Shell shock, trauma, and the First World War: the making of a diagnosis and its histories.
Loughran, Tracey
2012-01-01
During the First World War, thousands of soldiers were treated for "shell shock," a condition which encompassed a range of physical and psychological symptoms. Shell shock has most often been located within a "genealogy of trauma," and identified as an important marker in the gradual recognition of the psychological afflictions caused by combat. In recent years, shell shock has increasingly been viewed as a powerful emblem of the suffering of war. This article, which focuses on Britain, extends scholarly analyses which question characterizations of shell shock as an early form of post-traumatic stress disorder. It also considers some of the methodological problems raised by recasting shell shock as a wartime medical construction rather than an essentially timeless manifestation of trauma. It argues that shell shock must be analyzed as a diagnosis shaped by a specific set of contemporary concerns, knowledges, and practices. Such an analysis challenges accepted understandings of what shell shock "meant" in the First World War, and also offers new perspectives on the role of shell shock in shaping the emergence of psychology and psychiatry in the early part of the twentieth century. The article also considers what relation, if any, might exist between intellectual and other histories, literary approaches, and perceptions of trauma as timeless and unchanging.
Modelling of Innovation Diffusion
Arkadiusz Kijek
2010-01-01
Full Text Available Since the publication of the Bass model in 1969, research on the modelling of the diffusion of innovation resulted in a vast body of scientific literature consisting of articles, books, and studies of real-world applications of this model. The main objective of the diffusion model is to describe a pattern of spread of innovation among potential adopters in terms of a mathematical function of time. This paper assesses the state-of-the-art in mathematical models of innovation diffusion and procedures for estimating their parameters. Moreover, theoretical issues related to the models presented are supplemented with empirical research. The purpose of the research is to explore the extent to which the diffusion of broadband Internet users in 29 OECD countries can be adequately described by three diffusion models, i.e. the Bass model, logistic model and dynamic model. The results of this research are ambiguous and do not indicate which model best describes the diffusion pattern of broadband Internet users but in terms of the results presented, in most cases the dynamic model is inappropriate for describing the diffusion pattern. Issues related to the further development of innovation diffusion models are discussed and some recommendations are given. (original abstract
The relationship between the First World War and neurology: 100 years of "Shell Shock".
Pedroso, José Luiz; Linden, Stefanie C; Barsottini, Orlando G; Maranhão, Péricles; Lees, Andrew J
2017-05-01
The First World War was a global war, beginning on 28 July 1914, until 11 November 1918. Soon after the beginning of the war, there was an "epidemic" of neurological conversion symptoms. Soldiers on both sides started to present in large numbers with neurological symptoms, such as dizziness, tremor, paraplegia, tinnitus, amnesia, weakness, headache and mutism of psychosomatic origin. This condition was known as shell shock, or "war neurosis". Because medically unexplained symptoms remain a major challenge, and considering the close relationship of symptoms described in shell shock with clinical neurology, we should study their history in order to improve future care.
Anaesthetic and other treatments of shell shock: World War I and beyond.
McKenzie, A G
2012-03-01
Post-traumatic stress disorder (PTSD) is an important health risk factor for military personnel deployed in modern warfare. In World War I this condition (then known as shell shock or 'neurasthenia') was such a problem that 'forward psychiatry' was begun by French doctors in 1915. Some British doctors tried general anaesthesia as a treatment (ether and chloroform), while others preferred application of electricity. Four British 'forward psychiatric units' were set up in 1917. Hospitals for shell shocked soldiers were also established in Britain, including (for officers) Craiglockhart War Hospital in Edinburgh; patients diagnosed to have more serious psychiatric conditions were transferred to the Royal Edinburgh Asylum. Towards the end of 1918 anaesthetic and electrical treatments of shell shock were gradually displaced by modified Freudian methods psychodynamic intervention. The efficacy of 'forward psychiatry' was controversial. In 1922 the War Office produced a report on shell shock with recommendations for prevention of war neurosis. However, when World War II broke out in 1939, this seemed to have been ignored. The term 'combat fatigue' was introduced as breakdown rates became alarming, and then the value of pre-selection was recognised. At the Maudsley Hospital in London in 1940 barbiturate abreaction was advocated for quick relief from severe anxiety and hysteria, using i.v. anaesthetics: Somnifaine, paraldehyde, Sodium Amytal. 'Pentothal narcosis' and 'narco-analysis' were adopted by British and American military psychiatrists. However, by 1945 medical thinking gradually settled on the same approaches that had seemed to be effective in 1918. The term PTSD was introduced in 1980. In the UK the National Institute for Health and Clinical Excellence (NICE) guidelines for management (2005) recommend trauma-focussed Cognitive Behavioural Therapy and consideration of antidepressants.
On Diffusive Climatological Models.
Griffel, D. H.; Drazin, P. G.
1981-11-01
A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.
Models of diffuse solar radiation
Boland, John; Ridley, Barbara [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Brown, Bruce [Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546 (Singapore)
2008-04-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19-32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103-16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions. Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement. (author)
'His nerves gave way': Shell shock, history and the memory of the First World War in Britain.
Reid, Fiona
2014-06-01
During the First World War soldiers suffered from a wide range of debilitating nervous complaints as a result of the stresses and strains of modern warfare. These complaints--widely known as shell shock--were the subject of much medical-military debate during the war and became emblematic of the war and its sufferings afterwards. One hundred years after the war the diagnosis of PTSD has not resolved the issues initially raised by First World War shell shock. The stigma of mental illness remains strong and it is still difficult to commemorate and remember the mental wounds of war in a culture which tend to glory or glamorise military heroes. Copyright © 2014. Published by Elsevier Ltd.
Reid, Fiona; Van Everbroeck, Christine
2014-01-01
During the First World War combatants of all armies were prey to nervous disorders or psychological breakdown. These war neuroses were a response to the highly-industrialised nature of the warfare as well as to the fatigue engendered over four years of intense conflict. Yet while fear and mental breakdown were universal, national responses varied. A comparison of British and Belgian shell shock indicates that men suffered in very similar ways but that symptoms met with rather different responses: in Britain treatment and diagnostic regimes stressed the importance of class difference and shell shock was often linked to cowardice. These issues were not of overriding importance in the Belgian army. In the longer term shell shock became, and remained, a topic of political and social concern in Britain whereas in Belgium men suffering from kloppe (extreme fear) tended to be forgotten and the topic has not excited much popular interest or scholarly attention. Yet despite these differences one overarching theme remains clear, namely that despite the extensive experience of war neuroses during and after the First World War, there still remains a fierce stigma about the mental wounds of war.
Modeling the diffusion of scientific publications
D. Fok (Dennis); Ph.H.B.F. Franses (Philip Hans)
2005-01-01
textabstractThis paper illustrates that salient features of a panel of time series of annual citations can be captured by a Bass type diffusion model. We put forward an extended version of this diffusion model, where we consider the relation between key characteristics of the diffusion process and
Model of diffusers / permeators for hydrogen processing
Jacobs, W. D.; Hang, T.
2008-01-01
Palladium-silver (Pd-Ag) diffusers are mainstays of hydrogen processing. Diffusers separate hydrogen from inert species such as nitrogen, argon or helium. The tubing becomes permeable to hydrogen when heated to more than 250 C and a differential pressure is created across the membrane. The hydrogen diffuses better at higher temperatures. Experimental or experiential results have been the basis for determining or predicting a diffuser's performance. However, the process can be mathematically modeled, and comparison to experimental or other operating data can be utilized to improve the fit of the model. A reliable model-based diffuser system design is the goal which will have impacts on tritium and hydrogen processing. A computer model has been developed to solve the differential equations for diffusion given the operating boundary conditions. The model was compared to operating data for a low pressure diffuser system. The modeling approach and the results are presented in this paper. (authors)
Lagrangian-similarity diffusion-deposition model
Horst, T.W.
1979-01-01
A Lagrangian-similarity diffusion model has been incorporated into the surface-depletion deposition model. This model predicts vertical concentration profiles far downwind of the source that agree with those of a one-dimensional gradient-transfer model
MHD diffuser model test program
Idzorek, J J
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment.
MHD diffuser model test program
Idzorek, J.J.
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment
Homogenization of neutronic diffusion models
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)
Diffusion in condensed matter methods, materials, models
Kärger, Jörg
2005-01-01
Diffusion as the process of particle transport due to stochastic movement is a phenomenon of crucial relevance for a large variety of processes and materials. This comprehensive, handbook- style survey of diffusion in condensed matter gives detailed insight into diffusion as the process of particle transport due to stochastic movement. Leading experts in the field describe in 23 chapters the different aspects of diffusion, covering microscopic and macroscopic experimental techniques and exemplary results for various classes of solids, liquids and interfaces as well as several theoretical concepts and models. Students and scientists in physics, chemistry, materials science, and biology will benefit from this detailed compilation.
Symmetries and modelling functions for diffusion processes
Nikitin, A G; Spichak, S V; Vedula, Yu S; Naumovets, A G
2009-01-01
A constructive approach to the theory of diffusion processes is proposed, which is based on application of both symmetry analysis and the method of modelling functions. An algorithm for construction of the modelling functions is suggested. This algorithm is based on the error function expansion (ERFEX) of experimental concentration profiles. The high-accuracy analytical description of the profiles provided by ERFEX approximation allows a convenient extraction of the concentration dependence of diffusivity from experimental data and prediction of the diffusion process. Our analysis is exemplified by its employment in experimental results obtained for surface diffusion of lithium on the molybdenum (1 1 2) surface precovered with dysprosium. The ERFEX approximation can be directly extended to many other diffusion systems.
Double diffusivity model under stochastic forcing
Chattopadhyay, Amit K.; Aifantis, Elias C.
2017-05-01
The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into
Misha Kavka
1998-01-01
Full Text Available This paper undertakes to read Rebecca West's first novel, The Return of the Soldier (1918, as a critical exploration of masculine trauma on the one hand and an ambivalent engagement with Freudian psychoanalysis on the other. The novel proves interesting as a site in which two shifting cultural contexts intersect: the wartime culture of England facing the "shell shock" of its men, and the contemporaneous infusion of English intellectual culture with psychoanalytic ideas. Though the effects of new war technology and "a newer kind of doctor," West challenge existing notions of stable masculinity, West maintains that masculinity has all along been simply a construct, a shell built around inarticulable trauma. The fact that in this novel West, despite her early pugnaciously feminist journalism, remains as much within the masculine order as critical of it forces us to expand our notions of the forms feminist narrative can take. This paper argues that the novel is a feminist narrative in the sense that it positions masculine trauma as a mark of adherence to the social order for both men and women.
Saxton, Michael J
2007-01-01
Modeling obstructed diffusion is essential to the understanding of diffusion-mediated processes in the crowded cellular environment. Simple Monte Carlo techniques for modeling obstructed random walks are explained and related to Brownian dynamics and more complicated Monte Carlo methods. Random number generation is reviewed in the context of random walk simulations. Programming techniques and event-driven algorithms are discussed as ways to speed simulations.
A tracer diffusion model derived from microstructure
Lehikoinen, Jarmo; Muurinen, Arto; Olin, Markus
2012-01-01
Document available in extended abstract form only. Full text of publication follows: Numerous attempts have been made to explain the tracer diffusion of various solutes in compacted clays. These attempts have commonly suffered from an inability to describe the diffusion of uncharged and charged solutes with a single unified model. Here, an internally consistent approach to describing the diffusion of solutes in a heterogeneous porous medium, such as compacted bentonite, in terms of its microstructure is presented. The microstructure is taken to be represented by a succession of unit cells, which consist of two consecutive regions (Do, 1996). In the first region, the diffusion is viewed to occur in two parallel paths: one through microcrystalline units (micropores) and the other through meso-pores between the microcrystalline units. Solutes exiting these two paths are then joined together to continue diffusing through the second, disordered, region, connecting the two adjacent microcrystalline units. Adsorption (incl. co-ion exclusion) is thought to occur in the micropores, whereas meso-pores and the disordered region accommodate free species alone. Co-ions are also assumed to experience transfer resistance into and out of the micropores, which is characterized in the model by a transmission coefficient. Although the model is not new per se, its application to compacted clays has never been attempted before. It is shown that in the limit of strong adsorption, the effective diffusivity is limited from above only by the microstructural parameters of the model porous medium. As intuitive and logical as this result may appear, it has not been proven before. In the limit of vanishing disordered region, the effective diffusivity is no longer explicitly constrained by any of the model parameters. The tortuosity of the diffusion path, i.e. the quotient of the actual diffusion path length in the porous-medium coordinates and the characteristic length of the laboratory frame
Stochastic models for surface diffusion of molecules
Shea, Patrick, E-mail: patrick.shea@dal.ca; Kreuzer, Hans Jürgen [Department of Physics and Atmospheric Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5 (Canada)
2014-07-28
We derive a stochastic model for the surface diffusion of molecules, starting from the classical equations of motion for an N-atom molecule on a surface. The equation of motion becomes a generalized Langevin equation for the center of mass of the molecule, with a non-Markovian friction kernel. In the Markov approximation, a standard Langevin equation is recovered, and the effect of the molecular vibrations on the diffusion is seen to lead to an increase in the friction for center of mass motion. This effective friction has a simple form that depends on the curvature of the lowest energy diffusion path in the 3N-dimensional coordinate space. We also find that so long as the intramolecular forces are sufficiently strong, memory effects are usually not significant and the Markov approximation can be employed, resulting in a simple one-dimensional model that can account for the effect of the dynamics of the molecular vibrations on the diffusive motion.
Agent-based modelling of cholera diffusion
Augustijn-Beckers, Petronella; Doldersum, Tom; Useya, Juliana; Augustijn, Dionysius C.M.
2016-01-01
This paper introduces a spatially explicit agent-based simulation model for micro-scale cholera diffusion. The model simulates both an environmental reservoir of naturally occurring V.cholerae bacteria and hyperinfectious V. cholerae. Objective of the research is to test if runoff from open refuse
Stochastic diffusion models for substitutable technological innovations
Wang, L.; Hu, B.; Yu, X.
2004-01-01
Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the
Bag model with diffuse surface
Phatak, S.C.
1986-01-01
The constraint of a sharp bag boundary in the bag model is relaxed in the present work. This has been achieved by replacing the square-well potential of the bag model by a smooth scalar potential and introducing a term similar to the bag pressure term. The constraint of the conservation of the energy-momentum tensor is used to obtain an expression for the added bag pressure term. The model is then used to determine the static properties of the nucleon. The calculation shows that the rms charge radius and the nucleon magnetic moment are larger than the corresponding bag model values. Also, the axial vector coupling constant and the πNN coupling constant are in better agreement with the experimental values
Multiphase Microfluidics The Diffuse Interface Model
2012-01-01
Multiphase flows are typically described assuming that the different phases are separated by a sharp interface, with appropriate boundary conditions. This approach breaks down whenever the lengthscale of the phenomenon that is being studied is comparable with the real interface thickness, as it happens, for example, in the coalescence and breakup of bubbles and drops, the wetting and dewetting of solid surfaces and, in general, im micro-devices. The diffuse interface model resolves these probems by assuming that all quantities can vary continuously, so that interfaces have a non-zero thickness, i.e. they are "diffuse". The contributions in this book review the theory and describe some relevant applications of the diffuse interface model for one-component, two-phase fluids and for liquid binary mixtures, to model multiphase flows in confined geometries.
Parameter estimation in fractional diffusion models
Kubilius, Kęstutis; Ralchenko, Kostiantyn
2017-01-01
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides s...
Fractional diffusion models of nonlocal transport
Castillo-Negrete, D. del
2006-01-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments
Technological diffusion in the Ramsey model
Duczynski, Petr
2002-01-01
Roč. 1, č. 3 (2002), s. 243-250 ISSN 1607-0704 Institutional research plan: CEZ:AV0Z7085904 Keywords : neoclassical growth model * technological diffusion Subject RIV: AH - Economics http://www.ijbe.org/table%20of%20content/pdf/vol1-3/06.pdf
Modeling of Reaction Processes Controlled by Diffusion
Revelli, Jorge
2003-01-01
Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider different boundary conditions and transitions movements.We derive expressions that describe diffusion behaviors constrained to bulk restrictions and the dynamic of the particles.Finally it is important to mention that the theoretical results obtained from the models proposed in this work are compared with Monte Carlo simulations.We find, in general, excellent agreements between the theory and the simulations
Rae, Ruth
2007-08-01
The study of the disorders of the mind at the turn of the twentieth century offered useful knowledge about the psyche and the First World War (FWW) provided an avalanche of case studies. Prior to the war the mentally ill were treated with disdain and the social distrust of individuals who did not present as 'normal' was high. The level of diagnostic expertise of psychiatric illness by doctors and nurses was low and as a consequence medicine and nursing was ill-equipped to deal with the phenomenon initially referred to as 'shell shock'. However, the soldiers of the FWW who endured the varied and seemingly unrelated symptoms of shell-shock were respected men - occasional heroes - who were reduced to the status of 'mentals'. There is evidence that civilian trained health professionals altered their views about mental illness during the FWW but initially, the military imperatives inherent in a global conflict perpetuated the notion that mental illness was linked with defective morality. This paper provides an historical account of changes in attitude toward the mentally ill as a consequence of the FWW. The interregnum (1918-39) was a period of advancement in the field of mental health within the civilian sector. However, the imperatives of war negated these developments and there is evidence that the management of soldiers suffering from post-traumatic stress disorders in the Second World War did not benefit from the lessons learnt in the FWW.
Modeling the reemergence of information diffusion in social network
Yang, Dingda; Liao, Xiangwen; Shen, Huawei; Cheng, Xueqi; Chen, Guolong
2018-01-01
Information diffusion in networks is an important research topic in various fields. Existing studies either focus on modeling the process of information diffusion, e.g., independent cascade model and linear threshold model, or investigate information diffusion in networks with certain structural characteristics such as scale-free networks and small world networks. However, there are still several phenomena that have not been captured by existing information diffusion models. One of the prominent phenomena is the reemergence of information diffusion, i.e., a piece of information reemerges after the completion of its initial diffusion process. In this paper, we propose an optimized information diffusion model by introducing a new informed state into traditional susceptible-infected-removed model. We verify the proposed model via simulations in real-world social networks, and the results indicate that the model can reproduce the reemergence of information during the diffusion process.
Anomalous diffusion in a symbolic model
Ribeiro, H V; Lenzi, E K; Mendes, R S; Santoro, P A
2011-01-01
In this work, we investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following the power-law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach reveals a rich diffusive scenario characterized by non-Gaussian distribution and, depending on the power-law exponent or the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare the analytic results with the numerical data, thereby finding good agreement. Because of its simplicity and flexibility, this model can be a candidate for describing real systems governed by power-law probability densities.
Radiosity diffusion model in 3D
Riley, Jason D.; Arridge, Simon R.; Chrysanthou, Yiorgos; Dehghani, Hamid; Hillman, Elizabeth M. C.; Schweiger, Martin
2001-11-01
We present the Radiosity-Diffusion model in three dimensions(3D), as an extension to previous work in 2D. It is a method for handling non-scattering spaces in optically participating media. We present the extension of the model to 3D including an extension to the model to cope with increased complexity of the 3D domain. We show that in 3D more careful consideration must be given to the issues of meshing and visibility to model the transport of light within reasonable computational bounds. We demonstrate the model to be comparable to Monte-Carlo simulations for selected geometries, and show preliminary results of comparisons to measured time-resolved data acquired on resin phantoms.
Recent advances in modelling diffuse radiation
Boland, John; Ridley, Barbara [Centre for Industrial and Applied Mathematics, Univ. of South Australia, Mawson Lakes, SA (Australia)
2008-07-01
Boland et al (2001) developed a validated model for Australian conditions, using a logistic function instead of piecewise linear or simple nonlinear functions. Recently, Jacovides et al (2006) have verified that this model performs well for locations in Cyprus. Their analysis includes using moving average techniques to demonstrate the form of the relationship, which corresponds well to a logistic relationship. We have made significant advances in both the intuitive and theoretical justification of the use of the logistic function. In the theoretical development of the model utilising advanced non-parametric statistical methods. We have also constructed a method of identifying values that are likely to be erroneous. Using quadratic programming, we can eliminate outliers in diffuse radiation values, the data most prone to errors in measurement. Additionally, this is a first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors (see Boland and Ridley 2007). Our more recent investigations focus on examining the effects of adding additional explanatory variables to enhance the predictability of the model. Examples for Australian and other locations will be presented. (orig.)
Reaction-diffusion pulses: a combustion model
Campos, Daniel; Llebot, Josep Enric; Fort, Joaquim
2004-01-01
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations
Reaction-diffusion pulses: a combustion model
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.
Premuda, F.
1983-01-01
Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated
Stochastic Modelling of the Diffusion Coefficient for Concrete
Thoft-Christensen, Palle
In the paper, a new stochastic modelling of the diffusion coefficient D is presented. The modelling is based on physical understanding of the diffusion process and on some recent experimental results. The diffusion coefficients D is strongly dependent on the w/c ratio and the temperature....
Recommendation based on trust diffusion model.
Yuan, Jinfeng; Li, Li
2014-01-01
Recommender system is emerging as a powerful and popular tool for online information relevant to a given user. The traditional recommendation system suffers from the cold start problem and the data sparsity problem. Many methods have been proposed to solve these problems, but few can achieve satisfactory efficiency. In this paper, we present a method which combines the trust diffusion (DiffTrust) algorithm and the probabilistic matrix factorization (PMF). DiffTrust is first used to study the possible diffusions of trust between various users. It is able to make use of the implicit relationship of the trust network, thus alleviating the data sparsity problem. The probabilistic matrix factorization (PMF) is then employed to combine the users' tastes with their trusted friends' interests. We evaluate the algorithm on Flixster, Moviedata, and Epinions datasets, respectively. The experimental results show that the recommendation based on our proposed DiffTrust + PMF model achieves high performance in terms of the root mean square error (RMSE), Recall, and F Measure.
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO; HITTMEIR, SABINE; JÜ NGEL, ANSGAR
2012-01-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy
A spatial structural derivative model for ultraslow diffusion
Xu Wei
2017-01-01
Full Text Available This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function ex is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function ex in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.
Observational Constraints for Modeling Diffuse Molecular Clouds
Federman, S. R.
2014-02-01
Ground-based and space-borne observations of diffuse molecular clouds suggest a number of areas where further improvements to modeling efforts is warranted. I will highlight those that have the widest applicability. The range in CO fractionation caused by selective isotope photodissociation, in particular the large 12C16O/13C16O ratios observed toward stars in Ophiuchus, is not reproduced well by current models. Our ongoing laboratory measurements of oscillator strengths and predissociation rates for Rydberg transitions in CO isotopologues may help clarify the situtation. The CH+ abundance continues to draw attention. Small scale structure seen toward ζ Per may provide additional constraints on the possible synthesis routes. The connection between results from optical transitions and those from radio and sub-millimeter wave transitions requires further effort. A study of OH+ and OH toward background stars reveals that these species favor different environments. This brings to focus the need to model each cloud along the line of sight separately, and to allow the physical conditions to vary within an individual cloud, in order to gain further insight into the chemistry. Now that an extensive set of data on molecular excitation is available, the models should seek to reproduce these data to place further constraints on the modeling results.
Modeling dendrite density from magnetic resonance diffusion measurements
Jespersen, Sune Nørhøj; Kroenke, CD; Østergaard, Leif
2007-01-01
in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (DL) and perpendicular (DT) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.......e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides......Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal...
Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations
Arkhincheev, V.E.
2001-04-01
To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-01-01
Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.
A new model of anomalous phosphorus diffusion in silicon
Budil, M.; Poetzl, H.; Stingeder, G.; Grasserbauer, M.
1989-01-01
A model is presented to describe the 'kink and tail' diffusion of phosphorus. The diffusion behaviour of phosphorus is expplained by the motion of phosphorus-interstitial and phosphorus-vacancy pairs in different charge states. The model yields the enhancement of diffusion in the tail region depending on surface concentration. Furthermore it yields the same selfdiffusion coefficient for interstitials as the gold diffusion experiments. A transformation of the diffusion equation was found to reduce the number of simulation equations. (author) 7 refs., 5 figs
Kubaschewski, O.
1983-01-01
The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes
Structured inverse modeling in parabolic diffusion processess
Schulz, Volker; Siebenborn, Martin; Welker, Kathrin
2014-01-01
Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A novel shape gradient is derived in parabolic processes. Furthermore quasi-Newton techniques are used in order to accelerate shape gradient based iterations in shape space. Numerical investigations support the theoretical results.
Matrix diffusion model. In situ tests using natural analogues
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
Rasilainen, K.
1997-11-01
Matrix diffusion is an important retarding and dispersing mechanism for substances carried by groundwater in fractured bedrock. Natural analogues provide, unlike laboratory or field experiments, a possibility to test the model of matrix diffusion in situ over long periods of time. This thesis documents quantitative model tests against in situ observations, done to support modelling of matrix diffusion in performance assessments of nuclear waste repositories
Modelling Bourdieu: An extension of the Axelrod cultural diffusion model
Trigg, Andrew B.; Bertie, Andrew J.; Himmelweit, Susan F.
2008-01-01
The contribution to the social theory of consumption of the late Pierre Bourdieu has been widely recognized, but not fully absorbed by the economics discipline. To address this lacuna, an agent-based model of Bourdieu's social theory is developed by extending Axelrod's cultural diffusion model. Bourdieu's theory is decomposed into two components: a capital effect on social interaction and an innovation effect. Whereas simulations of the capital effect are found to have a key role in the repro...
Study of a diffusion flamelet model, with preferential diffusion effects included
Delhaye, S.; Somers, L.M.T.; Bongers, H.; Oijen, van J.A.; Goey, de L.P.H.; Dias, V.
2005-01-01
The non-premixed flamelet model of Peters [1] (model1), which does not include preferential diffusion effects is investigated. Two similar models are presented, but without the assumption of unity Lewis numbers. One of these models was derived by Peters & Pitsch [2] (model2), while the other one was
Diffusion coefficient adaptive correction in Lagrangian puff model
Tan Wenji; Wang Dezhong; Ma Yuanwei; Ji Zhilong
2014-01-01
Lagrangian puff model is widely used in the decision support system for nuclear emergency management. The diffusion coefficient is one of the key parameters impacting puff model. An adaptive method was proposed in this paper, which could correct the diffusion coefficient in Lagrangian puff model, and it aimed to improve the accuracy of calculating the nuclide concentration distribution. This method used detected concentration data, meteorological data and source release data to estimate the actual diffusion coefficient with least square method. The diffusion coefficient adaptive correction method was evaluated by Kincaid data in MVK, and was compared with traditional Pasquill-Gifford (P-G) diffusion scheme method. The results indicate that this diffusion coefficient adaptive correction method can improve the accuracy of Lagrangian puff model. (authors)
Diffusion models in metamorphic thermo chronology: philosophy and methods
Munha, Jose Manuel; Tassinari, Colombo Celso Gaeta
1999-01-01
Understanding kinetics of diffusion is of major importance to the interpretation of isotopic ages in metamorphic rocks. This paper provides a review of concepts and methodologies involved on the various diffusion models that can be applied to radiogenic systems in cooling rocks. The central concept of closure temperature is critically discussed and quantitative estimates for the various diffusion models are evaluated, in order to illustrate the controlling factors and the limits of their practical application. (author)
Modelling Nanoparticle Diffusion into Cancer Tumors
Podduturi, Vishwa Priya; Derosa, Pedro
2011-03-01
Cancer is one of the major, potentially deadly diseases and has been for years. Non-specific delivery of the drug can damage healthy tissue seriously affecting in many cases the patient's living condition. Nanoparticles are being used for a targeted drug delivery thereby reducing the dose. In addition, metallic nanoparticles are being used in thermal treatment of cancer cells where nanoparticles help concentrate heat in the tumor and away from living tissue. We proposed a model that combines random walk with diffusion principles. The particle drift velocity is taken from the Hagen-Poiseuille equation and the velocity profile of the particle at the pores in the capillary wall is obtained using the Coventorware software. Pressure gradient and concentration gradient through the capillary wall are considered. Simulations are performed in Matlab using the Monte Carlo technique. Number of particles leaving the blood vessel through a pore is obtained as a function of blood pressure, the osmotic pressure, temperature, particle concentration, blood vessel radius, and pore size, and the relative effect of each of the parameters is discussed.
A variable-order fractal derivative model for anomalous diffusion
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
A consistent transported PDF model for treating differential molecular diffusion
Wang, Haifeng; Zhang, Pei
2016-11-01
Differential molecular diffusion is a fundamentally significant phenomenon in all multi-component turbulent reacting or non-reacting flows caused by the different rates of molecular diffusion of energy and species concentrations. In the transported probability density function (PDF) method, the differential molecular diffusion can be treated by using a mean drift model developed by McDermott and Pope. This model correctly accounts for the differential molecular diffusion in the scalar mean transport and yields a correct DNS limit of the scalar variance production. The model, however, misses the molecular diffusion term in the scalar variance transport equation, which yields an inconsistent prediction of the scalar variance in the transported PDF method. In this work, a new model is introduced to remedy this problem that can yield a consistent scalar variance prediction. The model formulation along with its numerical implementation is discussed, and the model validation is conducted in a turbulent mixing layer problem.
Diffuse radiation models and monthly-average, daily, diffuse data for a wide latitude range
Gopinathan, K.K.; Soler, A.
1995-01-01
Several years of measured data on global and diffuse radiation and sunshine duration for 40 widely spread locations in the latitude range 36° S to 60° N are used to develop and test models for estimating monthly-mean, daily, diffuse radiation on horizontal surfaces. Applicability of the clearness-index (K) and sunshine fraction (SSO) models for diffuse estimation and the effect of combining several variables into a single multilinear equation are tested. Correlations connecting the diffuse to global fraction (HdH) with K and SSO predict Hd values more accurately than their separate use. Among clearness-index and sunshine-fraction models, SSO models are found to have better accuracy if correlations are developed for wide latitude ranges. By including a term for declinations in the correlation, the accuracy of the estimated data can be marginally improved. The addition of latitude to the equation does not help to improve the accuracy further. (author)
Diffuse interface methods for multiphase flow modeling
Jamet, D.
2004-01-01
Full text of publication follows:Nuclear reactor safety programs need to get a better description of some stages of identified incident or accident scenarios. For some of them, such as the reflooding of the core or the dryout of fuel rods, the heat, momentum and mass transfers taking place at the scale of droplets or bubbles are part of the key physical phenomena for which a better description is needed. Experiments are difficult to perform at these very small scales and direct numerical simulations is viewed as a promising way to give new insight into these complex two-phase flows. This type of simulations requires numerical methods that are accurate, efficient and easy to run in three space dimensions and on parallel computers. Despite many years of development, direct numerical simulation of two-phase flows is still very challenging, mostly because it requires solving moving boundary problems. To avoid this major difficulty, a new class of numerical methods is arising, called diffuse interface methods. These methods are based on physical theories dating back to van der Waals and mostly used in materials science. In these methods, interfaces separating two phases are modeled as continuous transitions zones instead of surfaces of discontinuity. Since all the physical variables encounter possibly strong but nevertheless always continuous variations across the interfacial zones, these methods virtually eliminate the difficult moving boundary problem. We show that these methods lead to a single-phase like system of equations, which makes it easier to code in 3D and to make parallel compared to more classical methods. The first method presented is dedicated to liquid-vapor flows with phase-change. It is based on the van der Waals' theory of capillarity. This method has been used to study nucleate boiling of a pure fluid and of dilute binary mixtures. We discuss the importance of the choice and the meaning of the order parameter, i.e. a scalar which discriminates one
Asymptotic solutions of diffusion models for risk reserves
S. Shao
2003-01-01
Full Text Available We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a special class of initial and boundary value problems defined by a linear diffusion equation. Armed with asymptotic analysis and perturbation theory, we obtain the asymptotic solutions of the diffusion models (possibly degenerate governing the conditional probability of ruin over a finite time in terms of interest rate.
Lévy flight with absorption: A model for diffusing diffusivity with long tails
Jain, Rohit; Sebastian, K. L.
2017-03-01
We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of "diffusing diffusivity" [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016), 10.1021/acs.jpcb.6b01527], it was shown that the mean square displacement of particle remains Fickian, i.e., ∝T at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of D in that model has a steady state limit which is exponential, i.e., πe(D ) ˜e-D /D0 . In the present study, we model the diffusivity of a particle as a Lévy flight process so that D has a power-law tailed distribution, viz., πe(D ) ˜D-1 -α with 0 <α <1 . We find that in the short time limit, the width of displacement distribution is proportional to √{T }, implying that the diffusion is Fickian. But for long times, the width is proportional to T1 /2 α which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index 2 α which preserves its shape at all times.
Fractional diffusion models of transport in magnetically confined plasmas
Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.
2005-01-01
Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model
Diffusion of hydrous species in model basaltic melt
Zhang, Li; Guo, Xuan; Wang, Qinxia; Ding, Jiale; Ni, Huaiwei
2017-10-01
Water diffusion in Fe-free model basaltic melt with up to 2 wt% H2O was investigated at 1658-1846 K and 1 GPa in piston-cylinder apparatus using both hydration and diffusion couple techniques. Diffusion profiles measured by FTIR are consistent with a model in which both molecular H2O (H2Om) and hydroxyl (OH) contribute to water diffusion. OH diffusivity is roughly 13% of H2Om diffusivity, showing little dependence on temperature or water concentration. Water diffusion is dominated by the motion of OH until total H2O (H2Ot) concentration reaches 1 wt%. The dependence of apparent H2Ot diffusivity on H2Ot concentration appears to be overestimated by a previous study on MORB melt, but H2Ot diffusivity at 1 wt% H2Ot in basaltic melt is still greater than those in rhyolitic to andesitic melts. The appreciable contribution of OH to water diffusion in basaltic melt can be explained by enhanced mobility of OH, probably associated with the development of free hydroxyl bonded with network-modifying cations, as well as higher OH concentration. Calculation based on the Nernst-Einstein equation demonstrates that OH may serve as an effective charge carrier in hydrous basaltic melt, which could partly account for the previously observed strong influence of water on electrical conductivity of basaltic melt.
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-12-15
Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber. Copyright © 2015 Elsevier B.V. All rights reserved.
Simple Brownian diffusion an introduction to the standard theoretical models
Gillespie, Daniel T
2013-01-01
Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.
Wind Power in Europe. A Simultaneous Innovation-Diffusion Model
Soederholm, P.; Klaassen, G.
2007-01-01
The purpose of this paper is to provide a quantitative analysis of innovation and diffusion in the European wind power sector. We derive a simultaneous model of wind power innovation and diffusion, which combines a rational choice model of technological diffusion and a learning curve model of dynamic cost reductions. These models are estimated using pooled annual time series data for four European countries (Denmark, Germany, Spain and the United Kingdom) over the time period 1986-2000. The empirical results indicate that reductions in investment costs have been important determinants of increased diffusion of wind power, and these cost reductions can in turn be explained by learning activities and public R and D support. Feed-in tariffs also play an important role in the innovation and diffusion processes. The higher the feed-in price the higher, ceteris paribus, the rate of diffusion, and we present some preliminary empirical support for the notion that the impact on diffusion of a marginal increase in the feed-in tariff will differ depending on the support system used. High feed-in tariffs, though, also have a negative effect on cost reductions as they induce wind generators to choose high-cost sites and provide fewer incentives for cost cuts. This illustrates the importance of designing an efficient wind energy support system, which not only promotes diffusion but also provides continuous incentives for cost-reducing innovations
Modelling of diffuse solar fraction with multiple predictors
Ridley, Barbara; Boland, John [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Lauret, Philippe [Laboratoire de Physique du Batiment et des Systemes, University of La Reunion, Reunion (France)
2010-02-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia. Boland et al. developed a validated model for Australian conditions. Boland et al. detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model. (author)
What Can the Diffusion Model Tell Us About Prospective Memory?
Horn, Sebastian S.; Bayen, Ute J.; Smith, Rebekah E.
2011-01-01
Cognitive process models, such as Ratcliff’s (1978) diffusion model, are useful tools for examining cost- or interference effects in event-based prospective memory (PM). The diffusion model includes several parameters that provide insight into how and why ongoing-task performance may be affected by a PM task and is ideally suited to analyze performance because both reaction time and accuracy are taken into account. Separate analyses of these measures can easily yield misleading interpretations in cases of speed-accuracy tradeoffs. The diffusion model allows us to measure possible criterion shifts and is thus an important methodological improvement over standard analyses. Performance in an ongoing lexical decision task (Smith, 2003) was analyzed with the diffusion model. The results suggest that criterion shifts play an important role when a PM task is added, but do not fully explain the cost effect on RT. PMID:21443332
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO
2012-12-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy functional, yielding gradient estimates for the cell density and chemical concentration. For arbitrarily small cross-diffusion coefficients and for suitable exponents of the nonlinear diffusion terms, the global-in-time existence of weak solutions is proved, thus preventing finite-time blow up of the cell density. The global existence result also holds for linear and fast diffusion of the cell density in a certain parameter range in three dimensions. Furthermore, we show L∞ bounds for the solutions to the parabolic-elliptic system. Sufficient conditions leading to the asymptotic stability of the constant steady state are given for a particular choice of the nonlinear diffusion exponents. Numerical experiments in two and three space dimensions illustrate the theoretical results. © 2012 World Scientific Publishing Company.
Pricing Participating Products under a Generalized Jump-Diffusion Model
Tak Kuen Siu
2008-01-01
Full Text Available We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.
WWER radial reflector modeling by diffusion codes
Petkov, P. T.; Mittag, S.
2005-01-01
The two commonly used approaches to describe the WWER radial reflectors in diffusion codes, by albedo on the core-reflector boundary and by a ring of diffusive assembly size nodes, are discussed. The advantages and disadvantages of the first approach are presented first, then the Koebke's equivalence theory is outlined and its implementation for the WWER radial reflectors is discussed. Results for the WWER-1000 reactor are presented. Then the boundary conditions on the outer reflector boundary are discussed. The possibility to divide the library into fuel assembly and reflector parts and to generate each library by a separate code package is discussed. Finally, the homogenization errors for rodded assemblies are presented and discussed (Author)
Dynamic Diffusion Estimation in Exponential Family Models
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
Weak diffusion limits of dynamic conditional correlation models
Hafner, Christian M.; Laurent, Sebastien; Violante, Francesco
The properties of dynamic conditional correlation (DCC) models are still not entirely understood. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized...... by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a non-degenerate diffusion limit can be obtained. Alternative sets of conditions are considered...
A simplified model exploration research of new anisotropic diffuse radiation model
Yao, Wanxiang; Li, Zhengrong; Wang, Xiao; Zhao, Qun; Zhang, Zhigang; Lin, Lin
2016-01-01
Graphical abstract: The specific process of measured diffuse radiation data. - Highlights: • Simplified diffuse radiation model is extremely important for solar radiation simulation and energy simulation. • A new simplified anisotropic diffuse radiation model (NSADR model) is proposed. • The accuracy of existing models and NSADR model is compared based on the measured values. • The accuracy of the NSADR model is higher than that of the existing models, and suitable for calculating diffuse radiation. - Abstract: More accurate new anisotropic diffuse radiation model (NADR model) has been proposed, but the parameters and calculation process of NADR model used in the process are complex. So it is difficult to widely used in the simulation software and engineering calculation. Based on analysis of the diffuse radiation model and measured diffuse radiation data, this paper put forward three hypotheses: (1) diffuse radiation from sky horizontal region is concentrated in a very thin layer which is close to the line source; (2) diffuse radiation from circumsolar region is concentrated in the point of the sun; (3) diffuse radiation from orthogonal region is concentrated in the point located at 90 degree angles with the Sun. Based on these hypotheses, NADR model is simplified to a new simplified anisotropic diffuse radiation model (NSADR model). Then the accuracy of NADR model and its simplified model (NSADR model) are compared with existing models based on the measured values, and the result shows that Perez model and its simplified model are relatively accurate among existing models. However, the accuracy of these two models is lower than the NADR model and NSADR model due to neglect the influence of the orthogonal diffuse radiation. The accuracy of the NSADR model is higher than that of the existing models, meanwhile, another advantage is that the NSADR model simplifies the process of solution parameters and calculation. Therefore it is more suitable for
Smirnova, E.S.; Chuvil'deev, V.N.
1998-01-01
The model is suggested which describes the influence of large-angle grain boundary migration on a diffusion controlled creep rate in polycrystalline materials (Coble creep). The model is based on the concept about changing the value of migrating boundary free volume when introducing dislocations distributed over the grain bulk into this boundary. Expressions are obtained to calculate the grain boundary diffusion coefficient under conditions of boundary migration and the parameter, which characterized the value of Coble creep acceleration. A comparison is made between calculated and experimental data for Cd, Co and Fe
Verification of atmospheric diffusion models with data of atmospheric diffusion experiments
Hato, Shinji; Homma, Toshimitsu
2009-02-01
The atmospheric diffusion experiments were implemented by Japan Atomic Energy Research Institute (JAERI) around Mount Tsukuba in 1989 and 1990, and the tracer gas concentration were monitored. In this study, the Gauss Plume Model and RAMS/HYPACT that are meteorological forecast code and atmospheric diffusion code with detailed physical law are made a comparison between monitored concentration. In conclusion, the Gauss Plume Model is better than RAM/HYPACT even complex topography if the estimation is around tens of kilometer form release point and the change in weather is constant for short time. This reason is difference of wind between RAMS and observation. (author)
Smith, Rachel A; Kim, Youllee; Zhu, Xun; Doudou, Dimi Théodore; Sternberg, Eleanore D; Thomas, Matthew B
2018-01-01
This study documents an investigation into the adoption and diffusion of eave tubes, a novel mosquito vector control, during a large-scale scientific field trial in West Africa. The diffusion of innovations (DOI) and the integrated model of behavior (IMB) were integrated (i.e., innovation attributes with attitudes and social pressures with norms) to predict participants' (N = 329) diffusion intentions. The findings showed that positive attitudes about the innovation's attributes were a consistent positive predictor of diffusion intentions: adopting it, maintaining it, and talking with others about it. As expected by the DOI and the IMB, the social pressure created by a descriptive norm positively predicted intentions to adopt and maintain the innovation. Drawing upon sharing research, we argued that the descriptive norm may dampen future talk about the innovation, because it may no longer be seen as a novel, useful topic to discuss. As predicted, the results showed that as the descriptive norm increased, the intention to talk about the innovation decreased. These results provide broad support for integrating the DOI and the IMB to predict diffusion and for efforts to draw on other research to understand motivations for social diffusion.
Diffuse Scattering Model of Indoor Wideband Propagation
Franek, Ondrej; Andersen, Jørgen Bach; Pedersen, Gert Frølund
2011-01-01
segments in total and approximately 2 min running time on average computer. Frequency independent power levels at the walls around the circumference of the room and at four receiver locations in the middle of the room are observed. It is demonstrated that after finite period of initial excitation the field...... radio coverage predictions.......This paper presents a discrete-time numerical algorithm for computing field distribution in indoor environment by diffuse scattering from walls. Calculations are performed for a rectangular room with semi-reflective walls. The walls are divided into 0.5 x 0.5 m segments, resulting in 2272 wall...
MODEL OF THE TOKAMAK EDGE DENSITY PEDESTAL INCLUDING DIFFUSIVE NEUTRALS
BURRELL, K.H.
2003-01-01
OAK-B135 Several previous analytic models of the tokamak edge density pedestal have been based on diffusive transport of plasma plus free-streaming of neutrals. This latter neutral model includes only the effect of ionization and neglects charge exchange. The present work models the edge density pedestal using diffusive transport for both the plasma and the neutrals. In contrast to the free-streaming model, a diffusion model for the neutrals includes the effect of both charge exchange and ionization and is valid when charge exchange is the dominant interaction. Surprisingly, the functional forms for the electron and neutral density profiles from the present calculation are identical to the results of the previous analytic models. There are some differences in the detailed definition of various parameters in the solution. For experimentally relevant cases where ionization and charge exchange rate are comparable, both models predict approximately the same width for the edge density pedestal
Reflector modelization for neutronic diffusion and parameters identification
Argaud, J.P.
