffusion is a rate-limiting process controlling U(VI) adsorption and desorption. The grain-scale reactive diffusion model was able to describe U(VI) adsorption/desorption kinetics that has been described using a semi-empirical, multi-rate model
Biggins, J D
2010-01-01
Results on the behaviour of the rightmost particle in the $n$th generation in the branching random walk are reviewed and the phenomenon of anomalous spreading speeds, noticed recently in related deterministic models, is considered. The relationship between such results and certain coupled reaction-diffusion equations is indicated.
A Data Flow Behavior Constraints Model for Branch Decisionmaking Variables
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.
Testing the Beat Frequency Model of Horizontal Branch Qpos
Hertz, Paul
The beat frequency modulated accretion (BFMA) model requires strong correlations in the horizontal branch quasiperiodic oscillations (HBO) and low frequency noise (LFN) amplitudes on time scales HBO and LFN amplitude predicted by the BFMA model and constrain some of the free observable parameters in the model. Any HBO model must account for these properties.
Anomalous scaling in an age-dependent branching model
Keller-Schmidt, Stephanie; Tugrul, Murat; Eguiluz, Victor M.; Hernandez-Garcia, Emilio; Klemm, Konstantin
2010-01-01
We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $\\tau$ as $\\tau^{-\\alpha}$. Depending on the exponent $\\alpha$, the scaling of tree depth with tree size $n$ displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition ($\\alpha=1$) tree depth grows as $(\\log n)^2$. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus p...
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...
Highlights: • Recovery of deuterium by thermal diffusion from water–isotope mixture has been investigated. • The undesirable remixing effect can be reduced by employing the device of branch columns. • Deuterium recoveries were compared with that in a single column of the same total column length. • Considerable recovery improvement is obtainable in the device of branch columns, instead of in a single-column device. - Abstract: Deuterium recovery from water–isotopes mixture using thermal diffusion can be improved by employing the branch column device, instead of single column devices, with the same total column length. The remixing effect due to convection currents in a thermal diffusion column for heavy water enrichment is thus reduced and separation improvement increases when the flow rate or the total column length increases. The improvement in separation can reach about 50% for the numerical example given
Oak Ridge Gaseous Diffusion Plant Biological Monitoring and Abatement Program for Mitchell Branch
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.
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.
A space-averaged model of branched structures
Lopez, Diego; Michelin, Sébastien
2014-01-01
Many biological systems and artificial structures are ramified, and present a high geometric complexity. In this work, we propose a space-averaged model of branched systems for conservation laws. From a one-dimensional description of the system, we show that the space-averaged problem is also one-dimensional, represented by characteristic curves, defined as streamlines of the space-averaged branch directions. The geometric complexity is then captured firstly by the characteristic curves, and secondly by an additional forcing term in the equations. This model is then applied to mass balance in a pipe network and momentum balance in a tree under wind loading.
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
Diffusion models and neural activity
Ricciardi, L. M.; Lánský, Petr
London : Nature publishing group, 2003 - (Nadel, L.), s. 968-972 ISBN 0-333-79261-0 R&D Projects: GA ČR GA309/02/0168 Institutional research plan: CEZ:AV0Z5011922 Keywords : Neuronal activity, Diffusion model Subject RIV: ED - Physiology
Anomalous scaling in an age-dependent branching model
Keller-Schmidt, Stephanie; Tugrul, Murat; Víctor M Eguíluz; Hernández-García, Emilio; Klemm, Konstantin
2015-01-01
© 2015 American Physical Society. We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ-α. Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)2. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus provid...
Anomalous scaling in an age-dependent branching model.
Keller-Schmidt, Stephanie; Tuğrul, Murat; Eguíluz, Víctor M; Hernández-García, Emilio; Klemm, Konstantin
2015-02-01
We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age τ as τ(-α). Depending on the exponent α, the scaling of tree depth with tree size n displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition (α=1) tree depth grows as (logn)(2). This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point. PMID:25768548
Eddy viscosity and diffusivity modeling
The standard Smagorinsky subgrid scale model for large eddy simulation can be derived from turbulent eddy viscosity models by assuming that the unresolved scales exhibit a Kolmogorov energy spectrum. The present work provides a general framework for developing eddy viscosity and corresponding subgrid models for flow problems in which Kolmogorov scaling cannot be assumed because additional physical mechanisms strongly modify the turbulence dynamics. Examples of such mechanisms include externally imposed time scales, compressibility, and intermittency. The general formalism is also applied to the turbulent thermal diffusivity. In special cases, this approach yields models that agree with those existing in the literature
Diffusion models for Knudsen compressors
Aoki, Kazuo; Degond, Pierre; Takata, Shigeru; Yoshida, Hiroaki
2007-01-01
A rarefied gas in a long straight pipe with a periodic structure consisting of alternately arranged narrow and wide pipes and with periodic temperature distribution, which is known as the Knudsen compressor (or pump), is considered. Under the assumption that the pipe is much thinner than the period, a diffusion model that describes the pressure distribution and mass flux of the gas in each pipe element is derived, together with the connection conditions at the junctions of the narrow and wide...
Pen Branch Delta and Savannah River Swamp Hydraulic Model
The proposed Savannah River Site (SRS) Wetlands Restoration Project area is located in Barnwell County, South Carolina on the southwestern boundary of the SRS Reservation. The swamp covers about 40.5 km2 and is bounded to the west and south by the Savannah River and to the north and east by low bluffs at the edge of the Savannah River floodplain. Water levels within the swamp are determined by stage along the Savannah River, local drainage, groundwater seepage, and inflows from four tributaries, Beaver Dam Creek, Fourmile Branch, Pen Branch, and Steel Creek. Historic discharges of heated process water into these tributaries scoured the streambed, created deltas in the adjacent wetland, and killed native vegetation in the vicinity of the delta deposits. Future releases from these tributaries will be substantially smaller and closer to ambient temperatures. One component of the proposed restoration project will be to reestablish indigenous wetland vegetation on the Pen Branch delta that covers about 1.0 km2. Long-term predictions of water levels within the swamp are required to determine the characteristics of suitable plants. The objective of the study was to predict water levels at various locations within the proposed SRS Wetlands Restoration Project area for a range of Savannah River flows and regulated releases from Pen Branch. TABS-MD, a United States Army Corps of Engineer developed two-dimensional finite element open channel hydraulic computer code, was used to model the SRS swamp area for various flow conditions
Pen Branch Delta and Savannah River Swamp Hydraulic Model
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.
Fusion by diffusion model revisited
A complete set of 27 excitation functions for synthesis of superheavy nuclei produced in cold fusion reactions was analyzed in terms of the "Fusion by Diffusion Model" of Swiatecki et al., modified to account for the angular momentum dependence of the fusion hindrance factor. The data on cold fusion reactions originate from experiments carried out at GSI Darmstadt, RIKEN Tokyo and LBNL Berkeley in which 208Pb and 209Bi targets were bombarded with the variety of projectiles ranging from 48,50Ti to 70Zn. (author)
Precision Polyolefin Structure: Modeling Polyethylene Containing Methyl and Ethyl Branches
Rojas, Giovanni; Wagener, Kenneth B.
Sequenced copolymers of ethylene and diverse species have been created using acyclic diene metathesis (ADMET) polymerization, a step growth, condensation- type polymerization driven to high conversion by the removal of ethylene. ADMET permits control over branch content and branch length, which can be predetermined during the monomer synthesis, allowing sequence control in the resultant unsaturated polymer. Monomers are symmetrical α,ωdienes with a pendant functionality. Diverse functional groups are compatible with ADMET polymerization when Schrock’s or first-generation Grubb’s catalysts are used. Saturation with hydrogen after ADMET polymerization affords a polyethylene (PE) backbone bearing specific functionalities in precise places. Varying both the pendant functional group and the spacing between functionalities alters the physical and chemical properties of the polymer. Incorporation of alkyl chains into the PE backbone via ADMET leads to the study of perfect structures modeling the copolymerization of ethylene with α-olefins such as 1-propene, 1-butene, 1-hexene, and 1-octene.
Updated stellar yields from Asymptotic Giant Branch models
Karakas, Amanda I.
2009-01-01
An updated grid of stellar yields for low to intermediate-mass thermally-pulsing Asymptotic Giant Branch (AGB) stars are presented. The models cover a range in metallicity Z = 0.02, 0.008, 0.004, and 0.0001, and masses between 1Msun to 6Msun. New intermediate-mass Z = 0.0001 AGB models are also presented, along with a finer mass grid than used in previous studies. The yields are computed using an updated reaction rate network that includes the latest NeNa and MgAl proton capture rates, with t...
Birth-death branching models. Application to African elephant populations.
Corbacho, Casimiro; Molina, Manuel; Mota, Manuel; Ramos, Alfonso
2013-09-01
Branching models have a long history of biological applications, particularly in population dynamics. In this work, our interest is the development of mathematical models to describe the demographic dynamics of socially structured animal populations, focusing our attention on lineages, usually matrilines, as the basic structure in the population. Significant efforts have been made to develop models based on the assumption that all individuals behave identically with respect to reproduction. However, the reproduction phase has a large random component that involves not only demographic but also environmental factors that change across range distribution of species. In the present work, we introduce new classes of birth-death branching models which take such factors into account. We assume that both, the offspring probability distribution and the death probabilities may be different in each generation, changing either predictably or unpredictably in relation to habitat features. We consider the genealogical tree generated by observation of the process until a pre-set generation. We determine the probability distributions of the random variables representing the number of dead or living individuals having at least one ancestor alive, living individuals whose ancestors are all dead, and dead individuals whose ancestors are all dead, explicitly obtaining their principal moments. Also, we derive the probability distributions corresponding to the partial and total numbers of such biological variables, obtaining in particular the distribution of the total number of matriarchs in the genealogical tree. We apply the proposed models to describe the demographic dynamics of African elephant populations living in different habitats. PMID:23648183
Stochastic models of technology diffusion
Horner, S.M.
1978-01-01
Simple stochastic models of epidemics have often been employed by economists and sociologists in the study of the diffusion of information or new technology. In the present theoretical inquiry the properties of a family of models related to these epidemic processes are investigated, and use of the results in the study of technical change phenomena is demonstrated. A moving limit to the level of productivity of capital is hypothesized, the exact increment is determined exogenously by basic or applied research carried on outside the industry. It is this level of latent productivity (LPRO) which fills the role of the ''disease'' which ''spreads'' through the industry. In the single advance models, LPRO is assumed to have moved forward at some point in time, after which an individual firm may advance to the limit by virtue of its own research and development or through imitation of the successful efforts of another firm. In the recurrent advance models, LPRO is assumed to increase at either a constant absolute or relative rate. The firms, in the course of their research and imitation efforts, follow behind LPRO. Using the methods of stochastic processes, it is shown that these models are equivalent to ergodic Markov chains. Based on an assumption of constant intensity of R and D effort, it is shown how the single and recurrent advance models reflect on Joseph Schumpeter's hypothesis that more concentrated industries tend to be more technologically advanced than less concentrated. The results corroborate the weakest version of the hypothesis: monopoly prices need not be higher than competitive prices.
Homogenization of neutronic diffusion models
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)
Chen, She; Zeng, Rong; Zhuang, Chijie; Zhou, Xuan; Ding, Yujian
2016-03-01
One of the main problems in the Ultra High Voltage (UHV) transmission project is to choose the external insulation distance, which requires a deep understanding of the long air gap discharge mechanism. The leader-streamer propagation is one of most important stages in long air gap discharge. In the conductor-tower lattice configuration, we have measured the voltage, the current on the high voltage side and the electric field in the gap. While the streamer in the leader-streamer system presented a conical or hyperboloid diffuse shape, the clear branch structure streamer in front of the leader was firstly observed by a high speed camera in the experiment. Besides, it is found that the leader velocity, width and injected charge for the branch type streamer are greater than those of a diffuse type. We propose that the phenomenon results from the high humidity, which was 15.5-16.5 g/m3 in our experiment. supported by the Fund of the National Priority Basic Research of China (2011CB209403) and National Natural Science Foundation of China (Nos. 51325703, 51377094, 51577098)
Updated stellar yields from Asymptotic Giant Branch models
Karakas, Amanda I
2009-01-01
An updated grid of stellar yields for low to intermediate-mass thermally-pulsing Asymptotic Giant Branch (AGB) stars are presented. The models cover a range in metallicity Z = 0.02, 0.008, 0.004, and 0.0001, and masses between 1Msun to 6Msun. New intermediate-mass Z = 0.0001 AGB models are also presented, along with a finer mass grid than used in previous studies. The yields are computed using an updated reaction rate network that includes the latest NeNa and MgAl proton capture rates, with the main result that between ~6 to 30 times less Na is produced by intermediate-mass models with hot bottom burning. In low-mass AGB models we investigate the effect on the production of light elements of including some partial mixing of protons into the intershell region during the deepest extent of each third dredge-up episode. The protons are captured by the abundant 12C to form a 13C pocket. The 13C pocket increases the yields of 19F, 23Na, the neutron-rich Mg and Si isotopes, 60Fe, and 31P. The increase in 31P is by f...
Multinational Diffusion Models: An Alternative Framework
V. Kumar; Trichy V. Krishnan
2002-01-01
The literature on cross-national diffusion models is gaining increased importance today due to the needs of present day managers. New product sales growth in a given nation or society is affected by many factors (Rogers 1995), and of these, sociocontagion (or word of mouth) has been found to be the most important factor that characterizes the diffusion process (Bass 1969, Moore 1995). Hence, it is interesting and perhaps challenging to analyze what would happen if a new product diffuses in pa...
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...
A diffusion model for service products
Shi, Xiaohui; Chumnumpan, Pattarin; Fernandes, Kiran
2014-01-01
Purpose – This paper aims to develop a diffusion model that can be used to understand and forecast the market growth of service products in a competitive environment. Despite the fast growth of the service sector, the existing literature has dedicated little effort to modeling the market growth of service products. Design/methodology/approach – The authors propose a choice-type diffusion model that links the issues of service product utility, customers’ choice preference, customer switching b...
