Journal articles: 'Diffusion drift models'

1

Glitzky, Annegret. "Analysis of spin-polarized drift-diffusion models." PAMM 8, no. 1 (December 2008): 10717–18. http://dx.doi.org/10.1002/pamm.200810717.

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Degond, Pierre, Florian M�hats, and Christian Ringhofer. "Quantum Energy-Transport and Drift-Diffusion Models." Journal of Statistical Physics 118, no. 3-4 (February 2005): 625–67. http://dx.doi.org/10.1007/s10955-004-8823-3.

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3

Hübner, Ronald, and Thomas Pelzer. "Improving parameter recovery for conflict drift-diffusion models." Behavior Research Methods 52, no. 5 (February 10, 2020): 1848–66. http://dx.doi.org/10.3758/s13428-020-01366-8.

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Abstract Several drift-diffusion models have been developed to account for the performance in conflict tasks. Although a common characteristic of these models is that the drift rate changes within a trial, their architecture is rather different. Comparative studies usually examine which model fits the data best. However, a good fit does not guarantee good parameter recovery, which is a necessary condition for a valid interpretation of any fit. A recent simulation study revealed that recovery performance varies largely between models and individual parameters. Moreover, recovery was generally not very impressive. Therefore, the aim of the present study was to introduce and test an improved fit procedure. It is based on a grid search for determining the initial parameter values and on a specific criterion for assessing the goodness of fit. Simulations show that not only the fit performance but also parameter recovery improved substantially by applying this procedure, compared to the standard one. The improvement was largest for the most complex model.

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Langner, M., J. Peinke, F. Flemisch, M. Baumann, and D. Beckmann. "Drift and diffusion based models of driver behavior." European Physical Journal B 76, no. 1 (June 4, 2010): 99–107. http://dx.doi.org/10.1140/epjb/e2010-00148-8.

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Chalub, Fabio A. C. C., Peter A. Markowich, Beno�t Perthame, and Christian Schmeiser. "Kinetic Models for Chemotaxis and their Drift-Diffusion Limits." Monatshefte f�r Mathematik 142, no. 1-2 (June 1, 2004): 123–41. http://dx.doi.org/10.1007/s00605-004-0234-7.

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Comte, Fabienne, and Valentine Genon-Catalot. "Drift estimation on non compact support for diffusion models." Stochastic Processes and their Applications 134 (April 2021): 174–207. http://dx.doi.org/10.1016/j.spa.2021.01.001.

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7

Kordt, Pascal, Sven Stodtmann, Alexander Badinski, Mustapha Al Helwi, Christian Lennartz, and Denis Andrienko. "Parameter-free continuous drift–diffusion models of amorphous organic semiconductors." Physical Chemistry Chemical Physics 17, no. 35 (2015): 22778–83. http://dx.doi.org/10.1039/c5cp03605d.

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Stevens, A., K. Kang, and H. J. Hwang. "Drift-diffusion limits of kinetic models for chemotaxis: A generalization." Discrete and Continuous Dynamical Systems - Series B 5, no. 2 (February 2005): 319–34. http://dx.doi.org/10.3934/dcdsb.2005.5.319.

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Labiod, Samir, Saida Latreche, Mourad Bella, and Christian Gontrand. "Combined Electromagnetic and Drift Diffusion Models for Microwave Semiconductor Device." Journal of Electromagnetic Analysis and Applications 03, no. 10 (2011): 423–29. http://dx.doi.org/10.4236/jemaa.2011.310067.

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10

Brezzi, Franco, Luisa Donatella Marini, and Paola Pietra. "Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models." SIAM Journal on Numerical Analysis 26, no. 6 (December 1989): 1342–55. http://dx.doi.org/10.1137/0726078.

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11

Wang, Wei-Min, and Jing Wang. "NONPARAMETRIC HYPOTHESIS OF DRIFT FUNCTION IN LOCALLY STATIONARY DIFFUSION MODELS." Far East Journal of Applied Mathematics 100, no. 3 (December 19, 2018): 181–96. http://dx.doi.org/10.17654/am100030181.