1993-04-01
Physical parameters of neutronic diffusion equations can be adjusted to decrease calculations-measurements errors. The reflector being always difficult to modelize, we choose to elaborate a new reflector model and to use the parameters of this model as adjustment coefficients in the identification procedure. Using theoretical results, and also the physical behaviour of neutronic flux solutions, the reflector model consists then in its replacement by boundary conditions for the diffusion equations on the core only. This theoretical result of non-local operator relations leads then to some discrete approximations by taking into account the multiscaled behaviour, on the core-reflector interface, of neutronic diffusion solutions. The resulting model of this approach is then compared with previous reflector modelizations, and first results indicate that this new model gives the same representation of reflector for the core than previous. (author). 12 refs
Microscopic modeling of the Raman diffusion
Benisti, D.; Morice, O.; Gremillet, L.; Strozzi, D.
2010-01-01
In the typical conditions of density and electronic temperature of the Laser Megajoule (LMJ), a quantitative assessment of the Raman reflectivity requires an accurate calculation of the non-linear movement of each electron submitted to the waves propagating in the plasma. The interaction of a laser beam with a plasma generates an electronic wave shifted in frequency (that can be back-scattered) and an electron plasma wave (OPE). The OPE can give to the electrons a strongly non-linear movement by trapping them in a potential well. This non-linearity of microscopic origin has an impact on the plasma electronic density. We have succeeded in computing this plasma electronic density in a very accurate way by combining the principles of a perturbative approach with those of an adiabatic theory. Results show that the Raman diffusion can grow on temperature and density ranges more important than expected. We have predicted the threshold and the behavior of the Raman diffusion above this threshold as accurately as we had done it with a Vlasov code but by being 10000 times more rapid. (A.C.)
A strongly nonlinear reaction-diffusion model for a deterministic diffusive epidemic
Kirane, M.; Kouachi, S.
1992-10-01
In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the diffusivities. (author). 7 refs
Tamura, Junji; Kido, Hiroko; Hato, Shinji; Homma, Toshimitsu
2009-03-01
Straight-line or segmented plume models as atmospheric diffusion models are commonly used in probabilistic accident consequence assessment (PCA) codes due to cost and time savings. The PCA code, OSCAAR developed by Japan Atomic Energy Research Institute (Present; Japan Atomic Energy Agency) uses the variable puff trajectory model to calculate atmospheric transport and dispersion of released radionuclides. In order to investigate uncertainties involved with the structure of the atmospheric dispersion/deposition model in OSCAAR, we have introduced the more sophisticated computer codes that included regional meteorological models RAMS and atmospheric transport model HYPACT, which were developed by Colorado State University, and comparative analyses between OSCAAR and RAMS/HYPACT have been performed. In this study, model verification of OSCAAR and RAMS/HYPACT was conducted using data of long term atmospheric diffusion experiments, which were carried out in Tokai-mura, Ibaraki-ken. The predictions by models and the results of the atmospheric diffusion experiments indicated relatively good agreements. And it was shown that model performance of OSCAAR was the same degree as it of RAMS/HYPACT. (author)
Mockler, Eva; Reaney, Simeon; Mellander, Per-Erik; Wade, Andrew; Collins, Adrian; Arheimer, Berit; Bruen, Michael
2017-04-01
The agricultural sector is the most common suspected source of nutrient pollution in Irish rivers. However, it is also often the most difficult source to characterise due to its predominantly diffuse nature. Particulate phosphorus in surface water and dissolved phosphorus in groundwater are of particular concern in Irish water bodies. Hence the further development of models and indices to assess diffuse sources of contaminants are required for use by the Irish Environmental Protection Agency (EPA) to provide support for river basin planning. Understanding connectivity in the landscape is a vital component of characterising the source-pathway-receptor relationships for water-borne contaminants, and hence is a priority in this research. The DIFFUSE Project will focus on connectivity modelling and incorporation of connectivity into sediment, nutrient and pesticide risk mapping. The Irish approach to understanding and managing natural water bodies has developed substantially in recent years assisted by outputs from multiple research projects, including modelling and analysis tools developed during the Pathways and CatchmentTools projects. These include the Pollution Impact Potential (PIP) maps, which are an example of research output that is used by the EPA to support catchment management. The PIP maps integrate an understanding of the pollution pressures and mobilisation pathways and, using the source-pathways-receptor model, provide a scientific basis for evaluation of mitigation measures. These maps indicate the potential risk posed by nitrate and phosphate from diffuse agricultural sources to surface and groundwater receptors and delineate critical source areas (CSAs) as a means of facilitating the targeting of mitigation measures. Building on this previous research, the DIFFUSE Project will develop revised and new catchment managements tools focused on connectivity, sediment, phosphorus and pesticides. The DIFFUSE project will strive to identify the state
Discrete random walk models for space-time fractional diffusion
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
Flux-limited diffusion models in radiation hydrodynamics
Pomraning, G.C.; Szilard, R.H.
1993-01-01
The authors discuss certain flux-limited diffusion theories which approximately describe radiative transfer in the presence of steep spatial gradients. A new formulation is presented which generalizes a flux-limited description currently in widespread use for large radiation hydrodynamic calculations. This new formation allows more than one Case discrete mode to be described by a flux-limited diffusion equation. Such behavior is not extant in existing formulations. Numerical results predicted by these flux-limited diffusion models are presented for radiation penetration into an initially cold halfspace. 37 refs., 5 figs
Convergence of surface diffusion parameters with model crystal size
Cohen, Jennifer M.; Voter, Arthur F.
1994-07-01
A study of the variation in the calculated quantities for adatom diffusion with respect to the size of the model crystal is presented. The reported quantities include surface diffusion barrier heights, pre-exponential factors, and dynamical correction factors. Embedded atom method (EAM) potentials were used throughout this effort. Both the layer size and the depth of the crystal were found to influence the values of the Arrhenius factors significantly. In particular, exchange type mechanisms required a significantly larger model than standard hopping mechanisms to determine adatom diffusion barriers of equivalent accuracy. The dynamical events that govern the corrections to transition state theory (TST) did not appear to be as sensitive to crystal depth. Suitable criteria for the convergence of the diffusion parameters with regard to the rate properties are illustrated.
When mechanism matters: Bayesian forecasting using models of ecological diffusion
Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.
2017-01-01
Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.
Capdebosq, Y
1999-09-01
In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)
Statistical model of a gas diffusion electrode. III. Photomicrograph study
Winsel, A W
1965-12-01
A linear section through a gas diffusion electrode produces a certain distribution function of sinews with the pores. From this distribution function some qualities of the pore structure are derived, and an automatic device to determine the distribution function is described. With a statistical model of a gas diffusion electrode the behavior of a DSK electrode is discussed and compared with earlier measurements of the flow resistance of this material.
Shao, Yuan; Ramachandran, Sandhya; Arnold, Susan; Ramachandran, Gurumurthy
2017-03-01
The use of the turbulent eddy diffusion model and its variants in exposure assessment is limited due to the lack of knowledge regarding the isotropic eddy diffusion coefficient, D T . But some studies have suggested a possible relationship between D T and the air changes per hour (ACH) through a room. The main goal of this study was to accurately estimate D T for a range of ACH values by minimizing the difference between the concentrations measured and predicted by eddy diffusion model. We constructed an experimental chamber with a spatial concentration gradient away from the contaminant source, and conducted 27 3-hr long experiments using toluene and acetone under different air flow conditions (0.43-2.89 ACHs). An eddy diffusion model accounting for chamber boundary, general ventilation, and advection was developed. A mathematical expression for the slope based on the geometrical parameters of the ventilation system was also derived. There is a strong linear relationship between D T and ACH, providing a surrogate parameter for estimating D T in real-life settings. For the first time, a mathematical expression for the relationship between D T and ACH has been derived that also corrects for non-ideal conditions, and the calculated value of the slope between these two parameters is very close to the experimentally determined value. The values of D T obtained from the experiments are generally consistent with values reported in the literature. They are also independent of averaging time of measurements, allowing for comparison of values obtained from different measurement settings. These findings make the use of turbulent eddy diffusion models for exposure assessment in workplace/indoor environments more practical.
Modelling and simulation of diffusive processes methods and applications
Basu, SK
2014-01-01
This book addresses the key issues in the modeling and simulation of diffusive processes from a wide spectrum of different applications across a broad range of disciplines. Features: discusses diffusion and molecular transport in living cells and suspended sediment in open channels; examines the modeling of peristaltic transport of nanofluids, and isotachophoretic separation of ionic samples in microfluidics; reviews thermal characterization of non-homogeneous media and scale-dependent porous dispersion resulting from velocity fluctuations; describes the modeling of nitrogen fate and transport
A model of non-Gaussian diffusion in heterogeneous media
Lanoiselée, Yann; Grebenkov, Denis S.
2018-04-01
Recent progress in single-particle tracking has shown evidence of the non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. Similar behavior has also been observed in granular materials, turbulent flows, gels and colloidal suspensions, suggesting that this is a general feature of diffusion in complex media. A possible interpretation of this phenomenon is that a tracer explores a medium with spatio-temporal fluctuations which result in local changes of diffusivity. We propose and investigate an ergodic, easily interpretable model, which implements the concept of diffusing diffusivity. Depending on the parameters, the distribution of displacements can be either flat or peaked at small displacements with an exponential tail at large displacements. We show that the distribution converges slowly to a Gaussian one. We calculate statistical properties, derive the asymptotic behavior and discuss some implications and extensions.
Modelling of monovacancy diffusion in W over wide temperature range
Bukonte, L.; Ahlgren, T.; Heinola, K.
2014-01-01
The diffusion of monovacancies in tungsten is studied computationally over a wide temperature range from 1300 K until the melting point of the material. Our modelling is based on Molecular Dynamics technique and Density Functional Theory. The monovacancy migration barriers are calculated using nudged elastic band method for nearest and next-nearest neighbour monovacancy jumps. The diffusion pre-exponential factor for monovacancy diffusion is found to be two to three orders of magnitude higher than commonly used in computational studies, resulting in attempt frequency of the order 10 15 Hz. Multiple nearest neighbour jumps of monovacancy are found to play an important role in the contribution to the total diffusion coefficient, especially at temperatures above 2/3 of T m , resulting in an upward curvature of the Arrhenius diagram. The probabilities for different nearest neighbour jumps for monovacancy in W are calculated at different temperatures
The parton model for the diffusion
Ducati, M.B. Gay; Machado, M.V.T.
1999-01-01
We analyze the Buchmueller-Hebecker model for diffraction processes, point out its predictions to the diffractive structure function F D(3) 2 (x IP , β,Q 2 ). The break of factorization for the F D93) 2 present in recent H1 data is well described introducing an extra soft (reggeon) contribution as an extension to the model. (author)
A combinatorial model of malware diffusion via bluetooth connections.
Merler, Stefano; Jurman, Giuseppe
2013-01-01
We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression.
A combinatorial model of malware diffusion via bluetooth connections.
Stefano Merler
Full Text Available We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy and closed form (more complex but efficiently computable expression.
Diffusion approximation for modeling of 3-D radiation distributions
Zardecki, A.; Gerstl, S.A.W.; De Kinder, R.E. Jr.
1985-01-01
A three-dimensional transport code DIF3D, based on the diffusion approximation, is used to model the spatial distribution of radiation energy arising from volumetric isotropic sources. Future work will be concerned with the determination of irradiances and modeling of realistic scenarios, relevant to the battlefield conditions. 8 refs., 4 figs
Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model
Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand); Fichtner, Horst; Walter, Dominik [Institut für Theoretische Physik IV, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum (Germany)
2017-05-20
We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatment of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.
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.
Diffuse solar radiation estimation models for Turkey's big cities
Ulgen, Koray; Hepbasli, Arif
2009-01-01
A reasonably accurate knowledge of the availability of the solar resource at any place is required by solar engineers, architects, agriculturists, and hydrologists in many applications of solar energy such as solar furnaces, concentrating collectors, and interior illumination of buildings. For this purpose, in the past, various empirical models (or correlations) have been developed in order to estimate the solar radiation around the world. This study deals with diffuse solar radiation estimation models along with statistical test methods used to statistically evaluate their performance. Models used to predict monthly average daily values of diffuse solar radiation are classified in four groups as follows: (i) From the diffuse fraction or cloudness index, function of the clearness index, (ii) From the diffuse fraction or cloudness index, function of the relative sunshine duration or sunshine fraction, (iii) From the diffuse coefficient, function of the clearness index, and (iv) From the diffuse coefficient, function of the relative sunshine duration or sunshine fraction. Empirical correlations are also developed to establish a relationship between the monthly average daily diffuse fraction or cloudness index (K d ) and monthly average daily diffuse coefficient (K dd ) with the monthly average daily clearness index (K T ) and monthly average daily sunshine fraction (S/S o ) for the three big cities by population in Turkey (Istanbul, Ankara and Izmir). Although the global solar radiation on a horizontal surface and sunshine duration has been measured by the Turkish State Meteorological Service (STMS) over all country since 1964, the diffuse solar radiation has not been measured. The eight new models for estimating the monthly average daily diffuse solar radiation on a horizontal surface in three big cites are validated, and thus, the most accurate model is selected for guiding future projects. The new models are then compared with the 32 models available in the
Diffusion theory model for optimization calculations of cold neutron sources
Azmy, Y.Y.
1987-01-01
Cold neutron sources are becoming increasingly important and common experimental facilities made available at many research reactors around the world due to the high utility of cold neutrons in scattering experiments. The authors describe a simple two-group diffusion model of an infinite slab LD 2 cold source. The simplicity of the model permits to obtain an analytical solution from which one can deduce the reason for the optimum thickness based solely on diffusion-type phenomena. Also, a second more sophisticated model is described and the results compared to a deterministic transport calculation. The good (particularly qualitative) agreement between the results suggests that diffusion theory methods can be used in parametric and optimization studies to avoid the generally more expensive transport calculations
Mizia, R.E.; Clark, D.E.; Glazoff, M.V.; Lister, Tedd E.; Trowbridge, T.L.
2011-01-01
A research effort was made to evaluate the usefulness of modern thermodynamic and diffusion computational tools, Thermo-Calc(copyright) and Dictra(copyright), in optimizing the parameters for diffusion welding of Alloy 800H. This would achieve a substantial reduction in the overall number of experiments required to achieve optimal welding and post-weld heat treatment conditions. This problem is important because diffusion welded components of Alloy 800H are being evaluated for use in assembling compact, micro-channel heat exchangers that are being proposed in the design of a high temperature gas-cooled reactor by the US Department of Energy. The modeling was done in close contact with experimental work. The latter included using the Gleeble 3500 System(reg sign) for welding simulation, mechanical property measurement, and light optical and Scanning Electron Microscopy. The modeling efforts suggested a temperature of 1150 C for 1 hour with an applied pressure of 5 MPa using a 15 μm Ni foil as a joint filler to reduce chromium oxidation on the welded surfaces. Good agreement between modeled and experimentally determined concentration gradients was achieved, and model refinements to account for the complexity of actual alloy materials are suggested.
Radon diffusion through multilayer earthen covers: models and simulations
Mayer, D.W.; Oster, C.A.; Nelson, R.W.; Gee, G.W.
1981-09-01
A capability to model and analyze the fundamental interactions that influence the diffusion of radon gas through uranium mill tailings and cover systems has been investigated. The purpose of this study is to develop the theoretical basis for modeling radon diffusion and to develop an understanding of the fundamental interactions that influence radon diffusion. This study develops the theoretical basis for modeling radon diffusion in one, two and three dimensions. The theory has been incorporated into three computer models that are used to analyze several tailings and cover configurations. This report contains a discussion of the theoretical basis for modeling radon diffusion, a discussion of the computer models used to analyze uranium mill tailings and multilayered cover systems, and presents the results that have been obtained. The study has been conducted using a four-phase approach. The first phase develops the solution to the steady-state radon-diffusion equation in one-dimensieered barriers; disposal charge analysis; analysis of spent fuel policy implementation; spent f water. Field measurements and observations are reported for each site. Analytical data and field measurements are presented in tables and maps. Uranium concentrations in the sediments which were above detection limits ranged from 0.10 t 51.2 ppM. The mean of the logarithms of the uranium concentrations was 0.53. A group of high uranium concentrations occurs near the junctions of quadrangles AB, AC, BB, a 200 mK. In case 2), x-ray studies of isotopic phase separation in 3 He-- 4 He bcc solids were carried out by B. A. Fraass
Modelling Ni diffusion in bentonite using different sorption models
Pfingsten, W.; Baeyens, B.; Bradbury, M.
2010-01-01
Document available in extended abstract form only. An important component of the multi barrier disposal concept for a radioactive waste repository is the bentonite backfill surrounding the canisters containing vitrified high-level waste and spent fuel located in the tunnels deep within the chosen host rock. The effectiveness of the compacted bentonite barrier is such that calculations have indicated that many radionuclides have decayed to insignificant levels before having diffused through the thickness of bentonite. These calculations are performed using the simple Kd sorption concept in which the values are taken from batch type experiments performed on dispersed systems performed for a single metal at a time, usually at trace concentrations. However, in such complex systems many radionuclides, inactive metal contaminants/ground water components may be simultaneously present in the aqueous phase at a range of concentrations varying with time during the temporal evolution of the repository system. An important aspect influencing the sorption of any radioactive metal under a set of given geochemical conditions is its competition with other metals present, and how this may vary as a function of concentration. Competitive sorption effects are not currently included in safety assessments and are thus an issue which needs to be addressed. Here we provide some first estimates of the potential influence of competitive sorption effects on the migration of radioactive metals through compacted bentonite as a function of their concentration and the concentration of competing metals. Ni(II) and Fe(II) were chosen as possible competing cations since their concentration levels are expected to have values greater than trace levels and effects might be maximal and canister corrosion represents a permanent Fe source at the bentonite interface which could influence bivalent radionuclide diffusion. The modelling of the Ni(II) diffusion/sorption has been carried out using three
A diffuse radar scattering model from Martian surface rocks
Calvin, W. M.; Jakosky, B. M.; Christensen, P. R.
1987-01-01
Remote sensing of Mars has been done with a variety of instrumentation at various wavelengths. Many of these data sets can be reconciled with a surface model of bonded fines (or duricrust) which varies widely across the surface and a surface rock distribution which varies less so. A surface rock distribution map from -60 to +60 deg latitude has been generated by Christensen. Our objective is to model the diffuse component of radar reflection based on this surface distribution of rocks. The diffuse, rather than specular, scattering is modeled because the diffuse component arises due to scattering from rocks with sizes on the order of the wavelength of the radar beam. Scattering for radio waves of 12.5 cm is then indicative of the meter scale and smaller structure of the surface. The specular term is indicative of large scale surface undulations and should not be causally related to other surface physical properties. A simplified model of diffuse scattering is described along with two rock distribution models. The results of applying the models to a planet of uniform fractional rock coverage with values ranging from 5 to 20% are discussed.
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
Diffusion in energy materials: Governing dynamics from atomistic modelling
Parfitt, D.; Kordatos, A.; Filippatos, P. P.; Chroneos, A.
2017-09-01
Understanding diffusion in energy materials is critical to optimising the performance of solid oxide fuel cells (SOFCs) and batteries both of which are of great technological interest as they offer high efficiency for cleaner energy conversion and storage. In the present review, we highlight the insights offered by atomistic modelling of the ionic diffusion mechanisms in SOFCs and batteries and how the growing predictive capability of high-throughput modelling, together with our new ability to control compositions and microstructures, will produce advanced materials that are designed rather than chosen for a given application. The first part of the review focuses on the oxygen diffusion mechanisms in cathode and electrolyte materials for SOFCs and in particular, doped ceria and perovskite-related phases with anisotropic structures. The second part focuses on disordered oxides and two-dimensional materials as these are very promising systems for battery applications.
Estimation and prediction under local volatility jump-diffusion model
Kim, Namhyoung; Lee, Younhee
2018-02-01
Volatility is an important factor in operating a company and managing risk. In the portfolio optimization and risk hedging using the option, the value of the option is evaluated using the volatility model. Various attempts have been made to predict option value. Recent studies have shown that stochastic volatility models and jump-diffusion models reflect stock price movements accurately. However, these models have practical limitations. Combining them with the local volatility model, which is widely used among practitioners, may lead to better performance. In this study, we propose a more effective and efficient method of estimating option prices by combining the local volatility model with the jump-diffusion model and apply it using both artificial and actual market data to evaluate its performance. The calibration process for estimating the jump parameters and local volatility surfaces is divided into three stages. We apply the local volatility model, stochastic volatility model, and local volatility jump-diffusion model estimated by the proposed method to KOSPI 200 index option pricing. The proposed method displays good estimation and prediction performance.
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.
A fractional motion diffusion model for grading pediatric brain tumors.
Karaman, M Muge; Wang, He; Sui, Yi; Engelhard, Herbert H; Li, Yuhua; Zhou, Xiaohong Joe
2016-01-01
To demonstrate the feasibility of a novel fractional motion (FM) diffusion model for distinguishing low- versus high-grade pediatric brain tumors; and to investigate its possible advantage over apparent diffusion coefficient (ADC) and/or a previously reported continuous-time random-walk (CTRW) diffusion model. With approval from the institutional review board and written informed consents from the legal guardians of all participating patients, this study involved 70 children with histopathologically-proven brain tumors (30 low-grade and 40 high-grade). Multi- b -value diffusion images were acquired and analyzed using the FM, CTRW, and mono-exponential diffusion models. The FM parameters, D fm , φ , ψ (non-Gaussian diffusion statistical measures), and the CTRW parameters, D m , α , β (non-Gaussian temporal and spatial diffusion heterogeneity measures) were compared between the low- and high-grade tumor groups by using a Mann-Whitney-Wilcoxon U test. The performance of the FM model for differentiating between low- and high-grade tumors was evaluated and compared with that of the CTRW and the mono-exponential models using a receiver operating characteristic (ROC) analysis. The FM parameters were significantly lower ( p < 0.0001) in the high-grade ( D fm : 0.81 ± 0.26, φ : 1.40 ± 0.10, ψ : 0.42 ± 0.11) than in the low-grade ( D fm : 1.52 ± 0.52, φ : 1.64 ± 0.13, ψ : 0.67 ± 0.13) tumor groups. The ROC analysis showed that the FM parameters offered better specificity (88% versus 73%), sensitivity (90% versus 82%), accuracy (88% versus 78%), and area under the curve (AUC, 93% versus 80%) in discriminating tumor malignancy compared to the conventional ADC. The performance of the FM model was similar to that of the CTRW model. Similar to the CTRW model, the FM model can improve differentiation between low- and high-grade pediatric brain tumors over ADC.
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...... we applied different thermodynamic models, such as the Soave-Redlich-Kwong and the Peng-Robinson equations of state. The necessity to try different thermo-dynamic models is caused by the high sensitivity of the thermal diffusion factors to the values of the partial molar properties. Two different...... corrections for the determination of the partial molar volumes have been implemented; the Peneloux correction and the correction based on the principle of corresponding states....
Diffusion model of delayed hydride cracking in zirconium alloys
Shmakov, AA; Kalin, BA; Matvienko, YG; Singh, RN; De, PK
2004-01-01
We develop a method for the evaluation of the rate of delayed hydride cracking in zirconium alloys. The model is based on the stationary solution of the phenomenological diffusion equation and the detailed analysis of the distribution of hydrostatic stresses in the plane of a sharp tensile crack.
Three dimensional simulated modelling of diffusion capacitance of ...
A three dimensional (3-D) simulated modelling was developed to analyse the excess minority carrier density in the base of a polycrystalline bifacial silicon solar cell. The concept of junction recombination velocity was ado-pted to quantify carrier flow through the junction, and to examine the solar cell diffusion capacitance for ...
Analytically solvable models of reaction-diffusion systems
Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)
2004-05-01
We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.
An improved analytical model of diffusion through the RIST target
Bennett, J R J
2003-01-01
The diffusion and effusion through the RIST target is calculated using a more realistic model than previously. Extremely good fits to the data are obtained and new values of the time constants of effusion through the target and the ioniser are found.
Modeling intragranular diffusion in low-connectivity granular media
Ewing, Robert P.; Liu, Chongxuan; Hu, Qinhong
2012-03-01
Characterizing the diffusive exchange of solutes between bulk water in an aquifer and water in the intragranular pores of the solid phase is still challenging despite decades of study. Many disparities between observation and theory could be attributed to low connectivity of the intragranular pores. The presence of low connectivity indicates that a useful conceptual framework is percolation theory. The present study was initiated to develop a percolation-based finite difference (FD) model, and to test it rigorously against both random walk (RW) simulations of diffusion starting from nonequilibrium, and data on Borden sand published by Ball and Roberts (1991a,b) and subsequently reanalyzed by Haggerty and Gorelick (1995) using a multirate mass transfer (MRMT) approach. The percolation-theoretical model is simple and readily incorporated into existing FD models. The FD model closely matches the RW results using only a single fitting parameter, across a wide range of pore connectivities. Simulation of the Borden sand experiment without pore connectivity effects reproduced the MRMT analysis, but including low pore connectivity effects improved the fit. Overall, the theory and simulation results show that low intragranular pore connectivity can produce diffusive behavior that appears as if the solute had undergone slow sorption, despite the absence of any sorption process, thereby explaining some hitherto confusing aspects of intragranular diffusion.
An alternative atmospheric diffusion model for control room habitability assessments
Ramsdell, J.V. Jr.
1990-01-01
The US Nuclear Regulatory (NRC) staff uses procedures to evaluate control room designs for compliance with General Design Criterion 19 of the Code of Federal Regulations, Appendix A, 10 CRF Part 50. These procedures deal primarily with radiation protection. However, other hazardous materials, for example, chlorine, pose a potential threat to control room habitability. The NRC is considering changes in their current procedures to update methods and extend their applicability. Two changes to the current procedures are suggested: using a puff diffusion model to estimate concentrations at air intakes and using a new method to estimate diffusion coefficients
Turing and Non-Turing patterns in diffusive plankton model
N. K. Thakur
2015-03-01
Full Text Available In this paper, we investigate a Rosenzweig-McAurthur model and its variant for phytoplankton, zooplankton and fish population dynamics with Holling type II and III functional responses. We present the theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with local diffusion. The choice of parameter values is important to study the effect of diffusion, also it depends more on the nonlinearity of the system. With the help of numerical simulations, we observe the formation of spatiotemporal patterns both inside and outside the Turing space.
On a Generalized Squared Gaussian Diffusion Model for Option Valuation
Edeki S.O.
2017-01-01
Full Text Available In financial mathematics, option pricing models are vital tools whose usefulness cannot be overemphasized. Modern approaches and modelling of financial derivatives are therefore required in option pricing and valuation settings. In this paper, we derive via the application of Ito lemma, a pricing model referred to as Generalized Squared Gaussian Diffusion Model (GSGDM for option pricing and valuation. Same approach can be considered via Stratonovich stochastic dynamics. We also show that the classical Black-Scholes, and the square root constant elasticity of variance models are special cases of the GSGDM. In addition, general solution of the GSGDM is obtained using modified variational iterative method (MVIM.
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.)
Leaky-box approximation to the fractional diffusion model
Uchaikin, V V; Sibatov, R T; Saenko, V V
2013-01-01
Two models based on fractional differential equations for galactic cosmic ray diffusion are applied to the leaky-box approximation. One of them (Lagutin-Uchaikin, 2000) assumes a finite mean free path of cosmic ray particles, another one (Lagutin-Tyumentsev, 2004) uses distribution with infinite mean distance between collision with magnetic clouds, when the trajectories have form close to ballistic. Calculations demonstrate that involving boundary conditions is incompatible with spatial distributions given by the second model.
Lai, Vincent; Khong, Pek Lan [University of Hong Kong, Department of Diagnostic Radiology, Li Ka Shing Faculty of Medicine, Queen Mary Hospital, Pok Fu Lam (China); Lee, Victor Ho Fun; Lam, Ka On; Sze, Henry Chun Kin [University of Hong Kong, Department of Clinical Oncology, Li Ka Shing Faculty of Medicine, Queen Mary Hospital, Pok Fu Lam (China); Chan, Queenie [Philips Healthcare, Hong Kong, Shatin, New Territories (China)
2015-06-01
To determine the utility of stretched exponential diffusion model in characterisation of the water diffusion heterogeneity in different tumour stages of nasopharyngeal carcinoma (NPC). Fifty patients with newly diagnosed NPC were prospectively recruited. Diffusion-weighted MR imaging was performed using five b values (0-2,500 s/mm{sup 2}). Respective stretched exponential parameters (DDC, distributed diffusion coefficient; and alpha (α), water heterogeneity) were calculated. Patients were stratified into low and high tumour stage groups based on the American Joint Committee on Cancer (AJCC) staging for determination of the predictive powers of DDC and α using t test and ROC curve analyses. The mean ± standard deviation values were DDC = 0.692 ± 0.199 (x 10{sup -3} mm{sup 2}/s) for low stage group vs 0.794 ± 0.253 (x 10{sup -3} mm{sup 2}/s) for high stage group; α = 0.792 ± 0.145 for low stage group vs 0.698 ± 0.155 for high stage group. α was significantly lower in the high stage group while DDC was negatively correlated. DDC and α were both reliable independent predictors (p < 0.001), with α being more powerful. Optimal cut-off values were (sensitivity, specificity, positive likelihood ratio, negative likelihood ratio) DDC = 0.692 x 10{sup -3} mm{sup 2}/s (94.4 %, 64.3 %, 2.64, 0.09), α = 0.720 (72.2 %, 100 %, -, 0.28). The heterogeneity index α is robust and can potentially help in staging and grading prediction in NPC. (orig.)
Lai, Vincent; Khong, Pek Lan; Lee, Victor Ho Fun; Lam, Ka On; Sze, Henry Chun Kin; Chan, Queenie
2015-01-01
To determine the utility of stretched exponential diffusion model in characterisation of the water diffusion heterogeneity in different tumour stages of nasopharyngeal carcinoma (NPC). Fifty patients with newly diagnosed NPC were prospectively recruited. Diffusion-weighted MR imaging was performed using five b values (0-2,500 s/mm 2 ). Respective stretched exponential parameters (DDC, distributed diffusion coefficient; and alpha (α), water heterogeneity) were calculated. Patients were stratified into low and high tumour stage groups based on the American Joint Committee on Cancer (AJCC) staging for determination of the predictive powers of DDC and α using t test and ROC curve analyses. The mean ± standard deviation values were DDC = 0.692 ± 0.199 (x 10 -3 mm 2 /s) for low stage group vs 0.794 ± 0.253 (x 10 -3 mm 2 /s) for high stage group; α = 0.792 ± 0.145 for low stage group vs 0.698 ± 0.155 for high stage group. α was significantly lower in the high stage group while DDC was negatively correlated. DDC and α were both reliable independent predictors (p < 0.001), with α being more powerful. Optimal cut-off values were (sensitivity, specificity, positive likelihood ratio, negative likelihood ratio) DDC = 0.692 x 10 -3 mm 2 /s (94.4 %, 64.3 %, 2.64, 0.09), α = 0.720 (72.2 %, 100 %, -, 0.28). The heterogeneity index α is robust and can potentially help in staging and grading prediction in NPC. (orig.)
Robust and fast nonlinear optimization of diffusion MRI microstructure models.
Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A
2017-07-15
Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of
Diffusion in higher dimensional SYK model with complex fermions
Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong
2018-01-01
We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.
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.
A Diffusion Model for Two-sided Service Systems
Homma, Koichi; Yano, Koujin; Funabashi, Motohisa
A diffusion model is proposed for two-sided service systems. ‘Two-sided’ refers to the existence of an economic network effect between two different and interrelated groups, e.g., card holders and merchants in an electronic money service. The service benefit for a member of one side depends on the number and quality of the members on the other side. A mathematical model by J. H. Rohlfs explains the network (or bandwagon) effect of communications services. In Rohlfs' model, only the users' group exists and the model is one-sided. This paper extends Rohlfs' model to a two-sided model. We propose, first, a micro model that explains individual behavior in regard to service subscription of both sides and a computational method that drives the proposed model. Second, we develop macro models with two diffusion-rate variables by simplifying the micro model. As a case study, we apply the models to an electronic money service and discuss the simulation results and actual statistics.
Characterization and modeling of thermal diffusion and aggregation in nanofluids.
Gharagozloo, Patricia E.; Goodson, Kenneth E. (Stanford University, Stanford, CA)
2010-05-01
Fluids with higher thermal conductivities are sought for fluidic cooling systems in applications including microprocessors and high-power lasers. By adding high thermal conductivity nanoscale metal and metal oxide particles to a fluid the thermal conductivity of the fluid is enhanced. While particle aggregates play a central role in recent models for the thermal conductivity of nanofluids, the effect of particle diffusion in a temperature field on the aggregation and transport has yet to be studied in depth. The present work separates the effects of particle aggregation and diffusion using parallel plate experiments, infrared microscopy, light scattering, Monte Carlo simulations, and rate equations for particle and heat transport in a well dispersed nanofluid. Experimental data show non-uniform temporal increases in thermal conductivity above effective medium theory and can be well described through simulation of the combination of particle aggregation and diffusion. The simulation shows large concentration distributions due to thermal diffusion causing variations in aggregation, thermal conductivity and viscosity. Static light scattering shows aggregates form more quickly at higher concentrations and temperatures, which explains the increased enhancement with temperature reported by other research groups. The permanent aggregates in the nanofluid are found to have a fractal dimension of 2.4 and the aggregate formations that grow over time are found to have a fractal dimension of 1.8, which is consistent with diffusion limited aggregation. Calculations show as aggregates grow the viscosity increases at a faster rate than thermal conductivity making the highly aggregated nanofluids unfavorable, especially at the low fractal dimension of 1.8. An optimum nanoparticle diameter for these particular fluid properties is calculated to be 130 nm to optimize the fluid stability by reducing settling, thermal diffusion and aggregation.
Modeling information diffusion in time-varying community networks
Cui, Xuelian; Zhao, Narisa
2017-12-01
Social networks are rarely static, and they typically have time-varying network topologies. A great number of studies have modeled temporal networks and explored social contagion processes within these models; however, few of these studies have considered community structure variations. In this paper, we present a study of how the time-varying property of a modular structure influences the information dissemination. First, we propose a continuous-time Markov model of information diffusion where two parameters, mobility rate and community attractiveness, are introduced to address the time-varying nature of the community structure. The basic reproduction number is derived, and the accuracy of this model is evaluated by comparing the simulation and theoretical results. Furthermore, numerical results illustrate that generally both the mobility rate and community attractiveness significantly promote the information diffusion process, especially in the initial outbreak stage. Moreover, the strength of this promotion effect is much stronger when the modularity is higher. Counterintuitively, it is found that when all communities have the same attractiveness, social mobility no longer accelerates the diffusion process. In addition, we show that the local spreading in the advantage group has been greatly enhanced due to the agglomeration effect caused by the social mobility and community attractiveness difference, which thus increases the global spreading.
An innovation diffusion model for new mobile technologies acceptance
Barkoczia Nadi
2017-01-01
Full Text Available This paper aims to approach the diffusion model developed in 1960 by Frank Bass has been utilized to study the distribution of different types of new products and services. The Bass Model helps by describing the process in which new products are adopted in a market. This model is a useful tool for predicting the first purchase of an innovative product for which there are competing alternatives on the market. It also provides the innovator with information regarding the size of customers and the adoption time for the product. The second part of the paper is dedicated to a monographic study of specific conceptual correlations between the diffusion of technology and marketing management that emphasizes technological uncertainty and market uncertainty as major risks to innovative projects. In the final section, the results of empirical research conducted in Baia-Mare, Romania will be presented in a way that uses diffusion Bass model to estimate the adoption period for new mobile technologies.
Social influence and perceptual decision making: a diffusion model analysis.
Germar, Markus; Schlemmer, Alexander; Krug, Kristine; Voss, Andreas; Mojzisch, Andreas
2014-02-01
Classic studies on social influence used simple perceptual decision-making tasks to examine how the opinions of others change individuals' judgments. Since then, one of the most fundamental questions in social psychology has been whether social influence can alter basic perceptual processes. To address this issue, we used a diffusion model analysis. Diffusion models provide a stochastic approach for separating the cognitive processes underlying speeded binary decisions. Following this approach, our study is the first to disentangle whether social influence on decision making is due to altering the uptake of available sensory information or due to shifting the decision criteria. In two experiments, we found consistent evidence for the idea that social influence alters the uptake of available sensory evidence. By contrast, participants did not adjust their decision criteria.
Modeling and Analysis of New Products Diffusion on Heterogeneous Networks
Shuping Li
2014-01-01
Full Text Available We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.
Modelling and control of a diffusion/LPCVD furnace
Dewaard, H.; Dekoning, W. L.
1988-12-01
Heat transfer inside a cylindrical resistance diffusion/Low Pressure Chemical Vapor Deposition (LPCVD) furnace is studied with the aim of developing an improved temperature controller. A model of the thermal behavior is derived, which covers the important class of furnaces equipped with semitransparent quartz process tubes. The model takes into account the thermal behavior of the thermocouples. Currently used temperature controllers are shown to be highly inefficient for very large scale integration applications. Based on the model an alternative temperature controller of the LQG (linear quadratic Gaussian) type is proposed which features direct wafer temperature control. Some simulation results are given.
Statistical models of a gas diffusion electrode: II. Current resistent
Proksch, D B; Winsel, O W
1965-07-01
The authors describe an apparatus for measuring the flow resistance of gas diffusion electrodes which is a mechanical analog of the Wheatstone bridge for measuring electric resistance. The flow resistance of a circular DSK electrode sheet, consisting of two covering layers and a working layer between them, was measured as a function of the gas pressure. While the pressure first was increased and then decreased, a hysteresis occurred, which is discussed and explained by a statistical model of a porous electrode.
Analysis of a diffuse interface model of multispecies tumor growth
Dai, M.; Feireisl, Eduard; Rocca, E.; Schimperna, G.; Schonbek, M.E.
2017-01-01
Roč. 30, č. 4 (2017), s. 1639-1658 ISSN 0951-7715 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Cahn-Hilliard equation * Darcy law * diffuse interface model Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6544/aa6063/meta
An epidemic model of rumor diffusion in online social networks
Cheng, Jun-Jun; Liu, Yun; Shen, Bo; Yuan, Wei-Guo
2013-01-01
So far, in some standard rumor spreading models, the transition probability from ignorants to spreaders is always treated as a constant. However, from a practical perspective, the case that individual whether or not be infected by the neighbor spreader greatly depends on the trustiness of ties between them. In order to solve this problem, we introduce a stochastic epidemic model of the rumor diffusion, in which the infectious probability is defined as a function of the strength of ties. Moreover, we investigate numerically the behavior of the model on a real scale-free social site with the exponent γ = 2.2. We verify that the strength of ties plays a critical role in the rumor diffusion process. Specially, selecting weak ties preferentially cannot make rumor spread faster and wider, but the efficiency of diffusion will be greatly affected after removing them. Another significant finding is that the maximum number of spreaders max( S) is very sensitive to the immune probability μ and the decay probability v. We show that a smaller μ or v leads to a larger spreading of the rumor, and their relationships can be described as the function ln(max( S)) = Av + B, in which the intercept B and the slope A can be fitted perfectly as power-law functions of μ. Our findings may offer some useful insights, helping guide the application in practice and reduce the damage brought by the rumor.
THE LOS ALAMOS NATIONAL LABORATORY ATMOSPHERIC TRANSPORT AND DIFFUSION MODELS
M. WILLIAMS [and others
1999-08-01
The LANL atmospheric transport and diffusion models are composed of two state-of-the-art computer codes. The first is an atmospheric wind model called HOThlAC, Higher Order Turbulence Model for Atmospheric circulations. HOTMAC generates wind and turbulence fields by solving a set of atmospheric dynamic equations. The second is an atmospheric diffusion model called RAPTAD, Random Particle Transport And Diffusion. RAPTAD uses the wind and turbulence output from HOTMAC to compute particle trajectories and concentration at any location downwind from a source. Both of these models, originally developed as research codes on supercomputers, have been modified to run on microcomputers. Because the capability of microcomputers is advancing so rapidly, the expectation is that they will eventually become as good as today's supercomputers. Now both models are run on desktop or deskside computers, such as an IBM PC/AT with an Opus Pm 350-32 bit coprocessor board and a SUN workstation. Codes have also been modified so that high level graphics, NCAR Graphics, of the output from both models are displayed on the desktop computer monitors and plotted on a laser printer. Two programs, HOTPLT and RAPLOT, produce wind vector plots of the output from HOTMAC and particle trajectory plots of the output from RAPTAD, respectively. A third CONPLT provides concentration contour plots. Section II describes step-by-step operational procedures, specifically for a SUN-4 desk side computer, on how to run main programs HOTMAC and RAPTAD, and graphics programs to display the results. Governing equations, boundary conditions and initial values of HOTMAC and RAPTAD are discussed in Section III. Finite-difference representations of the governing equations, numerical solution procedures, and a grid system are given in Section IV.
Yearly, seasonal and monthly daily average diffuse sky radiation models
Kassem, A.S.; Mujahid, A.M.; Turner, D.W.
1993-01-01
A daily average diffuse sky radiation regression model based on daily global radiation was developed utilizing two year data taken near Blytheville, Arkansas (Lat. =35.9 0 N, Long. = 89.9 0 W), U.S.A. The model has a determination coefficient of 0.91 and 0.092 standard error of estimate. The data were also analyzed for a seasonal dependence and four seasonal average daily models were developed for the spring, summer, fall and winter seasons. The coefficient of determination is 0.93, 0.81, 0.94 and 0.93, whereas the standard error of estimate is 0.08, 0.102, 0.042 and 0.075 for spring, summer, fall and winter, respectively. A monthly average daily diffuse sky radiation model was also developed. The coefficient of determination is 0.92 and the standard error of estimate is 0.083. A seasonal monthly average model was also developed which has 0.91 coefficient of determination and 0.085 standard error of estimate. The developed monthly daily average and daily models compare well with a selected number of previously developed models. (author). 11 ref., figs., tabs
Diffusion Modeling: A Study of the Diffusion of “Jatropha Curcas ...
Consequently, the study recommended the use of diffusion networks which integrate interpersonal networks, and multimedia strategies for the effective diffusion of innovation such as Jacodiesel in Adamawa State and other parts of the country. Keywords: Sustainability, Diffusion, Innovation, Communicative Influence, ...
Performance modeling of parallel algorithms for solving neutron diffusion problems
Azmy, Y.Y.; Kirk, B.L.
1995-01-01
Neutron diffusion calculations are the most common computational methods used in the design, analysis, and operation of nuclear reactors and related activities. Here, mathematical performance models are developed for the parallel algorithm used to solve the neutron diffusion equation on message passing and shared memory multiprocessors represented by the Intel iPSC/860 and the Sequent Balance 8000, respectively. The performance models are validated through several test problems, and these models are used to estimate the performance of each of the two considered architectures in situations typical of practical applications, such as fine meshes and a large number of participating processors. While message passing computers are capable of producing speedup, the parallel efficiency deteriorates rapidly as the number of processors increases. Furthermore, the speedup fails to improve appreciably for massively parallel computers so that only small- to medium-sized message passing multiprocessors offer a reasonable platform for this algorithm. In contrast, the performance model for the shared memory architecture predicts very high efficiency over a wide range of number of processors reasonable for this architecture. Furthermore, the model efficiency of the Sequent remains superior to that of the hypercube if its model parameters are adjusted to make its processors as fast as those of the iPSC/860. It is concluded that shared memory computers are better suited for this parallel algorithm than message passing computers
Thermodynamic modelling of fast dopant diffusion in Si
Saltas, V.; Chroneos, A.; Vallianatos, F.