Mathematical Modeling of Branching Morphogenesis and Vascular Tumor Growth
Yan, Huaming
Feedback regulation of cell lineages is known to play an important role in tissue size control, but the effect in tissue morphogenesis has yet to be explored. We first use a non-spatial model to show that a combination of positive and negative feedback on stem and/or progenitor cell self-renewal leads to bistable or bi-modal growth behaviors and ultrasensitivity to external growth cues. Next, a spatiotemporal model is used to demonstrate spatial patterns such as local budding and branching arise in this setting, and are not consequences of Turing-type instabilities. We next extend the model to a three-dimensional hybrid discrete-continuum model of tumor growth to study the effects of angiogenesis, tumor progression and cancer therapies. We account for the crosstalk between the vasculature and cancer stem cells (CSCs), and CSC transdifferentiation into vascular endothelial cells (gECs), as observed experimentally. The vasculature stabilizes tumor invasiveness but considerably enhances growth. A gEC network structure forms spontaneously within the hypoxic core, consistent with experimental findings. The model is then used to study cancer therapeutics. We demonstrate that traditional anti-angiogenic therapies decelerate tumor growth, but make the tumor highly invasive. Chemotherapies help to reduce tumor sizes, but cannot control the invasion. Anti-CSC therapies that promote differentiation or disturb the stem cell niche effectively reduce tumor invasiveness. However, gECs inherit mutations present in CSCs and are resistant to traditional therapies. We show that anti-gEC treatments block the support on CSCs by gECs, and reduce both tumor size and invasiveness. Our study suggests that therapies targeting the vasculature, CSCs and gECs, when combined, are highly synergistic and are capable of controlling both tumor size and shape.
The Bipolar Quantum Drift-diffusion Model
Xiu Qing CHEN; Li CHEN
2009-01-01
A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassical limit describes the relation between quantum and classical drift-diffusion models. Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.
Horton and Tokunaga self-similarity in basic models of branching, aggregation, time series
Zaliapin, I.; Kovchegov, Y.
2012-12-01
Hierarchical branching structures are readily seen in river and drainage networks, lightening, botanical trees, vein structure of leaves, snowflakes, and bronchial passages, to mention but a few. Empirical evidence reveals a surprising similarity among natural hierarchies of diverse origin; many of them are closely approximated by so-called self-similar trees (SSTs). A two-parametric subclass of Tokunaga SSTs plays a special role in theory and applications, as it has been shown to emerge in unprecedented variety of modeled and natural phenomena. The Tokunaga SSTs with a broad range of parameters are seen in studies of river networks, aftershock sequences, vein structure of botanical leaves, numerical analyses of diffusion limited aggregation, two dimensional site percolation, and nearest-neighbor clustering in Euclidean spaces. The omnipresence of Tokunaga self-similarity hints at the existence of universal underlying mechanisms responsible for its appearance and prompts the question: What basic probability models may generate Tokunaga self-similar trees? This paper reviews the existing results on Tokunaga self-similarity of the critical binary Galton-Watson process, also known as Shreve's random topology model or equiprobable binary tree model. We then present new analytic results that establish Horton and Tokunaga self-similarity in (i) level-set tree representation of white noise, (ii) level-set tree representation of random walk and Brownian motion, and (iii) Kingman's coalescent process. We also formulate a conjecture, based on extensive numerical experiments, about Tokunaga self-similarity for the (iv) additive and (v) multiplicative coalescents as well as (vi) fractional Brownian motion. The listed processes are among the essential building blocks in natural and computer sciences modeling. Accordingly, the results of this study may provide at least a partial explanation for the presence of Horton and Tokunaga self-similarity in observed and modeled branching
A Model for Locating Branches of Ghavamin Bank
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.
A Model for Locating Branches of Ghavamin Bank
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.
SERVICE QUALITY ASSESSMENT IN SELECTED BRANCHES OF SOCIAL SECURITY ORGANIZATION USING SERVQUAL MODEL
Shirkavand, Fereshteh; Hossein, Seyed Mahdi; Mokhtarihesar, Parisa
2015-01-01
This study aimed to assess the quality of four branches of social security organization in Tehran Province, using SERVQUAL model and assessing the gaps between expectations and perceptions of customers in each branch of the service quality dimensions (factors tangible, reliability, responsiveness, assurance, empathy and diversity). The population study was the daily costumers of four provincial branches, each group 120, total 480 people. Sampling was simple randomize and the study was cross s...
Description of the Risoe puff diffusion model
The Risoe National Laboratory, Roskilde, Denmark, atmospheric puff dispersion model is described. This three-dimensional model simulates the release of Gaussian pullutant puffs and predicts their concentration as they are diffused and advected downwind by a horizontally homogeneous, time-dependent wind. Atmospheric characteristics such as turbulence intensity, potential temperature gradient, buoyant heat flux and maximum mixing depth have been considered. (author)
Multiphase Microfluidics The Diffuse Interface Model
2012-01-01
Multiphase flows are typically described assuming that the different phases are separated by a sharp interface, with appropriate boundary conditions. This approach breaks down whenever the lengthscale of the phenomenon that is being studied is comparable with the real interface thickness, as it happens, for example, in the coalescence and breakup of bubbles and drops, the wetting and dewetting of solid surfaces and, in general, im micro-devices. The diffuse interface model resolves these probems by assuming that all quantities can vary continuously, so that interfaces have a non-zero thickness, i.e. they are "diffuse". The contributions in this book review the theory and describe some relevant applications of the diffuse interface model for one-component, two-phase fluids and for liquid binary mixtures, to model multiphase flows in confined geometries.
Growth model for large branched three-dimensional hydraulic crack system in gas or oil shale.
Chau, Viet T; Bažant, Zdeněk P; Su, Yewang
2016-10-13
Recent analysis of gas outflow histories at wellheads shows that the hydraulic crack spacing must be of the order of 0.1 m (rather than 1 m or 10 m). Consequently, the existing models, limited to one or several cracks, are unrealistic. The reality is 10(5)-10(6) almost vertical hydraulic cracks per fracking stage. Here, we study the growth of two intersecting near-orthogonal systems of parallel hydraulic cracks spaced at 0.1 m, preferably following pre-existing rock joints. One key idea is that, to model lateral cracks branching from a primary crack wall, crack pressurization, by viscous Poiseuille-type flow, of compressible (proppant-laden) frac water must be complemented with the pressurization of a sufficient volume of micropores and microcracks by Darcy-type water diffusion into the shale, to generate tension along existing crack walls, overcoming the strength limit of the cohesive-crack or crack-band model. A second key idea is that enforcing the equilibrium of stresses in cracks, pores and water, with the generation of tension in the solid phase, requires a new three-phase medium concept, which is transitional between Biot's two-phase medium and Terzaghi's effective stress and introduces the loading of the solid by pressure gradients of diffusing pore water. A computer program, combining finite elements for deformation and fracture with volume elements for water flow, is developed to validate the new model.This article is part of the themed issue 'Energy and the subsurface'. PMID:27597791
Analytical boron diffusivity model in silicon for thermal diffusion from boron silicate glass film
Kurachi, Ikuo; Yoshioka, Kentaro
2015-09-01
An analytical boron diffusivity model in silicon for thermal diffusion from a boron silicate glass (BSG) film has been proposed in terms of enhanced diffusion due to boron-silicon interstitial pair formation. The silicon interstitial generation is considered to be a result of the silicon kick-out mechanism by the diffused boron at the surface. The additional silicon interstitial generation in the bulk silicon is considered to be the dissociation of the diffused pairs. The former one causes the surface boron concentration dependent diffusion. The latter one causes the local boron concentration dependent diffusion. The calculated boron profiles based on the diffusivity model are confirmed to agree with the actual diffusion profiles measured by secondary ion mass spectroscopy (SIMS) for a wide range of the BSG boron concentration. This analytical diffusivity model is a helpful tool for p+ boron diffusion process optimization of n-type solar cell manufacturing.
A Viral Branching Model for Predicting the Spread of Electronic Word of Mouth
van der Lans, Ralf; Bruggen, Gerrit; Eliashberg, Jehoshua; Wierenga, Berend
2010-01-01
textabstractIn a viral marketing campaign an organization develops a marketing message, and stimulates customers to forward this message to their contacts. Despite its increasing popularity, there are no models yet that help marketers to predict how many customers a viral marketing campaign will reach, and how marketers can influence this process through marketing activities. This paper develops such a model using the theory of branching processes. The proposed Viral Branching Model allows cu...
Diffusive 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.
Modelling Diffusion of a Personalized Learning Framework
Karmeshu; Raman, Raghu; Nedungadi, Prema
2012-01-01
A new modelling approach for diffusion of personalized learning as an educational process innovation in social group comprising adopter-teachers is proposed. An empirical analysis regarding the perception of 261 adopter-teachers from 18 schools in India about a particular personalized learning framework has been made. Based on this analysis,…
A transformation approach to modelling multi-modal diffusions
Forman, Julie Lyng; Sørensen, Michael
2014-01-01
This paper demonstrates that flexible and statistically tractable multi-modal diffusion models can be attained by transformation of simple well-known diffusion models such as the Ornstein–Uhlenbeck model, or more generally a Pearson diffusion. The transformed diffusion inherits many properties of...
NEW CAR DEMAND MODELING AND FORECASTING USING BASS DIFFUSION MODEL
Zuhaimy Ismail; Noratikah Abu
2013-01-01
Forecasting model of new product demand has been developed and applied to forecast new vehicle demand in Malaysia. Since the publication of the Bass model in 1969, innovation of new diffusion theory has sparked considerable research among marketing science scholars, operational researchers and mathematicians. The building of Bass diffusion model for forecasting new product within the Malaysian society is presented in this study. The proposed model represents the spread level of new Proton car...
"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis
Arellano Gustavo; Argil Julián; Azpeitia Eugenio; Benítez Mariana; Carrillo Miguel; Góngora Pedro; Rosenblueth David A.; Alvarez-Buylla Elena R
2011-01-01
Abstract Background In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulat...
Modeling Demic and Cultural Diffusion: An Introduction.
Fort, Joaquim; Crema, Enrico R; Madella, Marco
2015-07-01
Identifying the processes by which human cultures spread across different populations is one of the most topical objectives shared among different fields of study. Seminal works have analyzed a variety of data and attempted to determine whether empirically observed patterns are the result of demic and/or cultural diffusion. This special issue collects articles exploring several themes (from modes of cultural transmission to drivers of dispersal mechanisms) and contexts (from the Neolithic in Europe to the spread of computer programming languages), which offer new insights that will augment the theoretical and empirical basis for the study of demic and cultural diffusion. In this introduction we outline the state of art in the modeling of these processes, briefly discuss the pros and cons of two of the most commonly used frameworks (equation-based models and agent-based models), and summarize the significance of each article in this special issue. PMID:26932566
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.
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...
A gravitational diffusion model without dark matter
Britten, Roy J.
1998-01-01
In this model, without dark matter, the flat rotation curves of galaxies and the mass-to-light ratios of clusters of galaxies are described quantitatively. The hypothesis is that the agent of gravitational force is propagated as if it were scattered with a mean free path of approx 5 kiloparsecs. As a result, the force between moderately distant masses, separated by more than the mean free path, diminishes as the inverse first power of the distance, following diffusion equations, and describes...
Relativistic diffusion processes and random walk models
Dunkel, Jörn; Talkner, Peter; Hänggi, Peter
2006-01-01
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As well-known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (non-continuous) d...
A Stochastic Cellular Automaton Model of Non-linear Diffusion and Diffusion with Reaction
Brieger, Leesa M.; Bonomi, Ernesto
1991-06-01
This article presents a stochastic cellular automaton model of diffusion and diffusion with reaction. The master equations for the model are examined, and we assess the difference between the implementation in which a single particle at a time moves (asynchronous dynamics) and one implementation in which all particles move simultaneously (synchronous dynamics). Biasing locally each particle's random walk, we alter the diffusion coefficients of the system. By appropriately choosing the biasing function, we can impose a desired non-linear diffusive behaviour in the model. We present an application of this model, adapted to include two diffusing species, two static species, and a chemical reaction in a prototypical simulation of carbonation in concrete.
NEW CAR DEMAND MODELING AND FORECASTING USING BASS DIFFUSION MODEL
Zuhaimy Ismail
2013-01-01
Full Text Available Forecasting model of new product demand has been developed and applied to forecast new vehicle demand in Malaysia. Since the publication of the Bass model in 1969, innovation of new diffusion theory has sparked considerable research among marketing science scholars, operational researchers and mathematicians. The building of Bass diffusion model for forecasting new product within the Malaysian society is presented in this study. The proposed model represents the spread level of new Proton car among a given set of the society in terms of a simple mathematical function that elapsed since the introduction of the new car. With the limited amount of data available for the new car, a robust Bass model was developed to forecast the sales volume. A procedure of the proposed diffusion model was designed and the parameters were estimated. Results obtained by applying the proposed model and numerical calculation shows that the proposed diffusion model is robust and effective for forecasting demand of new Proton car. The proposed diffusion model is shown to forecast more effectively and accurately even with insufficient previous data on the new product.
Diffusive description of lattice gas models
The authors have investigated a lattice gas model consisting of repulsive particles following deterministic dynamics. Two versions of the model are studied. In one case a finite open system is considered in which particles can leave and enter the lattice over the edge. In the other case periodic boundary conditions are used. In both cases the density fluctuations exhibit a 1/f power spectrum. The individual particles behave asymptotically like ordinary random walkers. The collective behavior of these particles shows that due to the deterministic dynamics the particles behave as if they are correlated in time. The authors have numerically investigated the power spectrum of the density fluctuations, the lifetime distribution, and the spatial correlation function. The appropriate Langevin-like diffusion equation are discussed which can reproduce the numerical findings. The 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 to be valid for a moderate boundary drive, fails altogether when the drive goes to zero. 25 refs., 13 figs
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.
Efficient model checking for duration calculus based on branching-time approximations
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......-elementary and thus impractical. We here investigate a similar approximation as frequently employed in model checking situation-based temporal logics, where linear-time problems are safely approximated by branching-time counterparts amenable to more efficient model-checking algorithms. Mimicking the role that a...... situation has in (A)CTL as origin of a set of linear traces, we define a branching-time counterpart to interval-based temporal logics building on situation pairs spanning sets of intervals. While this branching-time interval semantics yields the desired reduction in complexity of the model-checking problem...
Mathematical Modeling of the Process for Microbial Production of Branched Chained Amino Acids
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.
Distributed Wind Diffusion Model Overview (Presentation)
Preus, R.; Drury, E.; Sigrin, B.; Gleason, M.
2014-07-01
Distributed wind market demand is driven by current and future wind price and performance, along with several non-price market factors like financing terms, retail electricity rates and rate structures, future wind incentives, and others. We developed a new distributed wind technology diffusion model for the contiguous United States that combines hourly wind speed data at 200m resolution with high resolution electricity load data for various consumer segments (e.g., residential, commercial, industrial), electricity rates and rate structures for utility service territories, incentive data, and high resolution tree cover. The model first calculates the economics of distributed wind at high spatial resolution for each market segment, and then uses a Bass diffusion framework to estimate the evolution of market demand over time. The model provides a fundamental new tool for characterizing how distributed wind market potential could be impacted by a range of future conditions, such as electricity price escalations, improvements in wind generator performance and installed cost, and new financing structures. This paper describes model methodology and presents sample results for distributed wind market potential in the contiguous U.S. through 2050.