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12

de Falco, Carlo, Emilio Gatti, Andrea L. Lacaita, and Riccardo Sacco. "Quantum-corrected drift-diffusion models for transport in semiconductor devices." Journal of Computational Physics 204, no. 2 (April 2005): 533–61. http://dx.doi.org/10.1016/j.jcp.2004.10.029.

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13

Baro, M., H. Neidhardt, and J. Rehberg. "Current Coupling of Drift-Diffusion Models and Schrödinger--Poisson Systems: Dissipative Hybrid Models." SIAM Journal on Mathematical Analysis 37, no. 3 (January 2005): 941–81. http://dx.doi.org/10.1137/040611690.

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14

Elbanna, Amany R. "Strategic Systems Implementation: Diffusion through Drift." Journal of Information Technology 23, no. 2 (June 2008): 89–96. http://dx.doi.org/10.1057/palgrave.jit.2000130.

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The adoption of Enterprise Resource Planning (ERP) systems follows various paths in organisations and achieves diverse results. The traditional models of diffusion of innovation applied in information systems are not sufficient to explain such variations in adoption. This study examines the process of drift in an ERP project to answer the questions of how and why drift tends to occur in such projects. It applies Actor Network Theory to interpret the data. This analytical lens reveals that a software implementation project's fate depends on each move it takes and each party involved in handling that move. Every handling of the project by different parties could present either a positive modality (that strengthens it and pushes it forward on its track) or a negative modality (that weakens its initial form and drags it onto a different direction). The study provides an alternative view of diffusion, and an explanation of drift in the ERP case that could be extended to other technological projects. It invites practitioners to monitor the various movements of their projects and to allow strategic drift in order to achieve a successful implementation.

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15

Anile, A. M., O. Muscato, S. Rinaudo, and P. Vergari. "Testing Hydrodynamical Models on the Characteristics of a One-Dimensional Submicrometer Structure." VLSI Design 6, no. 1-4 (January 1, 1998): 155–60. http://dx.doi.org/10.1155/1998/63185.

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Recent advances in technology leads to increasing high speed performance of submicrometer electron devices by the scaling of both process and geometry. In order to aid the design of these devices it is necessary to utilize powerful numerical simulation tools. In an industrial environment the simulation codes based on the Drift-Diffusion models have been widely used. However the shrinking dimension of the devices causes the Drift-Diffusion based simulators to become less accurate. Then it is necessary to utilize more refined models (including higher order moments of the distribution function) in order to correctly predict the behaviour of these devices. Several hydrodynamical models have been considered as viable simulation tools. It is possible to discriminate among the several hydrodynamical models on the basis of their results on the output characteristics of the electron device which are measurable (I-V curves). We have analyzed two classes of hydrodynamical models: i) HFIELDS hydrodynamical models and HFIELDS drift-diffusion model; ii) self-consistent extended hydrodynamical models with relaxation times determined from Monte Carlo simulations.

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16

Lewis, Fraser I., Godfrey Guga, Paschal Mdoe, Esto Mduma, Cloupas Mahopo, Pascal Bessong, Stephanie A. Richard, and Benjamin J. J. McCormick. "Introducing a drift and diffusion framework for childhood growth research." Gates Open Research 4 (June 29, 2020): 71. http://dx.doi.org/10.12688/gatesopenres.13123.1.

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Background: Growth trajectories are highly variable between children, making epidemiological analyses challenging both to the identification of malnutrition interventions at the population level and also risk assessment at individual level. We introduce stochastic differential equation (SDE) models into child growth research. SDEs describe flexible dynamic processes comprising: drift - gradual smooth changes – such as physiology or gut microbiome, and diffusion - sudden perturbations, such as illness or infection. Methods: We present a case study applying SDE models to child growth trajectory data from the Haydom, Tanzania and Venda, South Africa sites within the MAL-ED cohort. These data comprise n=460 children aged 0-24 months. A comparison with classical curve fitting (linear mixed models) is also presented. Results: The SDE models offered a wide range of new flexible shapes and parameterizations compared to classical additive models, with performance as good or better than standard approaches. The predictions from the SDE models suggest distinct longitudinal clusters that form distinct ‘streams’ hidden by the large between-child variability. Conclusions: Using SDE models to predict future growth trajectories revealed new insights in the observed data, where trajectories appear to cluster together in bands, which may have a future risk assessment application. SDEs offer an attractive approach for child growth modelling and potentially offer new insights.