2018-04-01
In the present study, nickel and copper fast diffusion in silicon is investigated in the framework of the cBΩ thermodynamic model, which connects point defect parameters with the bulk elastic and expansion properties. All the calculated point defect thermodynamic properties (activation Gibbs free energy, activation enthalpy, activation entropy, and activation volume) exhibit temperature dependence due to the non-linear anharmonic behavior of the isothermal bulk modulus of Si. Calculated activation enthalpies (0.15-0.16 eV for Ni and 0.17-0.19 eV for Cu) are in agreement with the reported experimental results. Small values of calculated activation volumes for both dopants (˜4% of the mean atomic volume) are consistent with the interstitial diffusion of Ni and Cu in Si.
Computing diffusivities from particle models out of equilibrium
Embacher, Peter; Dirr, Nicolas; Zimmer, Johannes; Reina, Celia
2018-04-01
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have Gaussian fluctuations but it is otherwise allowed to undergo arbitrary out-of-equilibrium evolutions. This could be potentially relevant for particle data obtained from experimental applications. The key idea underlying the method is that finite, yet large, particle systems formally obey stochastic partial differential equations of gradient flow type satisfying a fluctuation-dissipation relation. The strategy is here applied to three classic particle models, namely independent random walkers, a zero-range process and a symmetric simple exclusion process in one space dimension, to allow the comparison with analytic solutions.
Continuum modelling of silicon diffusion in indium gallium arsenide
Aldridge, Henry Lee, Jr.
A possible method to overcome the physical limitations experienced by continued transistor scaling and continue improvements in performance and power consumption is integration of III-V semiconductors as alternative channel materials for logic devices. Indium Gallium Arsenide (InGaAs) is such a material from the III-V semiconductor family, which exhibit superior electron mobilities and injection velocities than that of silicon. In order for InGaAs integration to be realized, contact resistances must be minimized through maximizing activation of dopants in this material. Additionally, redistribution of dopants during processing must be clearly understood and ultimately controlled at the nanometer-scale. In this work, the activation and diffusion behavior of silicon, a prominent n-type dopant in InGaAs, has been characterized and subsequently modelled using the Florida Object Oriented Process and Device Simulator (FLOOPS). In contrast to previous reports, silicon exhibits non-negligible diffusion in InGaAs, even for smaller thermal budget rapid thermal anneals (RTAs). Its diffusion is heavily concentration-dependent, with broadening "shoulder-like" profiles when doping levels exceed 1-3x1019cm -3, for both ion-implanted and Molecular Beam Epitaxy (MBE)-grown cases. Likewise a max net-activation value of ˜1.7x1019cm -3 is consistently reached with enough thermal processing, regardless of doping method. In line with experimental results and several ab-initio calculation results, rapid concentration-dependent diffusion of Si in InGaAs and the upper limits of its activation is believed to be governed by cation vacancies that serve as compensating defects in heavily n-type regions of InGaAs. These results are ultimately in line with an amphoteric defect model, where the activation limits of dopants are an intrinsic limitation of the material, rather than governed by individual dopant species or their methods of incorporation. As a result a Fermi level dependent point
Diffusion of innovations in Axelrod’s model
Tilles, Paulo F. C.; Fontanari, José F.
2015-11-01
Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e., individuals interact preferentially with similar others). The strength of these social influences are controlled by two parameters: $F$, the number of features that characterizes the cultures and $q$, the common number of states each feature can assume. Here we assume that the innovation is a new state of a cultural feature of a single individual -- the innovator -- and study how the innovation spreads through the networks among the individuals. For infinite regular lattices in one (1D) and two dimensions (2D), we find that initially the successful innovation spreads linearly with the time $t$, but in the long-time limit it spreads diffusively ($\\sim t^{1/2}$) in 1D and sub-diffusively ($\\sim t/\\ln t$) in 2D. For finite lattices, the growth curves for the number of adopters are typically concave functions of $t$. For random graphs with a finite number of nodes $N$, we argue that the classical S-shaped growth curves result from a trade-off between the average connectivity $K$ of the graph and the per feature diversity $q$. A large $q$ is needed to reduce the pace of the initial spreading of the innovation and thus delimit the early-adopters stage, whereas a large $K$ is necessary to ensure the onset of the take-off stage at which the number of adopters grows superlinearly with $t$. In an infinite random graph we find that the number of adopters of a successful innovation scales with $t^\\gamma$ with $\\gamma =1$ for $K> 2$ and $1/2 < \\gamma < 1$ for $K=2$. We suggest that the exponent $\\gamma$ may be a useful index to characterize the process of diffusion of successful innovations in diverse scenarios.
A current induced diffusion model of gas sputtering
Hotston, E.S.
1980-01-01
A model is proposed to explain the experimental results on deuteron trapping in stainless steel targets at low temperatures carried out at Garching and Culham. The model proposes that the ions are trapped in two kinds of sites: Deep sites with high activation energy and shallow sites of low activation energy. Trapped deuterons reach the surface of the target by being expelled from shallow sites by the action of the ion beam and migrate to nearby sites in a random way, thus moving by a bombardment induced diffusion. Ions diffusing to the target surface and being released are said to be sputtered from the target. It has been necessary to assume numerical values for sizes of some of the processes which occur. With a suitable choice of values the model successfully predicts the numbers of deuterons trapped per unit area of the target, the obserbed density profile of the trapped ions and the threshold at which sputtering starts. The model also successfully describes the replacement of the trapped deuterons by protons, when the deuteron beam is replaced by a proton beam. The collision cross-section for beam ions and ions trapped in shallow sites is too large, 4 x 10 -13 cm 2 , for a binary collision and it is tentatively suggested that the ions in the shallow sites may be in small voids in the target which may be connected with blister formation. Comparison of the present model with one being developed to describe the trapping of deuterons in carbon suggests that it may be possible to describe all gas sputtering experiments in terms of diffusion processes. (orig.)
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Turbulent diffusion modelling for windflow and dispersion analysis
Bartzis, J.G.
1988-01-01
The need for simple but reliable models for turbulent diffusion for windflow and atmospheric dispersion analysis is a necessity today if one takes into consideration the relatively high demand in computer time and costs for such an analysis, arising mainly from the often large solution domains needed, the terrain complexity and the transient nature of the phenomena. In the accident consequence assessment often there is a need for a relatively large number of cases to be analysed increasing further the computer time and costs. Within the framework of searching for relatively simple and universal eddy viscosity/diffusivity models, a new three dimensional non isotropic model is proposed applicable to any domain complexity and any atmospheric stability conditions. The model utilizes the transport equation for turbulent kinetic energy but introduces a new approach in effective length scale estimation based on the flow global characteristics and local atmospheric stability. The model is discussed in detail and predictions are given for flow field and boundary layer thickness. The results are compared with experimental data with satisfactory results
A discrete model to study reaction-diffusion-mechanics systems.
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Marinak, M.
1990-02-01
The problem of deducing χ e from measurements of the propagation of a monopole heatpulse is considered. An extended diffusive model, which takes into account perturbed sources and sinks is extended to the case of a monopole heat input. χ e is expressed as a function of two observables, the heat pulse velocity and the radial damping rate. Two simple expressions valid for two different ranges of the radius of the poloidal waist of the beam power profile are given. The expressions are valid in the heat pulse measurement region, extending radially 0.05a beyond the beam power waist to near 0.6a. The inferred χ e is a local value, not an average value of the radial χ e profile. 7 refs., 6 figs., 1 tab
Sooting Characteristics and Modeling in Counterflow Diffusion Flames
Wang, Yu
2013-11-01
Soot formation is one of the most complex phenomena in combustion science and an understanding of the underlying physico-chemical mechanisms is important. This work adopted both experimental and numerical approaches to study soot formation in laminar counterfl ow diffusion flames. As polycyclic aromatic hydrocarbons (PAHs) are the precursors of soot particles, a detailed gas-phase chemical mechanism describing PAH growth upto coronene for fuels with 1 to 4 carbon atoms was validated against laminar premixed and counter- flow diffusion fl ames. Built upon this gas-phase mechanism, a soot model was then developed to describe soot inception and surface growth. This soot model was sub- sequently used to study fuel mixing effect on soot formation in counterfl ow diffusion flames. Simulation results showed that compared to the baseline case of the ethylene flame, the doping of 5% (by volume) propane or ethane in ethylene tends to increase the soot volume fraction and number density while keeping the average soot size almost unchanged. These results are in agreement with experimental observations. Laser light extinction/scattering as well as laser induced fluorescence techniques were used to study the effect of strain rate on soot and PAH formation in counterfl ow diffusion ames. The results showed that as strain rate increased both soot volume fraction and PAH concentrations decreased. The concentrations of larger PAH were more sensitive to strain rate compared to smaller ones. The effect of CO2 addition on soot formation was also studied using similar experimental techniques. Soot loading was reduced with CO2 dilution. Subsequent numerical modeling studies were able to reproduce the experimental trend. In addition, the chemical effect of CO2 addition was analyzed using numerical data. Critical conditions for the onset of soot were systematically studied in counterfl ow diffusion ames for various gaseous hydrocarbon fuels and at different strain rates. A sooting
Application of the evolution theory in modelling of innovation diffusion
Krstić Milan
2016-01-01
Full Text Available The theory of evolution has found numerous analogies and applications in other scientific disciplines apart from biology. In that sense, today the so-called 'memetic-evolution' has been widely accepted. Memes represent a complex adaptable system, where one 'meme' represents an evolutional cultural element, i.e. the smallest unit of information which can be identified and used in order to explain the evolution process. Among others, the field of innovations has proved itself to be a suitable area where the theory of evolution can also be successfully applied. In this work the authors have started from the assumption that it is also possible to apply the theory of evolution in the modelling of the process of innovation diffusion. Based on the conducted theoretical research, the authors conclude that the process of innovation diffusion in the interpretation of a 'meme' is actually the process of imitation of the 'meme' of innovation. Since during the process of their replication certain 'memes' show a bigger success compared to others, that eventually leads to their natural selection. For the survival of innovation 'memes', their manifestations are of key importance in the sense of their longevity, fruitfulness and faithful replicating. The results of the conducted research have categorically confirmed the assumption of the possibility of application of the evolution theory with the innovation diffusion with the help of innovation 'memes', which opens up the perspectives for some new researches on the subject.
Different approach to the modeling of nonfree particle diffusion
Buhl, Niels
2018-03-01
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.
Dense-gas dispersion advection-diffusion model
Ermak, D.L.
1992-07-01
A dense-gas version of the ADPIC particle-in-cell, advection- diffusion model was developed to simulate the atmospheric dispersion of denser-than-air releases. In developing the model, it was assumed that the dense-gas effects could be described in terms of the vertically-averaged thermodynamic properties and the local height of the cloud. The dense-gas effects were treated as a perturbation to the ambient thermodynamic properties (density and temperature), ground level heat flux, turbulence level (diffusivity), and windfield (gravity flow) within the local region of the dense-gas cloud. These perturbations were calculated from conservation of energy and conservation of momentum principles along with the ideal gas law equation of state for a mixture of gases. ADPIC, which is generally run in conjunction with a mass-conserving wind flow model to provide the advection field, contains all the dense-gas modifications within it. This feature provides the versatility of coupling the new dense-gas ADPIC with alternative wind flow models. The new dense-gas ADPIC has been used to simulate the atmospheric dispersion of ground-level, colder-than-ambient, denser-than-air releases and has compared favorably with the results of field-scale experiments
Diffusion and reaction within porous packing media: a phenomenological model.
Jones, W L; Dockery, J D; Vogel, C R; Sturman, P J
1993-04-25
A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion.
Modeling of 1D Anomalous Diffusion in Fractured Nanoporous Media
Albinali Ali
2016-07-01
Full Text Available Fractured nanoporous reservoirs include multi-scale and discontinuous fractures coupled with a complex nanoporous matrix. Such systems cannot be described by the conventional dual-porosity (or multi-porosity idealizations due to the presence of different flow mechanisms at multiple scales. More detailed modeling approaches, such as Discrete Fracture Network (DFN models, similarly suffer from the extensive data requirements dictated by the intricacy of the flow scales, which eventually deter the utility of these models. This paper discusses the utility and construction of 1D analytical and numerical anomalous diffusion models for heterogeneous, nanoporous media, which is commonly encountered in oil and gas production from tight, unconventional reservoirs with fractured horizontal wells. A fractional form of Darcy’s law, which incorporates the non-local and hereditary nature of flow, is coupled with the classical mass conservation equation to derive a fractional diffusion equation in space and time. Results show excellent agreement with established solutions under asymptotic conditions and are consistent with the physical intuitions.
Subgrid models for mass and thermal diffusion in turbulent mixing
Lim, H; Yu, Y; Glimm, J; Li, X-L; Sharp, D H
2010-01-01
We propose a new method for the large eddy simulation (LES) of turbulent mixing flows. The method yields convergent probability distribution functions (PDFs) for temperature and concentration and a chemical reaction rate when applied to reshocked Richtmyer-Meshkov (RM) unstable flows. Because such a mesh convergence is an unusual and perhaps original capability for LES of RM flows, we review previous validation studies of the principal components of the algorithm. The components are (i) a front tracking code, FronTier, to control numerical mass diffusion and (ii) dynamic subgrid scale (SGS) models to compensate for unresolved scales in the LES. We also review the relevant code comparison studies. We compare our results to a simple model based on 1D diffusion, taking place in the geometry defined statistically by the interface (the 50% isoconcentration surface between the two fluids). Several conclusions important to physics could be drawn from our study. We model chemical reactions with no closure approximations beyond those in the LES of the fluid variables itself, and as with dynamic SGS models, these closures contain no adjustable parameters. The chemical reaction rate is specified by the joint PDF for temperature and concentration. We observe a bimodal distribution for the PDF and we observe significant dependence on fluid transport parameters.
Compact Models for Defect Diffusivity in Semiconductor Alloys.
Wright, Alan F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Nanostructure Physics Department; Modine, Normand A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Nanostructure Physics Department; Lee, Stephen R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Advanced Materials Sciences Department; Foiles, Stephen M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computational Materials and Data Science Department
2017-09-01
Predicting transient effects caused by short - pulse neutron irradiation of electronic devices is an important part of Sandia's mission. For example , predicting the diffusion of radiation - induced point defects is needed with in Sandia's Qualification Alternative to the Sandia Pulsed Reactor (QASPR) pro gram since defect diffusion mediates transient gain recovery in QASPR electronic devices. Recently, the semiconductors used to fabricate radiation - hard electronic devices have begun to shift from silicon to III - V compounds such as GaAs, InAs , GaP and InP . An advantage of this shift is that it allows engineers to optimize the radiation hardness of electronic devices by using alloy s such as InGaAs and InGaP . However, the computer codes currently being used to simulate transient radiation effects in QASP R devices will need to be modified since they presume that defect properties (charge states, energy levels, and diffusivities) in these alloys do not change with time. This is not realistic since the energy and properties of a defect depend on the types of atoms near it and , therefore, on its location in the alloy. In particular, radiation - induced defects are created at nearly random locations in an alloy and the distribution of their local environments - and thus their energies and properties - evolves with time as the defects diffuse through the alloy . To incorporate these consequential effects into computer codes used to simulate transient radiation effects, we have developed procedures to accurately compute the time dependence of defect energies and properties and then formulate them within compact models that can be employed in these computer codes. In this document, we demonstrate these procedures for the case of the highly mobile P interstitial (I P ) in an InGaP alloy. Further dissemination only as authorized to U.S. Government agencies and their contractors; other requests shall be approved by the originating facility or higher DOE
Anomalous diffusion in neutral evolution of model proteins
Nelson, Erik D.; Grishin, Nick V.
2015-06-01
Protein evolution is frequently explored using minimalist polymer models, however, little attention has been given to the problem of structural drift, or diffusion. Here, we study neutral evolution of small protein motifs using an off-lattice heteropolymer model in which individual monomers interact as low-resolution amino acids. In contrast to most earlier models, both the length and folded structure of the polymers are permitted to change. To describe structural change, we compute the mean-square distance (MSD) between monomers in homologous folds separated by n neutral mutations. We find that structural change is episodic, and, averaged over lineages (for example, those extending from a single sequence), exhibits a power-law dependence on n . We show that this exponent depends on the alignment method used, and we analyze the distribution of waiting times between neutral mutations. The latter are more disperse than for models required to maintain a specific fold, but exhibit a similar power-law tail.
Residual sweeping errors in turbulent particle pair diffusion in a Lagrangian diffusion model.
Malik, Nadeem A
2017-01-01
Thomson, D. J. & Devenish, B. J. [J. Fluid Mech. 526, 277 (2005)] and others have suggested that sweeping effects make Lagrangian properties in Kinematic Simulations (KS), Fung et al [Fung J. C. H., Hunt J. C. R., Malik N. A. & Perkins R. J. J. Fluid Mech. 236, 281 (1992)], unreliable. However, such a conclusion can only be drawn under the assumption of locality. The major aim here is to quantify the sweeping errors in KS without assuming locality. Through a novel analysis based upon analysing pairs of particle trajectories in a frame of reference moving with the large energy containing scales of motion it is shown that the normalized integrated error [Formula: see text] in the turbulent pair diffusivity (K) due to the sweeping effect decreases with increasing pair separation (σl), such that [Formula: see text] as σl/η → ∞; and [Formula: see text] as σl/η → 0. η is the Kolmogorov turbulence microscale. There is an intermediate range of separations 1 < σl/η < ∞ in which the error [Formula: see text] remains negligible. Simulations using KS shows that in the swept frame of reference, this intermediate range is large covering almost the entire inertial subrange simulated, 1 < σl/η < 105, implying that the deviation from locality observed in KS cannot be atributed to sweeping errors. This is important for pair diffusion theory and modeling. PACS numbers: 47.27.E?, 47.27.Gs, 47.27.jv, 47.27.Ak, 47.27.tb, 47.27.eb, 47.11.-j.
The brush model - a new approach to numerical modeling of matrix diffusion in fractured clay stone
Lege, T.; Shao, H.
1998-01-01
A special approach for numerical modeling of contaminant transport in fractured clay stone is presented. The rock matrix and the fractures are simulated with individual formulations for FE grids and transport, coupled into a single model. The capacity of the rock matrix to take up contaminants is taken into consideration with a discrete simulation of matrix diffusion. Thus, the natural process of retardation due to matrix diffusion can be better simulated than by a standard introduction of an empirical parameter into the transport equation. Transport in groundwater in fractured clay stone can be simulated using a model called a 'brush model'. The 'brush handle' is discretized by 2-D finite elements. Advective-dispersive transport in groundwater in the fractures is assumed. The contaminant diffuses into 1D finite elements perpendicular to the fractures, i.e., the 'bristles of the brush'. The conclusion is drawn that matrix diffusion is an important property of fractured clay stone for contaminant retardation. (author)
Bayesian uncertainty quantification in linear models for diffusion MRI.
Sjölund, Jens; Eklund, Anders; Özarslan, Evren; Herberthson, Magnus; Bånkestad, Maria; Knutsson, Hans
2018-03-29
Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. Copyright © 2018 Elsevier Inc. All rights reserved.
A chaotic model for advertising diffusion problem with competition
Ip, W. H.; Yung, K. L.; Wang, Dingwei
2012-08-01
In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win-Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win-Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy.
Modeling the Determinants Influencing the Diffusion of Mobile Internet
Alwahaishi, Saleh; Snášel, Václav
2013-04-01
Understanding individual acceptance and use of Information and Communication Technology (ICT) is one of the most mature streams of information systems research. In Information Technology and Information System research, numerous theories are used to understand users' adoption of new technologies. Various models were developed including the Innovation Diffusion Theory, Theory of Reasoned Action, Theory of Planned Behavior, Technology Acceptance Model, and recently, the Unified Theory of Acceptance and Use of Technology. This research composes a new hybrid theoretical framework to identify the factors affecting the acceptance and use of Mobile Internet -as an ICT application- in a consumer context. The proposed model incorporates eight constructs: Performance Expectancy (PE), Effort Expectancy (EE), Facilitating Conditions (FC), Social Influences (SI), Perceived Value (PV), Perceived Playfulness (PP), Attention Focus (AF), and Behavioral intention (BI). Individual differences-namely, age, gender, education, income, and experience are moderating the effects of these constructs on behavioral intention and technology use.
Jyothi, D.; Murty, T.V.R.; Sarma, V.V.; Rao, D.P.
conditions. As the pollutant load on the estuary increases, the. water quality may deteriorate rapidly and therefore the scientific interests are centered on the analysis of water quality. The pollutants will be subjected to a number of physical, chemical... study we have applied one-dimensional advection-diffusion model for the waters of Gauthami Godavari estuary to determine the axial diffusion coefficients and thereby to predict the impact assessment. The study area (Fig. 1) is the lower most 32 km...
Introducing serendipity in a social network model of knowledge diffusion
Cremonini, Marco
2016-01-01
Highlights: • Serendipity as a control mechanism for knowledge diffusion in social network. • Local communication enhanced in the periphery of a network. • Prevalence of hub nodes in the network core mitigated. • Potential disruptive effect on network formation of uncontrolled serendipity. - Abstract: In this paper, we study serendipity as a possible strategy to control the behavior of an agent-based network model of knowledge diffusion. The idea of considering serendipity in a strategic way has been first explored in Network Learning and Information Seeking studies. After presenting the major contributions of serendipity studies to digital environments, we discuss the extension to our model: Agents are enriched with random topics for establishing new communication according to different strategies. The results show how important network properties could be influenced, like reducing the prevalence of hubs in the network’s core and increasing local communication in the periphery, similar to the effects of more traditional self-organization methods. Therefore, from this initial study, when serendipity is opportunistically directed, it appears to behave as an effective and applicable approach to social network control.
Zirconium - ab initio modelling of point defects diffusion
Gasca, Petrica
2010-01-01
Zirconium is the main element of the cladding found in pressurized water reactors, under an alloy form. Under irradiation, the cladding elongate significantly, phenomena attributed to the vacancy dislocation loops growth in the basal planes of the hexagonal compact structure. The understanding of the atomic scale mechanisms originating this process motivated this work. Using the ab initio atomic modeling technique we studied the structure and mobility of point defects in Zirconium. This led us to find four interstitial point defects with formation energies in an interval of 0.11 eV. The migration paths study allowed the discovery of activation energies, used as entry parameters for a kinetic Monte Carlo code. This code was developed for calculating the diffusion coefficient of the interstitial point defect. Our results suggest a migration parallel to the basal plane twice as fast as one parallel to the c direction, with an activation energy of 0.08 eV, independent of the direction. The vacancy diffusion coefficient, estimated with a two-jump model, is also anisotropic, with a faster process in the basal planes than perpendicular to them. Hydrogen influence on the vacancy dislocation loops nucleation was also studied, due to recent experimental observations of cladding growth acceleration in the presence of this element [fr
Wen, Zijuan; Fu, Shengmao
2016-01-01
This paper deals with a strongly coupled reaction-diffusion system modeling a competitor-competitor-mutualist three-species model with diffusion, self-diffusion and nonlinear cross-diffusion and subject to Neumann boundary conditions. First, we establish the persistence of a corresponding reaction-diffusion system without self- and cross-diffusion. Second, the global asymptotic stability of the unique positive equilibrium for weakly coupled PDE system is established by using a comparison method. Moreover, under certain conditions about the intra- and inter-species effects, we prove that the uniform positive steady state is linearly unstable for the cross-diffusion system when one of the cross-diffusions is large enough. The results indicate that Turing instability can be driven solely from strong diffusion effect of the first species (or the second species or the third species) due to the pressure of the second species (or the first species).
Modelling thermal radiation and soot formation in buoyant diffusion flames
Demarco Bull, R.A.
2012-01-01
The radiative heat transfer plays an important role in fire problems since it is the dominant mode of heat transfer between flames and surroundings. It controls the pyrolysis, and therefore the heat release rate, and the growth rate of the fire. In the present work a numerical study of buoyant diffusion flames is carried out, with the main objective of modelling the thermal radiative transfer and the soot formation/destruction processes. In a first step, different radiative property models were tested in benchmark configurations. It was found that the FSCK coupled with the Modest and Riazzi mixing scheme was the best compromise in terms of accuracy and computational requirements, and was a good candidate to be implemented in CFD codes dealing with fire problems. In a second step, a semi-empirical soot model, considering acetylene and benzene as precursor species for soot nucleation, was validated in laminar co flow diffusion flames over a wide range of hydrocarbons (C1-C3) and conditions. In addition, the optically-thin approximation was found to produce large discrepancies in the upper part of these small laminar flames. Reliable predictions of soot volume fractions require the use of an advanced radiation model. Then the FSCK and the semi-empirical soot model were applied to simulate laboratory-scale and intermediate-scale pool fires of methane and propane. Predicted flame structures as well as the radiant heat flux transferred to the surroundings were found to be in good agreement with the available experimental data. Finally, the interaction between radiation and turbulence was quantified. (author)
The development of radioactivity diffusion model in global ocean
Nakano, M.; Watanabe, H.; Katagiri, H.
2000-01-01
The radioactivity diffusion model in global ocean has been developing in order to assess the long-term behavior of radioactive materials for discharge from nuclear facility. The model system consists of two parts. One is to calculate current velocity; and the other is for particle chasing. Both systems are executed by Macintosh personal computer. A lot of techniques to estimate ocean current velocity were investigated in geophysical field. The robust diagnosis model advocated by Sarmiento and Bryan was applied to build the numerical calculation system for getting the current velocity field in global scale. The latitudinal and longitudinal lattices were 2 degrees each and the number of vertical layer was 15. The movement of radioactive materials by current and diffusion were calculated using the particle chasing system. The above-mentioned current velocity field and the initial particle positions at will were read by the system. The movement of a particle was calculated using the interpolated current data step by step. The diffusion of a particle was calculated by random walk method. The model was verified by using the fallout data from atmospheric nuclear test. Yearly and latitudinal fallout data was adopted from UNSCEAR1977. The calculation result was compared with the observation data that includes total amount and vertical profile of Cs-137 and Pu-239,240 in the North Pacific Ocean. The result of the verification was agreed with the following general knowledge. Though the fallout amount between 40N and 50N was the biggest in the world, the amount in the seawater between 40N and 50N was smaller than that in south of 40N because of horizontal transportation, which carried water from north to south. As for vertical profile, Cs-137 could be accurately calculated except the surface layer. However the observation peak of Pu-239,240 existed deeper than the calculation peak. This model could calculate the vertical profile of Cs-137 because most of Cs exists as dissolved
Pre-Clinical Models of Diffuse Intrinsic Pontine Glioma
Oren J Becher
2015-07-01
Full Text Available Diffuse Intrinsic Pontine Glioma (DIPG is a rare and incurable brain tumor that arises in the brainstem of children predominantly between the ages of six and eight. Its intricate morphology and involvement of normal pons tissue precludes surgical resection, and the standard of care today remains fractionated radiation alone. In the past 30 years, there have been no significant advances made in the treatment of DIPG. This is largely because we lack good models of DIPG and therefore have little biological basis for treatment. In recent years however, due to increased biopsy and acquisition of autopsy specimens, research is beginning to unravel the genetic and epigenetic drivers of DIPG. Insight gleaned from these studies has led to improvements in approaches to both model these tumors in the lab, as well as to potentially treat them in the clinic. This review will detail the initial strides towards modeling DIPG in animals, which included allograft and xenograft rodent models using non-DIPG glioma cells. Important advances in the field came with the development of in vitro cell and in vivo xenograft models derived directly from autopsy material of DIPG patients or from human embryonic stem cells. Lastly, we will summarize the progress made in the development of genetically engineered mouse models of DIPG. Cooperation of studies incorporating all of these modeling systems to both investigate the unique mechanisms of gliomagenesis in the brainstem and to test potential novel therapeutic agents in a preclinical setting will result in improvement in treatments for DIPG patients.
Cardon, Clement
2016-01-01
This Ph.D. topic is focused on the modelling of stratification kinetics for an oxide-metal corium pool (U-O-Zr-steel system) in terms of multicomponent and multiphase diffusion. This work is part of a larger research effort for the development of a detailed corium pool modelling based on a CFD approach for thermal hydraulics. The overall goal is to improve the understanding of the involved phenomena and obtain closure laws for integral macroscopic models. The phase-field method coupled with an energy functional using the CALPHAD method appears to be relevant for this purpose. In a first part, we have developed a diffuse interface model in order to describe the diffusion process in the U-O system. This model has been coupled with a CALPHAD thermodynamic database and its parameterization has been developed with, in particular, an up-scaling procedure related to the interface thickness. Then, within the framework of a modelling for the U-O-Zr ternary system, we have proposed a generalization of the diffuse interface model through an assumption of local equilibrium for redox mechanisms. A particular attention was paid to the model analysis by 1D numerical simulations with a special focus on the steady state composition profiles. Finally we have applied this model to the U-O-Zr-Fe system. For that purpose, we have considered a configuration close to small-scale experimental tests of oxide-metal corium pool stratification. (author) [fr
A Jump Diffusion Model for Volatility and Duration
Wei, Wei; Pelletier, Denis
by the market microstructure theory. Traditional measures of volatility do not utilize durations. I adopt a jump diffusion process to model the persistence of intraday volatility and conditional duration, and their interdependence. The jump component is disentangled from the continuous part of the price......, volatility and conditional duration process. I develop a MCMC algorithm for the inference of irregularly spaced multivariate process with jumps. The algorithm provides smoothed estimates of the latent variables such as spot volatility, jump times and jump sizes. I apply this model to IBM data and I find...... meaningful relationship between volatility and conditional duration. Also, jumps play an important role in the total variation, but the jump variation is smaller than traditional measures that use returns sampled at lower frequency....
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Manchon, Aurelien; Praetorius, Dirk; Suess, Dieter
2016-01-01
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas
2016-12-17
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
Decomposition in aluminium alloys: diffuse scattering and crystal modelling
Aslam-Malik, A.
1995-01-01
In the present study the microstructure of metastable precipitates in Al-Ag and Al-Cu, so called pre-precipitates or Guinier-Preston (GP) zones, was investigated. In both systems important aspects of the microstructure are still controversially discussed. In Al-Ag two forms of GP zones are suggested; depending on the aging temperatures above or below about 443 K, ε- or η-zones should evolve. Differences between these two types of zones may be due to differences in internal order and/or composition. In Al-Cu the characterization of GP I zones is difficult because of the strong atomic displacements around the zones. The proper separation of short-range order and displacement scattering within a diffuse scattering experiment is still under discussion. The technique used to determine the short-range order in both alloys was diffuse scattering with neutrons and X-rays. To separate short-range order and displacement scattering, the methods of Georgopoulos-Cohen (X-ray scattering) and Borie-Sparks (neutron scattering) were used. Of main importance is the optimization of the scattering contrast and thus the scattering contribution due to short-range order. Short-range order scattering is rationalized in terms of pair correlations. Crystals may subsequently be modelled to visualize the microstructure. The Al-Ag system was investigated by diffuse X-ray wide-angle scattering and small-angle neutron scattering. The small-angle neutron scattering measurement was necessary since the GP zones in Al-Ag are almost spherical and the main scattering contribution is found close to the origin of reciprocal space. The small-angle scattering is not that important in the case of Al-Cu because the main scattering extends along (100) owing to the planar character of the GP I zones on (100) lattice planes. (author) 24 figs., 10 tabs., refs
Modeling Periodic Impulsive Effects on Online TV Series Diffusion.
Fu, Peihua; Zhu, Anding; Fang, Qiwen; Wang, Xi
Online broadcasting substantially affects the production, distribution, and profit of TV series. In addition, online word-of-mouth significantly affects the diffusion of TV series. Because on-demand streaming rates are the most important factor that influences the earnings of online video suppliers, streaming statistics and forecasting trends are valuable. In this paper, we investigate the effects of periodic impulsive stimulation and pre-launch promotion on on-demand streaming dynamics. We consider imbalanced audience feverish distribution using an impulsive susceptible-infected-removed(SIR)-like model. In addition, we perform a correlation analysis of online buzz volume based on Baidu Index data. We propose a PI-SIR model to evolve audience dynamics and translate them into on-demand streaming fluctuations, which can be observed and comprehended by online video suppliers. Six South Korean TV series datasets are used to test the model. We develop a coarse-to-fine two-step fitting scheme to estimate the model parameters, first by fitting inter-period accumulation and then by fitting inner-period feverish distribution. We find that audience members display similar viewing habits. That is, they seek new episodes every update day but fade away. This outcome means that impulsive intensity plays a crucial role in on-demand streaming diffusion. In addition, the initial audience size and online buzz are significant factors. On-demand streaming fluctuation is highly correlated with online buzz fluctuation. To stimulate audience attention and interpersonal diffusion, it is worthwhile to invest in promotion near update days. Strong pre-launch promotion is also a good marketing tool to improve overall performance. It is not advisable for online video providers to promote several popular TV series on the same update day. Inter-period accumulation is a feasible forecasting tool to predict the future trend of the on-demand streaming amount. The buzz in public social communities
Modeling Periodic Impulsive Effects on Online TV Series Diffusion.
Peihua Fu
Full Text Available Online broadcasting substantially affects the production, distribution, and profit of TV series. In addition, online word-of-mouth significantly affects the diffusion of TV series. Because on-demand streaming rates are the most important factor that influences the earnings of online video suppliers, streaming statistics and forecasting trends are valuable. In this paper, we investigate the effects of periodic impulsive stimulation and pre-launch promotion on on-demand streaming dynamics. We consider imbalanced audience feverish distribution using an impulsive susceptible-infected-removed(SIR-like model. In addition, we perform a correlation analysis of online buzz volume based on Baidu Index data.We propose a PI-SIR model to evolve audience dynamics and translate them into on-demand streaming fluctuations, which can be observed and comprehended by online video suppliers. Six South Korean TV series datasets are used to test the model. We develop a coarse-to-fine two-step fitting scheme to estimate the model parameters, first by fitting inter-period accumulation and then by fitting inner-period feverish distribution.We find that audience members display similar viewing habits. That is, they seek new episodes every update day but fade away. This outcome means that impulsive intensity plays a crucial role in on-demand streaming diffusion. In addition, the initial audience size and online buzz are significant factors. On-demand streaming fluctuation is highly correlated with online buzz fluctuation.To stimulate audience attention and interpersonal diffusion, it is worthwhile to invest in promotion near update days. Strong pre-launch promotion is also a good marketing tool to improve overall performance. It is not advisable for online video providers to promote several popular TV series on the same update day. Inter-period accumulation is a feasible forecasting tool to predict the future trend of the on-demand streaming amount. The buzz in public
Modeling Periodic Impulsive Effects on Online TV Series Diffusion
Fang, Qiwen; Wang, Xi
2016-01-01
Background Online broadcasting substantially affects the production, distribution, and profit of TV series. In addition, online word-of-mouth significantly affects the diffusion of TV series. Because on-demand streaming rates are the most important factor that influences the earnings of online video suppliers, streaming statistics and forecasting trends are valuable. In this paper, we investigate the effects of periodic impulsive stimulation and pre-launch promotion on on-demand streaming dynamics. We consider imbalanced audience feverish distribution using an impulsive susceptible-infected-removed(SIR)-like model. In addition, we perform a correlation analysis of online buzz volume based on Baidu Index data. Methods We propose a PI-SIR model to evolve audience dynamics and translate them into on-demand streaming fluctuations, which can be observed and comprehended by online video suppliers. Six South Korean TV series datasets are used to test the model. We develop a coarse-to-fine two-step fitting scheme to estimate the model parameters, first by fitting inter-period accumulation and then by fitting inner-period feverish distribution. Results We find that audience members display similar viewing habits. That is, they seek new episodes every update day but fade away. This outcome means that impulsive intensity plays a crucial role in on-demand streaming diffusion. In addition, the initial audience size and online buzz are significant factors. On-demand streaming fluctuation is highly correlated with online buzz fluctuation. Conclusion To stimulate audience attention and interpersonal diffusion, it is worthwhile to invest in promotion near update days. Strong pre-launch promotion is also a good marketing tool to improve overall performance. It is not advisable for online video providers to promote several popular TV series on the same update day. Inter-period accumulation is a feasible forecasting tool to predict the future trend of the on-demand streaming amount
Modelling of diffusion from equilibrium diffraction fluctuations in ordered phases
Arapaki, E.; Argyrakis, P.; Tringides, M.C.
2008-01-01
Measurements of the collective diffusion coefficient D c at equilibrium are difficult because they are based on monitoring low amplitude concentration fluctuations generated spontaneously, that are difficult to measure experimentally. A new experimental method has been recently used to measure time-dependent correlation functions from the diffraction intensity fluctuations and was applied to measure thermal step fluctuations. The method has not been applied yet to measure superstructure intensity fluctuations in surface overlayers and to extract D c . With Monte Carlo simulations we study equilibrium fluctuations in Ising lattice gas models with nearest neighbor attractive and repulsive interactions. The extracted diffusion coefficients are compared to the ones obtained from equilibrium methods. The new results are in good agreement with the results from the other methods, i.e., D c decreases monotonically with coverage Θ for attractive interactions and increases monotonically with Θ for repulsive interactions. Even the absolute value of D c agrees well with the results obtained with the probe area method. These results confirm that this diffraction based method is a novel, reliable way to measure D c especially within the ordered region of the phase diagram when the superstructure spot has large intensity
Modeling of interstitial diffusion of ion-implanted boron
Velichko, O.I.; Knyazheva, N.V.
2009-01-01
A model of the interstitial diffusion of ion-implanted boron during rapid thermal annealing of silicon layers previously amorphized by implantation of germanium has been proposed. It is supposed that the boron interstitials are created continuously during annealing due to generation, dissolution, or rearrangement of the clusters of impurity atoms which are formed in the ion-implanted layers with impurity concentration above the solubility limit. The local elastic stresses arising due to the difference of boron atomic radius and atomic radius of silicon also contribute to the generation of boron interstitials. A simulation of boron redistribution during thermal annealing for 60 s at a temperature of 850 C has been carried out. The calculated profile agrees well with the experimental data. A number of the parameters of interstitial diffusion have been derived. In particular, the average migration length of nonequilibrium boron interstitials is equal to 12 nm. It was also obtained that approximately 1.94% of boron atoms were converted to the interstitial sites, participated in the fast interstitial migration, and then became immobile again transferring into a substitutional position or forming the electrically inactive complexes with crystal lattice defects. (authors)
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S A; Kugeiko, M M; Firago, V A [Belarusian State University, Minsk (Belarus); Sobchuk, A N [B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk (Belarus)
2014-01-31
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)
Nonequilibrium two-dimensional Ising model with stationary uphill diffusion
Colangeli, Matteo; Giardinà, Cristian; Giberti, Claudio; Vernia, Cecilia
2018-03-01
Usually, in a nonequilibrium setting, a current brings mass from the highest density regions to the lowest density ones. Although rare, the opposite phenomenon (known as "uphill diffusion") has also been observed in multicomponent systems, where it appears as an artificial effect of the interaction among components. We show here that uphill diffusion can be a substantial effect, i.e., it may occur even in single component systems as a consequence of some external work. To this aim we consider the two-dimensional ferromagnetic Ising model in contact with two reservoirs that fix, at the left and the right boundaries, magnetizations of the same magnitude but of opposite signs.We provide numerical evidence that a class of nonequilibrium steady states exists in which, by tuning the reservoir magnetizations, the current in the system changes from "downhill" to "uphill". Moreover, we also show that, in such nonequilibrium setup, the current vanishes when the reservoir magnetization attains a value approaching, in the large volume limit, the magnetization of the equilibrium dynamics, thus establishing a relation between equilibrium and nonequilibrium properties.
Study of superionic conductors dynamics by continued diffusion model
Bennai, M.
1993-12-01
The superionic conductors form a special category of solids characterized by their remarkable transport properties and are in general, Simplified as being constituted by the superposition of two inter penetrable crystal lattices. The ions of the first one form a rigid structure through which the other ions of opposite charge diffuse in quasi-liquid way. Basing on experimental and theoretical arguments, it was proved necessary to adopt a model of N-body continued diffusion which the basic theory is that of brownian movement. This thesis deals with the study of the dynamic structure factor S (q,w) and its line half width by the method of development in continued fractions issued from the Mori theory. With regard to the analytical difficulty met at the time of the static correlations functions calculation, the homogeneous approximation was applied and the notion of effective strength was introduced. So, it was obtained general relationships which give the static correlation functions, only in term of the static structure factor of liquids and effective potential. 98 refs.; 22 figs. (F.M.)
Postural control model interpretation of stabilogram diffusion analysis
Peterka, R. J.
2000-01-01
Collins and De Luca [Collins JJ. De Luca CJ (1993) Exp Brain Res 95: 308-318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.
Lanzafame, S; Giannelli, M; Garaci, F; Floris, R; Duggento, A; Guerrisi, M; Toschi, N
2016-05-01
An increasing number of studies have aimed to compare diffusion tensor imaging (DTI)-related parameters [e.g., mean diffusivity (MD), fractional anisotropy (FA), radial diffusivity (RD), and axial diffusivity (AD)] to complementary new indexes [e.g., mean kurtosis (MK)/radial kurtosis (RK)/axial kurtosis (AK)] derived through diffusion kurtosis imaging (DKI) in terms of their discriminative potential about tissue disease-related microstructural alterations. Given that the DTI and DKI models provide conceptually and quantitatively different estimates of the diffusion tensor, which can also depend on fitting routine, the aim of this study was to investigate model- and algorithm-dependent differences in MD/FA/RD/AD and anisotropy mode (MO) estimates in diffusion-weighted imaging of human brain white matter. The authors employed (a) data collected from 33 healthy subjects (20-59 yr, F: 15, M: 18) within the Human Connectome Project (HCP) on a customized 3 T scanner, and (b) data from 34 healthy subjects (26-61 yr, F: 5, M: 29) acquired on a clinical 3 T scanner. The DTI model was fitted to b-value =0 and b-value =1000 s/mm(2) data while the DKI model was fitted to data comprising b-value =0, 1000 and 3000/2500 s/mm(2) [for dataset (a)/(b), respectively] through nonlinear and weighted linear least squares algorithms. In addition to MK/RK/AK maps, MD/FA/MO/RD/AD maps were estimated from both models and both algorithms. Using tract-based spatial statistics, the authors tested the null hypothesis of zero difference between the two MD/FA/MO/RD/AD estimates in brain white matter for both datasets and both algorithms. DKI-derived MD/FA/RD/AD and MO estimates were significantly higher and lower, respectively, than corresponding DTI-derived estimates. All voxelwise differences extended over most of the white matter skeleton. Fractional differences between the two estimates [(DKI - DTI)/DTI] of most invariants were seen to vary with the invariant value itself as well as with MK
Individual differences in emotion word processing: A diffusion model analysis.
Mueller, Christina J; Kuchinke, Lars
2016-06-01
The exploratory study investigated individual differences in implicit processing of emotional words in a lexical decision task. A processing advantage for positive words was observed, and differences between happy and fear-related words in response times were predicted by individual differences in specific variables of emotion processing: Whereas more pronounced goal-directed behavior was related to a specific slowdown in processing of fear-related words, the rate of spontaneous eye blinks (indexing brain dopamine levels) was associated with a processing advantage of happy words. Estimating diffusion model parameters revealed that the drift rate (rate of information accumulation) captures unique variance of processing differences between happy and fear-related words, with highest drift rates observed for happy words. Overall emotion recognition ability predicted individual differences in drift rates between happy and fear-related words. The findings emphasize that a significant amount of variance in emotion processing is explained by individual differences in behavioral data.
Reaction-diffusion modeling of hydrogen in beryllium
Wensing, Mirko; Matveev, Dmitry; Linsmeier, Christian [Forschungszentrum Juelich GmbH, Institut fuer Energie- und Klimaforschung - Plasmaphysik (Germany)
2016-07-01
Beryllium will be used as first-wall material for the future fusion reactor ITER as well as in the breeding blanket of DEMO. In both cases it is important to understand the mechanisms of hydrogen retention in beryllium. In earlier experiments with beryllium low-energy binding states of hydrogen were observed by thermal desorption spectroscopy (TDS) which are not yet well understood. Two candidates for these states are considered: beryllium-hydride phases within the bulk and surface effects. The retention of deuterium in beryllium is studied by a reaction rate approach using a coupled reaction diffusion system (CRDS)-model relying on ab initio data from density functional theory calculations (DFT). In this contribution we try to assess the influence of surface recombination.