Modeling of Reaction Processes Controlled by Diffusion
Revelli, J
2003-01-01
Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider differe...
Reflector modelization for neutronic diffusion calculations
For neutron diffusion calculations in nuclear reactors, it is always difficult to modelize the reflector. There exist different ways to describe the neutrons density in non fissile areas like the reflector, each of them presenting some advantages and difficulties. The first part of this work gives a new reflector problem formulation, replacing the complete diffusion calculation of the reflector by boundary conditions using non-local operators, the Poincare-Steklov ones. They can be used for the eigenvectors and eigenvalues diffusion problem stated on reactive core only. This theoretical treatment of non fissile areas leads, in second part, to a new interpretation of response matrix methods and Green functions methods. These two methods are in fact the main numerical techniques used to treat reflector as boundary conditions, and an other point of view is given by the Poincare-Steklov operators. Then some simple physical cases are studied, giving explicit expressions of the Poincare-Steklov operators, and allowing numerical estimates of the reflector behaviour in a whole core-reflector PWR calculation. Finally, numerical results of Green functions for boundary perturbations illustrate the physical non-locality of the boundary operators. (author). 16 refs., 2 annexes
A diffusion-diffusion model for percutaneous drug absorption.
Kubota, K; Ishizaki, T
1986-08-01
Several theories describing percutaneous drug absorption have been proposed, incorporating the mathematical solutions of differential equations describing percutaneous drug absorption processes where the vehicle and skin are regarded as simple diffusion membranes. By a solution derived from Laplace transforms, the mean residence time MRT and the variance of the residence time VRT in the vehicle are expressed as simple elementary functions of the following five pharmacokinetic parameters characterizing the percutaneous drug absorption: kd, which is defined as the normalized diffusion coefficient of the skin, kc, which is defined as the normalized skin-capillary boundary clearance, the apparent length of diffusion of the skin 1d, the effective length of the vehicle lv, and the diffusion coefficient of the vehicle Dv. All five parameters can be obtained by the methods proposed here. Results of numerical computation indicate that: concentration-distance curves in the vehicle and skin approximate two curves which are simply expressed using trigonometric functions when sufficient time elapses after an ointment application; the most suitable condition for the assumption that the concentration of a drug in the uppermost epidermis can be considered unchanged is the case where the partition coefficient between vehicle and skin is small, and the constancy of drug concentration is even more valid when the effective length of the vehicle is large; and the amount of a drug in the vehicle or skin and the flow rate of the drug from vehicle into skin or from skin into blood becomes linear on a semilogarithmic scale, and the slopes of those lines are small when Dv is small, when the partition coefficient between vehicle and skin is small, when lv is large, or when kc is small. A simple simulation method is also proposed using a biexponential for the concentration-time curve for the skin near the skin-capillary boundary, that is, the flow rate-time curve for drug passing from skin
ANALYSIS OF THE MECHANISM MODELS OF TECHNOLOGICAL INNOVATION DIFFUSION
XU Jiuping; HU Minan
2004-01-01
This paper analyzes the mechanism and principle of diffusion of technology diffusion on the basis of quantitative analysis. Then it sets up the diffusion model of innovation incorporating price, advertising and distribution, the diffusion model of innovation including various kinds of consumers, and the substitute model between the new technology and the old one applied systems dynamics, optimization method, probabilistic method and simulation method on computer. Finally this paper concludes with some practical observations from a case study.
Correlation effects in sequential energy branching: an exactly solvable model of Fano statistics.
Subashiev, Arsen V; Luryi, Serge
2010-02-01
Correlation effects in the fluctuation of the number of particles in the process of energy branching by sequential impact ionizations are studied using an exactly soluble model of random parking on a line. The Fano factor F calculated in an uncorrelated final-state "shot-glass" model does not give an accurate answer even with the exact gap-distribution statistics. Allowing for the nearest-neighbor correlation effects gives a correction to F that brings F very close to its exact value. We discuss the implications of our results for energy resolution of semiconductor gamma detectors, where the value of F is of the essence. We argue that F is controlled by correlations in the cascade energy branching process and hence the widely used final-state model estimates are not reliable--especially in the practically relevant cases when the energy branching is terminated by competition between impact ionization and phonon emission. PMID:20365546
Reaction-diffusion pulses: a combustion model
Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-02
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.
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...
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.
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
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
American Association of University Women: Branch Operations Data Modeling Case
Harris, Ranida B.; Wedel, Thomas L.
2015-01-01
A nationally prominent woman's advocacy organization is featured in this case study. The scenario may be used as a teaching case, an assignment, or a project in systems analysis and design as well as database design classes. Students are required to document the system operations and requirements, apply logical data modeling concepts, and design…
Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated
Stochastic Modelling of the Diffusion Coefficient for Concrete
Thoft-Christensen, Palle
In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficients D is strongly dependent on the w/c ratio and the temperature....
Hendrickson, Eric B; Edgerton, Jeremy R; Jaeger, Dieter
2011-04-01
Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. Therefore, we analyzed the processing capabilities of full or partially branched reduced models. These models were created by collapsing the dendritic tree of a full morphological model of a globus pallidus (GP) neuron while preserving its total surface area and electrotonic length, as well as its passive and active parameters. Dendritic trees were either collapsed into single cables (unbranched models) or the full complement of branch points was preserved (branched models). Both reduction strategies allowed us to compare dynamics between all models using the same channel density settings. Full model responses to somatic inputs were generally preserved by both types of reduced model while dendritic input responses could be more closely preserved by branched than unbranched reduced models. However, features strongly influenced by local dendritic input resistance, such as active dendritic sodium spike generation and propagation, could not be accurately reproduced by any reduced model. Based on our analyses, we suggest that there are intrinsic differences in processing capabilities between unbranched and branched models. We also indicate suitable applications for different levels of reduction, including fast searches of full model parameter space. PMID:20623167
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
Markov-modulated diffusion risk models
Bäuerle, Nicole; Kötter, Mirko
2009-01-01
In this paper we consider Markov-modulated diffusion risk reserve processes. Using diffusion approximation we show the relation to classical Markov-modulated risk reserve processes. In particular we derive a representation for the adjustment coefficient and prove some comparison results. Among others we show that increasing the volatility of the diffusion increases the probability of ruin.
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 ...
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.
Matsumoto, T.; Aizawa, Y.
1999-11-01
A stochastic branching process model of phylogeny with niche space and interactions among species is considered. For an intermediate interaction range, the time series of diversity has long periods of stasis divided by periods of rapid increase. The concept of monophyletic size is introduced, and it is shown that the size distribution obeys Zipf's law.
Puzzle of W Leptonic Decay Branching Fractions and Gauge Model of Generation Nonuniversality
Li, Xiao-Yuan; Ma, Ernest
2005-01-01
Lepton generation universality holds very well in Z decays, but appears to be violated in recent LEP data of W leptonic decay branching fractions. If this trend persists, a consistent and natural explanation is a model of generation nonuniversality, based on the gauge group SU(2)_L X U(1)_R X U(1)_{B-L}.
Brodnick, Jacob; Richardson, Brian; Ramachandran, Narayanan
2015-01-01
The Low Profile Diffuser (LPD) project originated as an award from the Marshall Space Flight Center (MSFC) Advanced Development (ADO) office to the Main Propulsion Systems Branch (ER22). The task was created to develop and test an LPD concept that could produce comparable performance to a larger, traditionally designed, ullage gas diffuser while occupying a smaller volume envelope. Historically, ullage gas diffusers have been large, bulky devices that occupy a significant portion of the propellant tank, decreasing the tank volume available for propellant. Ullage pressurization of spacecraft propellant tanks is required to prevent boil-off of cryogenic propellants and to provide a positive pressure for propellant extraction. To achieve this, ullage gas diffusers must slow hot, high-pressure gas entering a propellant tank from supersonic speeds to only a few meters per second. Decreasing the incoming gas velocity is typically accomplished through expansion to larger areas within the diffuser which has traditionally led to large diffuser lengths. The Fluid Dynamics Branch (ER42) developed and applied advanced Computational Fluid Dynamics (CFD) analysis methods in order to mature the LPD design from and initial concept to an optimized test prototype and to provide extremely accurate pre-test predictions of diffuser performance. Additionally, the diffuser concept for the Core Stage of the Space Launch System (SLS) was analyzed in a short amount of time to guide test data collection efforts of the qualification of the device. CFD analysis of the SLS diffuser design provided new insights into the functioning of the device and was qualitatively validated against hot wire anemometry of the exterior flow field. Rigorous data analysis of the measurements was performed on static and dynamic pressure data, data from two microphones, accelerometers and hot wire anemometry with automated traverse. Feasibility of the LPD concept and validation of the computational model were
Hendrickson, Eric B.; Edgerton, Jeremy R.; Jaeger, Dieter
2010-01-01
Conductance-based neuron models are frequently employed to study the dynamics of biological neural networks. For speed and ease of use, these models are often reduced in morphological complexity. Simplified dendritic branching structures may process inputs differently than full branching structures, however, and could thereby fail to reproduce important aspects of biological neural processing. It is not yet well understood which processing capabilities require detailed branching structures. T...
Modeling dendrite density from magnetic resonance diffusion measurements
Jespersen, Sune Nørhøj; Kroenke, CD; Østergaard, Leif;
2007-01-01
Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal in this...... model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (DL) and perpendicular (DT) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.e., in...... extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides an...
The coupled radiative transport-diffusion model can be used as light transport model in situations in which the diffusion equation is not a valid approximation everywhere in the domain. In the coupled model, light propagation is modelled with the radiative transport equation in sub-domains in which the approximations of the diffusion equation are not valid, such as within low-scattering regions, and the diffusion approximation is used elsewhere in the domain. In this paper, an image reconstruction method for diffuse optical tomography based on using the coupled radiative transport-diffusion model is developed. In the approach, absorption and scattering distributions are estimated by minimising a regularised least-squares error between the measured data and solution of the coupled model. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the coupled radiative transport-diffusion model can be utilised in image reconstruction problem of diffuse optical tomography and that it produces as good quality reconstructions as the full radiative transport equation also in the presence of low-scattering regions.
A stepped leader model for lightning including charge distribution in branched channels
The stepped leader process in negative cloud-to-ground lightning plays a vital role in lightning protection analysis. As lightning discharge usually presents significant branched or tortuous channels, the charge distribution along the branched channels and the stochastic feature of stepped leader propagation were investigated in this paper. The charge density along the leader channel and the charge in the leader tip for each lightning branch were approximated by introducing branch correlation coefficients. In combination with geometric characteristics of natural lightning discharge, a stochastic stepped leader propagation model was presented based on the fractal theory. By comparing simulation results with the statistics of natural lightning discharges, it was found that the fractal dimension of lightning trajectory in simulation was in the range of that observed in nature and the calculation results of electric field at ground level were in good agreement with the measurements of a negative flash, which shows the validity of this proposed model. Furthermore, a new equation to estimate the lightning striking distance to flat ground was suggested based on the present model. The striking distance obtained by this new equation is smaller than the value estimated by previous equations, which indicates that the traditional equations may somewhat overestimate the attractive effect of the ground.
Theoretical Model of Transformation Superlastic Diffusion Bonding for Eutectoid Steel
无
2002-01-01
Based on current theories of diffusion and creep cavity closure at high temperature, a theoretical analysis of phase transformation diffusion bonding for T8/T8 eutectoid steel is carried out. The diffusion bonding is mainly described as two-stage process: Ⅰ The interfacial cavity with shape change from diamond to cylinder.Ⅱ The radius of the cylindrical cavity are reduced and eliminated gradually. A new theoretical model is established for the process of transformation superplastic diffusion bonding (TSDB) ...
Matrix diffusion model. In situ tests using natural analogues
Rasilainen, K. [VTT Energy, Espoo (Finland)
1997-11-01
Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories. 98 refs. The thesis includes also eight previous publications by author.
Matrix diffusion model. In situ tests using natural analogues
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
A branching model for the spread of infectious animal diseases in varying environments
Trapman, Pieter; Meester, R; Heesterbeek, J A P
2004-01-01
This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in ...
Leena Nieminen
Full Text Available Branching networks are ubiquitous in nature and their growth often responds to environmental cues dynamically. Using the antibiotic-producing soil bacterium Streptomyces as a model we have developed a flexible mathematical model platform for the study of branched biological networks. Streptomyces form large aggregates in liquid culture that can impair industrial antibiotic fermentations. Understanding the features of these could aid improvement of such processes. The model requires relatively few experimental values for parameterisation, yet delivers realistic simulations of Streptomyces pellet and is able to predict features, such as the density of hyphae, the number of growing tips and the location of antibiotic production within a pellet in response to pellet size and external nutrient supply. The model is scalable and will find utility in a range of branched biological networks such as angiogenesis, plant root growth and fungal hyphal networks.
"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis
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
Models to assess perfume diffusion from skin.
Schwarzenbach, R; Bertschi, L
2001-04-01
Temperature, fragrance concentration on the skin and power of ventilation have been determined as crucial parameters in fragrance diffusion from skin. A tool has been developed to simulate perfume diffusion from skin over time, allowing headspace analysis and fragrance profile assessments in a highly reproducible way. PMID:18498453
Diffusion coefficient adaptive correction in Lagrangian puff model
Lagrangian puff model is widely used in the decision support system for nuclear emergency management. The diffusion coefficient is one of the key parameters impacting puff model. An adaptive method was proposed in this paper, which could correct the diffusion coefficient in Lagrangian puff model, and it aimed to improve the accuracy of calculating the nuclide concentration distribution. This method used detected concentration data, meteorological data and source release data to estimate the actual diffusion coefficient with least square method. The diffusion coefficient adaptive correction method was evaluated by Kincaid data in MVK, and was compared with traditional Pasquill-Gifford (P-G) diffusion scheme method. The results indicate that this diffusion coefficient adaptive correction method can improve the accuracy of Lagrangian puff model. (authors)
THE BANKRUPT RISK IN FEED DISTRIBUTION BRANCH IN DOLJ DISTRICT – FDR MODEL
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.
Finite difference time domain modeling of phase grating diffusion
Kowalczyk K.; Van Walstijn M.
2010-01-01
In this paper, a method for modeling diffusion caused by non-smooth boundary surfaces in simulations of room acoustics using finite difference time domain (FDTD) technique is investigated. The proposed approach adopts the well-known theory of phase grating diffusers to efficiently model sound scattering from rough surfaces. The variation of diffuser well-depths is attained by nesting allpass filters within the reflection filters from which the digital impedance filters used in the boundary im...