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Lewis, Fraser I., Godfrey Guga, Paschal Mdoe, Esto Mduma, Cloupas Mahopo, Pascal Bessong, Stephanie A. Richard, and Benjamin J. J. McCormick. "Introducing a drift and diffusion framework for childhood growth research." Gates Open Research 4 (November 26, 2020): 71. http://dx.doi.org/10.12688/gatesopenres.13123.2.

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Background: Growth trajectories are highly variable between children, making epidemiological analyses challenging both to the identification of malnutrition interventions at the population level and also risk assessment at individual level. We introduce stochastic differential equation (SDE) models into child growth research. SDEs describe flexible dynamic processes comprising: drift - gradual smooth changes – such as physiology or gut microbiome, and diffusion - sudden perturbations, such as illness or infection. Methods: We present a case study applying SDE models to child growth trajectory data from the Haydom, Tanzania and Venda, South Africa sites within the MAL-ED cohort. These data comprise n=460 children aged 0-24 months. A comparison with classical curve fitting (linear mixed models) is also presented. Results: The SDE models offered a wide range of new flexible shapes and parameterizations compared to classical additive models, with performance as good or better than standard approaches. The predictions from the SDE models suggest distinct longitudinal clusters that form distinct ‘streams’ hidden by the large between-child variability. Conclusions: Using SDE models to predict future growth trajectories revealed new insights in the observed data, where trajectories appear to cluster together in bands, which may have a future risk assessment application. SDEs offer an attractive approach for child growth modelling and potentially offer new insights.

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18

Smith, Philip L., and Cameron R. L. McKenzie. "Diffusive Information Accumulation by Minimal Recurrent Neural Models of Decision Making." Neural Computation 23, no. 8 (August 2011): 2000–2031. http://dx.doi.org/10.1162/neco_a_00150.

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An important class of psychological models of decision making assumes that evidence is accumulated by a diffusion process to a response criterion. These models have successfully accounted for reaction time (RT) distributions and choice probabilities from a wide variety of experimental tasks. An outstanding theoretical problem is how the integration process that underlies diffusive evidence accumulation can be realized neurally. Wang ( 2001 , 2002 ) has suggested that long timescale neural integration may be implemented by persistent activity in reverberation loops. We analyze a simple recurrent decision making architecture and show that it leads to a diffusive accumulation process. The process has the form of a time-inhomogeneous Ornstein-Uhlenbeck velocity process with linearly increasing drift and diffusion coefficients. The resulting model predicts RT distributions and choice probabilities that closely approximate those found in behavioral data.

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Pisarenko, Ivan, and Eugeny Ryndin. "Drift-Diffusion Simulation of High-Speed Optoelectronic Devices." Electronics 8, no. 1 (January 18, 2019): 106. http://dx.doi.org/10.3390/electronics8010106.

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In this paper, we address the problem of research and development of the advanced optoelectronic devices designed for on-chip optical interconnections in integrated circuits. The development of the models, techniques, and applied software for the numerical simulation of carrier transport and accumulation in high-speed AIIIBV (A and B refer to group III and V semiconductors, respectively) optoelectronic devices is the purpose of the paper. We propose the model based on the standard drift-diffusion equations, rate equation for photons in an injection laser, and complex analytical models of carrier mobility, generation, and recombination. To solve the basic equations of the model, we developed the explicit and implicit techniques of drift-diffusion numerical simulation and applied software. These aids are suitable for the stationary and time-domain simulation of injection lasers and photodetectors with various electrophysical, constructive, and technological parameters at different control actions. We applied the model for the simulation of the lasers with functionally integrated amplitude and frequency modulators and uni-travelling-carrier photodetectors. According to the results of non-stationary simulation, it is reasonable to optimize the parameters of the lasers-modulators and develop new construction methods aimed at the improvement of photodetectors’ response time.

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20

Teunissen, Jannis. "Improvements for drift-diffusion plasma fluid models with explicit time integration." Plasma Sources Science and Technology 29, no. 1 (January 28, 2020): 015010. http://dx.doi.org/10.1088/1361-6595/ab6757.