Modeling of immision from power plants using stream-diffusion model
Kanevce, Lj.; Kanevce, G.; Markoski, A.
1996-01-01
Analyses of simple empirical and integral immision models, comparing with complex three dimensional differential models is given. Complex differential models needs huge computer power, so they can't be useful for practical engineering calculations. In this paper immision modeling, using stream-diffusion approach is presented. Process of dispersion is divided into two parts. First part is called stream part, it's near the source of the pollutants, and it's presented with defected turbulent jet in wind field. This part finished when the velocity of stream (jet) becomes equal with wind speed. Boundary conditions in the end of the first part, are initial for the second, called diffusion part, which is modeling with tri dimensional diffusion equation. Gradient of temperature, wind speed profile and coefficient of diffusion in this model must not be constants, they can change with the height. Presented model is much simpler than the complete meteorological differential models which calculates whole fields of meteorological parameters. Also, it is more complex and gives more valuable results for dispersion of pollutants from widely used integral and empirical models
Modelling thermal radiation in buoyant turbulent diffusion flames
Consalvi, J. L.; Demarco, R.; Fuentes, A.
2012-10-01
This work focuses on the numerical modelling of radiative heat transfer in laboratory-scale buoyant turbulent diffusion flames. Spectral gas and soot radiation is modelled by using the Full-Spectrum Correlated-k (FSCK) method. Turbulence-Radiation Interactions (TRI) are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA), the resulting time-averaged Radiative Transfer Equation (RTE) being solved by the Finite Volume Method (FVM). Emission TRIs and the mean absorption coefficient are then closed by using a presumed probability density function (pdf) of the mixture fraction. The mean gas flow field is modelled by the Favre-averaged Navier-Stokes (FANS) equation set closed by a buoyancy-modified k-ɛ model with algebraic stress/flux models (ASM/AFM), the Steady Laminar Flamelet (SLF) model coupled with a presumed pdf approach to account for Turbulence-Chemistry Interactions, and an acetylene-based semi-empirical two-equation soot model. Two sets of experimental pool fire data are used for validation: propane pool fires 0.3 m in diameter with Heat Release Rates (HRR) of 15, 22 and 37 kW and methane pool fires 0.38 m in diameter with HRRs of 34 and 176 kW. Predicted flame structures, radiant fractions, and radiative heat fluxes on surrounding surfaces are found in satisfactory agreement with available experimental data across all the flames. In addition further computations indicate that, for the present flames, the gray approximation can be applied for soot with a minor influence on the results, resulting in a substantial gain in Computer Processing Unit (CPU) time when the FSCK is used to treat gas radiation.
Agent-based Modeling Automated: Data-driven Generation of Innovation Diffusion Models
Jensen, T.; Chappin, E.J.L.
2016-01-01
Simulation modeling is useful to gain insights into driving mechanisms of diffusion of innovations. This study aims to introduce automation to make identification of such mechanisms with agent-based simulation modeling less costly in time and labor. We present a novel automation procedure in which
Technology diffusion in energy-economy models: The case of Danish vintage models
Klinge Jacobsen, Henrik
2000-01-01
the costs of greenhouse gas mitigation. This paper examines the effect on aggregate energy efficiency of using technological vintage models to describe technology diffusion. The focus is on short- to medium-term issues. Three different models of Danish energy supply and demand are used to illustrate...
Modelling of a diffusion-sorption experiment on sandstone
Smith, P.A.
1989-11-01
The results of a diffusion-sorption experiment on a sample of Darley Dale sandstone, using simulated groundwater spiked with a mixture of 125 I, 85 Sr and 137 Cs, are modelled by a one-dimensional porous medium approach in which sorption is described by Freundlich isotherms. The governing equations are solved analytically for the special case of a linear isotherm, and numerically using the computer code RANCHDIFF for non-linear isotherms. A set of time-dependent, ordinary differential equations is obtained using the Lagrange interpolation technique and integrated by Gear's variable order predictor-corrector method. It is shown that the sorption behaviour of 85 Sr can be modelled successfully by a linear isotherm, using a sorption parameter consistent with batch-sorption tests. The behaviour of 137 Cs may be modelled by a non-linear isotherm, but the amount of 137 Cs sorbed is less than that anticipated from batch-sorption tests. 125 I is assumed to be non-sorbing and is used to determine the porosity of the sandstone. (author) 10 figs., 4 tabs., 6 refs
The dynamics of multimodal integration: The averaging diffusion model.
Turner, Brandon M; Gao, Juan; Koenig, Scott; Palfy, Dylan; L McClelland, James
2017-12-01
We combine extant theories of evidence accumulation and multi-modal integration to develop an integrated framework for modeling multimodal integration as a process that unfolds in real time. Many studies have formulated sensory processing as a dynamic process where noisy samples of evidence are accumulated until a decision is made. However, these studies are often limited to a single sensory modality. Studies of multimodal stimulus integration have focused on how best to combine different sources of information to elicit a judgment. These studies are often limited to a single time point, typically after the integration process has occurred. We address these limitations by combining the two approaches. Experimentally, we present data that allow us to study the time course of evidence accumulation within each of the visual and auditory domains as well as in a bimodal condition. Theoretically, we develop a new Averaging Diffusion Model in which the decision variable is the mean rather than the sum of evidence samples and use it as a base for comparing three alternative models of multimodal integration, allowing us to assess the optimality of this integration. The outcome reveals rich individual differences in multimodal integration: while some subjects' data are consistent with adaptive optimal integration, reweighting sources of evidence as their relative reliability changes during evidence integration, others exhibit patterns inconsistent with optimality.
An efficient method for model refinement in diffuse optical tomography
Zirak, A. R.; Khademi, M.
2007-11-01
Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.
The EZ diffusion model provides a powerful test of simple empirical effects.
van Ravenzwaaij, Don; Donkin, Chris; Vandekerckhove, Joachim
2017-04-01
Over the last four decades, sequential accumulation models for choice response times have spread through cognitive psychology like wildfire. The most popular style of accumulator model is the diffusion model (Ratcliff Psychological Review, 85, 59-108, 1978), which has been shown to account for data from a wide range of paradigms, including perceptual discrimination, letter identification, lexical decision, recognition memory, and signal detection. Since its original inception, the model has become increasingly complex in order to account for subtle, but reliable, data patterns. The additional complexity of the diffusion model renders it a tool that is only for experts. In response, Wagenmakers et al. (Psychonomic Bulletin & Review, 14, 3-22, 2007) proposed that researchers could use a more basic version of the diffusion model, the EZ diffusion. Here, we simulate experimental effects on data generated from the full diffusion model and compare the power of the full diffusion model and EZ diffusion to detect those effects. We show that the EZ diffusion model, by virtue of its relative simplicity, will be sometimes better able to detect experimental effects than the data-generating full diffusion model.
Preisach hysteresis model for non-linear 2D heat diffusion
Jancskar, Ildiko; Ivanyi, Amalia
2006-01-01
This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way
Validation of a mixture-averaged thermal diffusion model for premixed lean hydrogen flames
Schlup, Jason; Blanquart, Guillaume
2018-03-01
The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.
Ochalek, M; Podhaisky, H; Ruettinger, H-H; Wohlrab, J; Neubert, R H H
2012-10-01
The barrier function of two quaternary stratum corneum (SC) lipid model membranes, which were previously characterized with regard to the lipid organization, was investigated based on diffusion studies of model drugs with varying lipophilicities. Diffusion experiments of a hydrophilic drug, urea, and more lipophilic drugs than urea (i.e. caffeine, diclofenac sodium) were conducted using Franz-type diffusion cells. The amount of permeated drug was analyzed using either HPLC or CE technique. The subjects of interest in the present study were the investigation of the influence of physicochemical properties of model drugs on their diffusion and permeation through SC lipid model membranes, as well as the study of the impact of the constituents of these artificial systems (particularly ceramide species) on their barrier properties. The diffusion through both SC lipid model membranes and the human SC of the most hydrophilic model drug, urea, was faster than the permeation of the more lipophilic drugs. The slowest rate of permeation through SC lipid systems occurred in the case of caffeine. The composition of SC lipid model membranes has a significant impact on their barrier function. Model drugs diffused and permeated faster through Membrane II (presence of Cer [EOS]). In terms of the barrier properties, Membrane II is much more similar to the human SC than Membrane I. Copyright © 2012 Elsevier B.V. All rights reserved.
Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.
Xiao, Perry; Imhof, Robert E
2012-10-01
Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.
Wu Rui; Zhu Xun; Liao Qiang; Wang Hong; Ding Yudong; Li Jun; Ye Dingding
2010-01-01
In proton exchange membrane fuel cell (PEMFC) models, oxygen effective diffusivity is the most important parameter to characterize the oxygen transport in the gas diffusion layer (GDL). However, its determination is a challenge due to its complex dependency on GDL structure. In the present study, a three-dimensional network consisting of spherical pores and cylindrical throats is developed and used to investigate the effects of GDL structural parameters on oxygen effective diffusivity under the condition with/without water invasion process. Oxygen transport in the throat is described by Fick's law and water invasion process in the network is simulated using the invasion percolation with trapping algorithm. The simulation results reveal that oxygen effective diffusivity is slightly affected by network size but increases with decreasing the network heterogeneity and with increasing the pore connectivity. Impacts of network anisotropy on oxygen transport are also investigated in this paper. The anisotropic network is constructed by constricting the throats in the through-plane direction with a constriction factor. It is found that water invasion has a more severe negative influence on oxygen transport in an anisotropic network. Finally, two new correlations are introduced to determine the oxygen effective diffusivity for the Toray carbon paper GDLs.
Vestergaard-Poulsen, Peter; Hansen, Brian; Ostergaard, Leif; Jakobsen, Rikke
2007-09-01
To understand the diffusion attenuated MR signal from normal and ischemic brain tissue in order to extract structural and physiological information using mathematical modeling, taking into account the transverse relaxation rates in gray matter. We fit our diffusion model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and exchange between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each compartment. A global optimum was found from a wide range of parameter permutations using cluster computing. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia. Our model estimates an extracellular volume fraction of 0.19 in accordance with the accepted value from histology. The absolute apparent diffusion coefficient obtained from the model was similar to that of experiments. The model and the experimental results indicate significant differences in diffusion and transverse relaxation between the tissue compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms. Our modeling suggests that transverse relaxation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling as the primary cause of the diffusion changes seen in the acute phase of brain ischemia. (c) 2007 Wiley-Liss, Inc.
Nonlinear variational models for reaction and diffusion systems
Tanyi, G.E.
1983-08-01
There exists a natural metric w.r.t. which the density dependent diffusion operator is harmonic in the sense of Eells and Sampson. A physical corollary of this statement is the property that any two regular points on the orbit of a reaction or diffusion operator can be connected by a path along which the reaction rate is constant. (author)
Diffusion in Liquids : Equilibrium Molecular Simulations and Predictive Engineering Models
Liu, X.
2013-01-01
The aim of this thesis is to study multicomponent diffusion in liquids using Molecular Dynamics (MD) simulations. Diffusion plays an important role in mass transport processes. In binary systems, mass transfer processes have been studied extensively using both experiments and molecular simulations.
Subgrid models for mass and thermal diffusion in turbulent mixing
Sharp, David H [Los Alamos National Laboratory; Lim, Hyunkyung [STONY BROOK UNIV; Li, Xiao - Lin [STONY BROOK UNIV; Gilmm, James G [STONY BROOK UNIV
2008-01-01
We are concerned with the chaotic flow fields of turbulent mixing. Chaotic flow is found in an extreme form in multiply shocked Richtmyer-Meshkov unstable flows. The goal of a converged simulation for this problem is twofold: to obtain converged solutions for macro solution features, such as the trajectories of the principal shock waves, mixing zone edges, and mean densities and velocities within each phase, and also for such micro solution features as the joint probability distributions of the temperature and species concentration. We introduce parameterized subgrid models of mass and thermal diffusion, to define large eddy simulations (LES) that replicate the micro features observed in the direct numerical simulation (DNS). The Schmidt numbers and Prandtl numbers are chosen to represent typical liquid, gas and plasma parameter values. Our main result is to explore the variation of the Schmidt, Prandtl and Reynolds numbers by three orders of magnitude, and the mesh by a factor of 8 per linear dimension (up to 3200 cells per dimension), to allow exploration of both DNS and LES regimes and verification of the simulations for both macro and micro observables. We find mesh convergence for key properties describing the molecular level of mixing, including chemical reaction rates between the distinct fluid species. We find results nearly independent of Reynolds number for Re 300, 6000, 600K . Methodologically, the results are also new. In common with the shock capturing community, we allow and maintain sharp solution gradients, and we enhance these gradients through use of front tracking. In common with the turbulence modeling community, we include subgrid scale models with no adjustable parameters for LES. To the authors' knowledge, these two methodologies have not been previously combined. In contrast to both of these methodologies, our use of Front Tracking, with DNS or LES resolution of the momentum equation at or near the Kolmogorov scale, but without
Synchronized stability in a reaction–diffusion neural network model
Wang, Ling; Zhao, Hongyong, E-mail: hongyongz@126.com
2014-11-14
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability.
Synchronized stability in a reaction–diffusion neural network model
Wang, Ling; Zhao, Hongyong
2014-01-01
The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability
Bounds for perpetual American option prices in a jump diffusion model
Ekström, Erik
2006-01-01
We provide bounds for perpetual American option prices in a jump diffusion model in terms of American option prices in the standard Black-Scholes model. We also investigate the dependence of the bounds on different parameters of the model.
Numerical modelling of random walk one-dimensional diffusion
Vamos, C.; Suciu, N.; Peculea, M.
1996-01-01
The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies
Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong
2016-12-09
Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2 = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.
Liang, Yingjie; Chen, Wen
2018-03-01
Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.
Numerical vs. turbulent diffusion in geophysical flow modelling
D'Isidoro, M.; Maurizi, A.; Tampieri, F.
2008-01-01
Numerical advection schemes induce the spreading of passive tracers from localized sources. The effects of changing resolution and Courant number are investigated using the WAF advection scheme, which leads to a sub-diffusive process. The spreading rate from an instantaneous source is compared with the physical diffusion necessary to simulate unresolved turbulent motions. The time at which the physical diffusion process overpowers the numerical spreading is estimated, and is shown to reduce as the resolution increases, and to increase as the wind velocity increases.
Small-polaron model of light atom diffusion
Emin, D.
1977-01-01
A number of researchers have treated the diffusion of light interstitials in metals in strict analogy with the theory for the hopping diffusion of electrons in low-mobility insulators. In other words, these authors view the diffusion of light atoms as simply being an example of small-polaron hopping motion. In this paper the motion of a small polaron is introduced, and the mechanism of its motion is described. The experimental results are then succinctly presented. Next the physical assumptions implicit in the theory are compared with the situation which is believed to characterize the existence and motion of light interstitial atoms in metals. Concomitantly, the modifications of the small-polaron theory required in applying it to light atom diffusion are ennumerated
A mathematical model in charactering chloride diffusivity in unsaturated cementitious material
Zhang, Y.; Ye, G.; Pecur, I.B.; Baricevic, A.; Stirmer, N; Bjegovic, D.
2017-01-01
In this paper, a new analytic model for predicting chloride diffusivity in unsaturated cementitious materials is developed based on conductivity theory and Nernst-Einstein equation. The model specifies that chloride diffusivity in unsaturated cementitious materials can be mathematically described as
A critical discussion of the vacancy diffusion model of ion beam induced epitaxial crystallization
Heera, V.
1989-01-01
A simple vacancy diffusion model of ion beam induced epitaxial crystallization of silicon including divacancy formation is developed. The model reproduces some of the experimental findings, as e.g. the dose rate dependence of the crystallization rate. However, the measured activation energy of the ion beam induced epitaxial crystallization cannot be accounted for by vacancy diffusion alone. (author)
Nuclear interaction potential in a folded-Yukawa model with diffuse densities
Randrup, J.
1975-09-01
The folded-Yukawa model for the nuclear interaction potential is generalized to diffuse density distributions which are generated by folding a Yukawa function into sharp generating distributions. The effect of a finite density diffuseness or of a finite interaction range is studied. The Proximity Formula corresponding to the generalized model is derived and numerical comparison is made with the exact results. (8 figures)
Long, T.B.; Blok, V.; Poldner, Kim
2017-01-01
r, CSA technological innovation diffusion is subject to socio-economic barriers. The success of innovations is partly dependent on the business models that are used to diffuse them. Within the context of innovations for CSA, the role that innovation providers’ business models play in the successful
Osei, Frank B.; Osei, F.B.; Duker, Alfred A.; Stein, A.
2011-01-01
This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint
Modeling Simple Driving Tasks with a One-Boundary Diffusion Model
Ratcliff, Roger; Strayer, David
2014-01-01
A one-boundary diffusion model was applied to the data from two experiments in which subjects were performing a simple simulated driving task. In the first experiment, the same subjects were tested on two driving tasks using a PC-based driving simulator and the psychomotor vigilance test (PVT). The diffusion model fit the response time (RT) distributions for each task and individual subject well. Model parameters were found to correlate across tasks which suggests common component processes were being tapped in the three tasks. The model was also fit to a distracted driving experiment of Cooper and Strayer (2008). Results showed that distraction altered performance by affecting the rate of evidence accumulation (drift rate) and/or increasing the boundary settings. This provides an interpretation of cognitive distraction whereby conversing on a cell phone diverts attention from the normal accumulation of information in the driving environment. PMID:24297620
Modeling bioluminescent photon transport in tissue based on Radiosity-diffusion model
Sun, Li; Wang, Pu; Tian, Jie; Zhang, Bo; Han, Dong; Yang, Xin
2010-03-01
Bioluminescence tomography (BLT) is one of the most important non-invasive optical molecular imaging modalities. The model for the bioluminescent photon propagation plays a significant role in the bioluminescence tomography study. Due to the high computational efficiency, diffusion approximation (DA) is generally applied in the bioluminescence tomography. But the diffusion equation is valid only in highly scattering and weakly absorbing regions and fails in non-scattering or low-scattering tissues, such as a cyst in the breast, the cerebrospinal fluid (CSF) layer of the brain and synovial fluid layer in the joints. A hybrid Radiosity-diffusion model is proposed for dealing with the non-scattering regions within diffusing domains in this paper. This hybrid method incorporates a priori information of the geometry of non-scattering regions, which can be acquired by magnetic resonance imaging (MRI) or x-ray computed tomography (CT). Then the model is implemented using a finite element method (FEM) to ensure the high computational efficiency. Finally, we demonstrate that the method is comparable with Mont Carlo (MC) method which is regarded as a 'gold standard' for photon transportation simulation.
Diffusion-controlled reactions modeling in Geant4-DNA
Karamitros, M., E-mail: matkara@gmail.com [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); CNRS, INCIA, UMR 5287, F-33400 Talence (France); Luan, S. [University of New Mexico, Department of Computer Science, Albuquerque, NM (United States); Bernal, M.A. [Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP (Brazil); Allison, J. [Geant4 Associates International Ltd (United Kingdom); Baldacchino, G. [CEA Saclay, IRAMIS, LIDYL, Radiation Physical Chemistry Group, F-91191 Gif sur Yvette Cedex (France); CNRS, UMR3299, SIS2M, F-91191 Gif sur Yvette Cedex (France); Davidkova, M. [Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Francis, Z. [Saint Joseph University, Faculty of Sciences, Department of Physics, Mkalles, Beirut (Lebanon); Friedland, W. [Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Radiation Protection, Ingolstädter Landstr. 1, 85764 Neuherberg (Germany); Ivantchenko, V. [Ecoanalytica, 119899 Moscow (Russian Federation); Geant4 Associates International Ltd (United Kingdom); Ivantchenko, A. [Geant4 Associates International Ltd (United Kingdom); Mantero, A. [SwHaRD s.r.l., via Buccari 9, 16153 Genova (Italy); Nieminem, P.; Santin, G. [ESA-ESTEC, 2200 AG Noordwijk (Netherlands); Tran, H.N. [Division of Nuclear Physics and Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Stepan, V. [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Incerti, S., E-mail: incerti@cenbg.in2p3.fr [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France)
2014-10-01
Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest reactants. The
Diffusion of PAH in potato and carrot slices and application for a potato model
Trapp, Stefan; Cammarano, A.; Capri, E.
2007-01-01
of water, potato tissue, and carrot tissue. Naphthalene, phenanthrene, anthracene, and fluoranthene served as model substances. Their transfer from source to sink disk was measured by HPLC to determine a velocity rate constant proportional to the diffusive conductivity. The diffusive flux through the plant...... of the chemical. The findings of this study provide a convenient method to estimate the diffusion of nonvolatile organic chemicals through various plant materials. The application to a radial diffusion model suggests that "growth dilution" renders the concentration of highly hydrophobic chemicals in potatoes...... below their equilibrium partitioning level. This is in agreement with field results for the bioconcentration of PAHs in potatoes....
Models for the estimation of diffuse solar radiation for typical cities in Turkey
Bakirci, Kadir
2015-01-01
In solar energy applications, diffuse solar radiation component is required. Solar radiation data particularly in terms of diffuse component are not readily affordable, because of high price of measurements as well as difficulties in their maintenance and calibration. In this study, new empirical models for predicting the monthly mean diffuse solar radiation on a horizontal surface for typical cities in Turkey are established. Therefore, fifteen empirical models from studies in the literature are used. Also, eighteen diffuse solar radiation models are developed using long term sunshine duration and global solar radiation data. The accuracy of the developed models is evaluated in terms of different statistical indicators. It is found that the best performance is achieved for the third-order polynomial model based on sunshine duration and clearness index. - Highlights: • Diffuse radiation is given as a function of clearness index and sunshine fraction. • The diffuse radiation is an important parameter in solar energy applications. • The diffuse radiation measurement is for limited periods and it is very rare. • The new models can be used to estimate monthly average diffuse solar radiation. • The accuracy of the models is evaluated on the basis of statistical indicators
Chu, Khim Hoong
2017-11-09
Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6 cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.
Free surface modelling with two-fluid model and reduced numerical diffusion of the interface
Strubelj, Luka; Tiselj, Izrok
2008-01-01
Full text of publication follows: The free surface flows are successfully modelled with one of existing free surface models, such as: level set method, volume of fluid method (with/without surface reconstruction), front tracking, two-fluid model (two momentum equations) with modified interphase force and others. The main disadvantage of two-fluid model used for simulations of free surface flows is numerical diffusion of the interface, which can be significantly reduced using the method presented in this paper. Several techniques for reduction of numerical diffusion of the interface have been implemented in the volume of fluid model and are based on modified numerical schemes for advection of volume fraction near the interface. The same approach could be used also for two-fluid method, but according to our experience more successful reduction of numerical diffusion of the interface can be achieved with conservative level set method. Within the conservative level set method, continuity equation for volume fraction is solved and after that the numerical diffusion of the interface is reduced in such a way that the thickness of the interface is kept constant during the simulation. Reduction of the interface diffusion can be also called interface sharpening. In present paper the two-fluid model with interface sharpening is validated on Rayleigh-Taylor instability. Under assumptions of isothermal and incompressible flow of two immiscible fluids, we simulated a system with the fluid of higher density located above the fluid of smaller density in two dimensions. Due to gravity in the system, fluid with higher density moves below the fluid with smaller density. Initial condition is not a flat interface between the fluids, but a sine wave with small amplitude, which develops into a mushroom-like structure. Mushroom-like structure in simulation of Rayleigh-Taylor instability later develops to small droplets as result of numerical dispersion of interface (interface sharpening
Stalled-Flow and Head-Loss Model for Diffuser Pumps
Meng, S. Y.
1984-01-01
Modeling procedure approximates inlet transition zone (blade leading edge to blade throat) of diffuser pump as two-dimensional cascade, properties of which are well known. Model applied to stators as well as rotors. Procedure much faster than previous methods.
Quantum-corrected drift-diffusion models for transport in semiconductor devices
De Falco, Carlo; Gatti, Emilio; Lacaita, Andrea L.; Sacco, Riccardo
2005-01-01
In this paper, we propose a unified framework for Quantum-corrected drift-diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical drift-diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum-correction to the electric potential. We examine two special, and relevant, examples of QCDD models; the first one is the modified DD model named Schroedinger-Poisson-drift-diffusion, and the second one is the quantum-drift-diffusion (QDD) model. For the decoupled solution of the two models, we introduce a functional iteration technique that extends the classical Gummel algorithm widely used in the iterative solution of the DD system. We discuss the finite element discretization of the various differential subsystems, with special emphasis on their stability properties, and illustrate the performance of the proposed algorithms and models on the numerical simulation of nanoscale devices in two spatial dimensions
A model for self-diffusion of guanidinium-based ionic liquids: a molecular simulation study.
Klähn, Marco; Seduraman, Abirami; Wu, Ping
2008-11-06
We propose a novel self-diffusion model for ionic liquids on an atomic level of detail. The model is derived from molecular dynamics simulations of guanidinium-based ionic liquids (GILs) as a model case. The simulations are based on an empirical molecular mechanical force field, which has been developed in our preceding work, and it relies on the charge distribution in the actual liquid. The simulated GILs consist of acyclic and cyclic cations that were paired with nitrate and perchlorate anions. Self-diffusion coefficients are calculated at different temperatures from which diffusive activation energies between 32-40 kJ/mol are derived. Vaporization enthalpies between 174-212 kJ/mol are calculated, and their strong connection with diffusive activation energies is demonstrated. An observed formation of cavities in GILs of up to 6.5% of the total volume does not facilitate self-diffusion. Instead, the diffusion of ions is found to be determined primarily by interactions with their immediate environment via electrostatic attraction between cation hydrogen and anion oxygen atoms. The calculated average time between single diffusive transitions varies between 58-107 ps and determines the speed of diffusion, in contrast to diffusive displacement distances, which were found to be similar in all simulated GILs. All simulations indicate that ions diffuse by using a brachiation type of movement: a diffusive transition is initiated by cleaving close contacts to a coordinated counterion, after which the ion diffuses only about 2 A until new close contacts are formed with another counterion in its vicinity. The proposed diffusion model links all calculated energetic and dynamic properties of GILs consistently and explains their molecular origin. The validity of the model is confirmed by providing an explanation for the variation of measured ratios of self-diffusion coefficients of cations and paired anions over a wide range of values, encompassing various ionic liquid classes
Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model
Ni, Wenjie; Shi, Junping; Wang, Mingxin
2018-06-01
A diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka-Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper-lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients.
Telfeyan, Katherine Christina [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ware, Stuart Douglas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Reimus, Paul William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Birdsell, Kay Hanson [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-11-06
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
Telfeyan, Katherine; Ware, S. Doug; Reimus, Paul W.; Birdsell, Kay H.
2018-02-01
Diffusion cell and diffusion wafer experiments were conducted to compare methods for estimating effective matrix diffusion coefficients in rock core samples from Pahute Mesa at the Nevada Nuclear Security Site (NNSS). A diffusion wafer method, in which a solute diffuses out of a rock matrix that is pre-saturated with water containing the solute, is presented as a simpler alternative to the traditional through-diffusion (diffusion cell) method. Both methods yielded estimates of effective matrix diffusion coefficients that were within the range of values previously reported for NNSS volcanic rocks. The difference between the estimates of the two methods ranged from 14 to 30%, and there was no systematic high or low bias of one method relative to the other. From a transport modeling perspective, these differences are relatively minor when one considers that other variables (e.g., fracture apertures, fracture spacings) influence matrix diffusion to a greater degree and tend to have greater uncertainty than effective matrix diffusion coefficients. For the same relative random errors in concentration measurements, the diffusion cell method yields effective matrix diffusion coefficient estimates that have less uncertainty than the wafer method. However, the wafer method is easier and less costly to implement and yields estimates more quickly, thus allowing a greater number of samples to be analyzed for the same cost and time. Given the relatively good agreement between the methods, and the lack of any apparent bias between the methods, the diffusion wafer method appears to offer advantages over the diffusion cell method if better statistical representation of a given set of rock samples is desired.
A microscopic model of ballistic-diffusive crossover
Bagchi, Debarshee; Mohanty, P K
2014-01-01
Several low-dimensional systems show a crossover from diffusive to ballistic heat transport when system size is decreased. Although there is some phenomenological understanding of this crossover phenomenon at the coarse-grained level, a microscopic picture that consistently describes both the ballistic and the diffusive transport regimes has been lacking. In this work we derive a scaling form for the thermal current in a class of one dimensional systems attached to heat baths at boundaries and rigorously show that the crossover occurs when the characteristic length scale of the system competes with the system size. (paper)
A fractional Fokker-Planck model for anomalous diffusion
Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
2014-12-15
In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
Kee, Kerk F; Sparks, Lisa; Struppa, Daniele C; Mannucci, Mirco A; Damiano, Alberto
2016-01-01
By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that coexist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data.
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
Characteristics and Diffusion Model of the Individual Knowledge in the WeChat Mode
Zhang Lingzhi
2017-12-01
Full Text Available [Purpose/significance] According to the model of the individual knowledge diffusion, we conduct a behavior research and analyze the characteristics of that based on WeChat which is the most popular communication platform in China.[Method/process] By analyzing the methods of the diffusion on WeChat, we analyzed the characteristics of the individual knowledge diffusion. [Result/conclusion]The characteristics of the individual knowledge diffusion include real-time, short-term, speciality, friendship and transmission.
Diffusion-controlled reactions modeling in Geant4-DNA
Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davídková, Marie; Francis, Z.; Friedland, W.; Ivanchenko, A.; Ivanchenko, V.; Mantero, A.; Nieminen, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.
2014-01-01
Roč. 274, OCT (2014), s. 841-882 ISSN 0021-9991 Institutional support: RVO:61389005 Keywords : chemical kinetics simulation * radiation chemistry * Fokker-Planck equation * Smoluchowski diffusion equation * Brownian bridge * dynamical time steps * k-d tree * radiolysis * radiobiology * Geant4-DNA * Brownian dynamics Subject RIV: BO - Biophysics Impact factor: 2.434, year: 2014
A model of modulated diffusion. I. Analytical results
Bazzani, A.; Turcchetti, G.; Vaienti, S.
1994-01-01
We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion
Comparison Of Diffuse Solar Radiation Models Using Data For ...
Measurements of global solar radiation and sunshine duration data during the period from 1984 to 1999 were supplied by IITA (International Institute of Tropical Agriculture) at Onne. The data were used to establish empirical relationships that would connect the daily monthly average diffuse irradiation with both relative ...
Ionic diffusion in the double layer at model electrode/molten salt interfaces
Tankeshwar, K.; Tosi, M.P.
1991-08-01
The anisotropic ionic diffusion coefficients in model electrochemical cells in the molten-salt regime for the electrolyte are evaluated from the ionic density profiles reported in simulation work of Grout and coworkers. A local description of the diffusion processes for counterions and coions in the electrical double layer is obtained from the data. (author). 10 refs, 1 fig., 1 tab
Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow
Gonzalez, M.
2018-04-01
The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.
Long, Thomas B.; Blok, Vincent; Poldner, Kim
2017-01-01
Technological innovations will play a prominent role in the transition to climate-smart agriculture (CSA). However, CSA technological innovation diffusion is subject to socio-economic barriers. The success of innovations is partly dependent on the business models that are used to diffuse them.
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
Maurin, D.
2001-02-01
Dark matter is present at numerous scale of the universe (galaxy, cluster of galaxies, universe in the whole). This matter plays an important role in cosmology and can not be totally explained by conventional physic. From a particle physic point of view, there exists an extension of the standard model - supersymmetry - which predicts under certain conditions the existence of new stable and massive particles, the latter interacting weakly with ordinary matter. Apart from direct detection in accelerators, various indirect astrophysical detection are possible. This thesis focuses on one particular signature: disintegration of these particles could give antiprotons which should be measurable in cosmic rays. The present study evaluates the background corresponding to this signal i. e. antiprotons produced in the interactions between these cosmic rays and interstellar matter. In particular, uncertainties of this background being correlated to the uncertainties of the diffusion parameter, major part of this thesis is devoted to nuclei propagation. The first third of the thesis introduces propagation of cosmic rays in our galaxy, emphasizing the nuclear reaction responsibles of the nuclei fragmentation. In the second third, different models are reviewed, and in particular links between the leaky box model and the diffusion model are recalled (re-acceleration and convection are also discussed). This leads to a qualitative discussion about information that one can infer from propagation of these nuclei. In the last third, we finally present detailed solutions of the bidimensional diffusion model, along with constrains obtained on the propagation parameters. The latter is applied on the antiprotons background signal and it concludes the work done in this thesis. The propagation code for nuclei and antiprotons used here has proven its ability in data analysis. It would probably be of interest for the analysis of the cosmic ray data which will be taken by the AMS experiment on
Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport.
Hendel, Nathan L; Thomson, Matthew; Marshall, Wallace F
2018-02-06
An important question in cell biology is whether cells are able to measure size, either whole cell size or organelle size. Perhaps cells have an internal chemical representation of size that can be used to precisely regulate growth, or perhaps size is just an accident that emerges due to constraint of nutrients. The eukaryotic flagellum is an ideal model for studying size sensing and control because its linear geometry makes it essentially one-dimensional, greatly simplifying mathematical modeling. The assembly of flagella is regulated by intraflagellar transport (IFT), in which kinesin motors carry cargo adaptors for flagellar proteins along the flagellum and then deposit them at the tip, lengthening the flagellum. The rate at which IFT motors are recruited to begin transport into the flagellum is anticorrelated with the flagellar length, implying some kind of communication between the base and the tip and possibly indicating that cells contain some mechanism for measuring flagellar length. Although it is possible to imagine many complex scenarios in which additional signaling molecules sense length and carry feedback signals to the cell body to control IFT, might the already-known components of the IFT system be sufficient to allow length dependence of IFT? Here we investigate a model in which the anterograde kinesin motors unbind after cargo delivery, diffuse back to the base, and are subsequently reused to power entry of new IFT trains into the flagellum. By mathematically modeling and simulating such a system, we are able to show that the diffusion time of the motors can in principle be sufficient to serve as a proxy for length measurement. We found that the diffusion model can not only achieve a stable steady-state length without the addition of any other signaling molecules or pathways, but also is able to produce the anticorrelation between length and IFT recruitment rate that has been observed in quantitative imaging studies. Copyright © 2017 Biophysical
Two-state random walk model of lattice diffusion - 1. Self-correlation function
Balakrishnan, V.; Venkataraman, G.
1981-01-01
Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (in d dimensions, and with arbitrary directional bias) for temporarily uncorrelated jump diffusion and for the fluid diffusion counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2. (author)
Juan Wang
2017-11-01
Full Text Available Understanding diffusion of intrinsically disordered proteins (IDPs under crowded environments is of ubiquitous importance to modelling related dynamics in biological systems. In the present work, we proposed a theoretical framework to study the diffusion behavior of IDPs in polymer solutions. IDP is modeled as an ensemble of particles with a wide range of gyration radius subject to Flory-Fisk distribution, where the collapse effect which leads to the shrink of IDP due to polymer crowding is included. The diffusion coefficient of IDP is calculated as the average, denoted by 〈D〉, over the values of the particle samples. By properly incorporating the scaling relations for diffusion coefficient of nanoparticle (NP in polymer solutions, we are able to evaluate 〈D〉 straightforwardly and reveal the disorder and collapse effects on IDP’s diffusion in an explicit manner. Particular attentions are paid on comparison between the diffusion coefficient of an IDP and that of a NP. Results demonstrate that both disorder and collapse can enhance IDP diffusion rate. Our analysis shows that the crossover behavior reported by experiments can be actually a general phenomenon, namely, while a NP with smaller size than that of an IDP diffuses faster in simple solutions, the IDP may become the faster one under crowded conditions. We apply our theory to analyze the diffusion of several types of IDP in a few different polymer solutions. Good agreements between the theoretical results and the experimental data are obtained.
Diffusion Forecasting Model with Basis Functions from QR-Decomposition
Harlim, John; Yang, Haizhao
2017-12-01
The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to Itô diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the Fokker-Planck equation with a discrete representation of the shift (Koopman) operator on a set of basis functions generated via the diffusion maps algorithm. While the choice of these basis functions is provably optimal under appropriate conditions, computing these basis functions is quite expensive since it requires the eigendecomposition of an N× N diffusion matrix, where N denotes the data size and could be very large. For large-scale forecasting problems, only a few leading eigenvectors are computationally achievable. To overcome this computational bottleneck, a new set of basis functions constructed by orthonormalizing selected columns of the diffusion matrix and its leading eigenvectors is proposed. This computation can be carried out efficiently via the unpivoted Householder QR factorization. The efficiency and effectiveness of the proposed algorithm will be shown in both deterministically chaotic and stochastic dynamical systems; in the former case, the superiority of the proposed basis functions over purely eigenvectors is significant, while in the latter case forecasting accuracy is improved relative to using a purely small number of eigenvectors. Supporting arguments will be provided on three- and six-dimensional chaotic ODEs, a three-dimensional SDE that mimics turbulent systems, and also on the two spatial modes associated with the boreal winter Madden-Julian Oscillation obtained from applying the Nonlinear Laplacian Spectral Analysis on the measured Outgoing Longwave Radiation.
Predicting the weathering of fuel and oil spills: A diffusion-limited evaporation model.
Kotzakoulakis, Konstantinos; George, Simon C
2018-01-01
The majority of the evaporation models currently available in the literature for the prediction of oil spill weathering do not take into account diffusion-limited mass transport and the formation of a concentration gradient in the oil phase. The altered surface concentration of the spill caused by diffusion-limited transport leads to a slower evaporation rate compared to the predictions of diffusion-agnostic evaporation models. The model presented in this study incorporates a diffusive layer in the oil phase and predicts the diffusion-limited evaporation rate. The information required is the composition of the fluid from gas chromatography or alternatively the distillation data. If the density or a single viscosity measurement is available the accuracy of the predictions is higher. Environmental conditions such as water temperature, air pressure and wind velocity are taken into account. The model was tested with synthetic mixtures, petroleum fuels and crude oils with initial viscosities ranging from 2 to 13,000 cSt. The tested temperatures varied from 0 °C to 23.4 °C and wind velocities from 0.3 to 3.8 m/s. The average absolute deviation (AAD) of the diffusion-limited model ranged between 1.62% and 24.87%. In comparison, the AAD of a diffusion-agnostic model ranged between 2.34% and 136.62% against the same tested fluids. Copyright © 2017 Elsevier Ltd. All rights reserved.
Cheng-Wu, Li; Hong-Lai, Xue; Cheng, Guan; Wen-biao, Liu
2018-04-01
Statistical analysis shows that in the coal matrix, the diffusion coefficient for methane is time-varying, and its integral satisfies the formula μt κ /(1 + β κ ). Therefore, a so-called dynamic diffusion coefficient model (DDC model) is developed. To verify the suitability and accuracy of the DDC model, a series of gas diffusion experiments were conducted using coal particles of different sizes. The results show that the experimental data can be accurately described by the DDC and bidisperse models, but the fit to the DDC model is slightly better. For all coal samples, as time increases, the effective diffusion coefficient first shows a sudden drop, followed by a gradual decrease before stabilizing at longer times. The effective diffusion coefficient has a negative relationship with the size of the coal particle. Finally, the relationship between the constants of the DDC model and the effective diffusion coefficient is discussed. The constant α (μ/R 2 ) denotes the effective coefficient at the initial time, and the constants κ and β control the attenuation characteristic of the effective diffusion coefficient.
Anomalous diffusion in a lattice-gas wind-tree model
Kong, X.P.; Cohen, E.G.D.
1989-01-01
Two new strictly deterministic lattice-gas automata derived from Ehrenfest's wind-tree model are studied. While in one model normal diffusion occurs, the other model exhibits abnormal diffusion in that the distribution function of the displacements of the wind particle is non-Gaussian, but its second moment, the mean-square displacement, is proportional to the time, so that a diffusion coefficient can be defined. A connection with the percolation problem and a self-avoiding random walk for the case in which the lattice is completely covered with trees is discussed
Atomistic models of Cu diffusion in CuInSe2 under variations in composition
Sommer, David E.; Dunham, Scott T.
2018-03-01
We construct an analytic model for the composition dependence of the vacancy-mediated Cu diffusion coefficient in undoped CuInSe2 using parameters from density functional theory. The applicability of this model is supported numerically with kinetic lattice Monte Carlo and Onsager transport tensors. We discuss how this model relates to experimental measurements of Cu diffusion, arguing that our results can account for significant contributions to the bulk diffusion of Cu tracers in non-stoichiometric CuInSe2.
Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion
Xinze Lian
2013-01-01
Full Text Available We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.
Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates
Marcus C. Christiansen
2013-10-01
Full Text Available In the actuarial literature, it has become common practice to model future capital returns and mortality rates stochastically in order to capture market risk and forecasting risk. Although interest rates often should and mortality rates always have to be non-negative, many authors use stochastic diffusion models with an affine drift term and additive noise. As a result, the diffusion process is Gaussian and, thus, analytically tractable, but negative values occur with positive probability. The argument is that the class of Gaussian diffusions would be a good approximation of the real future development. We challenge that reasoning and study the asymptotics of diffusion processes with affine drift and a general noise term with corresponding diffusion processes with an affine drift term and an affine noise term or additive noise. Our study helps to quantify the error that is made by approximating diffusive interest and mortality rate models with Gaussian diffusions and affine diffusions. In particular, we discuss forward interest and forward mortality rates and the error that approximations cause on the valuation of life insurance claims.
Modeling and Analysis of Epidemic Diffusion within Small-World Network
Ming Liu
2012-01-01
Full Text Available To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.
Vestergaard-Poulsen, Peter; Hansen, Brian; Østergaard, Leif
2007-01-01
compartment. A global optimum was found from a wide range of parameter permutations using cluster computing. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia. RESULTS: Our model estimates an extracellular volume...... compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms. CONCLUSION: Our modeling suggests that transverse relaxation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling...... model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and exchange between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each...
Diffusive flux in a model of stochastically gated oxygen transport in insect respiration
Berezhkovskii, Alexander M. [Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892 (United States); Shvartsman, Stanislav Y. [Department of Chemical and Biological Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544 (United States)
2016-05-28
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.
Maxwell's Law Based Models for Liquid and Gas Phase Diffusivities in Variably-Saturated Soil
Mamamoto, Shoichiro; Møldrup, Per; Kawamoto, Ken
2012-01-01
-s,D-l). Different percolation threshold terms adopted from recent studies for gas (D-s,D-g) and solute (D-s,D-l) diffusion were applied. For gas diffusion, epsilon(th) was a function of bulk density (total porosity), while for solute diffusion theta(th) was best described by volumetric content of finer soil...... particles (clay and organic matter), FINESvol. The resulting LIquid and GAs diffusivity and tortuosity (LIGA) models were tested against D-s,D-g and D-s,D-l data for differently-textured soils and performed well against the measured data across soil types. A sensitivity analysis using the new Maxwell's Law...... based LIGA models implied that the liquid phase but not the gaseous-phase tortuosity was controlled by soil type. The analyses also suggested very different pathways and fluid-phase connectivity for gas and solute diffusion in unsaturated soil...
A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal
Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying
2018-04-01
Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.
Anomalous transport regimes in a stochastic advection-diffusion model
Dranikov, I.L.; Kondratenko, P.S.; Matveev, L.V.
2004-01-01
A general solution to the stochastic advection-diffusion problem is obtained for a fractal medium with long-range correlated spatial fluctuations. A particular transport regime is determined by two basic parameters: the exponent 2h of power-law decay of the two-point velocity correlation function and the mean advection velocity u. The values of these parameters corresponding to anomalous diffusion are determined, and anomalous behavior of the tracer distribution is analyzed for various combinations of u and h. The tracer concentration is shown to decrease exponentially at large distances, whereas power-law decay is predicted by fractional differential equations. Equations that describe the essential characteristics of the solution are written in terms of coupled space-time fractional differential operators. The analysis relies on a diagrammatic technique and makes use of scale-invariant properties of the medium
Modeling Effectivity of Atmospheric Advection-Diffusion Processes
Brojewski, R.