Measurement and Modeling of Solute Diffusion Coefficients in Unsaturated Soils
Chou, Hsin-Yi
2010-01-01
Solute diffusion in unsaturated soils refers to the transport of dissolved constituents in liquid phase from a higher to a lower concentration point. Several empirical and conceptual models were proposed to predict the solute diffusion coefficients in unsaturated soils, but they were not systematically tested and evaluated under the same conditions using soils of different textures. Our experimental data showed that there is no perfect model that can depict the behavior of solute diffusion co...
Diffusion model of the non-stoichiometric uranium dioxide
Moore, Emily, E-mail: emily.moore@cea.fr [CEA Saclay, DEN-DPC-SCCME, 91191 Gif-sur-Yvette Cedex (France); Guéneau, Christine, E-mail: christine.gueneau@cea.fr [CEA Saclay, DEN-DPC-SCCME, 91191 Gif-sur-Yvette Cedex (France); Crocombette, Jean-Paul, E-mail: jean-paul.crocombette@cea.fr [CEA Saclay, DEN DEN, Service de Recherches de Métallurgie Physique, 91191 Gif-sur-Yvette Cedex (France)
2013-07-15
Uranium dioxide (UO{sub 2}), which is used in light water reactors, exhibits a large range of non-stoichiometry over a wide temperature scale up to 2000 K. Understanding diffusion behavior of uranium oxides under such conditions is essential to ensure safe reactor operation. The current understanding of diffusion properties is largely limited by the stoichiometric deviations inherent to the fuel. The present DICTRA-based model considers diffusion across non-stoichiometric ranges described by experimentally available data. A vacancy and interstitial model of diffusion is applied to the U–O system as a function of its defect structure derived from CALPHAD-type thermodynamic descriptions. Oxygen and uranium self and tracer diffusion coefficients are assessed for the construction of a mobility database. Chemical diffusion coefficients of oxygen are derived with respect to the Darken relation and migration energies of defects are evaluated as a function of stoichiometric deviation. - Graphical abstract: Complete description of Oxygen–Uranium diffusion as a function of composition at various temperatures according to the developed Dictra model. - Highlights: • Assessment of a uranium–oxygen diffusion model with Dictra. • Complete description of U–O diffusion over wide temperature and composition range. • Oxygen model includes terms for interstitial and vacancy migration. • Interaction terms between defects help describe non-stoichiometric domain of UO{sub 2±x}. • Uranium model is separated into mobility terms for the cationic species.
Diffusion model of the non-stoichiometric uranium dioxide
Uranium dioxide (UO2), which is used in light water reactors, exhibits a large range of non-stoichiometry over a wide temperature scale up to 2000 K. Understanding diffusion behavior of uranium oxides under such conditions is essential to ensure safe reactor operation. The current understanding of diffusion properties is largely limited by the stoichiometric deviations inherent to the fuel. The present DICTRA-based model considers diffusion across non-stoichiometric ranges described by experimentally available data. A vacancy and interstitial model of diffusion is applied to the U–O system as a function of its defect structure derived from CALPHAD-type thermodynamic descriptions. Oxygen and uranium self and tracer diffusion coefficients are assessed for the construction of a mobility database. Chemical diffusion coefficients of oxygen are derived with respect to the Darken relation and migration energies of defects are evaluated as a function of stoichiometric deviation. - Graphical abstract: Complete description of Oxygen–Uranium diffusion as a function of composition at various temperatures according to the developed Dictra model. - Highlights: • Assessment of a uranium–oxygen diffusion model with Dictra. • Complete description of U–O diffusion over wide temperature and composition range. • Oxygen model includes terms for interstitial and vacancy migration. • Interaction terms between defects help describe non-stoichiometric domain of UO2±x. • Uranium model is separated into mobility terms for the cationic species
Radon diffusion through multilayer earthen covers: models and simulations
Mayer, D.W.; Oster, C.A.; Nelson, R.W.; Gee, G.W.
1981-09-01
A capability to model and analyze the fundamental interactions that influence the diffusion of radon gas through uranium mill tailings and cover systems has been investigated. The purpose of this study is to develop the theoretical basis for modeling radon diffusion and to develop an understanding of the fundamental interactions that influence radon diffusion. This study develops the theoretical basis for modeling radon diffusion in one, two and three dimensions. The theory has been incorporated into three computer models that are used to analyze several tailings and cover configurations. This report contains a discussion of the theoretical basis for modeling radon diffusion, a discussion of the computer models used to analyze uranium mill tailings and multilayered cover systems, and presents the results that have been obtained.
Large scale behavior of a two-dimensional model of anisotropic branched polymers.
Knežević, Milan; Knežević, Dragica
2013-10-28
We study critical properties of anisotropic branched polymers modeled by semi-directed lattice animals on a triangular lattice. Using the exact transfer-matrix approach on strips of quite large widths and phenomenological renormalization group analysis, we obtained pretty good estimates of various critical exponents in the whole high-temperature region, including the point of collapse transition. Our numerical results suggest that this collapse transition belongs to the universality class of directed percolation. PMID:24182076
Large scale behavior of a two-dimensional model of anisotropic branched polymers
Knežević, Milan; Knežević, Dragica
2013-10-01
We study critical properties of anisotropic branched polymers modeled by semi-directed lattice animals on a triangular lattice. Using the exact transfer-matrix approach on strips of quite large widths and phenomenological renormalization group analysis, we obtained pretty good estimates of various critical exponents in the whole high-temperature region, including the point of collapse transition. Our numerical results suggest that this collapse transition belongs to the universality class of directed percolation.
The Standard Model Higgs : Discovery Potentials and Branching Fraction Measurements at the NLC
Sachwitz, M.; Schreiber, H. J.; Shichanin, S.
1997-01-01
We discuss discovery potentials for a 140 GeV Standard Model Higgs boson produced in e+e- collisions at 360 GeV, including all potential irreducible and reducible background contributions. In the second part of the study, we estimate the uncertainties expected for the branching fractions of the Higgs into bb-bar, tau+tau-, WW* and into cc-bar+gg including a realistic error estimation of the inclusive bremsstrahlung Higgs production cross section.
March, N. H.; Moreno, A. J.
2016-06-01
The critical exponent ν for randomly branched polymers with dimensionality d equal to 3, is known exactly as 1/2. Here, we invoke an already available string theory model to predict the remaining static critical exponents. Utilizing results of Hsu et al. (Comput Phys Commun. 2005;169:114-116), results are added for d = 8. Experiment plus simulation would now be important to confirm, or if necessary to refine, the proposed values.
Wavelet estimation of the diffusion coefficient in time dependent diffusion models
Ping; CHEN; Jin-de; WANG
2007-01-01
The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1-dimensional bounded Lipschitzian function of the state or the time only.There is no previous work for the nonparametric estimation of time-dependent diffusion models where the diffusion coefficient depends on both the state and the time.This paper introduces and studies a wavelet estimation of the time-dependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz function.Using the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the Lr convergence rate.A strong consistency of the estimate is established.With this result one can estimate the time-dependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability measure.For example,in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure.
Diffuse radiation models and monthly-average, daily, diffuse data for a wide latitude range
Several years of measured data on global and diffuse radiation and sunshine duration for 40 widely spread locations in the latitude range 36° S to 60° N are used to develop and test models for estimating monthly-mean, daily, diffuse radiation on horizontal surfaces. Applicability of the clearness-index (K) and sunshine fraction (SSO) models for diffuse estimation and the effect of combining several variables into a single multilinear equation are tested. Correlations connecting the diffuse to global fraction (HdH) with K and SSO predict Hd values more accurately than their separate use. Among clearness-index and sunshine-fraction models, SSO models are found to have better accuracy if correlations are developed for wide latitude ranges. By including a term for declinations in the correlation, the accuracy of the estimated data can be marginally improved. The addition of latitude to the equation does not help to improve the accuracy further. (author)
Restricted diffusion in a model acinar labyrinth by NMR: Theoretical and numerical results
Grebenkov, D. S.; Guillot, G.; Sapoval, B.
2007-01-01
A branched geometrical structure of the mammal lungs is known to be crucial for rapid access of oxygen to blood. But an important pulmonary disease like emphysema results in partial destruction of the alveolar tissue and enlargement of the distal airspaces, which may reduce the total oxygen transfer. This effect has been intensively studied during the last decade by MRI of hyperpolarized gases like helium-3. The relation between geometry and signal attenuation remained obscure due to a lack of realistic geometrical model of the acinar morphology. In this paper, we use Monte Carlo simulations of restricted diffusion in a realistic model acinus to compute the signal attenuation in a diffusion-weighted NMR experiment. We demonstrate that this technique should be sensitive to destruction of the branched structure: partial removal of the interalveolar tissue creates loops in the tree-like acinar architecture that enhance diffusive motion and the consequent signal attenuation. The role of the local geometry and related practical applications are discussed.
SEMICLASSICAL LIMIT FOR BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL
Ju Qiangchang; Chen Li
2009-01-01
Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit ofthis solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.
Parameter Variability and Distributional Assumptions in the Diffusion Model
Ratcliff, Roger
2013-01-01
If the diffusion model (Ratcliff & McKoon, 2008) is to account for the relative speeds of correct responses and errors, it is necessary that the components of processing identified by the model vary across the trials of a task. In standard applications, the rate at which information is accumulated by the diffusion process is assumed to be normally…
A branching model for the spread of infectious animal diseases in varying environments.
Trapman, Pieter; Meester, Ronald; Heesterbeek, Hans
2004-12-01
This paper is concerned with a stochastic model, describing outbreaks of infectious diseases that have potentially great animal or human health consequences, and which can result in such severe economic losses that immediate sets of measures need to be taken to curb the spread. During an outbreak of such a disease, the environment that the infectious agent experiences is therefore changing due to the subsequent control measures taken. In our model, we introduce a general branching process in a changing (but not random) environment. With this branching process, we estimate the probability of extinction and the expected number of infected individuals for different control measures. We also use this branching process to calculate the generating function of the number of infected individuals at any given moment. The model and methods are designed using important infections of farmed animals, such as classical swine fever, foot-and-mouth disease and avian influenza as motivating examples, but have a wider application, for example to emerging human infections that lead to strict quarantine of cases and suspected cases (e.g. SARS) and contact and movement restrictions. PMID:15565446
Modeling of Two-Phase Flow through a Rotating Tube with Twin Exit Branches
Sun-Wen Cheng
2000-01-01
Full Text Available A numerical model is proposed to determine the dynamic behavior of single-phase and twophase, two-component flows through a horizontal rotating tube with identical twin exit branches. The working fluid, oil, enters the tube through a radial duct attached at one end and exits into open air through the twin radial branches, one located at midway and the other at the end of the tube. The branch-to-tube diameter ratio, rotational speed, and total oil flow rate are varied. It is experimentally revealed in previous study that the air cavitation occurs at lower speeds, leading to a two-phase flow with the air-oil ratio (void fraction varying with the rotating speed. A unique characteristic in two-phase flow, i.e., hysteresis, is found to exist in both oil flow rates and inlet pressure. In theoretical modeling, the governing flow equations are incorporated by empirical equations for hydraulic head losses. The predicted and measured exit oil flow rates are compared with good agreement in both the single-phase and annular flow regimes. Only qualitative agreement is achieved in the bubbly and bubbly-slug flow regimes. The model can be applied to improve the design and thus enhance the performance of automatic transmission lines, and the cooling efficiency of rotating machines and petroleum drilling process.
Rapidity distribution and duality of a phase-space branching model for multiparticle production
A branching model is developed for the description of multiparticle production processes at high energy. The starting point is the essential phenomenological validity of approximate KNO scaling. A quasirapidity variable is introduced, in terms of which the exclusive distribution of the produced particles can be calculated. The model is then described in the context of s- and t-channel duality. The dual picture lends itself to a physical interpretation of the model, the contrast of which from dual topological unitarization is pointed out
Spatial Pattern of an Epidemic Model with Cross-diffusion
LI Li; JIN Zhen; SUN Gui-Quan
2008-01-01
Pattern formation of a spatial epidemic model with both serf- and cross-diffusion is investigated. From the Turing theory, it is well known that Thring pattern formation cannot occur for the equal self-diffusion coefficients.However, combined with cross-diffusion, the system will show emergence of isolated groups, i.e., stripe-like or spotted or coexistence of both, which we show by both mathematical ana/ysis and numerical simulations. Our study shows that the interaction of self- and cross-diffusion can be considered as an important mechanism for the appearance of complex spatiotemporal dynamics in epidemic models.
Ion diffusion modelling of Fricke-agarose dosemeter gels
In Fricke-agarose gels, an accurate determination of the spatial dose distribution is hindered by the diffusion of ferric ions. In this work, a model was developed to describe the diffusion process within gel samples of finite length and, thus, permit the reconstruction of the initial spatial distribution of the ferric ions. The temporal evolution of the ion concentration as a function of the initial concentration is derived by solving Fick's second law of diffusion in two dimensions with boundary reflections. The model was applied to magnetic resonance imaging data acquired at high spatial resolution (0.3 mm) and was found to describe accurately the observed diffusion effects. (authors)
Dynamic hysteresis modeling including skin effect using diffusion equation model
Hamada, Souad; Louai, Fatima Zohra; Nait-Said, Nasreddine; Benabou, Abdelkader
2016-07-01
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Large scale multi-zone creep finite element modelling of a main steam line branch intersection
Payten, Warwick [ANSTO Materials and Engineering Science, New Illawarra Road, Lucas Heights, Menai, NSW 2234 (Australia)]. E-mail: wmp@ansto.gov.au
2006-05-15
A number of papers detail the non-linear creep finite element analysis of branch pieces. Predominately these models have incorporated only a single material zone representing the parent material. Multi-zone models incorporating weld material and heat affected zones have primarily been two-dimensional analyses, in part due to the large number of elements required to adequately represent all of the zones. This paper describes a non-linear creep analysis of a main steam line branch intersection using creep properties to represent the parent metal, weld metal, and heat affected zone (HAZ), the stress redistribution over 100,000 h is examined. The results show that the redistribution leads to a complex stress state, particularly at the heat affected zone. Although, there is damage on the external surface of the branch piece as expected, the results indicate that the damage would be more widespread through extensive sections of the heat affected zone. This would appear to indicate that the time between damage indications on the surface using techniques such as replication and full thickness damage may be more limited then previously expected.