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21

Baccarani, Giorgio, Elena Gnani, Antonio Gnudi, Susanna Reggiani, and Massimo Rudan. "Theoretical foundations of the quantum drift-diffusion and density-gradient models." Solid-State Electronics 52, no. 4 (April 2008): 526–32. http://dx.doi.org/10.1016/j.sse.2007.10.051.

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22

JU, QIANGCHANG, and SHU WANG. "QUASI-NEUTRAL LIMIT OF THE MULTIDIMENSIONAL DRIFT-DIFFUSION MODELS FOR SEMICONDUCTORS." Mathematical Models and Methods in Applied Sciences 20, no. 09 (September 2010): 1649–79. http://dx.doi.org/10.1142/s021820251000474x.

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This paper is devoted to the rigorous justification of the quasi-neutral limit of bipolar transient drift-diffusion models for semiconductors with p–n junctions in the multidimensional space. The general initial data and smooth sign-changing doping profiles with good boundary conditions are considered. The limit is performed rigorously by using multiple scaling asymptotic analysis, in which one main point is the construction of a more accurate approximate solution involving the effect of initial layer. The uniform estimates with respect to the scaled Debye length are obtained through the elaborate energy method and the relative entropy functional method.

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23

Jüngel, Ansgar, and Nicola Zamponi. "Two spinorial drift-diffusion models for quantum electron transport in graphene." Communications in Mathematical Sciences 11, no. 3 (2013): 807–30. http://dx.doi.org/10.4310/cms.2013.v11.n3.a7.

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24

Alabau, Fatiha. "Structural properties of the one-dimensional drift-diffusion models for semiconductors." Transactions of the American Mathematical Society 348, no. 3 (1996): 823–71. http://dx.doi.org/10.1090/s0002-9947-96-01519-x.

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25

FUCHS, F., and F. POUPAUD. "ASYMPTOTICAL AND NUMERICAL ANALYSIS OF DEGENERACY EFFECTS ON THE DRIFT-DIFFUSION EQUATIONS FOR SEMICONDUCTORS." Mathematical Models and Methods in Applied Sciences 05, no. 08 (December 1995): 1093–111. http://dx.doi.org/10.1142/s0218202595000577.

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A current approximation for modeling electron transport in semiconductor devices is to assume small electron density. Through this method nondegenerate models are obtained. Here we present an asymptotical analysis of that approximation on the drift-diffusion equation. The numerical approximations of the degenerate and nondegenerate equations are then compared. A modified Scharfetter-Gummel scheme which integrates the degenerate drift-diffusion equation is proposed for comparison.

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26

Smith, Philip L., and Simon D. Lilburn. "Vision for the blind: visual psychophysics and blinded inference for decision models." Psychonomic Bulletin & Review 27, no. 5 (June 8, 2020): 882–910. http://dx.doi.org/10.3758/s13423-020-01742-7.

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Abstract Evidence accumulation models like the diffusion model are increasingly used by researchers to identify the contributions of sensory and decisional factors to the speed and accuracy of decision-making. Drift rates, decision criteria, and nondecision times estimated from such models provide meaningful estimates of the quality of evidence in the stimulus, the bias and caution in the decision process, and the duration of nondecision processes. Recently, Dutilh et al. (Psychonomic Bulletin & Review 26, 1051–1069, 2019) carried out a large-scale, blinded validation study of decision models using the random dot motion (RDM) task. They found that the parameters of the diffusion model were generally well recovered, but there was a pervasive failure of selective influence, such that manipulations of evidence quality, decision bias, and caution also affected estimated nondecision times. This failure casts doubt on the psychometric validity of such estimates. Here we argue that the RDM task has unusual perceptual characteristics that may be better described by a model in which drift and diffusion rates increase over time rather than turn on abruptly. We reanalyze the Dutilh et al. data using models with abrupt and continuous-onset drift and diffusion rates and find that the continuous-onset model provides a better overall fit and more meaningful parameter estimates, which accord with the known psychophysical properties of the RDM task. We argue that further selective influence studies that fail to take into account the visual properties of the evidence entering the decision process are likely to be unproductive.