1999-01-01
Some methods of solving the advection-diffusion problems useful in the field of atmospheric physics are presented and analyzed in the paper. The most effective one ( from the point of view of computer applications) was chosen. This is the method of problem decomposition with respect to the directions followed by secondary decomposition of the problem with respect to the physical phenomena. Introducing some corrections to the classical numerical methods of solving the problems, a hybrid composed of the finite element method for the advection problems and the implicit method with averaging for the diffusion processes was achieved. This hybrid method and application of the corrections produces a very effective means for solving the problems of substance transportation in atmosphere. (author)
Semi-Nonparametric Estimation and Misspecification Testing of Diffusion Models
Kristensen, Dennis
of the estimators and tests under the null are derived, and the power properties are analyzed by considering contiguous alternatives. Test directly comparing the drift and diffusion estimators under the relevant null and alternative are also analyzed. Markov Bootstrap versions of the test statistics are proposed...... to improve on the finite-sample approximations. The finite sample properties of the estimators are examined in a simulation study....
Thermomechanics of damageable materials under diffusion: modelling and analysis
Roubíček, Tomáš; Tomassetti, G.
2015-01-01
Roč. 66, č. 6 (2015), s. 3535-3572 ISSN 0044-2275 R&D Projects: GA ČR GAP201/10/0357 Institutional support: RVO:61388998 Keywords : visco-elastic porous solids * incomplete damage * diffusion driven by chemical-potential gradient Subject RIV: BA - General Mathematics Impact factor: 1.560, year: 2015 http://link.springer.com/article/10.1007/s00033-015-0566-2
Modeling the diffusion magnetic resonance imaging signal inside neurons
Nguyen, D V; Li, J R; Grebenkov, D S; Le Bihan, D
2014-01-01
The Bloch-Torrey partial differential equation (PDE) describes the complex transverse water proton magnetization due to diffusion-encoding magnetic field gradient pulses. The integral of the solution of this PDE yields the diffusion magnetic resonance imaging (dMRI) signal. In a complex medium such as cerebral tissue, it is difficult to explicitly link the dMRI signal to biological parameters such as the cellular geometry or the cellular volume fraction. Studying the dMRI signal arising from a single neuron can provide insight into how the geometrical structure of neurons influences the measured signal. We formulate the Bloch-Torrey PDE inside a single neuron, under no water exchange condition with the extracellular space, and show how to reduce the 3D simulation in the full neuron to a 3D simulation around the soma and 1D simulations in the neurites. We show that this latter approach is computationally much faster than full 3D simulation and still gives accurate results over a wide range of diffusion times
A model for diffuse and global irradiation on horizontal surface
Jain, P.C.
1984-01-01
The intensity of the direct radiation and the diffuse radiation at any time on a horizontal surface are each expressed as fractions of the intensity of the extraterrestrial radiation. Using these and assuming a random distribution of the bright sunshine hours and not too wide variations in the values of the transmission coefficients, a number of relations for estimating the global and the diffuse irradiation are derived. Two of the relations derived are already known empirically. The formulation lends more confidence in the use of the already empirically known relations providing them a theoretical basis, and affords more flexibility to the estimation techniques by supplying new equations. The study identifies three independent basic parameters and the constants appearing in the various equations as simple functions of these three basic parameters. Experimental data for the diffuse irradiation, the global irradiation and the bright sunshine duration for Macerata (Italy), Salisbury and Bulawayo (Zimbabwe) is found to show good correlation for the linear equations, and the nature and the interrelationships of the constants are found to be as predicted by the theory
A strongly nonlinear reaction diffusion model for a deterministic diffusive epidemic
Kirane, M.; Kouachi, S.
1993-04-01
In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. Moreover the large time behaviour of the global solutions is analyzed. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the data. (author). 9 refs
Time-Dependent Diffusion MRI in Cancer: Tissue Modeling and Applications
Olivier Reynaud
2017-11-01
Full Text Available In diffusion weighted imaging (DWI, the apparent diffusion coefficient (ADC has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times/frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a in the short time regime, disentangling structural and diffusive tissue properties, and (b near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts, a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS and diffusivities are assessed. The proper modeling of tissue membrane permeability—hardly a newcomer in the field, but lacking applications—and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter
Time-dependent diffusion MRI in cancer: tissue modeling and applications
Reynaud, Olivier
2017-11-01
In diffusion weighted imaging (DWI), the apparent diffusion coefficient has been recognized as a useful and sensitive surrogate for cell density, paving the way for non-invasive tumor staging, and characterization of treatment efficacy in cancer. However, microstructural parameters, such as cell size, density and/or compartmental diffusivities affect diffusion in various fashions, making of conventional DWI a sensitive but non-specific probe into changes happening at cellular level. Alternatively, tissue complexity can be probed and quantified using the time dependence of diffusion metrics, sometimes also referred to as temporal diffusion spectroscopy when only using oscillating diffusion gradients. Time-dependent diffusion (TDD) is emerging as a strong candidate for specific and non-invasive tumor characterization. Despite the lack of a general analytical solution for all diffusion times / frequencies, TDD can be probed in various regimes where systems simplify in order to extract relevant information about tissue microstructure. The fundamentals of TDD are first reviewed (a) in the short time regime, disentangling structural and diffusive tissue properties, and (b) near the tortuosity limit, assuming weakly heterogeneous media near infinitely long diffusion times. Focusing on cell bodies (as opposed to neuronal tracts), a simple but realistic model for intracellular diffusion can offer precious insight on diffusion inside biological systems, at all times. Based on this approach, the main three geometrical models implemented so far (IMPULSED, POMACE, VERDICT) are reviewed. Their suitability to quantify cell size, intra- and extracellular spaces (ICS and ECS) and diffusivities are assessed. The proper modeling of tissue membrane permeability – hardly a newcomer in the field, but lacking applications - and its impact on microstructural estimates are also considered. After discussing general issues with tissue modeling and microstructural parameter estimation (i
Specifying theories of developmental dyslexia: a diffusion model analysis of word recognition
Zeguers, M.H.T.; Snellings, P.; Tijms, J.; Weeda, W.D.; Tamboer, P.; Bexkens, A.; Huizenga, H.M.
2011-01-01
The nature of word recognition difficulties in developmental dyslexia is still a topic of controversy. We investigated the contribution of phonological processing deficits and uncertainty to the word recognition difficulties of dyslexic children by mathematical diffusion modeling of visual and
Asymptotic behaviour of a nonlinear model for the geographic diffusion of infections diseases
Kirane, M.; Kouachi, S.
1994-01-01
In this paper a nonlinear diffusion model for the geographical spread of infective diseases is studied. In addition to proving well-posedness of the associated initial-boundary value problem, the large time behaviour is analyzed. (author). 4 refs
Desvillettes, Laurent; Fellner, Klemens
2010-01-01
We study a continuous coagulation-fragmentation model with constant kernels for reacting polymers (see [M. Aizenman and T. Bak, Comm. Math. Phys., 65 (1979), pp. 203-230]). The polymers are set to diffuse within a smooth bounded one
Kan-On, Yukio
2007-04-01
This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.
Diffuse-interface model for rapid phase transformations in nonequilibrium systems.
Galenko, Peter; Jou, David
2005-04-01
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.
Woo, Jiyoung; Chen, Hsinchun
2016-01-01
As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums.
Claude Rodrigue Bambe Moutsinga
2018-01-01
Full Text Available Most existing multivariate models in finance are based on diffusion models. These models typically lead to the need of solving systems of Riccati differential equations. In this paper, we introduce an efficient method for solving systems of stiff Riccati differential equations. In this technique, a combination of Laplace transform and homotopy perturbation methods is considered as an algorithm to the exact solution of the nonlinear Riccati equations. The resulting technique is applied to solving stiff diffusion model problems that include interest rates models as well as two and three-factor stochastic volatility models. We show that the present approach is relatively easy, efficient and highly accurate.
An extended five-stream model for diffusion of ion-implanted dopants in monocrystalline silicon
Khina, B.B.
2007-01-01
Low-energy high-dose ion implantation of different dopants (P, Sb, As, B and others) into monocrystalline silicon with subsequent thermal annealing is used for the formation of ultra-shallow p-n junctions in modern VLSI circuit technology. During annealing, dopant activation and diffusion in silicon takes place. The experimentally observed phenomenon of transient enhanced diffusion (TED), which is typically ascribed to the interaction of diffusing species with non-equilibrium point defects accumulated in silicon due to ion damage, and formation of small clusters and extended defects, hinders further down scaling of p-n junctions in VLSI circuits. TED is currently a subject of extensive experimental and theoretical investigation in many binary and multicomponent systems. However, the state-of-the-art mathematical models of dopant diffusion, which are based on the so-called 'five-stream' approach, and modern TCAD software packages such as SUPREM-4 (by Silvaco Data Systems, Ltd.) that implement these models encounter severe difficulties in describing TED. Solving the intricate problem of TED suppression and development of novel regimes of ion implantation and rapid thermal annealing is impossible without elaboration of new mathematical models and computer simulation of this complex phenomenon. In this work, an extended five-stream model for diffusion in silicon is developed which takes into account all possible charge states of point defects (vacancies and silicon self-interstitials) and diffusing pairs 'dopant atom-vacancy' and 'dopant atom-silicon self-interstitial'. The model includes the drift terms for differently charged point defects and pairs in the internal electric field and the kinetics of interaction between unlike 'species' (generation and annihilation of pairs and annihilation of point defects). Expressions for diffusion coefficients and numerous sink/source terms that appear in the non-linear, non-steady-state reaction-diffusion equations are derived
Macromolecular diffusion in crowded media beyond the hard-sphere model.
Blanco, Pablo M; Garcés, Josep Lluís; Madurga, Sergio; Mas, Francesc
2018-04-25
The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlongversus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (α) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and α are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient.
Fractional Diffusion Equations and Anomalous Diffusion
Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin
2018-01-01
Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.
Jakob, A
2004-07-01
In this report a comprehensive overview on the matrix diffusion of solutes in fractured crystalline rocks is presented. Some examples from observations in crystalline bedrock are used to illustrate that matrix diffusion indeed acts on various length scales. Fickian diffusion is discussed in detail followed by some considerations on rock porosity. Due to the fact that the dual-porosity medium model is a very common and versatile method for describing solute transport in fractured porous media, the transport equations and the fundamental assumptions, approximations and simplifications are discussed in detail. There is a variety of geometrical aspects, processes and events which could influence matrix diffusion. The most important of these, such as, e.g., the effect of the flow-wetted fracture surface, channelling and the limited extent of the porous rock for matrix diffusion etc., are addressed. In a further section open issues and unresolved problems related to matrix diffusion are mentioned. Since matrix diffusion is one of the key retarding processes in geosphere transport of dissolved radionuclide species, matrix diffusion was consequently taken into account in past performance assessments of radioactive waste repositories in crystalline host rocks. Some issues regarding matrix diffusion are site-specific while others are independent of the specific situation of a planned repository for radioactive wastes. Eight different performance assessments from Finland, Sweden and Switzerland were considered with the aim of finding out how matrix diffusion was addressed, and whether a consistent picture emerges regarding the varying methodology of the different radioactive waste organisations. In the final section of the report some conclusions are drawn and an outlook is given. An extensive bibliography provides the reader with the key papers and reports related to matrix diffusion. (author)
Chen, Xueli; Yang, Defu; Qu, Xiaochao; Hu, Hao; Liang, Jimin; Gao, Xinbo; Tian, Jie
2012-06-01
Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.
Random variability in mesoscale wind observations and implications for diffusion models
Hanna, S.R. [Sigma Research Corp., Concord, MA (United States)
1994-12-31
The investigation reported in this paper grew out of a preliminary analysis of methods by which regional air quality models such as the Regional Oxidant Model account for horizontal transport and diffusion. It was discovered that there is a variety of often inconsistent methods used to parameterize horizontal diffusion at meso- and regional scales, and the time seemed ripe to review and compare and contrast these schemes. This paper provides a brief overview of the major issues that were uncovered and lists a few specific examples of the technical approaches that are used. Subsequent sections cover the basic physics of horizontal diffusion, the characteristics of observed wind fields, and methods of parameterizing horizontal diffusion in air quality models.
Model analysis of the influence of gas diffusivity in soil on CO and H2 uptake
Yonemura, S.; Yokozawa, M.; Kawashima, S.; Tsuruta, H.
2000-01-01
CO and H 2 uptake by soil was studied as a diffusion process. A diffusion model was used to determine how the surface fluxes (net deposition velocities) were controlled by in-situ microbial uptake rates and soil gas diffusivity calculated from the 3-phase system (solid, liquid, gas) in the soil. Analytical solutions of the diffusion model assuming vertical uniformity of soil properties showed that physical properties such as air-filled porosity and soil gas diffusivity were more important in the uptake process than in the emission process. To incorporate the distribution of in-situ microbial uptake, we used a 2-layer model incorporating 'a microbiologically inactive layer and an active layer' as suggested from experimental results. By numerical simulation using the 2-layer model, we estimated the effect of several factors on deposition velocities. The variations in soil gas diffusivity due to physical properties, i.e., soil moisture and air-filled porosity, as well as to the depth of the inactive layer and in-situ microbial uptake, were found to be important in controlling deposition velocities. This result shows that the diffusion process in soil is critically important for CO and H 2 uptake by soil, at least in soils with higher in-situ uptake rates and/or with large variation in soil moisture. Similar uptake rates and the difference in deposition velocity between CO and H 2 may be attributable to differences in CO and H 2 molecular diffusivity. The inactive layer is resistant to diffusion and creates uptake limits in CO and H 2 by soil. The coupling of high temperature and a thick inactive layer, common in arid soils, markedly lowers net CO deposition velocity. The temperature for maximum uptake of CO changes with depth of the inactive layer
Preliminary Hybrid Modeling of the Panama Canal: Operations and Salinity Diffusion
Luis Rabelo
2012-01-01
Full Text Available This paper deals with the initial modeling of water salinity and its diffusion into the lakes during lock operation on the Panama Canal. A hybrid operational model was implemented using the AnyLogic software simulation environment. This was accomplished by generating an operational discrete-event simulation model and a continuous simulation model based on differential equations, which modeled the salinity diffusion in the lakes. This paper presents that unique application and includes the effective integration of lock operations and its impact on the environment.
Impact of Social Network and Business Model on Innovation Diffusion of Electric Vehicles in China
D. Y. Kong
2014-01-01
Full Text Available The diffusion of electric vehicles (EVs involves not only the technological development but also the construction of complex social networks. This paper uses the theory of network control to analyze the influence of network forms on EV diffusion in China, especially focusing on the building of EV business models (BMs and the resulting effects and control on the diffusion of EVs. The Bass model is adopted to forecast the diffusion process of EVs and genetic algorithm is used to estimate the parameters based on the diffusion data of Hybrid Electric Vehicle (HEV in the United States and Japan. Two different social network forms and BMs are selected, that is, battery leasing model and vehicle purchasing model, to analyze how different network forms may influence the innovation coefficient and imitation coefficient in the Bass model, which will in turn result in different diffusion results. Thereby, we can find the appropriate network forms and BMs for EVs which is suitable to the local market conditions.
From Shell Shock to Combat Stress
Binneveld, Hans
1997-01-01
War confronts a soldier with extreme situations. Armed conflicts produce not only deaths and injuries but mental breakdowns as well. The field of military psychiatry was founded at the beginning of this century. This book presents a history of this field. The first part provides a historical survey
Ulfah, S.; Awalludin, S. A.; Wahidin
2018-01-01
Advection-diffusion model is one of the mathematical models, which can be used to understand the distribution of air pollutant in the atmosphere. It uses the 2D advection-diffusion model with time-dependent to simulate air pollution distribution in order to find out whether the pollutants are more concentrated at ground level or near the source of emission under particular atmospheric conditions such as stable, unstable, and neutral conditions. Wind profile, eddy diffusivity, and temperature are considered in the model as parameters. The model is solved by using explicit finite difference method, which is then visualized by a computer program developed using Lazarus programming software. The results show that the atmospheric conditions alone influencing the level of concentration of pollutants is not conclusive as the parameters in the model have their own effect on each atmospheric condition.
Ying Liu
2015-01-01
Full Text Available Unidirectional pedestrian movement is a special phenomenon in the evacuation process of large public buildings and urban environments at pedestrian scale. Several macroscopic models for collective behaviors have been built to predict pedestrian flow. However, current models do not explain the diffusion behavior in pedestrian crowd movement, which can be important in representing spatial-temporal crowd density differentiation in the movement process. This study builds a macroscopic model for describing crowd diffusion behavior and evaluating unidirectional pedestrian flow. The proposed model employs discretization of time and walking speed in geometric distribution to calculate downstream pedestrian crowd flow and analyze movement process based on upstream number of pedestrians and average walking speed. The simulated results are calibrated with video observation data in a baseball stadium to verify the model precision. Statistical results have verified that the proposed pedestrian diffusion model could accurately describe pedestrian macromovement behavior within the margin of error.
Wang, Jing [Iowa State Univ., Ames, IA (United States)
2013-01-11
We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.
Diffusion of a collaborative care model in primary care: a longitudinal qualitative study
Vedel Isabelle
2013-01-01
Full Text Available Background Although collaborative team models (CTM improve care processes and health outcomes, their diffusion poses challenges related to difficulties in securing their adoption by primary care clinicians (PCPs. The objectives of this study are to understand: (1 how the perceived characteristics of a CTM influenced clinicians' decision to adopt -or not- the model; and (2 the model's diffusion process. Methods We conducted a longitudinal case study based on the Diffusion of Innovations Theory. First, diffusion curves were developed for all 175 PCPs and 59 nurses practicing in one borough of Paris. Second, semi-structured interviews were conducted with a representative sample of 40 PCPs and 15 nurses to better understand the implementation dynamics. Results Diffusion curves showed that 3.5 years after the start of the implementation, 100% of nurses and over 80% of PCPs had adopted the CTM. The dynamics of the CTM's diffusion were different between the PCPs and the nurses. The slopes of the two curves are also distinctly different. Among the nurses, the critical mass of adopters was attained faster, since they adopted the CTM earlier and more quickly than the PCPs. Results of the semi-structured interviews showed that these differences in diffusion dynamics were mostly founded in differences between the PCPs' and the nurses' perceptions of the CTM's compatibility with norms, values and practices and its relative advantage (impact on patient management and work practices. Opinion leaders played a key role in the diffusion of the CTM among PCPs. Conclusion CTM diffusion is a social phenomenon that requires a major commitment by clinicians and a willingness to take risks; the role of opinion leaders is key. Paying attention to the notion of a critical mass of adopters is essential to developing implementation strategies that will accelerate the adoption process by clinicians.
A novel rumor diffusion model considering the effect of truth in online social media
Sun, Ling; Liu, Yun; Zeng, Qing-An; Xiong, Fei
2015-12-01
In this paper, we propose a model to investigate how truth affects rumor diffusion in online social media. Our model reveals a relation between rumor and truth — namely, when a rumor is diffusing, the truth about the rumor also diffuses with it. Two patterns of the agents used to identify rumor, self-identification and passive learning are taken into account. Combining theoretical proof and simulation analysis, we find that the threshold value of rumor diffusion is negatively correlated to the connectivity between nodes in the network and the probability β of agents knowing truth. Increasing β can reduce the maximum density of the rumor spreaders and slow down the generation speed of new rumor spreaders. On the other hand, we conclude that the best rumor diffusion strategy must balance the probability of forwarding rumor and the probability of agents losing interest in the rumor. High spread rate λ of rumor would lead to a surge in truth dissemination which will greatly limit the diffusion of rumor. Furthermore, in the case of unknown λ, increasing β can effectively reduce the maximum proportion of agents who do not know the truth, but cannot narrow the rumor diffusion range in a certain interval of β.
Atmospheric diffusion model for control room habitability assessments
Ramsdell, J.V.; Lee, J.Y.
1993-01-01
General Design Criterion 19 for nuclear power plants (Appendix A to 10CFR50) requires control room radiation protection adequate to limit radiation exposures to control room personnel. Murphy and Campe proposed the procedure currently used in evaluating control room habitability. However, data from building-wake diffusion experiments at nuclear power plants indicate that the Murphy-Campe procedure tends to overestimate concentrations, particularly during low wind speeds. This paper describes an alternative procedure developed by the Pacific Northwest Laboratory that is acceptable to U.S. Nuclear Regulatory Commission (NRC) staff. The procedure estimates control room air intake concentrations that are generally lower than those estimated by the Murphy-Campe procedure, yet are still conservative
Olena G. Filatova
2018-04-01
Full Text Available Better insight into white matter (WM alterations after stroke onset could help to understand the underlying recovery mechanisms and improve future interventions. MR diffusion imaging enables to assess such changes. Our goal was to investigate the relation of WM diffusion characteristics derived from diffusion models of increasing complexity with the motor function of the upper limb. Moreover, we aimed to evaluate the variation of such characteristics across different WM structures of chronic stroke patients in comparison to healthy subjects. Subjects were scanned with a two b-value diffusion-weighted MRI protocol to exploit multiple diffusion models: single tensor, single tensor with isotropic compartment, bi-tensor model, bi-tensor with isotropic compartment. From each model we derived the mean tract fractional anisotropy (FA, mean (MD, radial (RD and axial (AD diffusivities outside the lesion site based on a WM tracts atlas. Asymmetry of these measures was correlated with the Fugl-Meyer upper extremity assessment (FMA score and compared between patient and control groups. Eighteen chronic stroke patients and eight age-matched healthy individuals participated in the study. Significant correlation of the outcome measures with the clinical scores of stroke recovery was found. The lowest correlation of the corticospinal tract FAasymmetry and FMA was with the single tensor model (r = −0.3, p = 0.2 whereas the other models reported results in the range of r = −0.79 ÷ −0.81 and p = 4E-5 ÷ 8E-5. The corticospinal tract and superior longitudinal fasciculus showed most alterations in our patient group relative to controls. Multiple compartment models yielded superior correlation of the diffusion measures and FMA compared to the single tensor model.
Yoshikawa, T.; Kimura, F.; Koide, T.; Kurita, S.
1990-01-01
Since 1986, a simple computation model for a nuclear accident has been operating in the emergency information center of Japan Agency for Science and Technology. It was developed by introducing the variation method for wind and a random walk particle model for diffusion in 50-100 km scale. Furthermore, we developed a new model with dynamic equations and a diffusion equation to predict more accurately the wind and diffusion, including local thermal convection. The momentum equation and the continuity equation are solved numerically in nonhydrostatic and incompressible conditions, using a finite difference technique. Then, the equation of thermal energy preservation is solved for potential temperature in the predicted wind field of every time step. The diffusion of nuclear pollutants is computed numerically in the predicted wind field, using diffusion coefficients obtained from the predictive dynamic equations. These computations were verified with meteorological surveys and gas tracer diffusion experiments over flat land, along a sea shore and over a mountainous area. Horizontal circulations and vertical convections can be computed in any mesh size from several tens of meters to several kilometers, while small vertical convections less than 1 km or so cannot be represented with the former hydrostatic circulation models. (author)
O. H. Kapitonov
2010-05-01
Full Text Available A mathematical model of coulostatic relaxation of the potential for solid metallic electrode was presented. The solution in the case of limiting diffusion current was obtained. On the basis of this model the technique of concentration measurements for heavy metal ions in diluted solutions was suggested. The model adequacy was proved by experimental data.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, C; Vereecken, H
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.
Generalized random walk algorithm for the numerical modeling of complex diffusion processes
Vamos, Calin; Suciu, Nicolae; Vereecken, Harry
2003-01-01
A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested
Analysis of effective diffusivity of cement based materials by multi-scale modelling
Dridi, Wissem
2013-01-01
This paper presents a simplified composite model, which considers the contribution of each phase participating to the transport within OPC pastes and concretes. At the micrometer scale, the phases considered hereafter are capillary porosity (macro-porosity) and the Low Density and the High Density C-S-H both containing gel pores (nano-porosity). Predicted values of tritiated water (HTO) diffusivity in OPC pastes with various (w/c) ratios are confronted to experimental results with a good agreement. The approach is then extended to mortars and concretes scale where microstructure is described by a three phase composite sphere assemblage. Here, elementary phase distribution is assumed to change as a function of distance from aggregate surface. Model results about HTO diffusivities of mortars and concretes are presented with some experimental values. The competition between the more diffusing ITZ zone and the less diffusing bulk matrix is investigated from a sensitive analysis. The dominance of the ITZ control is confirmed. (authors)
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
Bernard Wong
2009-01-01
martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.
A minimally-resolved immersed boundary model for reaction-diffusion problems
Pal Singh Bhalla, A; Griffith, BE; Patankar, NA; Donev, A
2013-01-01
We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blo...
Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage
Allen, Rebecca
2015-04-01
ABSTRACT Modeling Diffusion and Buoyancy-Driven Convection with Application to Geological CO2 Storage Rebecca Allen Geological CO2 storage is an engineering feat that has been undertaken around the world for more than two decades, thus accurate modeling of flow and transport behavior is of practical importance. Diffusive and convective transport are relevant processes for buoyancy-driven convection of CO2 into underlying fluid, a scenario that has received the attention of numerous modeling studies. While most studies focus on Darcy-scale modeling of this scenario, relatively little work exists at the pore-scale. In this work, properties evaluated at the pore-scale are used to investigate the transport behavior modeled at the Darcy-scale. We compute permeability and two different forms of tortuosity, namely hydraulic and diffusive. By generating various pore ge- ometries, we find hydraulic and diffusive tortuosity can be quantitatively different in the same pore geometry by up to a factor of ten. As such, we emphasize that these tortuosities should not be used interchangeably. We find pore geometries that are characterized by anisotropic permeability can also exhibit anisotropic diffusive tortuosity. This finding has important implications for buoyancy-driven convection modeling; when representing the geological formation with an anisotropic permeabil- ity, it is more realistic to also account for an anisotropic diffusivity. By implementing a non-dimensional model that includes both a vertically and horizontally orientated 5 Rayleigh number, we interpret our findings according to the combined effect of the anisotropy from permeability and diffusive tortuosity. In particular, we observe the Rayleigh ratio may either dampen or enhance the diffusing front, and our simulation data is used to express the time of convective onset as a function of the Rayleigh ratio. Also, we implement a lattice Boltzmann model for thermal convective flows, which we treat as an analog for
Georgios C Manikis
Full Text Available The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer.Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2 at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG and non-Gaussian (MNG and BNG were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE. To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC and F-ratio.All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area.No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.
A generalized diffusion model for growth of nanoparticles synthesized by colloidal methods.
Wen, Tianlong; Brush, Lucien N; Krishnan, Kannan M
2014-04-01
A nanoparticle growth model is developed to predict and guide the syntheses of monodisperse colloidal nanoparticles in the liquid phase. The model, without any a priori assumptions, is based on the Fick's law of diffusion, conservation of mass and the Gibbs-Thomson equation for crystal growth. In the limiting case, this model reduces to the same expression as the currently accepted model that requires the assumption of a diffusion layer around each nanoparticle. The present growth model bridges the two limiting cases of the previous model i.e. complete diffusion controlled and adsorption controlled growth of nanoparticles. Specifically, the results show that a monodispersion of nanoparticles can be obtained both with fast monomer diffusion and with surface reaction under conditions of small diffusivity to surface reaction constant ratio that results is growth 'focusing'. This comprehensive description of nanoparticle growth provides new insights and establishes the required conditions for fabricating monodisperse nanoparticles critical for a wide range of applications. Copyright © 2013 Elsevier Inc. All rights reserved.
Marcon, J. [Laboratoire Electronique Microtechnologie et Instrumentation (LEMI), University of Rouen, 76821 Mont Saint Aignan (France)], E-mail: Jerome.Marcon@univ-rouen.fr; Merabet, A. [Laboratoire de Physique et Mecanique des Materiaux Metalliques, Departement d' O.M.P., Faculte des Sciences de l' Ingenieur, Universite de Setif, 19000 Setif (Algeria)
2008-12-05
We have investigated and modelled the diffusion of boron implanted into crystalline silicon in the form of boron difluoride BF{sub 2}{sup +}. We have used published data for BF{sub 2}{sup +} implanted with an energy of 2.2 keV in crystalline silicon. Fluorine effects are considered by using vacancy-fluorine pairs which are responsible for the suppression of boron diffusion in crystalline silicon. Following Uematsu's works, the simulations satisfactory reproduce the SIMS experimental profiles in the 800-1000 deg. C temperature range. The boron diffusion model in silicon of Uematsu has been improved taking into account the last experimental data.
Simulating watercolor by modeling diffusion, pigment, and paper fibers
Small, David
1991-08-01
This paper explores a parallel approach to the problem of predicting the actions of pigment and water when applied to paper fibers. This work was done on the Connection Machine II, whose parallel architecture allows one to cast the problem as that of a complex cellular automata. One defines simple rules for the behavior of each cell based on the state of that cell and its immediate neighbors. By repeating the computation for each cell in the paper over many time steps, elaborate and realistic behaviors can be achieved. The simulation takes into account diffusion, surface tension, gravity, humidity, paper absorbency and the molecular weight of each pigment. At each time step a processor associated with each fiber in the paper computes water and pigment gradients, surface tension and gravitational forces, and decides if there should be any movement of material. Pigment and water can be applied and removed (blotting) with masks created from type or scanned images. Use of a parallel processor simplifies the creation and testing of software, and variables can be stored and manipulated at highprecision. The resulting simulation runs at approximately one-tenth real time.
Green's function method and its application to verification of diffusion models of GASFLOW code
Xu, Z.; Travis, J.R.; Breitung, W.
2007-07-01
To validate the diffusion model and the aerosol particle model of the GASFLOW computer code, theoretical solutions of advection diffusion problems are developed by using the Green's function method. The work consists of a theory part and an application part. In the first part, the Green's functions of one-dimensional advection diffusion problems are solved in infinite, semi-infinite and finite domains with the Dirichlet, the Neumann and/or the Robin boundary conditions. Novel and effective image systems especially for the advection diffusion problems are made to find the Green's functions in a semi-infinite domain. Eigenfunction method is utilized to find the Green's functions in a bounded domain. In the case, key steps of a coordinate transform based on a concept of reversed time scale, a Laplace transform and an exponential transform are proposed to solve the Green's functions. Then the product rule of the multi-dimensional Green's functions is discussed in a Cartesian coordinate system. Based on the building blocks of one-dimensional Green's functions, the multi-dimensional Green's function solution can be constructed by applying the product rule. Green's function tables are summarized to facilitate the application of the Green's function. In the second part, the obtained Green's function solutions benchmark a series of validations to the diffusion model of gas species in continuous phase and the diffusion model of discrete aerosol particles in the GASFLOW code. Perfect agreements are obtained between the GASFLOW simulations and the Green's function solutions in case of the gas diffusion. Very good consistencies are found between the theoretical solutions of the advection diffusion equations and the numerical particle distributions in advective flows, when the drag force between the micron-sized particles and the conveying gas flow meets the Stokes' law about resistance. This situation is corresponding to a very small Reynolds number based on the particle
Multi-component fiber track modelling of diffusion-weighted magnetic resonance imaging data
Yasser M. Kadah
2010-01-01
Full Text Available In conventional diffusion tensor imaging (DTI based on magnetic resonance data, each voxel is assumed to contain a single component having diffusion properties that can be fully represented by a single tensor. Even though this assumption can be valid in some cases, the general case involves the mixing of components, resulting in significant deviation from the single tensor model. Hence, a strategy that allows the decomposition of data based on a mixture model has the potential of enhancing the diagnostic value of DTI. This project aims to work towards the development and experimental verification of a robust method for solving the problem of multi-component modelling of diffusion tensor imaging data. The new method demonstrates significant error reduction from the single-component model while maintaining practicality for clinical applications, obtaining more accurate Fiber tracking results.
Inclusion of the diffuseness in the schematic model of heavy ion collisions
Marta, H.D.
1989-01-01
The schematic model of central heavy ion collisions developed by Swiatecki includes the Coulomb and surface contributions to the potential energy of the system and one-body dissipation. This model is extended by considering the diffuseness of the nuclear surface; this has the implication that we must consider the proximity forces in the dynamics of the collisions. For the sake of simplicity we work with symmetrical systems. The results of the model studied are compared with experimental data and with other theoretical calculations. We conclude that the detailed consideration of the diffuseness of the nuclear surfaces does not substantially change the results of the schematic model for sharp surfaces in which the diffuseness is considered only through the parameters. (author) [pt
Application of Fokker-Planck equation in positron diffusion trapping model
Bartosova, I.; Ballo, P.
2015-01-01
This paper is a theoretical prelude to future work involving positron diffusion in solids for the purpose of positron annihilation lifetime spectroscopy (PALS). PALS is a powerful tool used to study defects present in materials. However, the behavior of positrons in solids is a process hard to describe. Various models have been established to undertake this task. Our preliminary model is based on the Diffusion Trapping Model (DTM) described by partial differential Fokker-Planck equation and is solved via time discretization. Fokker-Planck equation describes the time evolution of the probability density function of velocity of a particle under the influence of various forces. (authors)
Kochukhov, O.; Ryabchikova, T. A.
2018-02-01
A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.
Desvillettes, Laurent
2010-01-01
We study a continuous coagulation-fragmentation model with constant kernels for reacting polymers (see [M. Aizenman and T. Bak, Comm. Math. Phys., 65 (1979), pp. 203-230]). The polymers are set to diffuse within a smooth bounded one-dimensional domain with no-flux boundary conditions. In particular, we consider size-dependent diffusion coefficients, which may degenerate for small and large cluster-sizes. We prove that the entropy-entropy dissipation method applies directly in this inhomogeneous setting. We first show the necessary basic a priori estimates in dimension one, and second we show faster-than-polynomial convergence toward global equilibria for diffusion coefficients which vanish not faster than linearly for large sizes. This extends the previous results of [J.A. Carrillo, L. Desvillettes, and K. Fellner, Comm. Math. Phys., 278 (2008), pp. 433-451], which assumes that the diffusion coefficients are bounded below. © 2009 Society for Industrial and Applied Mathematics.
Modelling Of Eco-innovation Diffusion: The EU Eco-label
KIJEK TOMASZ
2015-03-01
Full Text Available The aim of this article is to carry out a theoretical and empirical analysis of the process of eco-label diffusion. Eco-labels allow consumers to identify products and services that have a reduced environmental impact during their life cycle. Thus, they are aimed at diminishing the information gap between sellers and buyers. The results of the estimation using the Bass model indicate that the diffusion of the EU eco-label has been most dynamic in countries such as Hungary, Poland, Denmark, Germany and France. In turn, the scope of diffusion (absolute saturation level reached the highest value for companies in France and Italy. In addition, the results of the study confirm the stimulating impact of the scope of eco-label diffusion on consumer awareness of environmental issues. This finding points to the need for environmental education among consumers, which could in turn encourage firms to undertake pro-environmental actions.
An agent-based model for diffusion of electric vehicles
Kangur, A.; Bockarjova, M.; Jager, W.; Verbrugge, R.
2017-01-01
The transition from fuel cars to electric cars is a large-scale process involving many interactions between consumers and other stakeholders over decades. To explore how policies may interfere with consumer behavior over such a long time period, we developed a social simulation model. In this model,
Jump diffusion models and the evolution of financial prices
Figueiredo, Annibal; Castro, Marcio T. de; Silva, Sergio da; Gleria, Iram
2011-01-01
We analyze a stochastic model to describe the evolution of financial prices. We consider the stochastic term as a sum of the Wiener noise and a jump process. We point to the effects of the jumps on the return time evolution, a central concern of the econophysics literature. The presence of jumps suggests that the process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. We then extend the De Finetti functions to a generalized nonlinear model and show the model to be capable of explaining return behavior. -- Highlights: → We analyze a stochastic model to describe the evolution of financial prices. → The stochastic term is considered as a sum of the Wiener noise and a jump process. → The process can be described by an infinitely divisible characteristic function belonging to the De Finetti class. → We extend the De Finetti functions to a generalized nonlinear model.
Modeling diffusion coefficients in binary mixtures of polar and non-polar compounds
Medvedev, Oleg; Shapiro, Alexander
2005-01-01
The theory of transport coefficients in liquids, developed previously, is tested on a description of the diffusion coefficients in binary polar/non-polar mixtures, by applying advanced thermodynamic models. Comparison to a large set of experimental data shows good performance of the model. Only f...
Wagenmakers, E.-J.
2009-01-01
The Ratcliff diffusion model for simple two-choice decisions (e.g., Ratcliff, 1978; Ratcliff & McKoon, 2008) has two outstanding advantages. First, the model generally provides an excellent fit to the observed data (i.e., response accuracy and the shape of RT distributions, both for correct and
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
On the well posedness and further regularity of a diffusive three species aquatic model
Parshad, R.D.
2012-01-01
We consider Upadhay\\'s three species aquatic food chain model, with the inclusion of spatial spread. This is a well established food chain model for the interaction of three given aquatic species. It exhibits rich dynamical behavior, including chaos. We prove the existence of a global weak solution to the diffusive system, followed by existence of local mild and strong solution.
Barbante, Paolo [Dipartimento di Matematica, Politecnico di Milano - Piazza Leonardo da Vinci 32 - 20133 Milano (Italy); Frezzotti, Aldo; Gibelli, Livio [Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano - Via La Masa 34 - 20156 Milano (Italy)
2014-12-09
The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviations of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.
Donkin, C.; Brown, S.; Heathcote, A.; Wagenmakers, E.-J.
2011-01-01
Quantitative models for response time and accuracy are increasingly used as tools to draw conclusions about psychological processes. Here we investigate the extent to which these substantive conclusions depend on whether researchers use the Ratcliff diffusion model or the Linear Ballistic
The effect of a realistic thermal diffusivity on numerical model of a subducting slab
Maierova, P.; Steinle-Neumann, G.; Cadek, O.
2010-12-01
A number of numerical studies of subducting slab assume simplified (constant or only depth-dependent) models of thermal conductivity. The available mineral physics data indicate, however, that thermal diffusivity is strongly temperature- and pressure-dependent and may also vary among different mantle materials. In the present study, we examine the influence of realistic thermal properties of mantle materials on the thermal state of the upper mantle and the dynamics of subducting slabs. On the basis of the data published in mineral physics literature we compile analytical relationships that approximate the pressure and temperature dependence of thermal diffusivity for major mineral phases of the mantle (olivine, wadsleyite, ringwoodite, garnet, clinopyroxenes, stishovite and perovskite). We propose a simplified composition of mineral assemblages predominating in the subducting slab and the surrounding mantle (pyrolite, mid-ocean ridge basalt, harzburgite) and we estimate their thermal diffusivity using the Hashin-Shtrikman bounds. The resulting complex formula for the diffusivity of each aggregate is then approximated by a simpler analytical relationship that is used in our numerical model as an input parameter. For the numerical modeling we use the Elmer software (open source finite element software for multiphysical problems, see http://www.csc.fi/english/pages/elmer). We set up a 2D Cartesian thermo-mechanical steady-state model of a subducting slab. The model is partly kinematic as the flow is driven by a boundary condition on velocity that is prescribed on the top of the subducting lithospheric plate. Reology of the material is non-linear and is coupled with the thermal equation. Using the realistic relationship for thermal diffusivity of mantle materials, we compute the thermal and flow fields for different input velocity and age of the subducting plate and we compare the results against the models assuming a constant thermal diffusivity. The importance of the
Modeling the oxygen diffusion of nanocomposite-based food packaging films.
Bhunia, Kanishka; Dhawan, Sumeet; Sablani, Shyam S
2012-07-01
Polymer-layered silicate nanocomposites have been shown to improve the gas barrier properties of food packaging polymers. This study developed a computer simulation model using the commercial software, COMSOL Multiphysics to analyze changes in oxygen barrier properties in terms of relative diffusivity, as influenced by configuration and structural parameters that include volume fraction (φ), aspect ratio (α), intercalation width (W), and orientation angle (θ) of nanoparticles. The simulation was performed at different φ (1%, 3%, 5%, and 7%), α (50, 100, 500, and 1000), and W (1, 3, 5, and 7 nm). The θ value was varied from 0° to 85°. Results show that diffusivity decreases with increasing volume fraction, but beyond φ = 5% and α = 500, diffusivity remained almost constant at W values of 1 and 3 nm. Higher relative diffusivity coincided with increasing W and decreasing α value for the same volume fraction of nanoparticles. Diffusivity increased as the rotational angle increased, gradually diminishing the influence of nanoparticles. Diffusivity increased drastically as θ changed from 15° to 30° (relative increment in relative diffusivity was almost 3.5 times). Nanoparticles with exfoliation configuration exhibited better oxygen barrier properties compared to intercalation. The finite element model developed in this study provides insight into oxygen barrier properties for nanocomposite with a wide range of structural parameters. This model can be used to design and manufacture an ideal nanocomposite-based food packaging film with improved gas barrier properties for industrial applications. The model will assist in designing nanocomposite polymeric structures of desired gas barrier properties for food packaging applications. In addition, this study will be helpful in formulating a combination of nanoparticle structural parameters for designing nanocomposite membranes with selective permeability for the industrial applications including membrane
Diffusion properties of a guiding center plasma in a model electrostatic turbulence
Pettini, M.; Vulpiani, A.; Misguich, J.H.; Balescu, R.; De Leener, M.; Orban, J.
1986-01-01
Numerical simulations have been performed to calculate the diffusion coefficient of several hundreds of charged particles across a strong magnetic field B, due to a known spectrum of electrostatic fluctuations. The results have been compared with the turbulent diffusion theory proposed by Misguich et al. The equation of motion is solved with a model electrostatic potential. This potential is also the Hamiltonian of this chaotic non-autonomous system: positive Lyapunov exponents are found in qualitative agreement with theoretical predictions. The absolute diffusion coefficients found in two different models exhibit a transition between two scaling regions: a classical scaling at low amplitudes (D ∼ E 2 /B 2 ), and a Bohm scaling at higher amplitudes (D ∼ E/B), in agreement with the predictions for these models. The value of the diffusion coefficient obtained in the isotropic model shows a satisfactory agreement with the theory. The study of the relative diffusion of initially close particles yields a clear quantitative confirmation of the clump effect and of the validity of the theoretical treatment of such nonlinearities. (26 fig, 20 refs)
Single-shot spiral imaging enabled by an expanded encoding model: Demonstration in diffusion MRI.