Diffusion model of the non-stoichiometric uranium dioxide
Moore, Emily; Guéneau, Christine; Crocombette, Jean-Paul
2013-07-01
Uranium dioxide (UO2), which is used in light water reactors, exhibits a large range of non-stoichiometry over a wide temperature scale up to 2000 K. Understanding diffusion behavior of uranium oxides under such conditions is essential to ensure safe reactor operation. The current understanding of diffusion properties is largely limited by the stoichiometric deviations inherent to the fuel. The present DICTRA-based model considers diffusion across non-stoichiometric ranges described by experimentally available data. A vacancy and interstitial model of diffusion is applied to the U-O system as a function of its defect structure derived from CALPHAD-type thermodynamic descriptions. Oxygen and uranium self and tracer diffusion coefficients are assessed for the construction of a mobility database. Chemical diffusion coefficients of oxygen are derived with respect to the Darken relation and migration energies of defects are evaluated as a function of stoichiometric deviation.
Models of Diffusion/Reaction in Dental Plaque
Dibdin, G. H.
2011-01-01
I have extended the originally requested title ‘Models of Diffusion in Dental Plaque’ to include reaction, as the two processes are so intimately linked for a system like dental plaque. This applies whether one is simply measuring diffusion or trying to understand its effects. For simplicity the following discussion is in terms of 1 -dimensional diffusion. In the laboratory we usually run experiments in well-stirred systems; the bench-top stirrer, although simple, is arguably one ...
Heat diffusion in a two-dimensional thermal fuse model
Tørå, Glenn; Hansen, Alex
2009-01-01
We present numerical studies of electrical breakdown in disordered materials using a two-dimensional thermal fuse model with heat diffusion. A conducting fuse is heated locally by a Joule heating term. Heat diffuses to neighbouring fuses by a diffusion term. When the temperature reaches a given threshold, the fuse breaks and turns into an insulator. The time dynamics is governed by the time scales related to the two terms, in the presence of quenched disorder in the conductances of the fuses....
Takehara, Yasuo; Sakahara, Harumi [Hamamatsu Univ., Shizuoka (Japan). School of Medicine; Takahashi, Mamoru; Ichijo, Katsutoshi; Tooyama, Norihiro; Yamamoto, Hideaki; Toki, Fumitake; Nishino, Takayoshi
2001-12-01
Detection of diffusely and irregularly dilated side branches of pancreatic ducts is a reliable criterion for the diagnosis of chronic pancreatitis (Japan Pancreas Society, revised 1995). This review deals with our experience with the utility of Magnetic resonance cholangiopancreatography (MRCP) in detecting this type of ductal abnormalities. Seventy patients with symptoms indicative of pancreatic or biliary diseases were evaluated using both MRCP and endoscopic retrograde chlangiopancreatography (ERCP) within an interval of three months or shorter. Using a 1.5 T unit, a multi-angle oblique multi-slab MRCP using a single-shot fast-spin-echo sequence was used to capture the pancreatic ducts. In 36 patients, MRCP was performed after administration of Gd-DTPA. The MRCP images were blindly and separately evaluated by two radiologists by counting the number of irregularly dilated side-branches in each segment. Two gastroenterologists in consensus evaluated the ERCP images as a standard of reference. The sensitivity, specificity and Az values for MRCP in the diagnosis of chronic pancreatitis were 0.33-0.50, 0.71-0.88 and 0.67-0.79 respectively without Gd-DTPA and 0.50-0.75, 0.78-0.93 and 0.82-0.89 with Gd-DTPA. Multi-angle oblique slab MRCP can be used for diagnosis of chronic pancreatitis with acceptable diagnostic accuracy when it is performed with intravenously administered of Gd chelates. (author)
Diffusive description of lattice gas models
Fiig, T.; Jensen, H.J.
1993-01-01
boundary conditions. In both cases the density fluctuations exhibit a 1/f power spectrum. The individual particles behave asymptotically like ordinary random walkers. The collective behavior of these particles shows that due to the deterministic dynamics the particles behave as if they are correlated 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...
Atom diffusion in furnaces - models and measurements
Sadagoff, Y. M.; Dědina, Jiří
2002-01-01
Roč. 57, č. 3 (2002), s. 535-549. ISSN 0584-8547 R&D Projects: GA ČR GA203/01/0453 Institutional research plan: CEZ:AV0Z4031919 Keywords : diffusion coefficients * graphite furnace * atomic absorption spectrometry Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 2.695, year: 2002
Diffuse Scattering Model of Indoor Wideband Propagation
Franek, Ondrej; Andersen, Jørgen Bach; Pedersen, Gert Frølund
2011-01-01
This paper presents a discrete-time numerical algorithm for computing field distribution in indoor environment by diffuse scattering from walls. Calculations are performed for a rectangular room with semi-reflective walls. The walls are divided into 0.5 x 0.5 m segments, resulting in 2272 wall se...
Model of moisture diffusion in fractal media
Fan Jie; Wang Li-Li; Liu Fu-Juan; Liu Zhi; Liu Yong; Zhang Sheng
2015-01-01
Moisture diffusion in fractal media does not obey the classical Fick’s law. In this paper, its fractal partner is proposed to investigate the phenomenon in fractal media. It reveals that the moisture transport strongly depends on fractal dimensions of the media.
Modeling dendrite density from magnetic resonance diffusion measurements
Jespersen, Sune Nørhøj; Kroenke, CD; Østergaard, Leif;
2007-01-01
Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal in this mo...
Diffusion imaging with stimulated echoes: signal models and experiment design
Alexander, Daniel C
2013-01-01
Purpose: Stimulated echo acquisition mode (STEAM) diffusion MRI can be advantageous over pulsed-gradient spin-echo (PGSE) for diffusion times that are long compared to $\\ttwo$. It is important therefore for biomedical diffusion imaging applications at 7T and above where $\\ttwo$ is short. However, imaging gradients in the STEAM sequence contribute much greater diffusion weighting than in PGSE, but are often ignored during post-processing. We demonstrate here that this can severely bias parameter estimates. Method: We present models for the STEAM signal for free and restricted diffusion that account for crusher and slice-select (butterfly) gradients to avoid such bias. The butterfly gradients also disrupt experiment design, typically by skewing gradient-vectors towards the slice direction. We propose a simple compensation to the diffusion gradient vector specified to the scanner that counterbalances the butterfly gradients to preserve the intended experiment design. Results: High-field data fixed monkey brain e...
Multiscale modelling of radiation-enhanced diffusion phenomena in metals
Chang, Zhongwen
2015-01-01
A multiscale modelling framework and an experiment campaign are used to study void swelling and Cu precipitation under irradiation. Several aspects regarding defect and solute diffusion under irradiation have been studied in this thesis. First, a self-diffusion model in bcc Fe has been constructed in order to describe the non-linear effects, especially the magnetic transition, around the Curie temperature. First principles calculations are applied to obtain the parameters in the model. The pa...
Hyperbolic reaction-diffusion equations for a forest fire model
Méndez López, Vicenç; Llebot, Josep Enric,
1997-01-01
Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail.
Modeling anomalous diffusion of dense fluids in carbon nanotubes
Wang, Gerald; Hadjiconstantinou, Nicolas
2015-11-01
Molecular diffusive mechanisms exhibited under nanoconfinement can differ considerably from the Fickian self-diffusion expected in a bulk fluid. We propose a theoretical description of this phenomenon in a nanofluidic system of considerable interest - namely, a dense fluid confined within a carbon nanotube (CNT). We show that the anomalous diffusion reported in the literature is closely related to the fluid layering widely observed in this system and recently theoretically described [Wang and Hadjiconstantinou, Physics of Fluids, 052006, 2015]. In particular, we find that the key to describing the anomalous molecular diffusion (within sufficiently large CNTs) lies in recognizing that the diffusion mechanism is spatially dependent: while fluid in the center of the nanotube (at least three molecular diameters away from the wall) exhibits Fickian diffusion, fluid near the CNT wall can demonstrate non-Fickian diffusive behavior. The previously reported anomalous diffusive behavior can be reproduced, to a good approximation level, by appropriately combining the bulk and near-wall behavior to form a model for the overall diffusion rate within the nanotube. Such models produce results in quantitative agreement with molecular dynamics simulations.
Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models
Yoder, Dennis A.
2016-01-01
This paper will include a detailed comparison of heat transfer models that rely upon the thermal diffusivity. The goals are to inform users of the development history of the various models and the resulting differences in model formulations, as well as to evaluate the models on a variety of validation cases so that users might better understand which models are more broadly applicable.
Bento, Ricardo Ferreira; Salomone, Raquel; Nascimento, Silvia Bona do; Ferreira, Ricardo Jose Rodriguez; Silva, Ciro Ferreira da; Costa, Heloisa Juliana Zabeu Rossi
2014-07-01
Introduction The ideal animal model for nerve regeneration studies is the object of controversy, because all models described by the literature have advantages and disadvantages. Objective To describe the histologic and functional patterns of the mandibular branch of the facial nerve of Wistar rats to create a new experimental model of facial nerve regeneration. Methods Forty-two male rats were submitted to a nerve conduction test of the mandibular branch to obtain the compound muscle action potential. Twelve of these rats had the mandibular branch surgically removed and submitted to histologic analysis (number, partial density, and axonal diameter) of the proximal and distal segments. Results There was no statistically significant difference in the functional and histologic variables studied. Conclusion These new histologic and functional standards of the mandibular branch of the facial nerve of rats establish an objective, easy, and greatly reproducible model for future facial nerve regeneration studies. PMID:25992106
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.
WWER radial reflector modeling by diffusion codes
The two commonly used approaches to describe the WWER radial reflectors in diffusion codes, by albedo on the core-reflector boundary and by a ring of diffusive assembly size nodes, are discussed. The advantages and disadvantages of the first approach are presented first, then the Koebke's equivalence theory is outlined and its implementation for the WWER radial reflectors is discussed. Results for the WWER-1000 reactor are presented. Then the boundary conditions on the outer reflector boundary are discussed. The possibility to divide the library into fuel assembly and reflector parts and to generate each library by a separate code package is discussed. Finally, the homogenization errors for rodded assemblies are presented and discussed (Author)
Dynamic Diffusion Estimation in Exponential Family Models
Dedecius, Kamil; Sečkárová, Vladimíra
2013-01-01
Roč. 20, č. 11 (2013), s. 1114-1117. ISSN 1070-9908 R&D Projects: GA MŠk 7D12004; GA ČR GA13-13502S Keywords : diffusion estimation * distributed estimation * paremeter estimation Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.639, year: 2013 http://library.utia.cas.cz/separaty/2013/AS/dedecius-0396518.pdf
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.
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.
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_...
A model for diffusive systems: Beyond the Arrhenius mechanism
Rosa, A. C. P.; Vaveliuk, Pablo; Mundim, Kleber C.; Moret, M. A.
2016-05-01
Diffusivity in supercooled liquids was observed to exhibit a non-Arrhenius behavior near the glass-transition temperature. This process, which occurs where the activation energy depends on the temperature, suggests the possibility of a metastable equilibrium. This peculiar phenomenon cannot be explained using the usual Markovian stochastic models. Based on a non-linear Fokker-Planck equation, we propose a diffusion coefficient that is proportional to the supercooled-liquid concentration. The proposed model allows us to explain the anomalous behavior of the diffusivity robustly. We demonstrate that this new approach is consistent with experimental patterns. Besides, it could be applied to non-Arrhenius chemical kinetics.
An Analytical Air Pollution Model with Time Dependent Eddy Diffusivity
Tiziano Tirabassi; Marco Túllio Vilhena; Daniela Buske; Gervásio Annes Degrazia
2013-01-01
Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressible flow. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation assuming turbulence parameterization for realistic physical scenarios. We present the general time dependent three-dimensional soluti...
Kronecker Product Approximation Preconditioners for Convection-diffusion Model Problems
Grigori, Laura; Xiang, Hua
2008-01-01
We consider the iterative solution of the linear systems arising from four convection-diffusion model problems: the scalar convection-diffusion problem, Stokes problem, Oseen problem, and Navier-Stokes problem. We give the explicit Kronecker product structure of the coefficient matrices, especially the Kronecker product structure for the convection term. For the latter three model cases, the coefficient matrices have a $2 \\times 2$ blocks, and each block is a Kronecker product or a summation ...
It is important to understand the coupled processes of sorption and diffusion of radionuclides (RNs) in compacted bentonite, and to develop mechanistic models that can aid in the prediction of the long-term performance of geological disposal systems of radioactive waste. The integrated sorption and diffusion (ISD) model was developed based on the consistent combination of clay–water interaction, sorption and diffusion models. The diffusion model based on the electrical double layer theory describing relative ionic concentrations and viscoelectric effects at the negatively charged clay surface was coupled with porewater chemistry and sorption models. This ISD model was successfully tested for various actinides with a complex chemistry (Np(V), Am(III), U(VI) under conditions where variably charged carbonate complexes are formed) considered in Part 1, by using published diffusion and sorption data (Da, De, Kd) as a function of partial montmorillonite density. Quantitative agreements were observed by considering uncertainty in porewater chemistry and dominant aqueous species. It can therefore be concluded that the ISD model developed here is able to adequately explain the sorption and diffusion behavior of various RNs with a complex chemistry in compacted bentonites. The performed modeling indicates that uncertainties are mainly related to porewater chemistry and RN speciation and that these parameters need to be carefully evaluated. (author)
Behaviour of tracer diffusion in simple atmospheric boundary layer models
P. S. Anderson
2006-12-01
Full Text Available 1-D profiles and time series from an idealised atmospheric boundary layer model are presented, which show agreement with measurements of polar photogenic NO and NO_{2}. Diffusion models are increasingly being used as the framework for studying tropospheric air chemistry dynamics. Models based on standard boundary layer diffusivity profiles have an intrinsic behaviour that is not necessarily intuitive, due to the variation of turbulent diffusivity with height. The relatively simple model provides both a programming and a conceptual tool in the analysis of observed trace gas evolution. A time scale inherent in the model can be tuned by fitting model time series to observations. This scale is then applicable to the more physically simple but chemically complex zeroth order or box models of chemical interactions.
Behaviour of tracer diffusion in simple atmospheric boundary layer models
P. S. Anderson
2007-10-01
Full Text Available 1-D profiles and time series from an idealised atmospheric boundary layer model are presented, which show agreement with boundary layer measurements of polar NO_{x}. Diffusion models are increasingly being used as the framework for studying tropospheric air chemistry dynamics. Models based on standard boundary layer diffusivity profiles have an intrinsic behaviour that is not necessarily intuitive, due to the variation of turbulent diffusivity with height. The simple model presented captures the essence of the evolution of a trace gas released at the surface, and thereby provides both a programming and a conceptual tool in the analysis of observed trace gas evolution. A time scale inherent in the model can be tuned by fitting model time series to observations. This scale is then applicable to the more physically simple but chemically complex zeroth order or box models of chemical interactions.