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27

Linetsky, Vadim. "On the transition densities for reflected diffusions." Advances in Applied Probability 37, no. 02 (June 2005): 435–60. http://dx.doi.org/10.1017/s0001867800000252.

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and should prove useful in applications.

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Linetsky, Vadim. "On the transition densities for reflected diffusions." Advances in Applied Probability 37, no. 2 (June 2005): 435–60. http://dx.doi.org/10.1239/aap/1118858633.

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and should prove useful in applications.

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Alasio, Luca, Maria Bruna, and Yves Capdeboscq. "Stability estimates for systems with small cross-diffusion." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 3 (May 2018): 1109–35. http://dx.doi.org/10.1051/m2an/2018036.

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We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems. We focus on stability estimates, that is, continuous dependence of solutions with respect to the nonlinearities in the diffusion and in the drift terms. We establish well-posedness and stability estimates in an appropriate Banach space. Under additional assumptions we show that these estimates are time independent. These results apply to several problems from mathematical biology; they allow comparisons between the solutions of different models a priori. For specific cell motility models from the literature, we illustrate the limit of the stability estimates we have derived numerically, and we document the behaviour of the solutions for extremal values of the parameters.

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ARABSHAHI, H., REZAEE ROKN-ABADI, and S. GOLAFROZ. "COMPARISON OF TWO-VALLEY HYDRODYNAMIC MODEL IN BULK SiC AND ZnO MATERIALS." Modern Physics Letters B 23, no. 23 (September 10, 2009): 2807–18. http://dx.doi.org/10.1142/s0217984909020916.

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This report reviews the feasibility of two-dimensional hydrodynamic models in bulk SiC and ZnO semiconductor materials. Although the single-gas hydrodynamic model is superior to the drift-diffusion or energy balance model, it is desirable to direct the efforts of future research in the direction of multi-valley hydrodynamic models. The hydrodynamic model is able to describe inertia effects which play an increasing role in different fields of micro and optoelectronics where simplified charge transport models like the drift-diffusion model and the energy balance model are no longer applicable. Results of extensive numerical simulations are shown for SiC and ZnO materials, which are in fair agreement with other theoretical or experimental methods.

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31

Dikalyuk, A. S., S. E. Kuratov, M. G. Lobok, and D. A. Storozhev. "Comparison of Results of Kinetic and Drift-Diffusion Models of Penning Discharge." Journal of Physics: Conference Series 1250 (June 2019): 012033. http://dx.doi.org/10.1088/1742-6596/1250/1/012033.

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32

Patil, Mahesh B., Y. Ohkura, T. Toyabe, and S. Ihara. "On coupling the drift-diffusion and Monte Carlo models for MOSFET simulation." Solid-State Electronics 38, no. 4 (April 1995): 935–36. http://dx.doi.org/10.1016/0038-1101(94)00206-u.

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33

Berger, Alexander, Simon Sanwald, Christian Montag, and Markus Kiefer. "The Influence of the BDNF Val66Met Polymorphism on Mechanisms of Semantic Priming: Analyses with Drift-Diffusion Models of Masked and Unmasked Priming." Advances in Cognitive Psychology 17, no. 1 (March 2021): 70–87. http://dx.doi.org/10.5709/acp-0318-z.

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Automatic and strategic processes in semantic priming can be investigated with masked and unmasked priming tasks. Unmasked priming is thought to enable strategic processes due to the conscious processing of primes, while masked priming exclusively depends on automatic processes due to the invisibility of the prime. Besides task properties, interindividual differences may alter priming effects. In a recent study, masked and unmasked priming based on mean response time (RT) and error rate (ER) differed as a function of the BDNF Val66Met polymorphism (Sanwald et al., 2020). The BDNF Val66Met polymorphism is related to the integrity of several cognitive executive functions and might thus influence the magnitude of priming. In the present study, we reanalyzed this data with drift-diffusion models. Drift-diffusion models conjointly analyze single trial RT and ER data and serve as a framework to elucidate cognitive processes underlying priming. Masked and unmasked priming effects were observed for the drift rates ν, presumably reflecting semantic preactivation. Priming effects on nondecision time t0 were especially pronounced in unmasked priming, suggesting additional conscious processes to be involved in the t0 modulation. Priming effects on the decision thresholds a may reflect a speed-accuracy tradeoff. Considering the BDNF Val66Met polymorphism, we found lowered drift rates and decision thresholds for Met allele carriers, possibly reflecting a superficial processing style in Met allele carriers. The present study shows that differences in cognitive tasks between genetic groups can be elucidated using drift-diffusion modeling.