Wilm, Bertram J; Barmet, Christoph; Gross, Simon; Kasper, Lars; Vannesjo, S Johanna; Haeberlin, Max; Dietrich, Benjamin E; Brunner, David O; Schmid, Thomas; Pruessmann, Klaas P
2017-01-01
The purpose of this work was to improve the quality of single-shot spiral MRI and demonstrate its application for diffusion-weighted imaging. Image formation is based on an expanded encoding model that accounts for dynamic magnetic fields up to third order in space, nonuniform static B 0 , and coil sensitivity encoding. The encoding model is determined by B 0 mapping, sensitivity mapping, and concurrent field monitoring. Reconstruction is performed by iterative inversion of the expanded signal equations. Diffusion-tensor imaging with single-shot spiral readouts is performed in a phantom and in vivo, using a clinical 3T instrument. Image quality is assessed in terms of artefact levels, image congruence, and the influence of the different encoding factors. Using the full encoding model, diffusion-weighted single-shot spiral imaging of high quality is accomplished both in vitro and in vivo. Accounting for actual field dynamics, including higher orders, is found to be critical to suppress blurring, aliasing, and distortion. Enhanced image congruence permitted data fusion and diffusion tensor analysis without coregistration. Use of an expanded signal model largely overcomes the traditional vulnerability of spiral imaging with long readouts. It renders single-shot spirals competitive with echo-planar readouts and thus deploys shorter echo times and superior readout efficiency for diffusion imaging and further prospective applications. Magn Reson Med 77:83-91, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
A dissolution-diffusion sliding model for soft rock grains with hydro-mechanical effect
Z. Liu
2018-06-01
Full Text Available The deformation and failure of soft rock affected by hydro-mechanical (HM effect are one of the most concerns in geotechnical engineering, which are basically attributed to the grain sliding of soft rock. This study tried to develop a dissolution-diffusion sliding model for the typical red bed soft rock in South China. Based on hydration film, mineral dissolution and diffusion theory, and geochemical thermodynamics, a dissolution-diffusion sliding model with the HM effect was established to account for the sliding rate. Combined with the digital image processing technology, the relationship between the grain size of soft rock and the amplitude of sliding surface was presented. An equation for the strain rate of soft rocks under steady state was also derived. The reliability of the dissolution-diffusion sliding model was verified by triaxial creep tests on the soft rock with the HM coupling effect and by the relationship between the inversion average disjoining pressure and the average thickness of the hydration film. The results showed that the sliding rate of the soft rock grains was affected significantly by the waviness of sliding surface, the shear stress, and the average thickness of hydration film. The average grain size is essential for controlling the steady-state creep rate of soft rock. This study provides a new idea for investigating the deformation and failure of soft rock with the HM effect. Keywords: Soft rock, Hydro-mechanical (HM effect, Mineral dissolution-diffusion, Grain sliding model
Tachi, Yukio; Suyama, Tadahiro; Ochs, Michael
2014-01-01
To predict the long-term migration of radionuclides (RNs) under variable conditions within the framework of safety analyses for geological disposal, thermodynamic sorption models are very powerful tools. The integrated sorption and diffusion (ISD) model for compacted bentonite was developed to achieve a consistent combination of clay–water interaction, sorption, and diffusion models. The basic premise considered in the ISD model was to consistently use the same simple surface model design and parameters for describing RNs sorption/diffusion as well as clay surface and porewater chemistry. A simple 1-site non-electrostatic surface complexation model in combination with a 1-site ion exchange model was selected to keep sorption model characteristics relatively robust for compacted systems. Fundamental parameters for the proposed model were evaluated from surface titration data for purified montmorillonite. The resulting basic model was then parameterized on the basis of selected published sorption data-sets for Np(V), Am(III), and U(VI) in dispersed systems, which cover a range of key geochemical conditions such as pH, ionic strength, and carbonate concentration. The sorption trends for these RNs can be quantitatively described by the model considering a full suite of surface species including hydrolytic and carbonate species. The application of these models to the description of diffusive-sorptive transport in compacted bentonites is presented in Part 2. (author)
Quantum Lattice-Gas Model for the Diffusion Equation
Yepez, J
2001-01-01
.... It is a minimal model with two qubits per node of a one-dimensional lattice and it is suitable for implementation on a large array of small quantum computers interconnected by nearest-neighbor...
Mathematical models for drug diffusion through the compartments of ...
M.A. Khanday
2016-07-26
Jul 26, 2016 ... partments have both favourable and adverse effects on human body. The researchers ... absorption, distribution and elimination process of the drug within the body ... models can be used to understand the transport processes.
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif; Ritter, Laura; Walton, Jay R.
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross
Mutual diffusion coefficient models for polymer-solvent systems based on the Chapman-Enskog theory
R. A. Reis
2004-12-01
Full Text Available There are numerous examples of the importance of small molecule migration in polymeric materials, such as in drying polymeric packing, controlled drug delivery, formation of films, and membrane separation, etc. The Chapman-Enskog kinetic theory of hard-sphere fluids with the Weeks-Chandler-Andersen effective hard-sphere diameter (Enskog-WCA has been the most fruitful in diffusion studies of simple fluids and mixtures. In this work, the ability of the Enskog-WCA model to describe the temperature and concentration dependence of the mutual diffusion coefficient, D, for a polystyrene-toluene system was evaluated. Using experimental diffusion data, two polymer model approaches and three mixing rules for the effective hard-sphere diameter were tested. Some procedures tested resulted in models that are capable of correlating the experimental data with the refereed system well for a solvent mass fraction greater than 0.3.
A thick-interface model for diffusive and massive phase transformation in substitutional alloys
Svoboda, J.; Vala, J.; Gamsjaeger, E.; Fischer, F.D.
2006-01-01
Based on the application of the thermodynamic extremal principle, a new model for the diffusive and massive phase transformation in multicomponent substitutional alloys is developed. Interfacial reactions such as the rearrangement of the lattice, solute drag and trans-interface diffusion are automatically considered by assigning a finite thickness and a finite mobility to the interface region. As an application of the steady-state solution of the derived evolution equations, the kinetics of the massive γ → α transformation in the Fe-rich Fe-Cr-Ni system is simulated. The thermodynamic properties of the interface may influence significantly the contact conditions at the interface as well as the conditions for the occurrence of the massive transformation and its kinetics. The model is also used for the simulation of the diffusion-induced grain boundary migration in the same system. By application of the model a realistic value for the Gibbs energy per unit interface area is obtained
Shrinkage Simulation of Holographic Grating Using Diffusion Model in PQ-PMMA Photopolymer
Wei Zepeng
2015-01-01
Full Text Available An extended model based on nonlocal polymerization-driven diffusion model is derived by introducing shrinkage process for describing photopolymerized dynamics in PQ-PMMA photopolymer. The kinetic parameters, polymerization rate and diffusion rate are experimentally determined to provide quantitative simulation. The numerical results show that the fringes at edge of grating are firstly shifted and consequently, it leads to a contrast reduction of holograms. Finally, theoretical results are experimentally checked by temporal evolution of diffraction efficiency, and the shrinkage coefficient 0.5% is approximately achieved under incident intensity 25.3mw/cm2. This work can enhance the applicability of diffusion model and contribute to the reasonable description of the grating formation in the photopolymer.
Gutierrez, R.; Nafidi, A.; Gutierrez Sanchez, R.
2005-01-01
The principal objective of the present study is to examine the possibilities of using a Gompertz-type innovation diffusion process as a stochastic growth model of natural-gas consumption in Spain, and to compare our results with those obtained, on the one hand, by stochastic logistic innovation modelling and, on the other, by using a stochastic lognormal growth model based on a non-innovation diffusion process. Such a comparison is carried out taking into account the macroeconomic characteristics and natural-gas consumption patterns in Spain, both of which reflect the current expansive situation characterizing the Spanish economy. From the technical standpoint a contribution is also made to the theory of the stochastic Gompertz Innovation diffusion process (SGIDP), as applied to the case in question. (author)
Kyte, W.S.
1980-01-01
The graphite moderator bricks which make up the moderator of an advanced gas-cooled nuclear reactor (AGR) are of many different and complex shapes. Many physico-chemical processes that occur within these porous bricks include a diffusional step and thus to model these processes it is necessary to solve the diffusion equation (with chemical reaction) in a porous medium of complex shape. A finite element technique is applied to calculating the rate at which nitrogen diffuses into and out of the porous moderator graphite during operation of a shutdown procedure for an AGR. However, the finite element method suffers from several disadvantages that undermine its general usefulness for calculating rates of diffusion in AGR moderator cores. A model which overcomes some of these disadvantages is presented (the equivalent cylinder model) and it is shown that this gives good results for a variety of different boundary and initial conditions
A new model of tail diffusion of phosphorus and boron in silicon
Morehead, F.F.; Lever, R.F.
1986-01-01
It is well known that high surface concentration phosphorus diffusion leads to deeply penetrating tails in its concentration profile. At 700 0 C the tail diffusivity exceeds that of low concentration phosphorus by a factor of a thousand. Less spectacular, but very significant tailing also affects boron, making the conventional models contained in commonly available process simulation programs quite inaccurate for boron diffusions with high surface concentrations. The authors show that the observed tailing can be accounted for by a model whose central assumption is the local equality of dopant and oppositely directed defect fluxes. As predicted by the model, the effect is greatest for normal processing at low temperatures for high surface concentrations. It is minimal for the high temperatures of rapid thermal annealing and unrelated to transient effects
Grey Box Modelling of Flow in Sewer Systems with State Dependent Diffusion
Breinholt, Anders; Thordarson, Fannar Örn; Møller, Jan Kloppenborg
2011-01-01
. It is shown that an additive diffusion noise term description leads to a violation of the physical constraints of the system, whereas a state dependent diffusion noise avoids this problem and should be favoured. It is also shown that a logarithmic transformation of the flow measurements secures positive lower...... flow prediction limits, because the observation noise is proportionally scaled with the modelled output. Finally it is concluded that a state proportional diffusion term best and adequately describes the one-step flow prediction uncertainty, and a proper description of the system noise is important......Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both...
Modelling the effect of diffusion into the rock matrix on radionuclide migration
Lever, D.A.; Bradbury, M.H.; Hemingway, S.J.
1983-01-01
Diffusion into the rock matrix is potentially an important retardation mechanism for nuclides leached from an underground radioactive waste repository in a fractured hard rock. Models of this diffusion process are discussed and incorporated into three-dimensional radionuclide migration models. Simple solutions to these models are derived for two regions: the region near to the repository where the nuclide is diffusing into effectively infinite rock, and that much further downstream where the concentrations in the rock and fractures are almost in equilibrium. These solutions are used to evaluate the possible impact on migration. It is shown that retardation factors in excess of 100 and reductions in the peak concentration at a given point on the flow path by three or four orders of magnitude are possibe for non-sorbed ions, which would otherwise be carried by the flow and not retarded at all. (author)
无
2001-01-01
Natural gas diffusion through the cap rock is mainly by means ofdissolving in water, so its concentration can be replaced by solubility, which varies with temperature, pressure and salinity in strata. Under certain geological conditions the maximal solubility is definite, so the diffusion com-putation can be handled approximately by stable state equation. Furthermore, on the basis of the restoration of the paleo-buried history, the diffusion is calculated with the dynamic method, and the result is very close to the real diffusion value in the geological history.
American Society for Testing and Materials. Philadelphia
2008-01-01
1.1 This test method provides procedures for measuring the leach rates of elements from a solidified matrix material, determining if the releases are controlled by mass diffusion, computing values of diffusion constants based on models, and verifying projected long-term diffusive releases. This test method is applicable to any material that does not degrade or deform during the test. 1.1.1 If mass diffusion is the dominant step in the leaching mechanism, then the results of this test can be used to calculate diffusion coefficients using mathematical diffusion models. A computer program developed for that purpose is available as a companion to this test method (Note 1). 1.1.2 It should be verified that leaching is controlled by diffusion by a means other than analysis of the leach test solution data. Analysis of concentration profiles of species of interest near the surface of the solid waste form after the test is recommended for this purpose. 1.1.3 Potential effects of partitioning on the test results can...
Advanced diffusion model in compacted bentonite based on modified Poisson-Boltzmann equations
Yotsuji, K.; Tachi, Y.; Nishimaki, Y.
2012-01-01
Document available in extended abstract form only. Diffusion and sorption of radionuclides in compacted bentonite are the key processes in the safe geological disposal of radioactive waste. JAEA has developed the integrated sorption and diffusion (ISD) model for compacted bentonite by coupling the pore water chemistry, sorption and diffusion processes in consistent way. The diffusion model accounts consistently for cation excess and anion exclusion in narrow pores in compacted bentonite by the electric double layer (EDL) theory. The firstly developed ISD model could predict the diffusivity of the monovalent cation/anion in compacted bentonite as a function of dry density. This ISD model was modified by considering the visco-electric effect, and applied for diffusion data for various radionuclides measured under wide range of conditions (salinity, density, etc.). This modified ISD model can give better quantitative agreement with diffusion data for monovalent cation/anion, however, the model predictions still disagree with experimental data for multivalent cation and complex species. In this study we extract the additional key factors influencing diffusion model in narrow charged pores, and the effects of these factors were investigated to reach a better understanding of diffusion processes in compacted bentonite. We investigated here the dielectric saturation effect and the excluded volume effect into the present ISD model and numerically solved these modified Poisson-Boltzmann equations. In the vicinity of the negatively charged clay surfaces, it is necessary to evaluate concentration distribution of electrolytes considering the dielectric saturation effects. The Poisson-Boltzmann (P-B) equation coupled with the dielectric saturation effects was solved numerically by using Runge-Kutta and Shooting methods. Figure 1(a) shows the concentration distributions of Na + as numerical solutions of the modified and original P-B equations for 0.01 M pore water, 800 kg m -3
Computing diffuse fraction of global horizontal solar radiation: A model comparison.
Dervishi, Sokol; Mahdavi, Ardeshir
2012-06-01
For simulation-based prediction of buildings' energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models' performance.
Fazeli, Mohammadreza; Hinebaugh, James; Bazylak, Aimy
2016-01-01
Highlights: • Pore network model for modeling PEMFC MPL-coated GDL effective diffusivity. • Bilayered GDL (substrate and MPL) is modeled with a hybrid network of block MPL elements combined with discrete substrate pores. • Diffusivities of MPL-coated GDLs agree with analytical solutions. - Abstract: In this work, a voxel-based methodology is introduced for the hybridization of a pore network with interspersed nano-porous material elements allowing pore network based oxygen diffusivity calculations in a 3D image of a polymer electrolyte membrane (PEM) fuel cell gas diffusion layer (GDL) with an embedded microporous layer (MPL). The composite GDL is modeled by combining a hybrid network of block MPL elements with prescribed bulk material properties and a topologically equivalent network of larger discrete pores and throats that are directly derived from the 3D image of the GDL substrate. This hybrid network was incorporated into a pore network model, and effective diffusivity predictions of GDL materials with MPL coatings were obtained. Stochastically generated numerical models of carbon paper substrates with and without MPLs were used, and the pore space was directly extracted from this realistic geometry as the input for the pore network model. The effective diffusion coefficient of MPL-coated GDL materials was predicted from 3D images in a pore network modeling environment without resolving the nano-scale structure of the MPL. This method is particularly useful due to the disparate length scales that are involved when attempting to capture pore-scale transport in the GDL. Validation was performed by comparing our predicted diffusivity values to analytical predictions, and excellent agreement was observed. Upon conducting a mesh sensitivity study, it was determined that an MPL element size of 7 μm provided sufficiently high resolution for accurately describing the MPL nano-structure.
Kwong, S.; Jivkov, A.P.
2013-01-01
Deep geologic disposal of high activity and long-lived radioactive waste is being actively considered and pursued in many countries, where low permeability geological formations are used to provide long term waste contaminant with minimum impact to the environment and risk to the biosphere. A multi-barrier approach that makes use of both engineered and natural barriers (i.e. geological formations) is often used to further enhance the containment performance of the repository. As the deep repository system subjects to a variety of thermo-hydro-chemo-mechanical (THCM) effects over its long 'operational' lifespan (e.g. 0.1 to 1.0 million years, the integrity of the barrier system will decrease over time (e.g. fracturing in rock or clay)). This is broadly referred as media degradation in the present study. This modelling study examines the effects of media degradation on diffusion dominant solute transport in fractured media that are typical of deep geological environment. In particular, reactive solute transport through fractured media is studied using a 2-D model, that considers advection and diffusion, to explore the coupled effects of kinetic and equilibrium chemical processes, while the effects of degradation is studied using a pore network model that considers the media diffusivity and network changes. Model results are presented to demonstrate the use of a 3D pore-network model, using a novel architecture, to calculate macroscopic properties of the medium such as diffusivity, subject to pore space changes as the media degrade. Results from a reactive transport model of a representative geological waste disposal package are also presented to demonstrate the effect of media property change on the solute migration behaviour, illustrating the complex interplay between kinetic biogeochemical processes and diffusion dominant transport. The initial modelling results demonstrate the feasibility of a coupled modelling approach (using pore-network model and reactive
Modeling photovoltaic diffusion: an analysis of geospatial datasets
Davidson, Carolyn; Drury, Easan; Lopez, Anthony; Elmore, Ryan; Margolis, Robert
2014-01-01
This study combines address-level residential photovoltaic (PV) adoption trends in California with several types of geospatial information—population demographics, housing characteristics, foreclosure rates, solar irradiance, vehicle ownership preferences, and others—to identify which subsets of geospatial information are the best predictors of historical PV adoption. Number of rooms, heating source and house age were key variables that had not been previously explored in the literature, but are consistent with the expected profile of a PV adopter. The strong relationship provided by foreclosure indicators and mortgage status have less of an intuitive connection to PV adoption, but may be highly correlated with characteristics inherent in PV adopters. Next, we explore how these predictive factors and model performance varies between different Investor Owned Utility (IOU) regions in California, and at different spatial scales. Results suggest that models trained with small subsets of geospatial information (five to eight variables) may provide similar explanatory power as models using hundreds of geospatial variables. Further, the predictive performance of models generally decreases at higher resolution, i.e., below ZIP code level since several geospatial variables with coarse native resolution become less useful for representing high resolution variations in PV adoption trends. However, for California we find that model performance improves if parameters are trained at the regional IOU level rather than the state-wide level. We also find that models trained within one IOU region are generally representative for other IOU regions in CA, suggesting that a model trained with data from one state may be applicable in another state. (letter)
Olague, N.E.; Price, L.L.
1991-01-01
The greater confinement disposal (GCD) project is an ongoing project examining the disposal of orphan wastes in Area 5 of the Nevada Test Site. One of the major tasks for the project is performance assessment. With regard to performance assessment, a preliminary conceptual model for ground-water flow and radionuclide transport to the accessible environment at the GCD facilities has been developed. One of the transport pathways that has been postulated is diffusion of radionuclides in the liquid phase upward to the land surface. This pathway is not usually considered in a performance assessment, but is included in the GCD conceptual model because of relatively low recharge estimates at the GCD site and the proximity of the waste to the land surface. These low recharge estimates indicate that convective flow downward to the water table may be negligible; thus, diffusion upward to the land surface may then become important. As part of a preliminary performance assessment which considered a basecase scenario and a climate-change scenario, a first approximation for modeling the liquid-diffusion pathway was formulated. The model includes an analytical solution that incorporates both diffusion and radioactivity decay. Overall, these results indicate that, despite the configuration of the GCD facilities that establishes the need for considering the liquid-diffusion pathway, the GCD disposal concept appears to be a technically feasible method for disposing of orphan wastes. Future analyses will consist of investigating the underlying assumptions of the liquid-diffusion model, refining the model is necessary, and reducing uncertainty in the input parameters. 11 refs., 6 figs
Nagamatsu, Akira; Watanabe, Chihiro; Shum, Kwok L.
2006-01-01
This paper first proposes a modeling framework to study diffusion of innovations which exhibit strong interaction with the institution systems across which they diffuse. A unique character of such generic innovation is that specific applications are continually developed during its diffusion. This self-propagation in continual applications generation, which is dependent upon the cumulative installed base of the technological innovation, can be modeled to lead to a dynamic changing carrying capacity in an otherwise simple logistic diffusion curve. The cumulative installed base is dependent upon the price of technology and the cost learning dynamics. This paper utilizes a multi-factors learning function to represent such learning dynamics. Empirical estimates from our model are compared with those from other logistics curve formulations and are shown to better fit the annual PV production data during the past quarter century in the case of Japan. The very fact that the potential of this class of innovation can be leveraged only if it interacts closely with the institution highlights the importance of institutional determinants of adoption and diffusion of such innovations like PV. We therefore attempt to put forward an institutional framework, based on viewing PV as a technology platform, to consider PV diffusion beyond mathematical and empirical modeling. Some future research directions are also proposed. (author)
Diffusion models for corona formation in metagabbros from the Western Grenville Province, Canada
Grant, Shona M.
1988-01-01
Metagabbro bodies in SW Grenville Province display a variety of disequilibrium corona textures between spinel-clouded plagioclase and primary olivine or opaque oxide. Textural evidence favours a single-stage, subsolidus origin for the olivine coronas and diffusive mass transfer is believed to have been the rate-controlling process. Irreversible thermodynamics have been used to model two different garnet symplectite-bearing corona sequences in terms of steady state diffusion. In the models the flux of each component is related to the chemical potential gradients of all diffusing species by the Onsager or L-coefficients for diffusion. These coefficients are analogous to experimentally determined diffusion coefficients ( d), but relate the flux of components to chemical potential rather than concentration gradients. The major constraint on the relative values of Onsager coefficients comes from the observed mole fraction, X, of garnet in the symplectites; in (amph-gt) symplectites X {Gt/Sym}˜0.80, compared with ˜0.75 in (cpx-gt) symplectites. Several models using simple oxide components, and two different modifications of the reactant plagioclase composition, give the following qualitative results: the very low mobility of aluminium appears to control the rate of corona formation. Mg and Fe have similar mobility, and Mg can be up to 6 8 times more mobile than sodium. Determination of calcium mobility is problematical because of a proposed interaction with cross-coefficient terms reflecting “uphill” Ca-diffusion, i.e., calcium diffusing up its own chemical potential gradient. If these terms are not introduced, it is difficult to generate the required proportions of garnet in the symplectite. However, at moderate values of the cross-coefficient ratios, Mg can be up to 4 6 times more mobile than calcium ( L MgMg/LCaCaCaCa/LAlAl>3).
Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric
2003-03-01
We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.
Fitting the CDO correlation skew: a tractable structural jump-diffusion model
Willemann, Søren
2007-01-01
We extend a well-known structural jump-diffusion model for credit risk to handle both correlations through diffusion of asset values and common jumps in asset value. Through a simplifying assumption on the default timing and efficient numerical techniques, we develop a semi-analytic framework...... allowing for instantaneous calibration to heterogeneous CDS curves and fast computation of CDO tranche spreads. We calibrate the model to CDX and iTraxx data from February 2007 and achieve a satisfactory fit. To price the senior tranches for both indices, we require a risk-neutral probability of a market...
Lumb, Matthew P. [The George Washington University, 2121 I Street NW, Washington, DC 20037 (United States); Naval Research Laboratory, Washington, DC 20375 (United States); Steiner, Myles A.; Geisz, John F. [National Renewable Energy Laboratory, Golden, Colorado 80401 (United States); Walters, Robert J. [Naval Research Laboratory, Washington, DC 20375 (United States)
2014-11-21
The analytical drift-diffusion formalism is able to accurately simulate a wide range of solar cell architectures and was recently extended to include those with back surface reflectors. However, as solar cells approach the limits of material quality, photon recycling effects become increasingly important in predicting the behavior of these cells. In particular, the minority carrier diffusion length is significantly affected by the photon recycling, with consequences for the solar cell performance. In this paper, we outline an approach to account for photon recycling in the analytical Hovel model and compare analytical model predictions to GaAs-based experimental devices operating close to the fundamental efficiency limit.
Continuous-time random-walk model for anomalous diffusion in expanding media
Le Vot, F.; Abad, E.; Yuste, S. B.
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Continuous-time random-walk model for anomalous diffusion in expanding media.
Le Vot, F; Abad, E; Yuste, S B
2017-09-01
Expanding media are typical in many different fields, e.g., in biology and cosmology. In general, a medium expansion (contraction) brings about dramatic changes in the behavior of diffusive transport properties such as the set of positional moments and the Green's function. Here, we focus on the characterization of such effects when the diffusion process is described by the continuous-time random-walk (CTRW) model. As is well known, when the medium is static this model yields anomalous diffusion for a proper choice of the probability density function (pdf) for the jump length and the waiting time, but the behavior may change drastically if a medium expansion is superimposed on the intrinsic random motion of the diffusing particle. For the case where the jump length and the waiting time pdfs are long-tailed, we derive a general bifractional diffusion equation which reduces to a normal diffusion equation in the appropriate limit. We then study some particular cases of interest, including Lévy flights and subdiffusive CTRWs. In the former case, we find an analytical exact solution for the Green's function (propagator). When the expansion is sufficiently fast, the contribution of the diffusive transport becomes irrelevant at long times and the propagator tends to a stationary profile in the comoving reference frame. In contrast, for a contracting medium a competition between the spreading effect of diffusion and the concentrating effect of contraction arises. In the specific case of a subdiffusive CTRW in an exponentially contracting medium, the latter effect prevails for sufficiently long times, and all the particles are eventually localized at a single point in physical space. This "big crunch" effect, totally absent in the case of normal diffusion, stems from inefficient particle spreading due to subdiffusion. We also derive a hierarchy of differential equations for the moments of the transport process described by the subdiffusive CTRW model in an expanding medium
Social Content Recommendation Based on Spatial-Temporal Aware Diffusion Modeling in Social Networks
Farman Ullah
2016-09-01
Full Text Available User interactions in online social networks (OSNs enable the spread of information and enhance the information dissemination process, but at the same time they exacerbate the information overload problem. In this paper, we propose a social content recommendation method based on spatial-temporal aware controlled information diffusion modeling in OSNs. Users interact more frequently when they are close to each other geographically, have similar behaviors, and fall into similar demographic categories. Considering these facts, we propose multicriteria-based social ties relationship and temporal-aware probabilistic information diffusion modeling for controlled information spread maximization in OSNs. The proposed social ties relationship modeling takes into account user spatial information, content trust, opinion similarity, and demographics. We suggest a ranking algorithm that considers the user ties strength with friends and friends-of-friends to rank users in OSNs and select highly influential injection nodes. These nodes are able to improve social content recommendations, minimize information diffusion time, and maximize information spread. Furthermore, the proposed temporal-aware probabilistic diffusion process categorizes the nodes and diffuses the recommended content to only those users who are highly influential and can enhance information dissemination. The experimental results show the effectiveness of the proposed scheme.
Yao, Yi; Berkowitz, Max L., E-mail: maxb@unc.edu, E-mail: ykanai@unc.edu; Kanai, Yosuke, E-mail: maxb@unc.edu, E-mail: ykanai@unc.edu [Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599 (United States)
2015-12-28
The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na{sup +} and K{sup +} ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.
Parker, L. N.; Zank, G. P.
2013-12-01
Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).
Chikhraj, E.V.; Tazhibaeva, I.L.; Shestakov, V.P.; Romanenko, O.G.; Klepikov, A.Kh.
1996-01-01
The programs for calculation of one-dimensional hydrogen distribution in diffusion media with traps are proposed. The programs have been described by the differential equations in partial derivatives, taking into account presence of convertible chemical reaction of the first order (model by Hurst-Gauss), presence of convertible chemical reaction of the second order (model by MacNabb and Forster) or presence of two different interchanging diffusion channels with traps under boundary conditions of first, second and third kinds. Programs allows to calculate and to show dynamic distribution and its flow in diffusion media and traps along the sample (both uniform and consisting of several different layers, distinguished by media structure and phase composition) in experiment on hydrogen permeability and thermodesorption. Conditions of flow continuity takes place on the borders of section layers. Code for resolving of inversive problem - extraction of diffusion parameters from an experimental curve of a gas permeation flow for specified above tree models of diffusion is developed also. The programs a written in Pascal in variants for DOS and for Windows-95. The programs could be applied for the analysis of gas release results being obtained from the structural materials samples of nuclear-power installation. 6 refs
Seo, Nieun; Chung, Yong Eun; Park, Yung Nyun; Kim, Eunju; Hwang, Jinwoo; Kim, Myeong-Jin
2018-07-01
To compare the ability of diffusion-weighted imaging (DWI) parameters acquired from three different models for the diagnosis of hepatic fibrosis (HF). Ninety-five patients underwent DWI using nine b values at 3 T magnetic resonance. The hepatic apparent diffusion coefficient (ADC) from a mono-exponential model, the true diffusion coefficient (D t ), pseudo-diffusion coefficient (D p ) and perfusion fraction (f) from a biexponential model, and the distributed diffusion coefficient (DDC) and intravoxel heterogeneity index (α) from a stretched exponential model were compared with the pathological HF stage. For the stretched exponential model, parameters were also obtained using a dataset of six b values (DDC # , α # ). The diagnostic performances of the parameters for HF staging were evaluated with Obuchowski measures and receiver operating characteristics (ROC) analysis. The measurement variability of DWI parameters was evaluated using the coefficient of variation (CoV). Diagnostic accuracy for HF staging was highest for DDC # (Obuchowski measures, 0.770 ± 0.03), and it was significantly higher than that of ADC (0.597 ± 0.05, p bi-exponential DWI model • Acquisition of six b values is sufficient to obtain accurate DDC and α.
Zhu, Yanjie; Peng, Xi; Wu, Yin; Wu, Ed X; Ying, Leslie; Liu, Xin; Zheng, Hairong; Liang, Dong
2017-02-01
To develop a new model-based method with spatial and parametric constraints (MB-SPC) aimed at accelerating diffusion tensor imaging (DTI) by directly estimating the diffusion tensor from highly undersampled k-space data. The MB-SPC method effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images using an L1-L2 norm and the smoothness of the diffusion tensor using a total variation seminorm. The undersampled k-space datasets were obtained from fully sampled DTI datasets of a simulated phantom and an ex-vivo experimental rat heart with acceleration factors ranging from 2 to 4. The diffusion tensor was directly reconstructed by solving a minimization problem with a nonlinear conjugate gradient descent algorithm. The reconstruction performance was quantitatively assessed using the normalized root mean square error (nRMSE) of the DTI indices. The MB-SPC method achieves acceptable DTI measures at an acceleration factor up to 4. Experimental results demonstrate that the proposed method can estimate the diffusion tensor more accurately than most existing methods operating at higher net acceleration factors. The proposed method can significantly reduce artifact, particularly at higher acceleration factors or lower SNRs. This method can easily be adapted to MR relaxometry parameter mapping and is thus useful in the characterization of biological tissue such as nerves, muscle, and heart tissue. © 2016 American Association of Physicists in Medicine.
Assessing Quasi-Steady State in Evaporation of Sessile Drops by Diffusion Models
Martin, Cameron; Nguyen, Hoa; Kelly-Zion, Peter; Pursell, Chris
2017-11-01
The vapor distributions surrounding sessile drops of methanol are modeled as the solutions of the steady-state and transient diffusion equations using Matlab's PDE Toolbox. The goal is to determine how quickly the transient diffusive transport reaches its quasi-steady state as the droplet geometry is varied between a Weber's disc, a real droplet shape, and a spherical cap with matching thickness or contact angle. We assume that the only transport mechanism at work is diffusion. Quasi-steady state is defined using several metrics, such as differences between the transient and steady-state solutions, and change in the transient solution over time. Knowing the vapor distribution, the gradient is computed to evaluate the diffusive flux. The flux is integrated along the surface of a control volume surrounding the drop to obtain the net rate of diffusion out of the volume. Based on the differences between the transient and steady-state diffusive fluxes at the discrete points along the control-volume surface, the time to reach quasi-steady state evaporation is determined and is consistent with other proposed measurements. By varying the dimensions of the control volume, we can also assess what regimes have equivalent or different quasi-steady states for different droplet geometries. Petroleum Research Fund.
A Jump-Diffusion Model with Stochastic Volatility and Durations
Wei, Wei; Pelletier, Denis
jumps in two ways: as exogenous sampling intervals, and through the interaction with volatility. We adopt a bivariate Ornstein-Ulenbeck process to model intraday volatility and conditional duration. We develop a MCMC algorithm for the inference on irregularly spaced multivariate processes with jumps...
K correlations and facet models in diffuse scattering
Hoenders, B.J.; Jakeman, E.; Baltes, H.P.; Steinle, B.
1979-01-01
The angular intensity distribution of radiation scattered by a wide range of random media can be accounted for by assuming effective source amplitude correlations involving modified Bessel functions Kv. We investigate how such correlations can be derived from physical models of stochastic scattering
Oxygen diffusion in a network model of the myocardial microcirculation
Wieringa, P. A.; Stassen, H. G.; van Kan, J. J.; Spaan, J. A.
1993-01-01
Oxygen supply was studied in a three-dimensional capillary network model of the myocardial microcirculation. Capillary networks were generated using one common strategy to locate the capillary branchings and segments, arterioles and venules. Flow paths developed with different capillary flow
An agent-based model for diffusion of electric vehicles
Kangur, Ayla; Jager, Wander; Verbrugge, Rineke; Bockarjova, Marija
2017-01-01
The transition from fuel cars to electric cars is a large-scale process involving many interactions between consumers and other stakeholders over decades. To explore how policies may interact with consumer behavior over such a long time period, we developed an agent-based social simulation model. In
STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies
Hepburn Iain
2012-05-01
Full Text Available Abstract Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins, conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates
A Chemo-Mechanical Model of Diffusion in Reactive Systems
Kerstin Weinberg
2018-02-01
Full Text Available The functional properties of multi-component materials are often determined by a rearrangement of their different phases and by chemical reactions of their components. In this contribution, a material model is presented which enables computational simulations and structural optimization of solid multi-component systems. Typical Systems of this kind are anodes in batteries, reactive polymer blends and propellants. The physical processes which are assumed to contribute to the microstructural evolution are: (i particle exchange and mechanical deformation; (ii spinodal decomposition and phase coarsening; (iii chemical reactions between the components; and (iv energetic forces associated with the elastic field of the solid. To illustrate the capability of the deduced coupled field model, three-dimensional Non-Uniform Rational Basis Spline (NURBS based finite element simulations of such multi-component structures are presented.
A Jump-Diffusion Model for Option Pricing
S. G. Kou
2002-01-01
Brownian motion and normal distribution have been widely used in the Black--Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called "volatility smile" in option markets. To incorporate both of them and to strike a balance between ...
MODELING OF SUPERCRITICAL FLUID EXTRACTION KINETIC OF FLAXSEED OIL BY DIFFUSION CONTROL METHOD
Emir Zafer HOŞGÜN
2013-06-01
Full Text Available In this study, Flaxseed oil was extracted by Supercritical Carbondioxide Extraction, and extractionkinetics was modelled using diffusion controlled method.The effect of process parameters, such as pressure (20, 35, 55 MPa, temperature (323 and 343 K, and CO2 flow rate (1 and 3 L CO2 /min on the extraction yield and effective diffusivity (De was investigated. The effective diffusion coefficient varied between 2.4 x10-12 and 10.8 x10-12 m2s-1 for the entire range of experiments and increased with the pressure and flow rate. The model fitted well theexperimental data (ADD varied between 2.35 and 7.48%.
A grain-boundary diffusion model of dynamic grain growth during superplastic deformation
Kim, Byung-Nam; Hiraga, Keijiro; Sakka, Yoshio; Ahn, Byung-Wook
1999-01-01
Dynamic grain growth during superplastic deformation is modelled on the basis of a grain-boundary diffusion mechanism. On the grain boundary where a static and a dynamic potential difference coexist, matter transport along the boundary is assumed to contribute to dynamic grain growth through depositing the matter on the grain surface located opposite to the direction of grain-boundary migration. The amount of the diffusive matter during deformation is calculated for an aggregate of spherical grains and is converted to the increment of mean boundary migration velocity. The obtained relationship between the strain rate and the dynamic grain growth rate is shown to be independent of deformation mechanisms, provided that the grain growth is controlled by grain-boundary diffusion. The strain dependence, strain-rate dependence and temperature dependence of grain growth predicted from this model are consistent with those observed in superplastic ZrO 2 -dispersed Al 2 O 3
The Illumination Model of the Valley Based on the Diffuse Reflect of Forest
He Guoliang
2016-01-01
Full Text Available In this paper, models are build to evaluate the impact of the forest on the valley’s illumination. Based on the assumes that all the light reach the ground comes from the diffuse reflection which comes from the sun directly and from the diffuse reflection of other points, One model is build to consider the impact of time and latitude on the direction of the sunlight. So we can get the direction of the sunlight at different time and latitude through the model. Besides, this paper develops a illumination model to evaluate the intensity of illumination of the ground. Combining the models above, this paper get a complete model which can not only evaluate the overall light intensity of the valley but also convert the light intensity to the intensity of illumination. Simulation of the intensity illumination of some basic terrains and finally gives a comprehensive results which is practical and close to the common sense.
Kojic, M; Milosevic, M; Kojic, N; Kim, K; Ferrari, M; Ziemys, A
2014-02-01
Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an aga-rose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts.
Kojic, M.; Milosevic, M.; Kojic, N.; Kim, K.; Ferrari, M.; Ziemys, A.
2014-01-01
Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an aga-rose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts. PMID:24578582
Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.
Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan
2018-05-30
Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.
A diffusive model for halo width growth during vertical displacement events
Eidietis, N.W.; Humphreys, D.A.
2011-01-01
The electromagnetic loads produced by halo currents during vertical displacement events (VDEs) impose stringent requirements on the strength of ITER in-vessel components. A predictive understanding of halo current evolution is essential for ensuring the robust design of these components. A significant factor determining that evolution is the plasma resistance, which is a function of three quantities: the resistivities of the core and halo regions, and the halo region width. A diffusive model of halo width growth during VDEs has been developed, which provides one part of a physics basis for predictive halo current simulations. The diffusive model was motivated by DIII-D observations that VDEs with cold post-thermal quench plasma and a current decay time much faster than the vertical motion (type I VDE) possess much wider halo region widths than warmer plasma VDEs, where the current decay is much slower than the vertical motion (type II). A 2D finite element code is used to model the diffusion of toroidal halo current during selected type I and type II DIII-D VDEs. The model assumes a core plasma region within the last closed flux surface (LCFS) diffusing current into a halo plasma filling the vessel outside the LCFS. LCFS motion and plasma temperature are prescribed from experimental observations. The halo width evolution produced by this model compares favourably with experimental measurements of type I and type II toroidal halo current width evolution.
Application of Parameter Estimation for Diffusions and Mixture Models
Nolsøe, Kim
The first part of this thesis proposes a method to determine the preferred number of structures, their proportions and the corresponding geometrical shapes of an m-membered ring molecule. This is obtained by formulating a statistical model for the data and constructing an algorithm which samples...... with the posterior score function. From an application point of view this methology is easy to apply, since the optimal estimating function G(;Xt1 ; : : : ;Xtn ) is equal to the classical optimal estimating function, plus a correction term which takes into account the prior information. The methology is particularly...
An Application of Epidemiological Modeling to Information Diffusion
McCormack, Robert; Salter, William
Messages often spread within a population through unofficial - particularly web-based - media. Such ideas have been termed "memes." To impede the flow of terrorist messages and to promote counter messages within a population, intelligence analysts must understand how messages spread. We used statistical language processing technologies to operationalize "memes" as latent topics in electronic text and applied epidemiological techniques to describe and analyze patterns of message propagation. We developed our methods and applied them to English-language newspapers and blogs in the Arab world. We found that a relatively simple epidemiological model can reproduce some dynamics of observed empirical relationships.
Marbán, Gregorio; Ramírez-Montoya, Luis A; García, Héctor; Menéndez, J Ángel; Arenillas, Ana; Montes-Morán, Miguel A
2018-02-01
The adsorption of cytochrome c in water onto organic and carbon xerogels with narrow pore size distributions has been studied by carrying out transient and equilibrium batch adsorption experiments. It was found that equilibrium adsorption exhibits a quasi-Langmuirian behavior (a g coefficient in the Redlich-Peterson isotherms of over 0.95) involving the formation of a monolayer of cyt c with a depth of ∼4nm on the surface of all xerogels for a packing density of the protein inside the pores of 0.29gcm -3 . A load-dependent surface diffusion model (LDSDM) has been developed and numerically solved to fit the experimental kinetic adsorption curves. The results of the LDSDM show better fittings than the standard homogeneous surface diffusion model. The value of the external mass transfer coefficient obtained by numerical optimization confirms that the process is controlled by the intraparticle surface diffusion of cyt c. The surface diffusion coefficients decrease with increasing protein load down to zero for the maximum possible load. The decrease is steeper in the case of the xerogels with the smallest average pore diameter (∼15nm), the limit at which the zero-load diffusion coefficient of cyt c also begins to be negatively affected by interactions with the opposite wall of the pore. Copyright © 2017 Elsevier Inc. All rights reserved.
Study of the applicability of the diffusion model of bentonite buffer material (2)
Matsumoto, Kazuhiro; Fujita, Tomoo
2011-03-01
Bentonite buffer material is envisaged as a component of the engineered barrier system for high-level radioactive waste disposal. As a result of its swelling property, the buffer may extrude into the surrounding host rock through open fractures. If this persists for extremely long periods of time, the buffer extrusion could lead to a reduction of buffer density, which may in turn degrade the expected performance. In this report, verification of the solid phase diffusion theory of the past was performed and future problems were extracted based on expertise. Results obtained from the studies are summarized as follows; 1) Verification of solid phase diffusion theory: Comparison with the solid phase diffusion coefficient based on an swelling experiment and the theoretical value was performed. As a result of simulation, the theoretical diffusion velocity had slower than the experimental one. 2) Simulation of an extrusion experiment: As a result of performing the simulation of an extrusion experiment using the fitting line based on an experiment, it was well in agreement in comparison. 3) Expert review: The expert propel an application of advection-diffusion equation to the extrusion model. It is necessary to attain optimization of a model, repeating the simulation of element experiment and those results and performing it based on the result of this experiment and a review. (author)
Theoretical model estimation of guest diffusion in Metal-Organic Frameworks (MOFs)
Zheng, Bin
2015-08-11
Characterizing molecule diffusion in nanoporous matrices is critical to understanding the novel chemical and physical properties of metal-organic frameworks (MOFs). In this paper, we developed a theoretical model to fastly and accurately compute the diffusion rate of guest molecules in a zeolitic imidazolate framework-8 (ZIF-8). The ideal gas or equilibrium solution diffusion model was modified to contain the effect of periodical media via introducing the possibility of guests passing through the framework gate. The only input in our model is the energy barrier of guests passing through the MOF’s gate. Molecular dynamics (MD) methods were employed to gather the guest density profile, which then was used to deduce the energy barrier values. This produced reliable results that require a simulation time of 5 picoseconds, which is much shorter when using pure MD methods (in the billisecond scale) . Also, we used density functional theory (DFT) methods to obtain the energy profile of guests passing through gates, as this does not require specification of a force field for the MOF degrees of freedom. In the DFT calculation, we only considered one gate of MOFs each time; as this greatly reduced the computational cost. Based on the obtained energy barrier values we computed the diffusion rate of alkane and alcohol in ZIF-8 using our model, which was in good agreement with experimental test results and the calculation values from standard MD model. Our model shows the advantage of obtaining accurate diffusion rates for guests in MOFs for a lower computational cost and shorter calculation time. Thus, our analytic model calculation is especially attractive for high-throughput computational screening of the dynamic performance of guests in a framework.
An approximation method for diffusion based leaching models
Shukla, B.S.; Dignam, M.J.
1987-01-01
In connection with the fixation of nuclear waste in a glassy matrix equations have been derived for leaching models based on a uniform concentration gradient approximation, and hence a uniform flux, therefore requiring the use of only Fick's first law. In this paper we improve on the uniform flux approximation, developing and justifying the approach. The resulting set of equations are solved to a satisfactory approximation for a matrix dissolving at a constant rate in a finite volume of leachant to give analytical expressions for the time dependence of the thickness of the leached layer, the diffusional and dissolutional contribution to the flux, and the leachant composition. Families of curves are presented which cover the full range of all the physical parameters for this system. The same procedure can be readily extended to more complex systems. (author)
Oliphant, Andrew J.; Stoy, Paul C.
2018-03-01
Photosynthesis is more efficient under diffuse than direct beam photosynthetically active radiation (PAR) per unit PAR, but diffuse PAR is infrequently measured at research sites. We examine four commonly used semiempirical models (Erbs et al., 1982, https://doi.org/10.1016/0038-092X(82)90302-4; Gu et al., 1999, https://doi.org/10.1029/1999JD901068; Roderick, 1999, https://doi.org/10.1016/S0168-1923(99)00028-3; Weiss & Norman, 1985, https://doi.org/10.1016/0168-1923(85)90020-6) that partition PAR into diffuse and direct beam components based on the negative relationship between atmospheric transparency and scattering of PAR. Radiation observations at 58 sites (140 site years) from the La Thuille FLUXNET data set were used for model validation and coefficient testing. All four models did a reasonable job of predicting the diffuse fraction of PAR (ϕ) at the 30 min timescale, with site median r2 values ranging between 0.85 and 0.87, model efficiency coefficients (MECs) between 0.62 and 0.69, and regression slopes within 10% of unity. Model residuals were not strongly correlated with astronomical or standard meteorological variables. We conclude that the Roderick (1999, https://doi.org/10.1016/S0168-1923(99)00028-3) and Gu et al. (1999, https://doi.org/10.1029/1999JD901068) models performed better overall than the two older models. Using the basic form of these models, the data set was used to find both individual site and universal model coefficients that optimized predictive accuracy. A new universal form of the model is presented in section 5 that increased site median MEC to 0.73. Site-specific model coefficients increased median MEC further to 0.78, indicating usefulness of local/regional training of coefficients to capture the local distributions of aerosols and cloud types.