Reflector modelization for neutronic diffusion and parameters identification
Physical parameters of neutronic diffusion equations can be adjusted to decrease calculations-measurements errors. The reflector being always difficult to modelize, we choose to elaborate a new reflector model and to use the parameters of this model as adjustment coefficients in the identification procedure. Using theoretical results, and also the physical behaviour of neutronic flux solutions, the reflector model consists then in its replacement by boundary conditions for the diffusion equations on the core only. This theoretical result of non-local operator relations leads then to some discrete approximations by taking into account the multiscaled behaviour, on the core-reflector interface, of neutronic diffusion solutions. The resulting model of this approach is then compared with previous reflector modelizations, and first results indicate that this new model gives the same representation of reflector for the core than previous
The advection of thermonuclear ashes by magnetized domains emerging near the H shell was suggested to explain asymptotic giant branch (AGB) star abundances. Here we verify this idea quantitatively through exact MHD models. Starting with a simple two-dimensional (2D) geometry and in an inertia frame, we study plasma equilibria avoiding the complications of numerical simulations. We show that below the convective envelope of an AGB star, variable magnetic fields induce a natural expansion, permitted by the almost ideal MHD conditions, in which the radial velocity grows as the second power of the radius. We then study the convective envelope, where the complexity of macroturbulence allows only for a schematic analytical treatment. Here the radial velocity depends on the square root of the radius. We then verify the robustness of our results with 3D calculations for the velocity, showing that for both studied regions the solution previously found can be seen as a planar section of a more complex behavior, in which the average radial velocity retains the same dependency on the radius found in 2D. As a final check, we compare our results to approximate descriptions of buoyant magnetic structures. For realistic boundary conditions, the envelope crossing times are sufficient to disperse in the huge convective zone any material transported, suggesting magnetic advection as a promising mechanism for deep mixing. The mixing velocities are smaller than for convection but larger than for diffusion and adequate for extra mixing in red giants.
Nucci, M. C. [Department of Mathematics and Informatics, University of Perugia, via Vanvitelli 1, Perugia, I-06123 (Italy); Busso, M., E-mail: mariaclara.nucci@unipg.it, E-mail: busso@fisica.unipg.it [INFN, Section of Perugia, via Pascoli, Perugia, I-06123 (Italy)
2014-06-01
The advection of thermonuclear ashes by magnetized domains emerging near the H shell was suggested to explain asymptotic giant branch (AGB) star abundances. Here we verify this idea quantitatively through exact MHD models. Starting with a simple two-dimensional (2D) geometry and in an inertia frame, we study plasma equilibria avoiding the complications of numerical simulations. We show that below the convective envelope of an AGB star, variable magnetic fields induce a natural expansion, permitted by the almost ideal MHD conditions, in which the radial velocity grows as the second power of the radius. We then study the convective envelope, where the complexity of macroturbulence allows only for a schematic analytical treatment. Here the radial velocity depends on the square root of the radius. We then verify the robustness of our results with 3D calculations for the velocity, showing that for both studied regions the solution previously found can be seen as a planar section of a more complex behavior, in which the average radial velocity retains the same dependency on the radius found in 2D. As a final check, we compare our results to approximate descriptions of buoyant magnetic structures. For realistic boundary conditions, the envelope crossing times are sufficient to disperse in the huge convective zone any material transported, suggesting magnetic advection as a promising mechanism for deep mixing. The mixing velocities are smaller than for convection but larger than for diffusion and adequate for extra mixing in red giants.
Development and validation of Apros multigroup nodal diffusion model
Rintala, Antti
2015-01-01
The development of a steady state and transient multigroup nodal diffusion model for process simulation software Apros was continued and the models were validated. The initial implementation of the model was performed in 2009 and it has not been under continuous development afterwards. Some errors in the steady state model were corrected. The transient model was found to be incorrect. The solution method of the transient model was derived, and the program code not common with the steady s...
Zhigao Liao; Jiuping Xu; Liming Yao
2013-01-01
This paper studies the innovation diffusion problem with the affection of urbanization, proposing a dynamical innovation diffusion model with fuzzy coefficient, and uses the shifting rate of people from rural areas stepping into urban areas to show the process of urbanization. The numerical simulation shows the diffusion process for telephones in China with Genetic Algorithms and this model is effective to show the process of innovation diffusion with the condition of urbanization process.
Hidetaka Tobita
2015-01-01
Polymers are the products of processes and their microstructure can be changed significantly by the reactor systems employed, especially for nonlinear polymers. The Monte Carlo simulation technique, based on the random sampling technique, is used to explore the effect of reactor types on the branched polymer structure, formed through free-radical polymerization with simultaneous long-chain branching and scission, as in the case of low-density polyethylene synthesis. As a simplified model for...
Adversarial Scheduling Analysis of Game Theoretic Models of Norm Diffusion
Istrate, Gabriel; Ravi, S S
2008-01-01
In (Istrate, Marathe, Ravi SODA 2001) we advocated the investigation of robustness of results in the theory of learning in games under adversarial scheduling models. We provide evidence that such an analysis is feasible and can lead to nontrivial results by investigating, in an adversarial scheduling setting, Peyton Young's model of diffusion of norms. In particular, our main result incorporates into Peyton Young's model.
Jump-Diffusion Models for Option Pricing versus the Black Scholes Model
Storeng, Håkon Båtnes
2014-01-01
In general, the daily logarithmic returns of individual stocks are not normally distributed. This poses a challenge when trying to compute the most accurate option prices. This thesis investigates three different models for option pricing, The Black Scholes Model (1973), the Merton Jump-Diffusion Model (1975) and the Kou Double-Exponential Jump-Diffusion Model (2002). The jump-diffusion models do not make the same assumption as the Black Scholes model regarding the behavior of the underlyi...
Scaling in the Diffusion Limited Aggregation Model
Menshutin, Anton
2012-01-01
We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/Rdep(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/Rdep) function on an ensemble with 1000 clusters of 5×107 particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.
Toward Information Diffusion Model for Viral Marketing in Business
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.
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 ...
GLOBAL ATTRACTIVITY OF POPULATION MODELS WITH DELAYS AND DIFFUSION
QIU Zhipeng
2005-01-01
In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patchΩand periodic environment and with delays recruitment, the second models a single species dispersal among the m patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators.Some earlier results are extended to population models with delays and diffusion.
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…
Numerical Simulation Model of Laminar Hydrogen/Air Diffusion Flame
于溯源; 吕雪峰
2002-01-01
A numerical simulation model is developed for a laminar hydrogen/air diffusion flame. Nineteen species and twenty chemical reactions are considered. The chemical kinetics package (CHEMKIN) subroutines are employed to calculate species thermodynamic properties and chemical reaction rate constants. The flow field is calculated by simultaneously solving a continuity equation, an axial momentum equation and an energy equation in a cylindrical coordinate system. Thermal diffusion and Brownian diffusion are considered in the radial direction while they are neglected in the axial direction. The results suggest that the main flame is buoyancy-controlled.
Underwood, Thomas; Loebner, Keith; Cappelli, Mark
2015-11-01
Detailed measurements of the thermodynamic and electrodynamic plasma state variables within the plume of a pulsed plasma accelerator are presented. A quadruple Langmuir probe operating in current-saturation mode is used to obtain time resolved measurements of the plasma density, temperature, potential, and velocity along the central axis of the accelerator. This data is used in conjunction with a fast-framing, intensified CCD camera to develop and validate a model predicting the existence of two distinct types of ionization waves corresponding to the upper and lower solution branches of the Hugoniot curve. A deviation of less than 8% is observed between the quasi-steady, one-dimensional theoretical model and the experimentally measured plume velocity. This work is supported by the U.S. Department of Energy Stewardship Science Academic Program in addition to the National Defense Science Engineering Graduate Fellowship.
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)
Weak diffusion limits of dynamic conditional correlation models
Hafner, Christian M.; Laurent, Sebastien; Violante, Francesco
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 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...... 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...
Evaluation of the Thermodynamic Models for the Thermal Diffusion Factor
Gonzalez-Bagnoli, Mariana G.; Shapiro, Alexander; Stenby, Erling Halfdan
2003-01-01
Over the years, several thermodynamic models for the thermal diffusion factors for binary mixtures have been proposed. The goal of this paper is to test some of these models in combination with different equations of state. We tested the following models: those proposed by Rutherford and Drickamer...... 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 we applied different thermodynamic models, such as the Soave-Redlich-Kwong and the Peng-Robinson equations of state. The necessity to try different thermo-dynamic models is caused by the high sensitivity of the thermal diffusion factors to the values of the partial molar properties. Two different...
A WORKING INTEGRATED MODEL FOR THE DIFFUSION OF CONSTRUCTION INNOVATION
Ahmad Rahman Songip; Lau, B. H.; Kamaruzaman Jusoff; Hayati Nor Ramli
2013-01-01
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 ...
Ostwald ripening on a substrate : modeling local interparticle diffusion
Zheng, Xin; Bigot, Bernard
1994-01-01
A model with local interparticle diffusion is considered, in contrast with the classical model of Ostwald ripening (the mean field model) and its multiparticle extensions which have long range interactions. Simulations of the evolution of the system show that the asymptotic behavior obeys a power law. It is also found that the scaled asymptotic distribution of particle radii is broader than in the previous models, even at low initial coverage where the multiparticle models have the same narro...
A Generalized Norton-Bass Model for Multigeneration Diffusion
Zhengrui Jiang; Dipak C. Jain
2012-01-01
The Norton-Bass (NB) model is often credited as the pioneering multigeneration diffusion model in marketing. However, as acknowledged by the authors, when counting the number of adopters who substitute an old product generation with a new generation, the NB model does not differentiate those who have already adopted the old generation from those who have not. In this study, we develop a generalized Norton-Bass (GNB) model that separates the two different types of substitutions. The GNB model ...
A Vertical Two-Dimensional Model to Simulate Tidal Hydrodynamics in A Branched Estuary
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.
A comparison of Gaussian and diffusivity models of atmospheric dispersion
The Gaussian plume diffusion model of Smith and a diffusivity model by Maul are compared over the full range of atmospheric stability. The models' predictions for ground level concentration are found to agree well a) for ground level releases of materials, and b) for elevated releases of material at distances comparable to or greater than the distance of maximum ground level concentration. Surface layer, ground roughness, and dry deposition effects are examined and a simple ground deposition model used in the Gaussian plume model is found to be adequate over most of the stability range. Uncertainties due to the models themselves and the meteorological input data are estimated and the advantages and limitations of both types of model are discussed. It is concluded that the models are suitable for a variety of applications and that they are fast and inexpensive to run as computer models. (author)
Numerical modelling of swirling diffusive flames
Parra-Santos Teresa; Perez Ruben; Szasz Robert Z.; Gutkowski Artur N.; Castro Francisco
2016-01-01
Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing...
Cohabitation reaction-diffusion model for virus focal infections
Amor, Daniel R.; Fort, Joaquim
2014-12-01
The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction-diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction-diffusion equations may lead to unrealistic descriptions. We argue that previous virus infection models also have this limitation, because they assume that a virion can simultaneously reproduce inside a cell and diffuse away from it. For this reason, we build a several-species cohabitation model that does not have this limitation. Furthermore, we perform a sensitivity analysis for the most relevant parameters of the model, and we compare the predicted infection speed with observed data for two different strains of the T7 virus.
RETADD: a Regional Trajectory And Diffusion-Deposition model
Begovich, C. L.; Murphy, B. D.; Nappo, Jr., C. J.
1978-06-01
The Regional Trajectory and Diffusion-Deposition Model (RETADD) is based upon a version of the National Oceanic and Atmospheric Administration Air Resources Laboratory's Regional-Continental Scale Transport, Diffusion, and Deposition Model. The FORTRAN IV computer model uses a trajectory analysis technique for estimating the transport and long-range diffusion of material emitted from a point source. The wind trajectory portion of the code uses observed upper air winds to compute the transport of the material. Ground level concentrations and depositions are computed by using the Gaussian plume equation for wind trajectories projected forward in time. Options are included to specify an upper bound for the mixed layer and a chemical decomposition rate for the effluent. The limitations to the technique are discussed, the equations and model are described, and listings of the program, input, and output are included.
Modelling and simulation of diffusive processes methods and applications
Basu, SK
2014-01-01
This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport
A Patient-Specific Airway Branching Model for Mechanically Ventilated Patients
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.
A spatial model of the diffusion of mobile communications within the European Union
Frank, Lauri Dieter
2002-01-01
Innovation diffusion studies have been popular. However, usually the focus has been on two dimensions: Either the innovation's diffusion is studied on the micro level by examining the individual's adoption of an innovation, or on the macro-level by modelling the sigmoid diffusion curve. The third dimension of the diffusion of an innovation, spatial diffusion, has gained less attention. Spatial diffusion models mostly base on the effect of distance on an innovation's diffusion process. General...
The parton model for the diffusion
We analyze the Buchmueller-Hebecker model for diffraction processes, point out its predictions to the diffractive structure function FD(3)2 (xIP, β,Q2). The break of factorization for the FD93)2 present in recent H1 data is well described introducing an extra soft (reggeon) contribution as an extension to the model. (author)
Modeling diffusion of innovations with probabilistic cellular automata
Boccara, Nino; Fuks, Henryk
1997-01-01
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a second-order phase transition. We show that the number of individuals who eventually keep adopting the innovation strongly depends on connectivity between individuals.
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
Diffusion approximation for modeling of 3-D radiation distributions
A three-dimensional transport code DIF3D, based on the diffusion approximation, is used to model the spatial distribution of radiation energy arising from volumetric isotropic sources. Future work will be concerned with the determination of irradiances and modeling of realistic scenarios, relevant to the battlefield conditions. 8 refs., 4 figs
A combinatorial model of malware diffusion via bluetooth connections.
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.
Langevin equation with fluctuating diffusivity: A two-state model.
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool. PMID:27575079
Langevin equation with fluctuating diffusivity: A two-state model
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
Modeling Copper Diffusion in Polycrystalline CdTe Solar Cells
Akis, Richard [Arizona State University; Brinkman, Daniel [Arizona State University; Sankin, Igor [First Solar; Fang, Tian [First Solar; Guo, Da [Arizona State Univeristy; Vasileska, Dragica [Arizona State University; Ringhofer, Christain [Arizona State University
2014-06-06
It is well known that Cu plays an important role in CdTe solar cell performance as a dopant. In this work, a finite-difference method is developed and used to simulate Cu diffusion in CdTe solar cells. In the simulations, which are done on a two-dimensional (2D) domain, the CdTe is assumed to be polycrystalline, with the individual grains separated by grain boundaries. When used to fit experimental Cu concentration data, bulk and grain boundary diffusion coefficients and activation energies for CdTe can be extracted. In the past, diffusion coefficients have been typically obtained by fitting data to simple functional forms of limited validity. By doing full simulations, the simplifying assumptions used in those analytical models are avoided and diffusion parameters can thus be determined more accurately
Numerical modelling of swirling diffusive flames
Parra-Santos Teresa
2016-01-01
Full Text Available Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing in mind the annular jet has swirl number over 0.5, a vortex breakdown appears in the axis of the burner. Besides, the sudden expansion with a ratio of 2 in diameter between nozzle exits and the test chamber produces the boundary layer separation with the corresponding torus shape recirculation. Contrasting the mixing and combustion models, the last one produces the reduction of the vortex breakdown.