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Muscato, Orazio, and Vincenza Di Stefano. "A hierarchy of hydrodynamic models for silicon carbide semiconductors." Communications in Applied and Industrial Mathematics 8, no. 1 (December 20, 2017): 251–64. http://dx.doi.org/10.1515/caim-2017-0013.

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Abstract The electro-thermal transport in silicon carbide semiconductors can be described by an extended hydrodynamic model, obtained by taking moments from kinetic equations, and using the Maximum Entropy Principle. By performing appropriate scaling, one can obtain reduced transport models such as the Energy transport and the drift-diffusion ones, where the transport coefficients are explicitly determined.

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Khadir, Abdelkader, Nouredine Sengouga, and Mohamed Kamel Abdelhafidi. "Germanium Gradient Optimization for High-Speed Silicon Germanium Hetero-Junction Bipolar Transistors." Annals of West University of Timisoara - Physics 61, no. 1 (December 1, 2019): 22–32. http://dx.doi.org/10.2478/awutp-2019-0002.

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AbstractThe effect of germanium trapezoidal profile shape on the direct current (DC) current gain (βF), cut-off frequency (fT) and maximum oscillation frequency (fMAX) of silicon-germanium (SiGe) hetero-junction bipolar transistors (HBTs) has been investigated. The energy balance (EB), hydrodynamic (HD) and drift-diffusion (DD) physical transport models in SILVACO technology computer aided design (T-CAD) simulator were used. It was found that the current gain values using energy balance model are higher than hydrodynamic and much higher than those corresponding to drift-diffusion. Moreover, decreasing the germanium gradient slope towards the collector side of the base enhances the maximum oscillation frequencies using HD and EB models whilst, they remain stable for DD model.

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Rus, Florina Stefania, Stefan Danica Novaconi, Paulina Vlazan, and Madalina Ivanovici. "Removal of Methylene Blue by Activated Glass Foams with TiO2 in Dark and Simulated Solar Light." Annals of West University of Timisoara - Physics 61, no. 1 (December 1, 2019): 33–43. http://dx.doi.org/10.2478/awutp-2019-0003.

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AbstractThe effect of germanium trapezoidal profile shape on the direct current (DC) current gain (βF), cut-off frequency (fT) and maximum oscillation frequency (fMAX) of silicon-germanium (SiGe) hetero-junction bipolar transistors (HBTs) has been investigated. The energy balance (EB), hydrodynamic (HD) and drift-diffusion (DD) physical transport models in SILVACO technology computer aided design (T-CAD) simulator were used. It was found that the current gain values using energy balance model are higher than hydrodynamic and much higher than those corresponding to drift-diffusion. Moreover, decreasing the germanium gradient slope towards the collector side of the base enhances the maximum oscillation frequencies using HD and EB models whilst, they remain stable for DD model.

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37

Knessl, Charles. "Exact and asymptotic solutions to a PDE that arises in time-dependent queues." Advances in Applied Probability 32, no. 01 (March 2000): 256–83. http://dx.doi.org/10.1017/s0001867800009873.

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We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection-diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.

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Knessl, Charles. "Exact and asymptotic solutions to a PDE that arises in time-dependent queues." Advances in Applied Probability 32, no. 1 (March 2000): 256–83. http://dx.doi.org/10.1239/aap/1013540033.

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We consider a diffusing particle in one dimension that is subject to a time-dependent drift or potential field. A reflecting barrier constrains the particle's position to the half-line X ≥ 0. Such models arise naturally in the study of queues with time-dependent arrival rates, as well as in advection-diffusion problems of mathematical physics. We solve for the probability distribution of the particle as a function of space and time. Then we do a detailed study of the asymptotic properties of the solution, for various ranges of space and time. We also relate our asymptotic results to those obtained by probabilistic approaches, such as central limit theorems and large deviations. We consider drifts that are either piecewise constant or linear functions of time.