Developing a laser shockwave model for characterizing diffusion bonded interfaces
Lacy, Jeffrey M.; Smith, James A.; Rabin, Barry H.
2015-01-01
The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) with the goal of reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU in high-power research reactors. The new LEU fuel is a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to support the fuel qualification process, the Laser Shockwave Technique (LST) is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However, because the deposition of laser energy into the containment layer on a specimen's surface is intractably complex, the shock wave energy is inferred from the surface velocity measured on the backside of the fuel plate and the depth of the impression left on the surface by the high pressure plasma pulse created by the shock laser. To help quantify the stresses generated at the interfaces, a finite element method (FEM) model is being utilized. This paper will report on initial efforts to develop and validate the model by comparing numerical and experimental results for back surface velocities and front surface depressions in a single aluminum plate representative of the fuel cladding
Developing a laser shockwave model for characterizing diffusion bonded interfaces
Lacy, Jeffrey M., E-mail: Jeffrey.Lacy@inl.gov; Smith, James A., E-mail: Jeffrey.Lacy@inl.gov; Rabin, Barry H., E-mail: Jeffrey.Lacy@inl.gov [Idaho National Laboratory, Idaho Falls, ID (United States)
2015-03-31
The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) with the goal of reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU in high-power research reactors. The new LEU fuel is a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to support the fuel qualification process, the Laser Shockwave Technique (LST) is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However, because the deposition of laser energy into the containment layer on a specimen's surface is intractably complex, the shock wave energy is inferred from the surface velocity measured on the backside of the fuel plate and the depth of the impression left on the surface by the high pressure plasma pulse created by the shock laser. To help quantify the stresses generated at the interfaces, a finite element method (FEM) model is being utilized. This paper will report on initial efforts to develop and validate the model by comparing numerical and experimental results for back surface velocities and front surface depressions in a single aluminum plate representative of the fuel cladding.
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
Ranger, Jochen; Kuhn, Jörg-Tobias; Szardenings, Carsten
2017-05-01
Cognitive psychometric models embed cognitive process models into a latent trait framework in order to allow for individual differences. Due to their close relationship to the response process the models allow for profound conclusions about the test takers. However, before such a model can be used its fit has to be checked carefully. In this manuscript we give an overview over existing tests of model fit and show their relation to the generalized moment test of Newey (Econometrica, 53, 1985, 1047) and Tauchen (J. Econometrics, 30, 1985, 415). We also present a new test, the Hausman test of misspecification (Hausman, Econometrica, 46, 1978, 1251). The Hausman test consists of a comparison of two estimates of the same item parameters which should be similar if the model holds. The performance of the Hausman test is evaluated in a simulation study. In this study we illustrate its application to two popular models in cognitive psychometrics, the Q-diffusion model and the D-diffusion model (van der Maas, Molenaar, Maris, Kievit, & Boorsboom, Psychol Rev., 118, 2011, 339; Molenaar, Tuerlinckx, & van der Maas, J. Stat. Softw., 66, 2015, 1). We also compare the performance of the test to four alternative tests of model fit, namely the M 2 test (Molenaar et al., J. Stat. Softw., 66, 2015, 1), the moment test (Ranger et al., Br. J. Math. Stat. Psychol., 2016) and the test for binned time (Ranger & Kuhn, Psychol. Test. Asess. , 56, 2014b, 370). The simulation study indicates that the Hausman test is superior to the latter tests. The test closely adheres to the nominal Type I error rate and has higher power in most simulation conditions. © 2017 The British Psychological Society.
Interpretation of the quasi-elastic neutron scattering on PAA by rotational diffusion models
Bata, L.; Vizi, J.; Kugler, S.
1974-10-01
First the most important data determined by other methods for para azoxy anisolon (PAA) are collected. This molecule makes a rotational oscillational motion around the mean molecular direction. The details of this motion can be determined by inelastic neutron scattering. Quasielastic neutron scattering measurements were carried out without orienting magnetic field on a time-of-flight facility with neutron beam of 4.26 meV. For the interpretation of the results two models, the spherical rotation diffusion model and the circular random walk model are investigated. The comparison shows that the circular random walk model (with N=8 sites, d=4A diameter and K=10 10 s -1 rate constant) fits very well with the quasi-elastic neutron scattering, while the spherical rotational diffusion model seems to be incorrect. (Sz.N.Z.)
On diffusion processes with variable drift rates as models for decision making during learning
Eckhoff, P; Holmes, P; Law, C; Connolly, P M; Gold, J I
2008-01-01
We investigate Ornstein-Uhlenbeck and diffusion processes with variable drift rates as models of evidence accumulation in a visual discrimination task. We derive power-law and exponential drift-rate models and characterize how parameters of these models affect the psychometric function describing performance accuracy as a function of stimulus strength and viewing time. We fit the models to psychophysical data from monkeys learning the task to identify parameters that best capture performance as it improves with training. The most informative parameter was the overall drift rate describing the signal-to-noise ratio of the sensory evidence used to form the decision, which increased steadily with training. In contrast, secondary parameters describing the time course of the drift during motion viewing did not exhibit steady trends. The results indicate that relatively simple versions of the diffusion model can fit behavior over the course of training, thereby giving a quantitative account of learning effects on the underlying decision process
Catching gas with droplets : modelling and simulation of a diffusion-reaction process
Mourik, van S.; Gennip, van Y.; Peletier, M.A.; Hlod, A.V.; Shcherbakov, V.; Panhuis, in 't P.H.M.W.; Vondenhoff, E.; Eendebak, P.; Berg, van den J.B.; Fledderus, E.R.; Hofstad, van der R.W.; Jochemsz, E.; Molenaar, J.; Mussche, T.J.J.; Peletier, M.A.; Prokert, G.
2006-01-01
The packaging industry wants to produce a foil for food packaging purposes, which is transparent and lets very little oxygen pass. To accomplish this they add a scavenger material to the foil which reacts with the oxygen that diffuses through the foil. We model this process by a system of partial
Filtering and smoothing of stae vector for diffuse state space models
Koopman, S.J.; Durbin, J.
2003-01-01
This paper presents exact recursions for calculating the mean and mean square error matrix of the state vector given the observations for the multi-variate linear Gaussian state-space model in the case where the initial state vector is (partially) diffuse.
A diffusion decision model analysis of evidence variability in the lexical decision task
Tillman, Gabriel; Osth, Adam F.; van Ravenzwaaij, Don; Heathcote, Andrew
2017-01-01
The lexical-decision task is among the most commonly used paradigms in psycholinguistics. In both the signal-detection theory and Diffusion Decision Model (DDM; Ratcliff, Gomez, & McKoon, Psychological Review, 111, 159–182, 2004) frameworks, lexical-decisions are based on a continuous source of
Derivation and Numerical Approximation of the Quantum Drift Diffusion Model for Semiconductors
Ohnmar Nwe
2004-06-01
This paper is concerned with the study of the quantum drift diffusion equation for semiconductors. Derivation of the mathematical model, which describes the electeon flow through a semiconductor device due to the application of a voltage, is considered and studied in numerical point of view by using some methods
Numerical modeling of turbulent jet diffusion flames in the atmospheric surface layer
Hernández, J.; Crespo, A.; Duijm, N.J.
1995-01-01
The evolution of turbulent jet diffusion flames of natural gas in air is predicted using a finite-volume procedure for solving the flow equations. The model is three dimensional, elliptic and based on the conserved-scalar approach and the laminar flamelet concept. A laminar flamelet prescription for
Vagstad, N.; French, H. K.; Andersen, H. E.; Behrendt, H.; Grizzetti, B.; Groenendijk, P.; Lo Porto, A.; Reisser, H.; Siderius, C.; Stromquist, J.; Hejzlar, Josef; Deelstra, J.
2009-01-01
Roč. 11, č. 3 (2009), s. 594-601 ISSN 1464-0325 Grant - others:EC(XE) EVK1-CT-2001-00096 Institutional research plan: CEZ:AV0Z60170517 Keywords : catchment modelling * phosphorus and nitrogen losses * agriculture practice * diffuse sources Subject RIV: DJ - Water Pollution ; Quality Impact factor: 2.225, year: 2009
Hopf bifurcations in a fractional reaction–diffusion model for the ...
The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...
Exact solution of a model for diffusion particles and longitudinal dispersion in packed beds
Rasmuson, A.; Neretnieks, I.
1979-08-01
An analytical solution of a model for diffusion in particles and longitudinal despersion in porous media is derived. The solution is obtained by the method of Laplace transform. The result is expressed as an infinite integral of five deminsionless quanitities. The extension for a decaying species is given. (authors)
Weber, Adam
2010-03-05
A macroscopic-modeling methodology to account for the chemical and structural properties of fuel-cell diffusion media is developed. A previous model is updated to include for the first time the use of experimentally measured capillary pressure -- saturation relationships through the introduction of a Gaussian contact-angle distribution into the property equations. The updated model is used to simulate various limiting-case scenarios of water and gas transport in fuel-cell diffusion media. Analysis of these results demonstrate that interfacial conditions are more important than bulk transport in these layers, where the associated mass-transfer resistance is the result of higher capillary pressures at the boundaries and the steepness of the capillary pressure -- saturation relationship. The model is also used to examine the impact of a microporous layer, showing that it dominates the response of the overall diffusion medium. In addition, its primary mass-transfer-related effect is suggested to be limiting the water-injection sites into the more porous gas-diffusion layer.
Numerical method for a 2D drift diffusion model arising in strained n ...
Abstract. This paper reports the calculation of electron transport in metal oxide semiconductor field effects transistors (MOSFETs) with biaxially tensile strained silicon channel. The calculation is formulated based on two-dimensional drift diffusion model (DDM) including strain effects. The carrier mobility dependence on the ...
Numerical method for a 2D drift diffusion model arising in strained n ...
This paper reports the calculation of electron transport in metal oxide semiconductor field effects transistors (MOSFETs) with biaxially tensile strained silicon channel. The calculation is formulated based on two-dimensional drift diffusion model (DDM) including strain effects. The carrier mobility dependence on the lateral and ...
El-Khouly, Fatma E; van Vuurden, Dannis G; Stroink, Thom; Hulleman, Esther; Kaspers, Gertjan J L; Hendrikse, N Harry; Veldhuijzen van Zanten, Sophie E M
2017-01-01
Despite decades of clinical trials for diffuse intrinsic pontine glioma (DIPG), patient survival does not exceed 10% at two years post-diagnosis. Lack of benefit from systemic chemotherapy may be attributed to an intact bloodbrain barrier (BBB). We aim to develop a theoretical model including
A surface diffuse scattering model for the mobility of electrons in surface charge coupled devices
Ionescu, M.
1977-01-01
An analytical model for the mobility of electrons in surface charge coupled devices is studied on the basis of the results previously obtained, considering a surface diffuse scattering; the importance of the results obtained for a better understanding of the influence of the fringing field in surface charge coupled devices is discussed. (author)
Modeling Cryptosporidium spp. Oocyst Inactivation in Bubble-Diffuser Ozone Contactors
1998-07-01
requirements for Giardia lamblia (G. lamblia) and viruses under the Surface Water Treatment Rule (SWTR). Minimum CT requirements include relatively...parvum and C. muris ) oocysts in ozone bubble-diffuser contactors. The model is calibrated with semi-batch kinetic data, verified with pilot-scale
First Principles Diffusion Modeling Final Report CRADA No. TC-1540-98
delaRubia, T. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Foad, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Giles, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-10-19
The CRADA participants built on the capabilities LLNL had already developed for ab initio diffusion modeling, extending them to higher doping and damage levels, and applying them to improve the understanding of implant and annealing tradeoffs for technology-relevant conditions. The calculation results and some of the simulation capabilities developed here were transferred to Intel and Applied Materials.
Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model
Donnelly, Catherine, E-mail: C.Donnelly@hw.ac.uk [Heriot-Watt University, Department of Actuarial Mathematics and Statistics (United Kingdom)
2011-10-15
We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem.
Sufficient Stochastic Maximum Principle in a Regime-Switching Diffusion Model
Donnelly, Catherine
2011-01-01
We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be used to solve a mean-variance portfolio selection problem.
Method of moments approach to pricing double barrier contracts in polynomial jump-diffusion models
Eriksson, B.; Pistorius, M.
2011-01-01
Abstract: We present a method of moments approach to pricing double barrier contracts when the underlying is modelled by a polynomial jump-diffusion. By general principles the price is linked to certain infinite dimensional linear programming problems. Subsequently approximating these by finite
Bos, Charles S.
2008-01-01
When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing
3-D Spherical Convection Modeling Applied to Mercury: Dislocation Versus Diffusion Rheology
Robertson, S. D.; King, S. D.
2016-12-01
Mercury is the smallest among the terrestrial planets and, prior to NASA's MESSENGER mission was thought to be the least tectonically and volcanically active body. Gravity and moment of inertia from MESSENGER constrain Mercury to have a thin silicate mantle shell of approximately 400 km over a massive iron core. This mantle is thinner than previously thought and the smallest end-member in comparison with the other terrestrial planets. Although Mercury currently has a stagnant lid and the present day mantle is likely not convecting, a significant proportion of Mercury's surface features could have been derived from convection in the viscous mantle. Given Mercury's small size, the amount of volcanism and tectonic activity was a surprise. We investigate the effect of dislocation creep rheology in olivine on the dynamics of Mercury. At the pressures and temperatures of Mercury's mantle, laboratory creep studies indicate that olivine deforms by dislocation creep. Previous studies using diffusion creep rheology find that the thin mantle shell of Mercury quickly becomes diffusive and, this is difficult to reconcile with the surface observations. We use the three-dimensional spherical code, CitcomS, to compare numerical models with both dislocation and diffusion creep. We compare gravity, topography, and mantle temperature as a function of time from the models with constraints on the timing of volcanic and tectonic activity on Mercury. The results show that with the dislocation creep mechanism, there is potential for convective flow in the mantle over billions of years. In contrast, models with the diffusion creep mechanism start with a convecting mantle that transitions to global diffusive cooling within 500 Myrs. Diffusion creep rheology does not adequately produce a dynamic interior that is consistent with the historical volcanic and tectonic evolution of the planet. This research is the result of participation in GLADE, a nine-week summer REU program directed by Dave
Sparse estimation of model-based diffuse thermal dust emission
Irfan, Melis O.; Bobin, Jérôme
2018-03-01
Component separation for the Planck High Frequency Instrument (HFI) data is primarily concerned with the estimation of thermal dust emission, which requires the separation of thermal dust from the cosmic infrared background (CIB). For that purpose, current estimation methods rely on filtering techniques to decouple thermal dust emission from CIB anisotropies, which tend to yield a smooth, low-resolution, estimation of the dust emission. In this paper, we present a new parameter estimation method, premise: Parameter Recovery Exploiting Model Informed Sparse Estimates. This method exploits the sparse nature of thermal dust emission to calculate all-sky maps of thermal dust temperature, spectral index, and optical depth at 353 GHz. premise is evaluated and validated on full-sky simulated data. We find the percentage difference between the premise results and the true values to be 2.8, 5.7, and 7.2 per cent at the 1σ level across the full sky for thermal dust temperature, spectral index, and optical depth at 353 GHz, respectively. A comparison between premise and a GNILC-like method over selected regions of our sky simulation reveals that both methods perform comparably within high signal-to-noise regions. However, outside of the Galactic plane, premise is seen to outperform the GNILC-like method with increasing success as the signal-to-noise ratio worsens.
The mirrors model: macroscopic diffusion without noise or chaos
Chiffaudel, Yann; Lefevere, Raphaël
2016-01-01
Before stating our main result, we first clarify through classical examples the status of the laws of macroscopic physics as laws of large numbers. We next consider the mirrors model in a finite d-dimensional domain and connected to particles reservoirs at fixed chemical potentials. The dynamics is purely deterministic and non-ergodic but takes place in a random environment. We study the macroscopic current of particles in the stationary regime. We show first that when the size of the system goes to infinity, the behaviour of the stationary current of particles is governed by the proportion of orbits crossing the system. This allows us to formulate a necessary and sufficient condition on the distribution of the set of orbits that ensures the validity of Fick’s law. Using this approach, we show that Fick’s law relating the stationary macroscopic current of particles to the concentration difference holds in three dimensions and above. The negative correlations between crossing orbits play a key role in the argument. (letter)
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross, atherogenesis is viewed as an inflammatory spiral with a positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved, giving conditions on system parameters guaranteeing stability of the health state, and a general framework is developed for constructing perturbations from a healthy state that exhibit blow-up, which are interpreted as corresponding to disease initiation. The analysis reveals key features that arterial geometry, antioxidant levels, and the source of inflammatory components (through coupled third-kind boundary conditions or through body sources) play in disease initiation. © 2010 Society for Industrial and Applied Mathematics.
Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model
Zhao, Hongyong; Zhu, Linhe
2016-06-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.
An axisymmetric non-hydrostatic model for double-diffusive water systems
Hilgersom, Koen; Zijlema, Marcel; van de Giesen, Nick
2018-02-01
The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier-Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.
Lei, Mingfeng; Lin, Dayong; Liu, Jianwen; Shi, Chenghua; Ma, Jianjun; Yang, Weichao; Yu, Xiaoniu
2018-03-01
For the purpose of investigating lining concrete durability, this study derives a modified chloride diffusion model for concrete based on the odd continuation of boundary conditions and Fourier transform. In order to achieve this, the linear stress distribution on a sectional structure is considered, detailed procedures and methods are presented for model verification and parametric analysis. Simulation results show that the chloride diffusion model can reflect the effects of linear stress distribution of the sectional structure on the chloride diffusivity with reliable accuracy. Along with the natural environmental characteristics of practical engineering structures, reference value ranges of model parameters are provided. Furthermore, a chloride diffusion model is extended for the consideration of multi-factor coupling of linear stress distribution, chloride concentration and diffusion time. Comparison between model simulation and typical current research results shows that the presented model can produce better considerations with a greater universality.
Mathematical modelling of pasta dough dynamic viscosity, thermal conductivity and diffusivity
Andrei Ionuţ SIMION
2015-08-01
Full Text Available This work aimed to study the mathematical variation of three main thermodynamic properties (dynamic viscosity, thermal conductivity and thermal diffusivity of pasta dough obtained by mixing wheat semolina and water with dough humidity and deformation speed (for dynamic viscosity, respectively with dough humidity and temperature (for thermal diffusivity and conductivity. The realized regression analysis of existing graphical data led to the development of mathematical models with a high degree of accuracy. The employed statistical tests (least squares, relative error and analysis of variance revealed that the obtained equations are able to describe and predict the tendency of the dough thermodynamic properties.
Modeling of Ni Diffusion Induced Austenite Formation in Ferritic Stainless Steel Interconnects
Chen, Ming; Alimadadi, Hossein; Molin, Sebastian
2017-01-01
Ferritic stainless steel interconnect plates are widely used in planar solid oxide fuel cell and electrolysis cell stacks. During stack production and operation, nickel from the Ni/yttria stabilized zirconia fuel electrode or from the Ni contact component layer diffuses into the interconnect plate......, causing transformation of the ferritic phase into an austenitic phase in the interface region. This is accompanied with changes in volume, and in mechanical and corrosion properties of the interconnect plates. In this work, kinetic modeling of the inter-diffusion between Ni and FeCr based ferritic...
Modeling of Ni Diffusion Induced Austenite Formation in Ferritic Stainless Steel Interconnects
Chen, Ming; Molin, Sebastian; Zhang, L.
2015-01-01
Ferritic stainless steel interconnect plates are widely used in planar solid oxide fuel cell (SOFC) or electrolysis cell (SOEC) stacks. During stack production and operation, nickel from the Ni/YSZ fuel electrode or from the Ni contact component diffuses into the IC plate, causing transformation...... of the ferritic phase into an austenitic phase in the interface region. This is accompanied with changes in volume and in mechanical and corrosion properties of the IC plates. In this work, kinetic modeling of the inter-diffusion between Ni and FeCr based ferritic stainless steel was conducted, using the CALPHAD...
Traveling waves in a diffusive predator-prey model with holling type-III functional response
Li Wantong; Wu Shiliang
2008-01-01
We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-III functional response. The analysis is in the three-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator-prey system in the traveling wave variable. The methods used to prove the results are the shooting argument, invariant manifold theory and the Hopf bifurcation theorem
A diffusive ink transport model for lipid dip-pen nanolithography
Urtizberea, A.; Hirtz, M.
2015-09-01
Despite diverse applications, phospholipid membrane stacks generated by dip-pen nanolithography (DPN) still lack a thorough and systematic characterization that elucidates the whole ink transport process from writing to surface spreading, with the aim of better controlling the resulting feature size and resolution. We report a quantitative analysis and modeling of the dependence of lipid DPN features (area, height and volume) on dwell time and relative humidity. The ink flow rate increases with humidity in agreement with meniscus size growth, determining the overall feature size. The observed time dependence indicates the existence of a balance between surface spreading and the ink flow rate that promotes differences in concentration at the meniscus/substrate interface. Feature shape is controlled by the substrate surface energy. The results are analyzed within a modified model for the ink transport of diffusive inks. At any humidity the dependence of the area spread on the dwell time shows two diffusion regimes: at short dwell times growth is controlled by meniscus diffusion while at long dwell times surface diffusion governs the process. The critical point for the switch of regime depends on the humidity.Despite diverse applications, phospholipid membrane stacks generated by dip-pen nanolithography (DPN) still lack a thorough and systematic characterization that elucidates the whole ink transport process from writing to surface spreading, with the aim of better controlling the resulting feature size and resolution. We report a quantitative analysis and modeling of the dependence of lipid DPN features (area, height and volume) on dwell time and relative humidity. The ink flow rate increases with humidity in agreement with meniscus size growth, determining the overall feature size. The observed time dependence indicates the existence of a balance between surface spreading and the ink flow rate that promotes differences in concentration at the meniscus
The Water-Induced Linear Reduction Gas Diffusivity Model Extended to Three Pore Regions
Chamindu, T. K. K. Deepagoda; de Jonge, Lis Wollesen; Kawamoto, Ken
2015-01-01
. Characterization of soil functional pore structure is an essential prerequisite to understand key gas transport processes in variably saturated soils in relation to soil ecosystems, climate, and environmental services. In this study, the water-induced linear reduction (WLR) soil gas diffusivity model originally...... gas diffusivity from moist to dry conditions across differently structured porous media, including narrow soil size fractions, perforated plastic blocks, fractured limestone, peaty soils, aggregated volcanic ash soils, and particulate substrates for Earth- or space-based applications. The new Cip...
Sittel, Wiebke; Basuki, Widodo W.; Aktaa, Jarir
2015-01-01
A modeling based optimization process of the solid state diffusion bonding is presented for joining ferritic oxide dispersion strengthened steels PM2000. An optimization study employing varying bonding temperatures and pressures results in almost the same strength and toughness of the bonded compared to the as received material. TEM investigations of diffusion bonded samples show a homogeneous distribution of oxide particles at the bonding seam similar to that in the bulk. Hence, no loss in strength or creep resistance due to oxide particle agglomeration is found, as verified by the mechanical properties observed for the joint.
On thermal vibration effects in diffusion model calculations of blocking dips
Fuschini, E.; Ugozzoni, A.
1983-01-01
In the framework of the diffusion model, a method for calculating blocking dips is suggested that takes into account thermal vibrations of the crystal lattice. Results of calculations of the diffusion factor and the transverse energy distribution taking into accoUnt scattering of the channeled particles at thermal vibrations of lattice nuclei, are presented. Calculations are performed for α-particles with the energy of 2.12 MeV at 300 K scattered by Al crystal. It is shown that calculations performed according to the above method prove the necessity of taking into account effects of multiple scattering under blocking conditions
MR perfusion/diffusion-weighted imaging of acute ischemia in an animal model with PET correlation
Pickens, D.R.; Dawson, R.C.; Votaw, J.R.; Lorenz, C.H.; Holburn, G.E.; Price, R.R.
1990-01-01
This paper evaluates acute cerebral ischemia in an animal model with MR perfusion/diffusion-sensitive pulse sequences and to compare the results with PET regional cerebral blood flow (rCBF) measurements. An embolizing agent was injected into the proximal middle cerebral artery (MCA) of a dog, and this was followed by DSA. Next, the animal was imaged in a 1.5-T MR system with perfusion/diffusion-sensitive spin-echo pulse sequence. Then, PET imaging was performed with H 2 O 15 at corresponding levels of the brain
Analysis of nonlinear parabolic equations modeling plasma diffusion across a magnetic field
Hyman, J.M.; Rosenau, P.
1984-01-01
We analyse the evolutionary behavior of the solution of a pair of coupled quasilinear parabolic equations modeling the diffusion of heat and mass of a magnetically confined plasma. The solutions's behavior, due to the nonlinear diffusion coefficients, exhibits many new phenomena. In short time, the solution converges into a highly organized symmetric pattern that is almost completely independent of initial data. The asymptotic dynamics then become very simple and take place in a finite dimensional space. These conclusions are backed by extensive numerical experimentation
Gutierrez, E; Huang, Y; Haglid, K; Bao, F; Hansson, H A; Hamberger, A; Viano, D
2001-03-01
Rapid head rotation is a major cause of brain damage in automobile crashes and falls. This report details a new model for rotational acceleration about the center of mass of the rabbit head. This allows the study of brain injury without translational acceleration of the head. Impact from a pneumatic cylinder was transferred to the skull surface to cause a half-sine peak acceleration of 2.1 x 10(5) rad/s2 and 0.96-ms pulse duration. Extensive subarachnoid hemorrhages and small focal bleedings were observed in the brain tissue. A pronounced reactive astrogliosis was found 8-14 days after trauma, both as networks around the focal hemorrhages and more diffusely in several brain regions. Astrocytosis was prominent in the gray matter of the cerebral cortex, layers II-V, and in the granule cell layer and around the axons of the pyramidal neurons in the hippocampus. The nuclei of cranial nerves, such as the hypoglossal and facial nerves, also showed intense astrocytosis. The new model allows study of brain injuries from head rotation in the absence of translational influences.
A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network.
Lufang Zhou
2010-01-01
Full Text Available Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS. Here, we develop a mathematical model of ROS-induced ROS release (RIRR based on reaction-diffusion (RD-RIRR in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA cycle, oxidative phosphorylation, and Ca(2+ handling. Local mitochondrial interaction is mediated by superoxide (O2.- diffusion and the O2.(--dependent activation of an inner membrane anion channel (IMAC. In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.- diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m depolarization is mediated specifically by O2.-. The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the
Berlowitz, D.R.
1996-11-01
In the last few decades the negative impact by humans on the thin atmospheric layer enveloping the earth, the basis for life on this planet, has increased steadily. In order to halt, or at least slow down this development, the knowledge and study of these anthropogenic influence has to be increased and possible remedies have to be suggested. An important tool for these studies are computer models. With their help the atmospheric system can be approximated and the various processes, which have led to the current situation can be quantified. They also serve as an instrument to assess short or medium term strategies to reduce this human impact. However, to assure efficiency as well as accuracy, a careful analysis of the numerous processes involved in the dispersion of pollutants in the atmosphere is called for. This should help to concentrate on the essentials and also prevent excessive usage of sometimes scarce computing resources. The basis of the presented work is the EUMAC Zooming Model (ETM), and particularly the component calculating the dispersion of pollutants in the atmosphere, the model MARS. The model has two main parts: an explicit solver, where the advection and the horizontal diffusion of pollutants are calculated, and an implicit solution mechanism, allowing the joint computation of the change of concentration due to chemical reactions, coupled with the respective influence of the vertical diffusion of the species. The aim of this thesis is to determine particularly the influence of the horizontal components of the turbulent diffusion on the existing implicit solver of the model. Suggestions for a more comprehensive inclusion of the full three dimensional diffusion operator in the implicit solver are made. This is achieved by an appropriate operator splitting. A selection of numerical approaches to tighten the coupling of the diffusion processes with the calculation of the applied chemical reaction mechanisms are examined. (author) figs., tabs., refs.
A scatter model for fast neutron beams using convolution of diffusion kernels
Moyers, M.F.; Horton, J.L.; Boyer, A.L.
1988-01-01
A new model is proposed to calculate dose distributions in materials irradiated with fast neutron beams. Scattered neutrons are transported away from the point of production within the irradiated material in the forward, lateral and backward directions, while recoil protons are transported in the forward and lateral directions. The calculation of dose distributions, such as for radiotherapy planning, is accomplished by convolving a primary attenuation distribution with a diffusion kernel. The primary attenuation distribution may be quickly calculated for any given set of beam and material conditions as it describes only the magnitude and distribution of first interaction sites. The calculation of energy diffusion kernels is very time consuming but must be calculated only once for a given energy. Energy diffusion distributions shown in this paper have been calculated using a Monte Carlo type of program. To decrease beam calculation time, convolutions are performed using a Fast Fourier Transform technique. (author)
Memory Effects and Coverage Dependence of Surface Diffusion in a Model Adsorption System
Vattulainen, Ilpo Tapio; Ying, S. C.; Ala-Nissila, T.
1999-01-01
in tracer and collective diffusion. We show that memory effects can be very pronounced deep inside the ordered phases and in regions close to first and second order phase transition boundaries. Particular attention is paid to the details of the time dependence of memory effects. The memory effect in tracer......We study the coverage dependence of surface diffusion coefficients for a strongly interacting adsorption system O/W(110) via Monte Carlo simulations of a lattice-gas model. In particular, we consider the nature and emergence of memory effects as contained in the corresponding correlation factors...... diffusion is found to decay following a power law after an initial transient period. This behavior persists until the hydrodynamic regime is reached, after which the memory effect decays exponentially. The time required to reach the hydrodynamical regime and the related exponential decay is strongly...
Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young
2017-03-14
Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
Diffusion layer modeling for condensation with multi-component noncondensable gases
Peterson, P.F.
1999-01-01
Many condensation problems involving noncondensable gases have multiple noncondensable species, for example air (with nitrogen, oxygen, and other gases); and other problems where light gases like hydrogen may mix with heavier gases like nitrogen. Particularly when the binary mass diffusion coefficients of the noncondensable species are substantially different, the noncondensable species tend to segregate in the condensation boundary layer. This paper presents a fundamental analysis of the mass transport with multiple noncondensable species, identifying a simple method to calculate an effective mass diffusion coefficient that can be used with the simple diffusion layer model, and discusses in detail the effects of using mass and mole based quantities, and various simplifying approximations, on predicted condensation rates. The results are illustrated with quantitative examples to demonstrate the potential importance of multi-component noncondensable gas effects
External field effects on diffusion and solidification derived from the free-volume model
Miller, R. I.; Ruff, R. C.
1975-01-01
Expressions for the diffusion coefficient and the solidification rate from the free-volume model of liquids developed by Turnbull and Cohen have been used to estimate the effects which microgravity and magnetic fields will have on these quantities. The mathematical formalism describing changes of the diffusion coefficient and the solidification rate is the same for both the microgravity and magnetic field cases, but the difference between the magnitudes of the two effects is quite large. The change in the two parameters is found to be less than .0001% for the microgravity case and on the order of 0.1 to 1.1% for the magnetic field case for four representative materials. The diffusion coefficient and the solidification rate are found to increase under the influence of an applied magnetic field, and this is in agreement with experimental observations.
Gavrilin, A V
2001-01-01
Low temperature composite superconductors stabilized with extra large cross-section pure aluminum are currently in use for the Large Helical Device in Japan, modern big detectors such as ATLAS at CERN, and other large magnets. In these types of magnet systems, the rated average current density is not high and the peak field in a region of interest is about 2-4 T. Aluminum stabilized superconductors result in high stability margins and relatively long quench times. Appropriate quench analyses, both for longitudinal and transverse propagation, have to take into account a rather slow diffusion of current from the superconductor into the thick aluminum stabilizer. An exact approach to modeling of the current diffusion would be based on directly solving the Maxwell's equations in parallel with thermal diffusion and conduction relations. However, from a practical point of view, such an approach should be extremely time consuming due to obvious restrictions of computation capacity. At the same time, there exist cert...
Oxygen diffusion in soils: Understanding the factors and processes needed for modeling
José Neira
2015-08-01
Full Text Available Oxygen is an important element for plant growth. Reducing its concentration in the soil affects plant physiological processes such as nutrient and water uptake as well as respiration, the redox potential of soil elements and the activity of microorganisms. The main mechanism of oxygen transport in the soil is by diffusion, a dynamic process greatly influenced by soil physical properties such as texture and structure, conditioning, pore size distribution, tortuosity and connectivity. Organic matter is a modifying agent of the soil's chemical and physical properties, affecting its structure and the porous matrix, which are determinants of oxygen transport. This study reviews the theory of soil gas diffusion and the effect of soil organic matter on the soil's physical properties and transport of gases. It also reviews gas diffusion models, particularly those including the effect of soil organic matter.
Numerical computation of the linear stability of the diffusion model for crystal growth simulation
Yang, C.; Sorensen, D.C. [Rice Univ., Houston, TX (United States); Meiron, D.I.; Wedeman, B. [California Institute of Technology, Pasadena, CA (United States)
1996-12-31
We consider a computational scheme for determining the linear stability of a diffusion model arising from the simulation of crystal growth. The process of a needle crystal solidifying into some undercooled liquid can be described by the dual diffusion equations with appropriate initial and boundary conditions. Here U{sub t} and U{sub a} denote the temperature of the liquid and solid respectively, and {alpha} represents the thermal diffusivity. At the solid-liquid interface, the motion of the interface denoted by r and the temperature field are related by the conservation relation where n is the unit outward pointing normal to the interface. A basic stationary solution to this free boundary problem can be obtained by writing the equations of motion in a moving frame and transforming the problem to parabolic coordinates. This is known as the Ivantsov parabola solution. Linear stability theory applied to this stationary solution gives rise to an eigenvalue problem of the form.
Modeling of heat transfer in a horizontal heat-generating layer by an effective diffusivity approach
Cheung, F.B.; Shiah, S.W.
1994-01-01
The concept of effective diffusivity is employed to model various processes of heat transfer in a volumetrically heated fluid layer subjected to different initial and boundary conditions. The approach, which involves the solution of only heat diffusion equations, is found to give rather accurate predictions of the transient response of an initially stagnant fluid layer to a step input of power as well as the developing and decaying nature of the flow following a step change in the internal Rayleigh number from one state of steady convection to another. The approach is also found to be applicable to various flow regions of a heat-generating fluid layer, and is not limited to the case in which the entire layer is in turbulent motion. The simplicity and accuracy of the method are clearly illustrated in the analysis. Validity of the effective diffusivity approach is demonstrated by comparing the predicted results with corresponding experimental data
A priori analysis of differential diffusion for model development for scale-resolving simulations
Hunger, Franziska; Dietzsch, Felix; Gauding, Michael; Hasse, Christian
2018-01-01
The present study analyzes differential diffusion and the mechanisms responsible for it with regard to the turbulent/nonturbulent interface (TNTI) with special focus on model development for scale-resolving simulations. In order to analyze differences between resolved and subfilter phenomena, direct numerical simulation (DNS) data are compared with explicitly filtered data. The DNS database stems from a temporally evolving turbulent plane jet transporting two passive scalars with Schmidt numbers of unity and 0.25 presented by Hunger et al. [F. Hunger et al., J. Fluid Mech. 802, R5 (2016), 10.1017/jfm.2016.471]. The objective of this research is twofold: (i) to compare the position of the turbulent-nonturbulent interface between the original DNS data and the filtered data and (ii) to analyze differential diffusion and the impact of the TNTI with regard to scale resolution in the filtered DNS data. For the latter, differential diffusion quantities are studied, clearly showing the decrease of differential diffusion at the resolved scales with increasing filter width. A transport equation for the scalar differences is evaluated. Finally, the existence of large scalar gradients, gradient alignment, and the diffusive fluxes being the physical mechanisms responsible for the separation of the two scalars are compared between the resolved and subfilter scales.
Model-free and analytical EAP reconstruction via spherical polar Fourier diffusion MRI.
Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid
2010-01-01
How to estimate the diffusion Ensemble Average Propagator (EAP) from the DWI signals in q-space is an open problem in diffusion MRI field. Many methods were proposed to estimate the Orientation Distribution Function (ODF) that is used to describe the fiber direction. However, ODF is just one of the features of the EAP. Compared with ODF, EAP has the full information about the diffusion process which reflects the complex tissue micro-structure. Diffusion Orientation Transform (DOT) and Diffusion Spectrum Imaging (DSI) are two important methods to estimate the EAP from the signal. However, DOT is based on mono-exponential assumption and DSI needs a lot of samplings and very large b values. In this paper, we propose Spherical Polar Fourier Imaging (SPFI), a novel model-free fast robust analytical EAP reconstruction method, which almost does not need any assumption of data and does not need too many samplings. SPFI naturally combines the DWI signals with different b-values. It is an analytical linear transformation from the q-space signal to the EAP profile represented by Spherical Harmonics (SH). We validated the proposed methods in synthetic data, phantom data and real data. It works well in all experiments, especially for the data with low SNR, low anisotropy, and non-exponential decay.
Yuvan, Steven; Bier, Martin
2018-02-01
Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.
Coste, P.; Bestion, D. [Commissariat a l Energie Atomique, Grenoble (France)
1995-09-01
This paper presents a simple modelling of mass diffusion effects on condensation. In presence of noncondensable gases, the mass diffusion near the interface is modelled using the heat and mass transfer analogy and requires normally an iterative procedure to calculate the interface temperature. Simplifications of the model and of the solution procedure are used without important degradation of the predictions. The model is assessed on experimental data for both film condensation in vertical tubes and direct contact condensation in horizontal tubes, including air-steam, Nitrogen-steam and Helium-steam data. It is implemented in the Cathare code, a french system code for nuclear reactor thermal hydraulics developed by CEA, EDF, and FRAMATOME.
Martin, R.C.
1991-01-01
A simple model for diffusion through the silicon carbide layer of TRISO particles is applied to the data for accident condition testing of fuel spheres for the High-Temperature Reactor program of the Federal Republic of Germany (FRG). Categorization of sphere release of 137 Cs based on fast neutron fluence permits predictions of release with an accuracy comparable to that of the US/FRG accident condition fuel performance model. Calculations are also performed for 85 Kr, 90 Sr, and 110m Ag. Diffusion of cesium through SiC suggests that models of fuel failure should consider fuel performance during repeated accident condition thermal cycling. Microstructural considerations in models of fission product release are discussed. The neutron-induced segregation of silicon within the SiC structure is postulated as a mechanism for enhanced fission product release during accident conditions. As oxygen-enhanced SiC decomposition mechanism is also discussed. (author). 12 refs, 11 figs, 2 tabs
Buske, D.
2011-01-01
The present contribution focuses on the question of radioactive material dispersion after discharge from a nuclear power plant in the context of micro-meteorology, i.e. an atmospheric dispersion model. The advection-diffusion equation with Fickian closure for the turbulence is solved for the atmospheric boundary layer where the eddy diffusivity coefficients and the wind profile are assumed to be space dependent. The model is solved in closed form using integral transform and spectral theory. Convergence of the solution is discussed in terms of a convergence criterion using a new interpretation of the Cardinal Theorem of Interpolation theory and Parseval's theorem. The solution is compared to other methods and model adequacy is analyzed. Model validation is performed against experimental data from a controlled release of radioactive material at the Itaorna Beach (Angra dos Reis, Rio de Janeiro state, Brazil, 1985). (author)
The first-passage time distribution for the diffusion model with variable drift
Blurton, Steven Paul; Kesselmeier, Miriam; Gondan, Matthias
2017-01-01
across trials. This extra flexibility allows accounting for slow errors that often occur in response time experiments. So far, the predicted response time distributions were obtained by numerical evaluation as analytical solutions were not available. Here, we present an analytical expression...... for the cumulative first-passage time distribution in the diffusion model with normally distributed trial-to-trial variability in the drift. The solution is obtained with predefined precision, and its evaluation turns out to be extremely fast.......The Ratcliff diffusion model is now arguably the most widely applied model for response time data. Its major advantage is its description of both response times and the probabilities for correct as well as incorrect responses. The model assumes a Wiener process with drift between two constant...
Bioheat model evaluations of laser effects on tissues: role of water evaporation and diffusion
Nagulapally, Deepthi; Joshi, Ravi P.; Thomas, Robert J.
2011-03-01
A two-dimensional, time-dependent bioheat model is applied to evaluate changes in temperature and water content in tissues subjected to laser irradiation. Our approach takes account of liquid-to-vapor phase changes and a simple diffusive flow of water within the biotissue. An energy balance equation considers blood perfusion, metabolic heat generation, laser absorption, and water evaporation. The model also accounts for the water dependence of tissue properties (both thermal and optical), and variations in blood perfusion rates based on local tissue injury. Our calculations show that water diffusion would reduce the local temperature increases and hot spots in comparison to simple models that ignore the role of water in the overall thermal and mass transport. Also, the reduced suppression of perfusion rates due to tissue heating and damage with water diffusion affect the necrotic depth. Two-dimensional results for the dynamic temperature, water content, and damage distributions will be presented for skin simulations. It is argued that reduction in temperature gradients due to water diffusion would mitigate local refractive index variations, and hence influence the phenomenon of thermal lensing. Finally, simple quantitative evaluations of pressure increases within the tissue due to laser absorption are presented.
Nafidi, A.; Gutiérrez, R.; Gutiérrez-Sánchez, R.; Ramos-Ábalos, E.; El Hachimi, S.
2016-01-01
The aim of this study is to model electric power consumption during a period of economic crisis, characterised by declining gross domestic product. A novel aspect of this study is its use of a Gamma-type diffusion process for short and medium-term forecasting – other techniques that have been used to describe such consumption patterns are not valid in this situation. In this study, we consider a new extension of the stochastic Gamma diffusion process by introducing time functions (exogenous factors) that affect its trend. This extension is defined in terms of Kolmogorov backward and forward equations. After obtaining the transition probability density function and the moments (specifically, the trend function), the inference on the process parameters is obtained by discrete sampling of the sample paths. Finally, this stochastic process is applied to model total net electricity consumption in Spain, when affected by the following set of exogenous factors: Gross Domestic Product (GDP), Gross Fixed Capital Formation (GFCF) and Final Domestic Consumption (FDC). - Highlights: • The aim is modelling and predicting electricity consumption in Spain. • We propose a Gamma-type diffusion process for short and medium-term forecasting. • We compared the fit using diffusion processes with different exogenous factors.
Burkes, Douglas [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Casella, Amanda J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Gardner, Levi D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Casella, Andrew M. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Huber, Tanja K. [Technische Universität München, Munich (Germany); Breitkreutz, Harald [Technische Universität München, Munich (Germany)
2015-02-11
The Office of Material Management and Minimization Fuel Thermo-physical Characterization Project at Pacific Northwest National Laboratory (PNNL) is tasked with using PNNL facilities and processes to receive irradiated low enriched uranium-molybdenum fuel plate samples and perform analyses in support of the Office of Material Management and Minimization Reactor Conversion Program. This work is in support of the Fuel Development Pillar that is managed by Idaho National Laboratory. A key portion of the scope associated with this project was to measure the thermal properties of fuel segments harvested from plates that were irradiated in the Advanced Test Reactor. Thermal diffusivity of samples prepared from the fuel segments was measured using laser flash analysis. Two models, one developed by PNNL and the other developed by the Technische Universität München (TUM), were evaluated to extract the thermal diffusivity of the uranium-molybdenum alloy from measurements made on the irradiated, layered composites. The experimental data of the “TC” irradiated fuel segment was evaluated using both models considering a three-layer and five-layer system. Both models are in acceptable agreement with one another and indicate that the zirconium diffusion barrier has a minimal impact on the overall thermal diffusivity of the monolithic U-Mo fuel.