Numerical modelling of swirling diffusive flames
Parra-Santos, Teresa; Perez, Ruben; Szasz, Robert Z.; Gutkowski, Artur N.; Castro, Francisco
2016-03-01
Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing in mind the annular jet has swirl number over 0.5, a vortex breakdown appears in the axis of the burner. Besides, the sudden expansion with a ratio of 2 in diameter between nozzle exits and the test chamber produces the boundary layer separation with the corresponding torus shape recirculation. Contrasting the mixing and combustion models, the last one produces the reduction of the vortex breakdown.
Modelling on cavitation in a diffuser with vortex generator
Jablonská J.
2013-04-01
Full Text Available Based on cavitation modelling in Laval nozzle results and experience, problem with the diffuser with vortex generator was defined. The problem describes unsteady multiphase flow of water. Different cavitation models were used when modelling in Fluent, flow condition is inlet and pressure condition is outlet. Boundary conditions were specified by Energy Institute, Victor Kaplan’s Department of Fluid Engineering, Faculty of Mechanical Engineering, Brno University of Technology. Numerical modelling is compared with experiment.
COMPUTATION OF GREEKS FOR JUMP-DIFFUSION MODELS
M'Hamed Eddahbi; SIDI MOHAMED LALAOUI BEN CHERIF; ABDELAZIZ NASROALLAH
2015-01-01
In the present paper, we compute the Greeks for a class of jump diffusion models by using Malliavin calculus techniques. More precisely, the model under consideration is governed by a Brownian component and a jump part described by a compound Poisson process. Our approach consists of approximating the compound Poisson process by a suitable sequence of standard Poisson processes. The Greeks of the original model are obtained as limits or weighted limits of the Greeks of the approximate model. ...
Mathematical models of a diffusion-convection in porous media
Anvarbek M. Meirmanov
2012-06-01
Full Text Available Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory. We start with the mathematical model on the microscopic level, which consist of the Stokes system for a weakly compressible viscous liquid occupying a pore space, coupled with a diffusion-convection equation for the admixture. We suppose that the viscosity of the liquid depends on a concentration of the admixture and for this nonlinear system we prove the global in time existence of a weak solution. Next we rigorously fulfil the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous media.
Diffuse solar radiation estimation models for Turkey's big cities
A reasonably accurate knowledge of the availability of the solar resource at any place is required by solar engineers, architects, agriculturists, and hydrologists in many applications of solar energy such as solar furnaces, concentrating collectors, and interior illumination of buildings. For this purpose, in the past, various empirical models (or correlations) have been developed in order to estimate the solar radiation around the world. This study deals with diffuse solar radiation estimation models along with statistical test methods used to statistically evaluate their performance. Models used to predict monthly average daily values of diffuse solar radiation are classified in four groups as follows: (i) From the diffuse fraction or cloudness index, function of the clearness index, (ii) From the diffuse fraction or cloudness index, function of the relative sunshine duration or sunshine fraction, (iii) From the diffuse coefficient, function of the clearness index, and (iv) From the diffuse coefficient, function of the relative sunshine duration or sunshine fraction. Empirical correlations are also developed to establish a relationship between the monthly average daily diffuse fraction or cloudness index (Kd) and monthly average daily diffuse coefficient (Kdd) with the monthly average daily clearness index (KT) and monthly average daily sunshine fraction (S/So) for the three big cities by population in Turkey (Istanbul, Ankara and Izmir). Although the global solar radiation on a horizontal surface and sunshine duration has been measured by the Turkish State Meteorological Service (STMS) over all country since 1964, the diffuse solar radiation has not been measured. The eight new models for estimating the monthly average daily diffuse solar radiation on a horizontal surface in three big cites are validated, and thus, the most accurate model is selected for guiding future projects. The new models are then compared with the 32 models available in the literature in
Modelling Ni diffusion in bentonite using different sorption models
Document available in extended abstract form only. An important component of the multi barrier disposal concept for a radioactive waste repository is the bentonite backfill surrounding the canisters containing vitrified high-level waste and spent fuel located in the tunnels deep within the chosen host rock. The effectiveness of the compacted bentonite barrier is such that calculations have indicated that many radionuclides have decayed to insignificant levels before having diffused through the thickness of bentonite. These calculations are performed using the simple Kd sorption concept in which the values are taken from batch type experiments performed on dispersed systems performed for a single metal at a time, usually at trace concentrations. However, in such complex systems many radionuclides, inactive metal contaminants/ground water components may be simultaneously present in the aqueous phase at a range of concentrations varying with time during the temporal evolution of the repository system. An important aspect influencing the sorption of any radioactive metal under a set of given geochemical conditions is its competition with other metals present, and how this may vary as a function of concentration. Competitive sorption effects are not currently included in safety assessments and are thus an issue which needs to be addressed. Here we provide some first estimates of the potential influence of competitive sorption effects on the migration of radioactive metals through compacted bentonite as a function of their concentration and the concentration of competing metals. Ni(II) and Fe(II) were chosen as possible competing cations since their concentration levels are expected to have values greater than trace levels and effects might be maximal and canister corrosion represents a permanent Fe source at the bentonite interface which could influence bivalent radionuclide diffusion. The modelling of the Ni(II) diffusion/sorption has been carried out using three
Mizia, Ronald E.; Clark, Denis E.; Glazoff, Michael V.; Lister, Tedd E.; Trowbridge, Tammy L.
2013-01-01
A research effort was made to evaluate the usefulness of modern thermodynamic and diffusion computational tools, Thermo-Calc and Dictra (Thermo_Calc Software, Inc., McMurray, PA), in optimizing the parameters for diffusion welding of Alloy 800H. This would achieve a substantial reduction in the overall number of experiments required to achieve optimal welding and post-weld heat treatment conditions. This problem is important because diffusion-welded components of Alloy 800H are being evaluated for use in assembling compact, micro-channel heat exchangers that are being proposed in the design of a high-temperature, gas-cooled reactor by the U.S. Department of Energy. The modeling was done in close contact with experimental work. The latter included using the Gleeble 3500 System (Dynamic Systems, Inc., Poestenkill, NY) for welding simulation, mechanical property measurement, and light optical and scanning electron microscopy. The modeling efforts suggested a temperature of 1423 K (1150 °C) for 1 hour with an applied pressure of 5 MPa using a 15- μm Ni foil as joint filler to reduce chromium oxidation on the welded surfaces. Good agreement between modeled and experimentally determined concentration gradients was achieved, and model refinements to account for the complexity of actual alloy materials are suggested.
A research effort was made to evaluate the usefulness of modern thermodynamic and diffusion computational tools, Thermo-Calc(copyright) and Dictra(copyright), in optimizing the parameters for diffusion welding of Alloy 800H. This would achieve a substantial reduction in the overall number of experiments required to achieve optimal welding and post-weld heat treatment conditions. This problem is important because diffusion welded components of Alloy 800H are being evaluated for use in assembling compact, micro-channel heat exchangers that are being proposed in the design of a high temperature gas-cooled reactor by the US Department of Energy. The modeling was done in close contact with experimental work. The latter included using the Gleeble 3500 System(reg sign) for welding simulation, mechanical property measurement, and light optical and Scanning Electron Microscopy. The modeling efforts suggested a temperature of 1150 C for 1 hour with an applied pressure of 5 MPa using a 15 μm Ni foil as a joint filler to reduce chromium oxidation on the welded surfaces. Good agreement between modeled and experimentally determined concentration gradients was achieved, and model refinements to account for the complexity of actual alloy materials are suggested.
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.
Model checking Branching-Time Properties of Multi-Pushdown Systems is Hard
Atig, Mohamed Faouzi; Kumar, K Narayan; Saivasan, Prakash
2012-01-01
We address the model checking problem for shared memory concurrent programs modeled as multi-pushdown systems. We consider here boolean programs with a finite number of threads and recursive procedures. It is well-known that the model checking problem is undecidable for this class of programs. In this paper, we investigate the decidability and the complexity of this problem under the assumption of bounded context-switching defined by Qadeer and Rehof, and of phase-boundedness proposed by La Torre et al. On the model checking of such systems against temporal logics and in particular branching time logics such as the modal $\\mu$-calculus or CTL has received little attention. It is known that parity games, which are closely related to the modal $\\mu$-calculus, are decidable for the class of bounded-phase systems (and hence for bounded-context switching as well), but with non-elementary complexity (Seth). A natural question is whether this high complexity is inevitable and what are the ways to get around it. This...
Modeling Dynamics of Diffusion Across Heterogeneous Social Networks: News Diffusion in Social Media
Peter Christen
2013-10-01
Full Text Available Diverse online social networks are becoming increasingly interconnected by sharing information. Accordingly, emergent macro-level phenomena have been observed, such as the synchronous spread of information across different types of social media. Attempting to analyze the emergent global behavior is impossible from the examination of a single social platform, and dynamic influences between different social networks are not negligible. Furthermore, the underlying structural property of networks is important, as it drives the diffusion process in a stochastic way. In this paper, we propose a macro-level diffusion model with a probabilistic approach by combining both the heterogeneity and structural connectivity of social networks. As real-world phenomena, we explore instances of news diffusion across different social media platforms from a dataset that contains over 386 million web documents covering a one-month period in early 2011. We find that influence between different media types is varied by the context of information. News media are the most influential in the arts and economy categories, while social networking sites (SNS and blog media are in the politics and culture categories, respectively. Furthermore, controversial topics, such as political protests and multiculturalism failure, tend to spread concurrently across social media, while entertainment topics, such as film releases and celebrities, are more likely driven by interactions within single social platforms. We expect that the proposed model applies to a wider class of diffusion phenomena in diverse fields and that it provides a way of interpreting the dynamics of diffusion in terms of the strength and directionality of influences among populations.
Do Coupled Climate Models Correctly SImulate the Upward Branch of the Deept Ocean Global Conveyor?
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 WORKING INTEGRATED MODEL FOR THE DIFFUSION OF CONSTRUCTION INNOVATION
Ahmad Rahman Songip
2013-01-01
Full Text Available Construction industry is said to be low in innovation and adoption of innovations is necessary to gain competitive advantage in a liberalized and globalized marketplace. This study investigated the factors that influenced the diffusion of construction innovations and developed an integrated framework to improve the diffusion process. A conceptual model was developed to guide the study and the modification of a questionnaire used in previous study of similar nature. The dependent variable was extent of diffusion and 10 independent factors were identified and categorized into industry characteristics, innovation attributes, adopter innovative characteristics and environmental interventions. A questionnaire survey was conducted on large and established construction firms in Malaysia. A randomized sample of 525 firms was selected and the primary data were collected by self-administered postal survey. The response rate was 28%. Data analysis was carried out using Statistical Package for Social Science (SPSS Version 12. Among the factors, innovative culture was found to be most significant and influenced diffusion positively. In contrast with most of the previous studies conducted in developed countries, this study was conducted in Malaysia. It is likely to benefit the construction industry of developing countries of similar settings. The integrated framework of innovation diffusion will benefit homegrown innovation developers in more successful diffusion of their future construction innovations.
A Diffusion Model for Spatially Dependent Photopolymerization
Mackey, Dana; Babeva, Tzvetanka; Naydenova, Izabela; Toal, Vincent
2010-01-01
Photopolymers represent an attractive class of optical recording materials due to properties such as high refractive index modulation, dry film processing, long shelf life, etc. Applications include holographically based devices for optical storage disks, optical interconnections, optical memories and filters. This paper will address the dynamics of short-exposure holographic grating formation; a new mathematical model is proposed with the aim of understanding the experimental observations of...
Diffusion approximation of neuronal models revisited
Čupera, Jakub
2014-01-01
Roč. 11, č. 1 (2014), s. 11-25. ISSN 1547-1063. [International Workshop on Neural Coding (NC) /10./. Praha, 02.09.2012-07.09.2012] R&D Projects: GA ČR(CZ) GAP103/11/0282 Institutional support: RVO:67985823 Keywords : stochastic model * neuronal activity * first-passage time Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.840, year: 2014
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Monika Žecová; Ján Terpák
2015-01-01
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 d...
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
Forecasting with a Repeat Purchase Diffusion Model
Ambar G. Rao; Masataka Yamada
1988-01-01
A methodology for forecasting the sales of an ethical drug as a function of marketing effort before any sales data are available and for updating the forecast with a few periods of sales data is presented. Physicians' perceptions of the drug on a number of attributes, e.g. effectiveness, range of ailments for which appropriate, frequency of prescriptions, are used to estimate the parameters of a model originally proposed by Lilien, Rao and Kalish (Lilien, G. L., A. G. Rao, S. Kalish. 1981. Ba...
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...
Modelling the sound transmission through partition walls using a diffusion model
Billon, A.; Foy, C; VALEAU, V; Picaut, J.; Sakout, A.
2007-01-01
The diffusion model has been used successfully to evaluate the acoustic behaviour of a system of coupled rooms connected through a coupling aperture. In this paper, an extension of this model is proposed to deal with the propagation of sound energy through a partition wall. The diffusion model can be considered as a extension of the statistical theory to none diffuse sound fields. Numerical comparisons with the statistical theory are then carried out. The following parameters are varied : its...
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...
Asymmetric diffusion model for oblique-incidence reflectometry
Yaqin Chen; Liji Cao; Liqun Sun
2011-01-01
A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectom-etry. By fitting to this asymmetric diffusion model, the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10% from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp') away from the incident point; particularly, μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10% accuracy. The method is verified by Monte Carlo simulations and experimentally tested on a phantom.%A diffusion theory model induced by a line source distribution is presented for oblique-incidence reflectometry.By fitting to this asymmetric diffusion model,the absorption and reduced scattering coefficients μa and μ's of the turbid medium can both be determined with accuracy of 10％ from the absolute profile of the diffuse reflectance in the incident plane at the negative position -1.5 transport mean free path (mfp')away from the incident point;particularly,μ's can be estimated from the data at positive positions within 0-1.0 mfp' with 10％ accuracy.The method is verified by Monte Carlo simulations and experimentally tested on a phantom.Knowledge about the optical properties,including the absorption coefficient (μa) and the reduced scattering coefficient (μ's =μs(1-g)),where μs is the scattering coefficient and g is the anisotropy factor of scattering,of biological tissues plays an important role for optical therapeutic and diagnostic techniques in medicine.