Xu, Xiaochun; Kang, Soyoung; Navarro-Comes, Eric; Wang, Yu; Liu, Jonathan T. C.; Tichauer, Kenneth M.
2018-03-01
Intraoperative tumor/surgical margin assessment is required to achieve higher tumor resection rate in breast-conserving surgery. Though current histology provides incomparable accuracy in margin assessment, thin tissue sectioning and the limited field of view of microscopy makes histology too time-consuming for intraoperative applications. If thick tissue, wide-field imaging can provide an acceptable assessment of tumor cells at the surface of resected tissues, an intraoperative protocol can be developed to guide the surgery and provide immediate feedback for surgeons. Topical staining of margins with cancer-targeted molecular imaging agents has the potential to provide the sensitivity needed to see microscopic cancer on a wide-field image; however, diffusion and nonspecific retention of imaging agents in thick tissue can significantly diminish tumor contrast with conventional methods. Here, we present a mathematical model to accurately simulate nonspecific retention, binding, and diffusion of imaging agents in thick tissue topical staining to guide and optimize future thick tissue staining and imaging protocol. In order to verify the accuracy and applicability of the model, diffusion profiles of cancer targeted and untargeted (control) nanoparticles at different staining times in A431 tumor xenografts were acquired for model comparison and tuning. The initial findings suggest the existence of nonspecific retention in the tissue, especially at the tissue surface. The simulator can be used to compare the effect of nonspecific retention, receptor binding and diffusion under various conditions (tissue type, imaging agent) and provides optimal staining and imaging protocols for targeted and control imaging agent.
Second generation diffusion model of interacting gravity waves on the surface of deep fluid
A. Pushkarev
2004-01-01
Full Text Available We propose a second generation phenomenological model for nonlinear interaction of gravity waves on the surface of deep water. This model takes into account the effects of non-locality of the original Hasselmann diffusion equation still preserving important properties of the first generation model: physically consistent scaling, adherence to conservation laws and the existence of Kolmogorov-Zakharov solutions. Numerical comparison of both models with the original Hasselmann equation shows that the second generation models improves the angular distribution in the evolving wave energy spectrum.
Regression-based model of skin diffuse reflectance for skin color analysis
Tsumura, Norimichi; Kawazoe, Daisuke; Nakaguchi, Toshiya; Ojima, Nobutoshi; Miyake, Yoichi
2008-11-01
A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.
Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
Armesto, Nestor; Bondarenko, Sergey; Quiroga-Arias, Paloma; Milhano, Jose Guilherme
2008-01-01
We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined-Reggeon Field Theory, Directed Percolation and Reversible Processes-only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
Flegg, Mark B.
2013-01-01
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, "The two-regime method for optimizing stochastic reaction-diffusion simulations," J. R. Soc., Interface 9, 859-868 (2012)] in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration
Continuous versus discontinuous albedo representations in a simple diffusive climate model
Simmons, P. A.; Griffel, D. H.
1988-07-01
A one-dimensional annually and zonally averaged energy-balance model, with diffusive meridional heat transport and including icealbedo feedback, is considered. This type of model is found to be very sensitive to the form of albedo used. The solutions for a discontinuous step-function albedo are compared to those for a more realistic smoothly varying albedo. The smooth albedo gives a closer fit to present conditions, but the discontinuous form gives a better representation of climates in earlier epochs.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
The Diffusion Decision Model: Theory and Data for Two-Choice Decision Tasks
Ratcliff, Roger; McKoon, Gail
2008-01-01
The diffusion decision model allows detailed explanations of behavior in two-choice discrimination tasks. In this article, the model is reviewed to show how it translates behavioral data—accuracy, mean response times, and response time distributions—into components of cognitive processing. Three experiments are used to illustrate experimental manipulations of three components: stimulus difficulty affects the quality of information on which a decision is based; instructions emphasizing either ...
Trojan War displayed as a full annihilation-diffusion-reaction model
Flores, J. C.
2017-02-01
The diffusive pair annihilation model with embedded topological domains and archaeological data is applied in an analysis of the hypothetical Trojan-Greek war during the late Bronze Age. Estimations of parameter are explicitly made for critical dynamics of the model. In particular, the 8-metre walls of Troy could be viewed as the effective shield that provided the technological difference between the two armies. Suggestively, the numbers in The Iliad are quite sound, being in accord with Lanchester's laws of warfare.
Savoye, S.; Beaucaire, C.; Grenut, B.; Fayette, A.
2015-01-01
Highlights: • HTO and 85 Sr diffusion is studied in clayrocks under increasing ionic strengths. • Sr diffusive flux is 5 times higher than HTO under standard porewater ionic strength. • Sr diffusive flux is reduced when the porewater ionic strength increases. • The Sr diffusive evolution is qualitatively reproduced by a surface diffusion model. - Abstract: Diffusion of cations in clayrocks is widely investigated, because deep clay-rich formations are currently considered as one of the potential host rocks for radioactive waste repositories. However, several authors have already reported that sorbing cations seem to diffuse at rates larger than those predicted by a simple pore diffusion model from their sorption coefficients and from the diffusive flux of non-sorbing water tracers. This process has been attributed to the migration of cations within the electrical double layer, next to the mineral surfaces, called the surface diffusion phenomenon. The aim of this work was to verify whether this “enhanced” cation diffusion compared to neutral species was observed for strontium and, if so, to what extent this effect might vary with the salinity of the synthetic solutions. These questions were addressed by performing batch sorption, through-diffusion and out-diffusion experiments on rock samples from the Callovo-Oxfordian claystone formation (France). The results showed that there was a good agreement of the distribution ratios (R D ) determined on crushed and intact rocks by batch and through-diffusion methods with a R D decrease related to the increase of the sodium concentration, a sorption competitor. Such a trend was also well reproduced by means of a geochemical modeling based on the multi-site ion exchange (MSIE) theory. Moreover, the “enhanced” diffusion for strontium was clearly observed in this study: the Sr diffusive flux was almost five times higher than that for HTO in the cell with the lowest ionic strength, and diminished to less than 1
Fatma E. El-Khouly
2017-10-01
Full Text Available Despite decades of clinical trials for diffuse intrinsic pontine glioma (DIPG, patient survival does not exceed 10% at two years post-diagnosis. Lack of benefit from systemic chemotherapy may be attributed to an intact bloodbrain barrier (BBB. We aim to develop a theoretical model including relevant physicochemical properties in order to review whether applied chemotherapeutics are suitable for passive diffusion through an intact BBB or whether local administration via convection-enhanced delivery (CED may increase their therapeutic potential. Physicochemical properties (lipophilicity, molecular weight, and charge in physiological environment of anticancer drugs historically and currently administered to DIPG patients, that affect passive diffusion over the BBB, were included in the model. Subsequently, the likelihood of BBB passage of these drugs was ascertained, as well as their potential for intratumoral administration via CED. As only non-molecularly charged, lipophilic, and relatively small sized drugs are likely to passively diffuse through the BBB, out of 51 drugs modeled, only 8 (15%—carmustine, lomustine, erlotinib, vismodegib, lenalomide, thalidomide, vorinostat, and mebendazole—are theoretically qualified for systemic administration in DIPG. Local administration via CED might create more therapeutic options, excluding only positively charged drugs and drugs that are either prodrugs and/or only available as oral formulation. A wide variety of drugs have been administered systemically to DIPG patients. Our model shows that only few are likely to penetrate the BBB via passive diffusion, which may partly explain the lack of efficacy. Drug distribution via CED is less dependent on physicochemical properties and may increase the therapeutic options for DIPG.
Islam, Towhidul
2014-01-01
We focus on predicting the adoption time probabilities of photo-voltaic solar panels by households using discrete choice experiments and an innovation diffusion model. The primary objective of this research is cohesively mapping the theory of disruptive innovation into diffusion of innovations to aid policy makers by linking two critical uncertainties of new technology: (1) whether households prefer the new attributes of the new technology and how these preferences vary by market segments? and (2) when are they going to adopt (if at all)? Our study uses recent developments of discrete choice experiments and establishes a causal link between the attributes of the technology, attitudinal constructs and socio-demographics, and adoption time probabilities using the Bass diffusion model. The data was collected from Ontario, a province of Canada. The innovation diffusion model allows us to compute the cumulative probability of adoption over time per household. Technology awareness and energy cost saving have a significant effect on the adoption probability, reinforcing the need for effective education. These findings also suggest that campaigns should explain more about investment criteria, feed-in tariffs and environmental attributes. This study findings call for a need to use seeding strategies to accelerate exogenous Word-of-Mouth (WOM) for this new technology. - Highlights: • Adoption of renewable energy (i.e. solar PV panels) and theory of disruptive innovations. • Household level innovation diffusion model from discrete choice experiments with time intent questions. • Variation in adoption probabilities by market segments. • Promotions should explain new attributes and lack of consistency of households especially on market develop policies. • Data from Ontario, province of Canada, with generous feed-in tariff for solar households
A new empirical model to estimate hourly diffuse photosynthetic photon flux density
Foyo-Moreno, I.; Alados, I.; Alados-Arboledas, L.
2018-05-01
Knowledge of the photosynthetic photon flux density (Qp) is critical in different applications dealing with climate change, plant physiology, biomass production, and natural illumination in greenhouses. This is particularly true regarding its diffuse component (Qpd), which can enhance canopy light-use efficiency and thereby boost carbon uptake. Therefore, diffuse photosynthetic photon flux density is a key driving factor of ecosystem-productivity models. In this work, we propose a model to estimate this component, using a previous model to calculate Qp and furthermore divide it into its components. We have used measurements in urban Granada (southern Spain), of global solar radiation (Rs) to study relationships between the ratio Qpd/Rs with different parameters accounting for solar position, water-vapour absorption and sky conditions. The model performance has been validated with experimental measurements from sites having varied climatic conditions. The model provides acceptable results, with the mean bias error and root mean square error varying between - 0.3 and - 8.8% and between 9.6 and 20.4%, respectively. Direct measurements of this flux are very scarce so that modelling simulations are needed, this is particularly true regarding its diffuse component. We propose a new parameterization to estimate this component using only measured data of solar global irradiance, which facilitates its use for the construction of long-term data series of PAR in regions where continuous measurements of PAR are not yet performed.
Diffusion and sorption on hardened cement pastes - experiments and modelling results
Jakob, A.; Sarott, F.-A.; Spieler, P.
1999-08-01
Large parts of repositories for low and intermediate level radioactive waste consist of cementitious materials. Radionuclides are transported by diffusion in the cement matrix or, in case of fractured or highly permeable cement, by advection and dispersion. In this work we aim at a mechanistic understanding of diffusion processes of some reactive tracers. On the laboratory scale, ten through-diffusion experiments were performed to study these processes for Cl{sup -}, I{sup -}, Cs{sup +} and Ni{sup 2+} ions in a Sulphate Resisting Portland Cement (SRPC) equilibrated with an artificial pore water. Some of the experiments continued up to nearly three years with daily measurements. In all the experiments, a cement disk initially saturated with an artificial pore water was exposed on one side to a highly diluted solution containing the species of interest. On the second side, a near-zero concentration boundary was maintained to drive through-diffusion of the tracer. The changes of concentrations on both sides of the samples were monitored, allowing careful mass balances. From these data, values of the diffusive flux and the mass of tracer taken up by the cementitious material were determined as a function of time. In the subsequent modelling, the time histories of these tracer breakthroughs were fitted using five different models. The simplest model neglects all retarding mechanisms except pure diffusion. More complex models either account for instantaneous equilibrium sorption in form of linear or non-linear (Freundlich) sorption or for first-order sorption kinetics where the forward reaction may be linear or non-linear according to the Freundlich isotherm, while the back-reaction is linear. Hence, the analysis allows the extraction of the diffusion coefficient and parameter values for the sorption isotherm or rate-constants for sorption and desorption. The fits to the experimental data were carried out by an automated Marquardt-Levenberg procedure yielding error
Czárán, Tamás; Rattray, Fergal P.; Møller, Cleide O.de A.
2018-01-01
The influence of metabolite diffusion within the cheese matrix on growth of non-starter lactic acid bacteria (NSLAB) during Cheddar cheese ripening was mathematically modelled. The model was calibrated at a realistic range of diffusion of metabolites and the decay and growth parameters...
de Mul, Frits F. M.; Blaauw, Judith; Smit, Andries J.; Rakhorst, Gerhard
2007-01-01
We present a physical model to describe iontophoresis time recordings. The model is a combination of monodimensional material diffusion and decay, probably due to transport by blood flow. It has four adjustable parameters, the diffusion coefficient, the decay constant, the height of the response,
A diffusive ink transport model for lipid dip-pen nanolithography.
Urtizberea, A; Hirtz, M
2015-10-14
Despite diverse applications, phospholipid membrane stacks generated by dip-pen nanolithography (DPN) still lack a thorough and systematic characterization that elucidates the whole ink transport process from writing to surface spreading, with the aim of better controlling the resulting feature size and resolution. We report a quantitative analysis and modeling of the dependence of lipid DPN features (area, height and volume) on dwell time and relative humidity. The ink flow rate increases with humidity in agreement with meniscus size growth, determining the overall feature size. The observed time dependence indicates the existence of a balance between surface spreading and the ink flow rate that promotes differences in concentration at the meniscus/substrate interface. Feature shape is controlled by the substrate surface energy. The results are analyzed within a modified model for the ink transport of diffusive inks. At any humidity the dependence of the area spread on the dwell time shows two diffusion regimes: at short dwell times growth is controlled by meniscus diffusion while at long dwell times surface diffusion governs the process. The critical point for the switch of regime depends on the humidity.
Lee, J.H.; Andrews, R.W.; Chambre, P.L.
1996-01-01
A robust engineered barrier system (EBS) is employed in the current design concept for the potential high-level nuclear waste repository at Yucca Mountain, Nevada, US. The primary component of the EBS is a multi-barrier waste package container. Simplifying the geometry of the cylindrical waste package container and the underlying invert into the equivalent spherical configuration, mathematical models are developed for steady-state and transient diffusive releases from the failed waste container with multiple perforations (or pit penetrations) at the boundary of the invert. Using the models the steady-state and transient diffusive release behaviors form the failed waste container are studied. The analyses show that the number of perforations, the size of perforation, the container wall thickness, the geometry of the waste container and invert, and the adsorption of radionuclide in the invert are the important parameters that control the diffusive release rate. It is emphasized that the failed (or perforated) waste package container can still perform as a potentially important barrier (or diffusion barrier) to radionuclide release
Quast, T.; Schirmacher, A.; Hauer, K.-O.; Koo, A.
2018-02-01
To elucidate the influence of polarization in diffuse reflectometry, we performed a series of measurements in several bidirectional geometries and determined the Stokes parameters of the diffusely reflected radiation. Different types of matte reflection standards were used, including several common white standards and ceramic colour standards. The dependence of the polarization on the sample type, wavelength and geometry have been studied systematically, the main influence factors have been identified: The effect is largest at large angles of incidence or detection and at wavelengths where the magnitude of the reflectance is small. The results for the colour standards have been modelled using a microfacet-based reflection theory which is derived from the well-known model of Torrance and Sparrow. Although the theory is very simple and only has three free parameters, the agreement with the measured data is very good, all essential features of the data can be reproduced by the model.
The drift diffusion model as the choice rule in reinforcement learning.
Pedersen, Mads Lund; Frank, Michael J; Biele, Guido
2017-08-01
Current reinforcement-learning models often assume simplified decision processes that do not fully reflect the dynamic complexities of choice processes. Conversely, sequential-sampling models of decision making account for both choice accuracy and response time, but assume that decisions are based on static decision values. To combine these two computational models of decision making and learning, we implemented reinforcement-learning models in which the drift diffusion model describes the choice process, thereby capturing both within- and across-trial dynamics. To exemplify the utility of this approach, we quantitatively fit data from a common reinforcement-learning paradigm using hierarchical Bayesian parameter estimation, and compared model variants to determine whether they could capture the effects of stimulant medication in adult patients with attention-deficit hyperactivity disorder (ADHD). The model with the best relative fit provided a good description of the learning process, choices, and response times. A parameter recovery experiment showed that the hierarchical Bayesian modeling approach enabled accurate estimation of the model parameters. The model approach described here, using simultaneous estimation of reinforcement-learning and drift diffusion model parameters, shows promise for revealing new insights into the cognitive and neural mechanisms of learning and decision making, as well as the alteration of such processes in clinical groups.
Kutner, R.; Sosnowska, I.
1977-01-01
A Multi-Sublattice Jump Diffusion Model (MSJD) for hydrogen diffusion through interstitial-site lattices is presented. The MSJD approach may, in principle, be considered as an extension of the Rowe et al (J. Phys. Chem. Solids; 32:41 (1971)) model. Jump diffusion to any neighbours with different jump times which may be asymmetric in space is discussed. On the basis of the model a new method of calculating the diffusion tensor is advanced. The quasielastic, double differential cross section for thermal neutron scattering is obtained in terms of the MSJD model. The model can be used for systems in which interstitial jump diffusion of impurity particles occurs. In Part II the theoretical results are compared with those for quasielastic neutron scattering from the αNbHsub(x) system. (author)
Equilibrium Asset and Option Pricing under Jump-Diffusion Model with Stochastic Volatility
Xinfeng Ruan
2013-01-01
Full Text Available We study the equity premium and option pricing under jump-diffusion model with stochastic volatility based on the model in Zhang et al. 2012. We obtain the pricing kernel which acts like the physical and risk-neutral densities and the moments in the economy. Moreover, the exact expression of option valuation is derived by the Fourier transformation method. We also discuss the relationship of central moments between the physical measure and the risk-neutral measure. Our numerical results show that our model is more realistic than the previous model.
Fractional single-phase-lagging heat conduction model for describing anomalous diffusion
T.N. Mishra
2016-03-01
Full Text Available The fractional single-phase-lagging (FSPL heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging (SPL heat conduction model. Based on the FSPL heat conduction model, anomalous diffusion within a finite thin film is investigated. The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model. The analytical solution is obtained using Laplace transform method. The whole analysis is presented in dimensionless form. Numerical examples of particular interest have been studied and discussed in details.
Role of spatial inhomogenity in GPCR dimerisation predicted by receptor association-diffusion models
Deshpande, Sneha A.; Pawar, Aiswarya B.; Dighe, Anish; Athale, Chaitanya A.; Sengupta, Durba
2017-06-01
G protein-coupled receptor (GPCR) association is an emerging paradigm with far reaching implications in the regulation of signalling pathways and therapeutic interventions. Recent super resolution microscopy studies have revealed that receptor dimer steady state exhibits sub-second dynamics. In particular the GPCRs, muscarinic acetylcholine receptor M1 (M1MR) and formyl peptide receptor (FPR), have been demonstrated to exhibit a fast association/dissociation kinetics, independent of ligand binding. In this work, we have developed a spatial kinetic Monte Carlo model to investigate receptor homo-dimerisation at a single receptor resolution. Experimentally measured association/dissociation kinetic parameters and diffusion coefficients were used as inputs to the model. To test the effect of membrane spatial heterogeneity on the simulated steady state, simulations were compared to experimental statistics of dimerisation. In the simplest case the receptors are assumed to be diffusing in a spatially homogeneous environment, while spatial heterogeneity is modelled to result from crowding, membrane micro-domains and cytoskeletal compartmentalisation or ‘corrals’. We show that a simple association-diffusion model is sufficient to reproduce M1MR association statistics, but fails to reproduce FPR statistics despite comparable kinetic constants. A parameter sensitivity analysis is required to reproduce the association statistics of FPR. The model reveals the complex interplay between cytoskeletal components and their influence on receptor association kinetics within the features of the membrane landscape. These results constitute an important step towards understanding the factors modulating GPCR organisation.
Ji Zhilong; Ma Yuanwei; Wang Dezhong
2014-01-01
Background: In radioactive nuclides atmospheric diffusion models, the empirical dispersion coefficients were deduced under certain experiment conditions, whose difference with nuclear accident conditions is a source of deviation. A better estimation of the radioactive nuclide's actual dispersion process could be done by correcting dispersion coefficients with observation data, and Genetic Algorithm (GA) is an appropriate method for this correction procedure. Purpose: This study is to analyze the fitness functions' influence on the correction procedure and the forecast ability of diffusion model. Methods: GA, coupled with Lagrange dispersion model, was used in a numerical simulation to compare 4 fitness functions' impact on the correction result. Results: In the numerical simulation, the fitness function with observation deviation taken into consideration stands out when significant deviation exists in the observed data. After performing the correction procedure on the Kincaid experiment data, a significant boost was observed in the diffusion model's forecast ability. Conclusion: As the result shows, in order to improve dispersion models' forecast ability using GA, observation data should be given different weight in the fitness function corresponding to their error. (authors)
Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling
Yudovsky, Dmitry; Durkin, Anthony J.
2011-07-01
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.
Wiecki, Thomas V; Sofer, Imri; Frank, Michael J
2013-01-01
The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python
Thomas V Wiecki
2013-08-01
Full Text Available The diffusion model is a commonly used tool to infer latent psychological processes underlying decision making, and to link them to neural mechanisms based on reaction times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of reaction time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model, which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject / condition than non-hierarchical method, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g. fMRI influence decision making parameters. This paper will first describe the theoretical background of drift-diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the chi-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs
Munoz-Jaramillo, Andres; Martens, Petrus C. H.; Nandy, Dibyendu
2011-01-01
The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double-step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory, which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work, we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main features of this solution can be reproduced by a dynamo simulation using a prescribed (kinematic) diffusivity profile that is based on the spatiotemporal geometric average of the dynamically quenched diffusivity. This bridges the gap between dynamically quenched and kinematic dynamo models, supporting their usage as viable tools for understanding the solar magnetic cycle.
Wu Jie
Full Text Available This paper presents an experimental and numerical model describing the effects of the aggregate shapes and exposure duration of chloride diffusion into cement-based materials. A simple chloride diffusion test was performed on a concrete specimen composed of a mixture of cement mortar with crushed granites and round gravels. A simulation was done and the numerical model developed was applied to the matrix at the meso-scale level and the chloride diffusivity was investigated at 30, 60, and 90 days. The experimental and simulation results showed that the aggregate shape and the exposure duration of chloride diffusing into concrete are of high significance. It was indicated that the model with crushed granite presents a good resistance against chloride ingress, while the model with rounded gravels shows some sensitivity to the chloride penetration. It was also found out that when the time dependence of the diffusion coefficient is not taken into account, the diffusion rate will be overestimated. The meso-scale model developed in this study also provides a new method applied in the analysis of the chloride and water transport that causes damage to concrete considering the particle inclusion and the diffusion duration. Keywords: Meso-scale modeling, Chloride diffusivity, Concrete, Effects of aggregates shape and exposure duration, FEM
Lynn, K. J.; Warren, J. M.
2017-12-01
Nominally anhydrous minerals (NAMs) are important for characterizing deep-Earth water reservoirs, but the water contents of olivine (ol), orthopyroxene (opx), and clinopyroxene (cpx) in peridotites generally do not reflect mantle equilibrium conditions. Ol is typically "dry" and decoupled from H in cpx and opx, which is inconsistent with models of partial melting and/or diffusive loss of H during upwelling beneath mid-ocean ridges. The rehydration of mantle pyroxenes via late-stage re-fertilization has been invoked to explain their relatively high water contents. Here, we use sophisticated 3D diffusion models (after Shea et al., 2015, Am Min) of H in ol, opx, and cpx to investigate the timescales of rehydration across a range of conditions relevant for melt-rock interaction and serpentinization of peridotites. Numerical crystals with 1 mm c-axis lengths and realistic crystal morphologies are modeled using recent H diffusivities that account for compositional variation and diffusion anisotropy. Models were run over timescales of minutes to millions of years and temperatures from 300 to 1200°C. Our 3D models show that, at the high-T end of the range, H concentrations in the cores of NAMs are partially re-equilibrated in as little as a few minutes, and completely re-equilibrated within hours to weeks. At low-T (300°C), serpentinization can induce considerable diffusion in cpx and opx. H contents are 30% re-equilibrated after continuous exposure to hydrothermal fluids for 102 and 105 years, respectively, which is inconsistent with previous interpretations that there is no effect on H in opx under similar conditions. Ol is unaffected after 1 Myr due to the slower diffusivity of the proton-vacancy mechanism at 300°C (2-4 log units lower than for opx). In the middle of the T range (700-1000°C), rehydration of opx and cpx occurs over hours to days, while ol is somewhat slower to respond (days to weeks), potentially allowing the decoupling observed in natural samples to
Carbon dioxide sequestration: Modeling the diffusive and convective transport under a CO2 cap
Allen, Rebecca
2012-01-01
A rise in carbon dioxide levels from industrial emissions is contributing to the greenhouse effect and global warming. CO2 sequestration in saline aquifers is a strategy to reduce atmospheric CO2 levels. Scientists and researchers rely on numerical simulators to predict CO2 storage by modeling the fluid transport behaviour. Studies have shown that after CO2 is injected into a saline aquifer, undissolved CO2 rises due to buoyant forces and will spread laterally away from the injection site under an area of low permeability. CO2 from this ‘capped\\' region diffuses into the fluid underlying it, and the resulting CO2-fluid mixture increases in density. This increase in density leads to gravity-driven convection. Accordingly, diffusive-convective transport is important to model since it predicts an enhanced storage capacity of the saline aquifer. This work incorporates the diffusive and convective transport processes into the transport modeling equation, and uses a self-generated code. Discretization of the domain is done with a cell-centered finite difference method. Cases are set up using similar parameters from published literature in order to compare results. Enhanced storage capacity is predicted in this work, similar to work done by others. A difference in the onset of convective transport between this work and published results is noticed and discussed in this paper. A sensitivity analysis is performed on the density model used in this work, and on the diffusivity value assumed. The analysis shows that the density model and diffusivity value is a key component on simulation results. Also, perturbations are added to porosity and permeability in order to see the effect of perturbations on the onset of convection, and results agree with similar findings by others. This work provides a basis for studying other cases, such as the impact of heterogeneity on the diffusion-convective transport. An extension of this work may involve the use of an equation of state to
Zhang, De-Long; Zhang, Qun; Zhang, Pei; Kang, Jian; Wong, Wing-Han; Yu, Dao-Yin
2016-01-01
Graphical abstract: Diffusion growth of Ga"3"+-doped LiTaO_3(LT) thin film was studied thermodynamically. Some Ga"3"+-doped LT thin films were grown on LT surface by in-diffusion of homogeneously coated Ga_2O_3 film at the temperature range of (1273 to 1473) K. The Ga"3"+ profile in the grown thin film was analyzed by secondary ion mass spectrometry. Form the measured Ga"3"+ profiles, some thermodynamic parameters were obtained. These include diffusivity, diffusion constant, chemical activation energy, solubility, solubility constant and enthalpy of solution. These parameters are crucial to design and growth of a Ga"3"+-doped LT thin film with desired Ga"3"+ profile for integrated optics application. A thermodynamic model is suggested for the growth and verified experimentally. - Highlights: • Diffusion growth of Ga"3"+-doped LiTaO_3 thin film were studied thermodynamically. • Diffusion constant is 1.41 · 10"−"6 m"2/s and activation energy is 237.2 kJ/mol. • Solubility constant is 22.9 · 10"2"6 ions/m"3 and enthalpy of solution is 28.9 kJ/mol. • Ga"3"+ dopant has small effect on LiTaO_3 refractive index. • Ga"3"+ growth can be described by a Fick-type equation with a constant diffusivity. - Abstract: A thermodynamic study was performed on diffusion growth of Ga"3"+-doped LiTaO_3(LT) thin film for integrated optics. Some Ga"3"+-doped LT thin films were grown on LT surface by in-diffusion of homogeneously coated Ga_2O_3 film at the temperature range of (1273 to 1473) K. After growth, the refractive indices at Ga"3"+-doped and un-doped surface parts were measured by prism coupling technique and Li composition there was evaluated from the measured refractive indices. The results show that Ga"3"+ dopant has small effect on the LT index. Li_2O out-diffusion is not measurable. The Ga"3"+ profile in the grown thin film was analysed by secondary ion mass spectrometry. It is found that the grown Ga"3"+ ions follow a complementary error function profile. A
Renny; Supriyanto
2018-04-01
Nutrition is the chemical compounds that needed by the organism for the growth process. In plants, nutrients are organic or inorganic compounds that are absorbed from the roots of the soil. It consist of macro and micro nutrient. Macro nutrients are nutrition that needed by plants in large quantities, such as, nitrogen, calcium, pottacium, magnesium, and sulfur. The total soil nutrient is the difference between the input nutrient and the output nutrients. Input nutrients are nutrient that derived from the decomposition of organic substances. Meanwhile, the output nutrient consists of the nutrients that absorbed by plant roots (uptake), the evaporated nutrients (volatilized) and leached nutrients. The nutrient transport can be done through diffusion process. The diffusion process is essential in removing the nutrient from one place to the root surface. It will cause the rate of absorption of nutrient by the roots will be greater. Nutrient concept in paddy filed can be represented into a mathematical modelling, by making compartment models. The rate of concentration change in the compartment model forms a system of homogeneous linear differential equations. In this research, we will use Laplaces transformation to solve the compartment model and determined the dynamics of macro nutrition due to diffusion process.
Christien, F.; Barbu, A.
2005-01-01
A model based on the cluster dynamics approach was proposed in [A. Hardouin Duparc, C. Moingeon, N. Smetniansky-de-Grande, A. Barbu, J. Nucl. Mater. 302 (2002) 143] to describe point defect agglomeration in metals under irradiation. This model is restricted to materials where point defect diffusion is isotropic and is thus not applicable to anisotropic metals such as zirconium. Following the approach proposed by Woo [C.H. Woo, J. Nucl. Mater. 159 (1988) 237], we extended in this work the model to the case where self-interstitial atoms (SIA) diffusion is anisotropic. The model was then applied to the loop microstructure evolution of a zirconium thin foil irradiated with electrons in a high-voltage microscope. First, the inputs were validated by comparing the numerical results with Hellio et al. experimental results [C. Hellio, C.H. de Novion, L. Boulanger, J. Nucl. Mater. 159 (1988) 368]. Further calculations were made to evidence the effect of the thin foil orientation on the dislocation loop microstructure under irradiation. The result is that it is possible to reproduce for certain orientations the 'unexpected' vacancy loop growth experimentally observed in electron-irradiated zirconium [M. Griffiths, M.H. Loretto, R.E. Sallmann, J. Nucl. Mater. 115 (1983) 313; J. Nucl. Mater. 115 (1983) 323; Philos. Mag. A 49 (1984) 613]. This effect is directly linked to SIA diffusion anisotropy
Cucumo, M.; De Rosa, A.; Ferraro, V.; Kaliakatsos, D.; Marinelli, V.
2009-01-01
Measurements of natural global and diffuse illuminance on four vertical surfaces exposed to north, east, south and west have been carried out at Arcavacata di Rende (Italy). In the work the mean hourly values of the global and diffuse luminous efficacy measured in the period of a year are presented. The hourly data have been compared with the predictions of many calculation models. The comparisons show that, for global efficacy, the differences among the various models are not significant, and the use of a model with a constant value of efficacy gives good predictions of global illuminance. For the prediction of diffuse illuminance the different models behave in a similar way if their coefficients are recalculated and, again, the use of a constant diffuse efficacy provides a good estimate of diffuse illuminance on vertical surfaces
Word-of-mouth marketing and enterprise strategies: a bottom-up diffusion model
Marco REMONDINO
2011-06-01
Full Text Available A comprehensive simulation model is presented, aimed to show the dynamics of social diffusion based on the word of mouth (e.g.: viral marketing over a social network of interconnected individuals. The model is build following a bottom-up approach and the agent based paradigm; this means that the dynamics of the diffusion is simulated in real time and generated at the micro level, not calculated by using mathematical formulas. This allows both to follow – step by step – the emergent process and to be able – if needed – to add complex behavior for the agents and analyze how this impacts the phenomenon at the macro level.
Hybrid transport and diffusion modeling using electron thermal transport Monte Carlo SNB in DRACO
Chenhall, Jeffrey; Moses, Gregory
2017-10-01
The iSNB (implicit Schurtz Nicolai Busquet) multigroup diffusion electron thermal transport method is adapted into an Electron Thermal Transport Monte Carlo (ETTMC) transport method to better model angular and long mean free path non-local effects. Previously, the ETTMC model had been implemented in the 2D DRACO multiphysics code and found to produce consistent results with the iSNB method. Current work is focused on a hybridization of the computationally slower but higher fidelity ETTMC transport method with the computationally faster iSNB diffusion method in order to maximize computational efficiency. Furthermore, effects on the energy distribution of the heat flux divergence are studied. Work to date on the hybrid method will be presented. This work was supported by Sandia National Laboratories and the Univ. of Rochester Laboratory for Laser Energetics.
Radial diffusion in the Uranian radiatian belts - Inferences from satellite absorption loss models
Hood, L. L.
1989-01-01
Low-energy charged particle (LECP) phase space density profiles available from the Voyager/1986 Uranus encounter are analyzed, using solutions of the time-averaged radial diffusion equation for charged particle transport in a dipolar planetary magnetic field. Profiles for lower-energy protons and electrons are first analyzed to infer radial diffusion rate as a function of L, assuming that satellite absorption is the dominant loss process and local sources for these particles are negligible. Satellite macrosignatures present in the experimentally derived profiles are approximately reproduced in several cases, lending credence to the loss model and indicating that magnetospheric distributed losses are not as rapid as satellite absorption near the minimum satellite L shells for the particles. Diffusion rates and L dependences are found to be similar to those previously inferred in the inner Jovian magnetosphere (Thomsen et al., 1977) and for the inner Saturnian magnetosphere (Hood, 1985). Profiles for higher energy electrons and protons are also analyzed using solutions that allow for the existence of significant particle sources as well as sinks. Possible implications for radial diffusion mechanisms in the Uranian radiation belts are discussed.
López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin
2017-09-01
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
A simple model of carcinogenic mutations with time delay and diffusion.
Piotrowska, Monika Joanna; Foryś, Urszula; Bodnar, Marek; Poleszczuk, Jan
2013-06-01
In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. The model essentially follows the idea of Ahangar and Lin (2003) where mutations in three different environmental conditions, namely favorable, competitive and unfavorable, were considered. We focus on the unfavorable conditions that can result from a given treatment, e.g. chemotherapy. Included delay stands for the interactions between benign and other cells. We compare the dynamics of ODEs system, the system with delay and the system with delay and diffusion. We mainly focus on the dynamics when a positive steady state exists. The system which is globally stable in the case without the delay and diffusion is destabilized by increasing delay, and therefore the underlying kinetic dynamics becomes oscillatory due to a Hopf bifurcation for appropriate values of the delay. This suggests the occurrence of spatially non-homogeneous periodic solutions for the system with the delay and diffusion.
A Network Diffusion Model of Food Safety Scare Behavior considering Information Transparency
Tingqiang Chen
2017-01-01
Full Text Available This study constructs the network diffusion model of food safety scare behavior under the effect of information transparency and examines the network topology and evolution characteristics of food safety scare behavior in a numerical simulation. The main conclusions of this study are as follows. (1 Under the effect of information transparency, the network degree distribution of food safety scare behavior diffusion demonstrates the decreasing characteristics of diminishing margins. (2 Food safety scare behavior diffusion increases with the information dissemination rate and consumer concern about food safety incidents and shows the characteristics of monotone increasing. And with the increasing of the government food safety supervision information transparency and media food safety supervision information transparency, the whole is declining characteristic of diminishing marginal. In addition, the extinction of food safety scare behavior cannot be achieved gradually given a single regulation of government food safety supervision information transparency and media food safety supervision information transparency. (3 The interaction effects between improving government food safety supervision information transparency or media food safety supervision information transparency and declining consumer concerns about food safety incidents or information transmission rate can engender the suppression of food safety scare behavior diffusion.
Mueller, A.
1985-01-01
The advantage of the Gauss-function-based models doubtlessly consists in their proven propagation parameter sets and empirical stack plume rise formulas and in their easy matchability and handability. However, grid models based on trace matter transport equation are more convincing concerning their fundamental principle. Grid models of the MODIS type are to acquire a practical applicability comparable to Gauss models by developing techniques allowing to consider the vertical self-movement of the plumes in grid models and to secure improved diffusion co-efficient determination. (orig./PW) [de
Yadav, P.; Chandel, S.S.
2014-01-01
Tilt angle and orientation greatly are influenced on the performance of the solar photo voltaic panels. The tilt angle of solar photovoltaic panels is one of the important parameters for the optimum sizing of solar photovoltaic systems. This paper analyses six different isotropic and anisotropic diffused solar radiation models for optimum tilt angle determination. The predicted optimum tilt angles are compared with the experimentally measured values for summer season under outdoor conditions. The Liu and Jordan model is found to exhibit t lowest error as compared to other models for the location. (author)
Modeling and control of diffusion and low-pressure chemical vapor deposition furnaces
De Waard, H.; De Koning, W. L.
1990-03-01
In this paper a study is made of the heat transfer inside cylindrical resistance diffusion and low-pressure chemical vapor deposition furnaces, aimed at developing an improved temperature controller. A model of the thermal behavior is derived which also covers the important class of furnaces equipped with semitransparent quartz process tubes. The model takes into account the thermal behavior of the thermocouples. It is shown that currently used temperature controllers are highly inefficient for very large scale integration applications. Based on the model an alternative temperature controller of the linear-quadratic-Gaussian type is proposed which features direct wafer temperature control. Some simulation results are given.
Mixed-order phase transition in a minimal, diffusion-based spin model.
Fronczak, Agata; Fronczak, Piotr
2016-07-01
In this paper we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model diffusion based because its Hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.
Jensen, Morten B; Guldberg, Trine L; Harbøll, Anja
2017-01-01
the microscopic tumor cell spread. Gliomas favor spread along the white matter fiber tracts. Tumor growth models incorporating the MRI diffusion tensors (DTI) allow to account more consistently for the glioma growth. The aim of the study was to investigate the potential of a DTI driven growth model to improve...... target definition in glioblastoma (GBM). MATERIAL AND METHODS: Eleven GBM patients were scanned using T1w, T2w FLAIR, T1w + Gd and DTI. The brain was segmented into white matter, gray matter and cerebrospinal fluid. The Fisher-Kolmogorov growth model was used assuming uniform proliferation...
Mueller, Christina J; White, Corey N; Kuchinke, Lars
2017-11-27
The goal of this study was to replicate findings of diffusion model parameters capturing emotion effects in a lexical decision task and investigating whether these findings extend to other tasks of implicit emotion processing. Additionally, we were interested in the stability of diffusion model parameters across emotional stimuli and tasks for individual subjects. Responses to words in a lexical decision task were compared with responses to faces in a gender categorization task for stimuli of the emotion categories: happy, neutral and fear. Main effects of emotion as well as stability of emerging response style patterns as evident in diffusion model parameters across these tasks were analyzed. Based on earlier findings, drift rates were assumed to be more similar in response to stimuli of the same emotion category compared to stimuli of a different emotion category. Results showed that emotion effects of the tasks differed with a processing advantage for happy followed by neutral and fear-related words in the lexical decision task and a processing advantage for neutral followed by happy and fearful faces in the gender categorization task. Both emotion effects were captured in estimated drift rate parameters-and in case of the lexical decision task also in the non-decision time parameters. A principal component analysis showed that contrary to our hypothesis drift rates were more similar within a specific task context than within a specific emotion category. Individual response patterns of subjects across tasks were evident in significant correlations regarding diffusion model parameters including response styles, non-decision times and information accumulation.
Efficient and Enhanced Diffusion of Vector Field for Active Contour Model
Liu, Guoqi; Sun, Lin; Liu, Shangwang
2015-01-01
Gradient vector flow (GVF) is an important external force field for active contour models. Various vector fields based on GVF have been proposed. However, these vector fields are obtained with many iterations and have difficulty in capturing the whole image area. On the other hand, the ability to converge to deep and complex concavity with these vector fields is also needed to improve. In this paper, by analyzing the diffusion equation of GVF, a normalized set is defined and a dynamically nor...
Markowich, Peter; Lorz, Alexander; Francesco, Marco
2010-01-01
We study the system ct + u · ∇c = ∇c -nf(c) nt + u · ∇n = ∇n m - ∇ · (n×(c) ∇c) ut + u·∇u + ∇P - η∇u + n∇φ/ = 0 ∇·u = 0. arising in the modelling of the motion of swimming bacteria under the effect of diffusion, oxygen-taxis and transport through
Dynamics of a Diffusive Predator-Prey Model with Allee Effect on Predator
Xiaoqin Wang
2013-01-01
Full Text Available The reaction-diffusion Holling-Tanner prey-predator model considering the Allee effect on predator, under zero-flux boundary conditions, is discussed. Some properties of the solutions, such as dissipation and persistence, are obtained. Local and global stability of the positive equilibrium and Turing instability are studied. With the help of the numerical simulations, the rich Turing patterns, including holes, stripes, and spots patterns, are obtained.
On weak solutions to a diffuse interface model of a binary mixture of compressible fluids
Feireisl, Eduard
2016-01-01
Roč. 9, č. 1 (2016), s. 173-183 ISSN 1937-1632 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Euler-Cahn-Hilliard system * weak solution * diffuse interface model Subject RIV: BA - General Mathematics Impact factor: 0.781, year: 2016 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=12093
The Attentional Drift Diffusion Model of Simple Perceptual Decision-Making
Gabriela Tavares; Pietro Perona; Antonio Rangel; Antonio Rangel
2017-01-01
Perceptual decisions requiring the comparison of spatially distributed stimuli that are fixated sequentially might be influenced by fluctuations in visual attention. We used two psychophysical tasks with human subjects to investigate the extent to which visual attention influences simple perceptual choices, and to test the extent to which the attentional Drift Diffusion Model (aDDM) provides a good computational description of how attention affects the underlying decision processes. We find e...
Carrillo, J. A.; Desvillettes, L.; Fellner, K.
2009-01-01
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Carrillo, J. A.
2009-10-30
Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [5], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters. © Taylor & Francis Group, LLC.
Ganeshan, S.; Hector, L.G.; Liu, Z.-K.
2011-01-01
Research highlights: → Implemented the eight frequency model for impurity diffusion in hexagonal metals. → Model inputs were energetics/vibrational properties from first princples. → Predicted diffusion coefficients for Al, Ca, Zn and Sn impurity diffusion in Mg. → Successful prediction of partial correlation factors and jump frequencies. → Good agreement between calculated and experimental results. - Abstract: Diffusion in dilute Mg-X alloys, where X denotes Al, Zn, Sn and Ca impurities, was investigated with first-principles density functional theory in the local density approximation. Impurity diffusion coefficients were computed as a function of temperature using the 8-frequency model which provided the relevant impurity and solvent (Mg) jump frequencies and correlation factors. Minimum energy pathways for impurity diffusion and associated saddle point structures were computed with the climbing image nudged elastic band method. Vibrational properties were obtained with the supercell (direct) method for lattice dynamics. Calculated diffusion coefficients were compared with available experimental data. For diffusion between basal planes, we find D Mg-Ca > D Mg-Zn > D Mg-Sn > D Mg-Al, where D is the diffusion coefficient. For diffusion within a basal plane, the same trend holds except that D Mg-Zn overlaps with D Mg-Al at high temperatures and D Mg-Sn at low temperatures. These trends were explored with charge density contours in selected planes of each Mg-X alloy, the variation of the activation energy for diffusion with the atomic radius of each impurity and the electronic density of states. The theoretical methodology developed herein can be applied to impurity diffusion in other hexagonal materials.