Computer modelling of nanoscale diffusion phenomena at epitaxial interfaces
The present study outlines an important area in the application of computer modelling to interface phenomena. Being relevant to the fundamental physical problem of competing atomic interactions in systems with reduced dimensionality, these phenomena attract special academic attention. On the other hand, from a technological point of view, detailed knowledge of the fine atomic structure of surfaces and interfaces correlates with a large number of practical problems in materials science. Typical examples are formation of nanoscale surface patterns, two-dimensional superlattices, atomic intermixing at an epitaxial interface, atomic transport phenomena, structure and stability of quantum wires on surfaces. We discuss here a variety of diffusion mechanisms that control surface-confined atomic exchange, formation of alloyed atomic stripes and islands, relaxation of pure and alloyed atomic terraces, diffusion of clusters and their stability in an external field. The computational model refines important details of diffusion of adatoms and clusters accounting for the energy barriers at specific atomic sites: smooth domains, terraces, steps and kinks. The diffusion kinetics, integrity and decomposition of atomic islands in an external field are considered in detail and assigned to specific energy regions depending on the cluster stability in mass transport processes. The presented ensemble of diffusion scenarios opens a way for nanoscale surface design towards regular atomic interface patterns with exotic physical features.
GIS-BASED 1-D DIFFUSIVE WAVE OVERLAND FLOW MODEL
KALYANAPU, ALFRED [Los Alamos National Laboratory; MCPHERSON, TIMOTHY N. [Los Alamos National Laboratory; BURIAN, STEVEN J. [NON LANL
2007-01-17
This paper presents a GIS-based 1-d distributed overland flow model and summarizes an application to simulate a flood event. The model estimates infiltration using the Green-Ampt approach and routes excess rainfall using the 1-d diffusive wave approximation. The model was designed to use readily available topographic, soils, and land use/land cover data and rainfall predictions from a meteorological model. An assessment of model performance was performed for a small catchment and a large watershed, both in urban environments. Simulated runoff hydrographs were compared to observations for a selected set of validation events. Results confirmed the model provides reasonable predictions in a short period of time.
Active Versus Passive: Receiver Model Transforms for Diffusive Molecular Communication
Noel, Adam; Makrakis, Dimitrios; Hafid, Abdelhakim
2016-01-01
This paper presents an analytical comparison of the active and passive receiver models in diffusive molecular communication. In the active model, molecules are absorbed when they collide with the receiver surface. In the passive model, the receiver is a virtual boundary that does not affect molecule behavior. Two approaches are presented to derive transforms between the active and passive receiver signals. As an example, we unify the two models for an unbounded diffusion-only molecular communication system with a spherical receiver. As time increases in the three-dimensional system, the transform functions have constant scaling factors, such that the receiver models are effectively equivalent. Methods are presented to enable the transformation of stochastic simulations, which are used to verify the transforms and demonstrate that transforming the simulation of a passive receiver can be more efficient and more accurate than the direct simulation of an absorbing receiver.
Turing instability in reaction-diffusion models on complex networks
Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya
2016-09-01
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.
A Mixed-Culture Biofilm Model with Cross-Diffusion.
Rahman, Kazi A; Sudarsan, Rangarajan; Eberl, Hermann J
2015-11-01
We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system. PMID:26582360
A Short Note on Non-isothermal Diffusion Models
T. Ficker
2003-01-01
Full Text Available Asymptotic behaviour of the DIAL and DRAL non-isothermal models, derived previously for the diffusion of water vapour through a porous building structure, is studied under the assumption that the initially non-isothermal structure becomes purely isothermal.
A Jump Diffusion Model for Volatility and Duration
Wei, Wei; Pelletier, Denis
the market microstructure theory. Traditional measures of volatility do not utilize durations. I adopt a jump diffusion process to model the persistence of intraday volatility and conditional duration, and their interdependence. The jump component is disentangled from the continuous part of the price...
Quasineutral limit of a standard drift diffusion model for semiconductors
无
2002-01-01
The limit of vanishing Debye length (charge neutral limit ) in a nonlinear bipolar drift-diffusion model for semiconductors without pn-junction (i.e. without a bipolar background charge ) is studied. The quasineutral limit (zero-Debye-length limit) is performed rigorously by using the weak compactness argument and the so-called entropy functional which yields appropriate uniform estimates.
Traveling Wave Solutions in a Reaction-Diffusion Epidemic Model
Sheng Wang; Wenbin Liu; Zhengguang Guo; Weiming Wang
2013-01-01
We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.
Probability of induced nuclear fission in diffusion model
The apparatus of the fission diffusion model taking into account nonequilibrium stage of the process as applied to the description of the probability of induced nuclear fission is described. The results of calculation of the energy dependence of 212Po nuclear fissility according to the new approach are presented
Decomposing Task-Switching Costs with the Diffusion Model
Schmitz, Florian; Voss, Andreas
2012-01-01
In four experiments, task-switching processes were investigated with variants of the alternating runs paradigm and the explicit cueing paradigm. The classical diffusion model for binary decisions (Ratcliff, 1978) was used to dissociate different components of task-switching costs. Findings can be reconciled with the view that task-switching…
Computational Modeling of Turbulent Swirling Diffusion Flames
Vondál, Jiří
2012-01-01
Schopnost predikovat tepelné toky do stěn v oblasti spalování, konstrukce pecí a procesního průmyslu je velmi důležitá pro návrh těchto zařízení. Je to často klíčový požadavek pro pevnostní výpočty. Cílem této práce je proto získat kvalitní naměřená data na experimentálním zařízení a využít je pro validaci standardně využívaných modelů počítačového modelování turbulentního vířivého difúzního spalování zemního plynu. Experimentální měření bylo provedeno na vodou chlazené spalovací komoře průmy...
Gitter, K., E-mail: kurt.gitter@tu-dresden.de [TU Dresden, Institute of Fluid Mechanics, Chair of Magnetofluiddynamics, 01062 Dresden (Germany); Odenbach, S. [TU Dresden, Institute of Fluid Mechanics, Chair of Magnetofluiddynamics, 01062 Dresden (Germany)
2011-12-15
Magnetic drug targeting (MDT), because of its high targeting efficiency, is a promising approach for tumour treatment. Unwanted side effects are considerably reduced, since the nanoparticles are concentrated within the target region due to the influence of a magnetic field. Nevertheless, understanding the transport phenomena of nanoparticles in an artery system is still challenging. This work presents experimental results for a branched tube model. Quantitative results describe, for example, the net amount of nanoparticles that are targeted towards the chosen region due to the influence of a magnetic field. As a result of measurements, novel drug targeting maps, combining, e.g. the magnetic volume force, the position of the magnet and the net amount of targeted nanoparticles, are presented. The targeting maps are valuable for evaluation and comparison of setups and are also helpful for the design and the optimisation of a magnet system with an appropriate strength and distribution of the field gradient. The maps indicate the danger of accretion within the tube and also show the promising result of magnetic drug targeting that up to 97% of the nanoparticles were successfully targeted. - Highlights: > Quantitative targeting maps summarise a series of measurements. > Targeting maps combine quantitative data, magnetic volume forces and magnet position. > Here, up to 97% of injected particles were targeted towards the tumour region. > High concentration of injected ferrofluid brings the danger of accretion. > Low miscibility of ferrofluid by water modelling the blood flow is detected.
Modeling the diffusion of phosphorus in silicon in 3-D
Baker, K.R. [Univ. of Texas, Austin, TX (United States)
1994-12-31
The use of matrix preconditioning in semiconductor process simulation is examined. The simplified nonlinear single-species model for the diffusion of phosphorus into silicon is considered. The experimental three-dimensional simulator, PEPPER3, which uses finite differences and the numerical method of lines to implement the reaction-diffusion equation is modified to allow NSPCG to be called to solve the linear system in the inner Newton loop. Use of NSPCG allowed various accelerators such as Generalized Minimal Residual (GMRES) and Conjugate Gradient (CG) to be used in conjunction with preconditioners such as Richardson, Jacobi, and Incomplete Cholesky.
Two ARCH Models and Their Limitations as Diffusion Processes
杨海波; 叶俊
2002-01-01
Two typical ARCH models: the ASDARCH model and the APARCH model are analyzed. Let Yk and σ2k denote the log returns and the volatility. When the time interval h goes to zero, (Yk,σ2k), as a discrete time Markov chain system, weakly converges to a continuous time diffusion process. The continuous time approximation of the ASDARCH model is done using two different methods. With some transformation, these two results are equivalent to high frequency data. The continuous time approximation of the APARCH model is obtained by a different procedure.
Macroscopic diffusion models for precipitation in crystalline gallium arsenide
Kimmerle, Sven-Joachim Wolfgang
2009-09-21
Based on a thermodynamically consistent model for precipitation in gallium arsenide crystals including surface tension and bulk stresses by Dreyer and Duderstadt, we propose two different mathematical models to describe the size evolution of liquid droplets in a crystalline solid. The first model treats the diffusion-controlled regime of interface motion, while the second model is concerned with the interface-controlled regime of interface motion. Our models take care of conservation of mass and substance. These models generalise the well-known Mullins- Sekerka model for Ostwald ripening. We concentrate on arsenic-rich liquid spherical droplets in a gallium arsenide crystal. Droplets can shrink or grow with time but the centres of droplets remain fixed. The liquid is assumed to be homogeneous in space. Due to different scales for typical distances between droplets and typical radii of liquid droplets we can derive formally so-called mean field models. For a model in the diffusion-controlled regime we prove this limit by homogenisation techniques under plausible assumptions. These mean field models generalise the Lifshitz-Slyozov-Wagner model, which can be derived from the Mullins-Sekerka model rigorously, and is well understood. Mean field models capture the main properties of our system and are well adapted for numerics and further analysis. We determine possible equilibria and discuss their stability. Numerical evidence suggests in which case which one of the two regimes might be appropriate to the experimental situation. (orig.)
A hierarchy of models related to nanoflows and surface diffusion
Aoki, Kazuo; Degond, Pierre
2010-01-01
In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker proposed to use kinetic theory in order to analyze the mechanisms that determine mobility of molecules in nanoscale channels. This approach proved to be remarkably useful to give new insight on these issues, such as density dependence of the diffusion coefficient. In this paper we revisit these works to derive the kinetic and diffusion models introduced by V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J. M. Beenakker by using classical tools of kinetic theory such as scaling and systematic asymptotic analysis. Some results are extended to less restrictive hypothesis.
Branches of the essential spectrum of the lattice spin-boson model with at most two photons
Rasulov, T. Kh.
2016-02-01
We consider a lattice analogue of the A m model of light radiation with a fixed atom and at most m photons ( m = 1, 2). We describe the essential spectrum of the operator A 2 in terms of the spectrum of the operator A 1, i.e., we find the "two-particle" and "three-particle" branches of the essential spectrum of A 2. We prove that the essential spectrum is a union of at most six intervals, and we study their positions. We derive an estimate for the lower bound of the "two-particle" and "three-particle" branches.
Regularization modeling for large-eddy simulation of diffusion flames
Geurts, Bernard J.; Wesseling, P.; OÑate, E.; Périaux, J.
2006-01-01
We analyze the evolution of a diffusion flame in a turbulent mixing layer using large-eddy simulation. The large-eddy simulation includes Leray regularization of the convective transport and approximate inverse filtering to represent the chemical source terms. The Leray model is compared to the more conventional dynamic mixed model. The location of the flame-center is defined by the 'stoichiometric' interface. Geometrical properties such as its surface-area and wrinkling are characterized usi...
Polynomial Preserving Diffusion Models for Life Insurance Liabilities
Biagini, Francesca; Zhang, Yinglin
2016-01-01
In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial preserving diffusion on a compact state space. Such a model guarantees not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and hedging strategy of a large class of life insurance products by e...
A Lattice Boltzmann model for diffusion of binary gas mixtures
Bennett, Sam
2010-01-01
This thesis describes the development of a Lattice Boltzmann (LB) model for a binary gas mixture. Specifically, channel flow driven by a density gradient with diffusion slip occurring at the wall is studied in depth. The first part of this thesis sets the foundation for the multi-component model used in the subsequent chapters. Commonly used single component LB methods use a non-physical equation of state, in which the relationship between pressure and density varies according to the sca...
Hidetaka Tobita
2015-11-01
Full Text Available Polymers are the products of processes and their microstructure can be changed significantly by the reactor systems employed, especially for nonlinear polymers. The Monte Carlo simulation technique, based on the random sampling technique, is used to explore the effect of reactor types on the branched polymer structure, formed through free-radical polymerization with simultaneous long-chain branching and scission, as in the case of low-density polyethylene synthesis. As a simplified model for a tower-type multi-zone reactor, a series of continuous stirred-tank reactors, consisting of one big tank and the same N-1 small tanks is considered theoretically. By simply changing the tank arrangement, various types of branched polymers, from star-like globular structure to a more randomly branched structure, can be obtained, while keeping the following properties of the final products, the monomer conversion to polymer, the average branching and scission densities, and the relationship between the mean-square radius of gyration and molecular weight.
Vester, Steen
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...
Hub and spoke: A community model for child branch students at the University of Southampton
Wigley, W.
2006-01-01
Whilst existing health care education provides a foundation in public health there is a need to enhance the knowledge and skills of practitioners expected to contribute to the new public health agenda. Child branch graduates will be important to delivering this agenda as most children are cared for in a community setting. Previously child health students would receive little community experience as part of their training and on qualifying child branch students applying to work in communi...
Premixed turbulent combustion modelling with FGM including preferential diffusion effects
Goey, L.P.H. de; Oijen, J.A. van; Bastiaans, R.J.M. [Eindhoven University of Technology (Netherlands). Mechanical Engineering Dept.
2009-07-01
The FGM technique is a new method to reduce chemical kinetics. It has already proven to be accurate for modelling (partially-) premixed flames in DNS, LES and RANS settings. Previous research has focussed on flames with unit Lewis number transport models, thereby neglecting preferential diffusion effects. The method is extended in the present contribution by introducing an additional mixing parameter W in the manifold, describing the combined fluctuations in enthalpy and element mass fractions due to flame stretch and preferential diffusion. The resulting 2D FGM is used in 2D DNS of a circular flame and compared with detailed chemistry. The agreement is near perfect thereby opening the way to model 3D turbulent CH{sub 4}-H{sub 2}-air flames on a slot burner with realistic non-unit Lewis numbers. A significant increase in flame wrinkling occurs due to local changes in burning intensity. (orig.)
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Monika Žecová
2015-01-01
Full Text Available The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.