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39

Bees, Martin A., and Ottavio A. Croze. "Dispersion of biased swimming micro-organisms in a fluid flowing through a tube." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (February 10, 2010): 2057–77. http://dx.doi.org/10.1098/rspa.2009.0606.

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Classical Taylor–Aris dispersion theory is extended to describe the transport of suspensions of self-propelled dipolar cells in a tubular flow. General expressions for the mean drift and effective diffusivity are determined exactly in terms of axial moments and compared with an approximation a la Taylor. As in the Taylor–Aris case, the skewness of a finite distribution of biased swimming cells vanishes at long times. The general expressions can be applied to particular models of swimming micro-organisms, and thus be used to predict swimming drift and diffusion in tubular bioreactors, and to elucidate competing unbounded swimming drift and diffusion descriptions. Here, specific examples are presented for gyrotactic swimming algae.

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40

Pedersen, Mads L., and Michael J. Frank. "Simultaneous Hierarchical Bayesian Parameter Estimation for Reinforcement Learning and Drift Diffusion Models: a Tutorial and Links to Neural Data." Computational Brain & Behavior 3, no. 4 (May 26, 2020): 458–71. http://dx.doi.org/10.1007/s42113-020-00084-w.

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AbstractCognitive models have been instrumental for generating insights into the brain processes underlying learning and decision making. In reinforcement learning it has recently been shown that not only choice proportions but also their latency distributions can be well captured when the choice function is replaced with a sequential sampling model such as the drift diffusion model. Hierarchical Bayesian parameter estimation further enhances the identifiability of distinct learning and choice parameters. One caveat is that these models can be time-consuming to build, sample from, and validate, especially when models include links between neural activations and model parameters. Here we describe a novel extension to the widely used hierarchical drift diffusion model (HDDM) toolbox, which facilitates flexible construction, estimation, and evaluation of the reinforcement learning drift diffusion model (RLDDM) using hierarchical Bayesian methods. We describe the types of experiments most applicable to the model and provide a tutorial to illustrate how to perform quantitative data analysis and model evaluation. Parameter recovery confirmed that the method can reliably estimate parameters with varying numbers of synthetic subjects and trials. We also show that the simultaneous estimation of learning and choice parameters can improve the sensitivity to detect brain–behavioral relationships, including the impact of learned values and fronto-basal ganglia activity patterns on dynamic decision parameters.

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BANASIAK, JACEK. "MATHEMATICAL PROPERTIES OF INELASTIC SCATTERING MODELS IN LINEAR KINETIC THEORY." Mathematical Models and Methods in Applied Sciences 10, no. 02 (March 2000): 163–86. http://dx.doi.org/10.1142/s0218202500000112.

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In this paper we analyse properties of collision operators which occur in linear Boltzmann–Maxwell models with inelastic scattering. In particular, we prove the solvability of the Cauchy problem for such models. These results form a basis for further applications of these models and, in particular, for their asymptotic analysis and the derivation of the drift–diffusion approximation.

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Holmes, Geoffrey R., Giles Dixon, Sean R. Anderson, Constantino Carlos Reyes-Aldasoro, Philip M. Elks, Stephen A. Billings, Moira K. B. Whyte, Visakan Kadirkamanathan, and Stephen A. Renshaw. "Drift-Diffusion Analysis of Neutrophil Migration during Inflammation Resolution in a Zebrafish Model." Advances in Hematology 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/792163.

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Neutrophils must be removed from inflammatory sites for inflammation to resolve. Recent work in zebrafish has shown neutrophils can migrate away from inflammatory sites, as well as die in situ. The signals regulating the process of reverse migration are of considerable interest, but remain unknown. We wished to study the behaviour of neutrophils during reverse migration, to see whether they moved away from inflamed sites in a directed fashion in the same way as they are recruited or whether the inherent random component of their migration was enough to account for this behaviour. Using neutrophil-driven photoconvertible Kaede protein in transgenic zebrafish larvae, we were able to specifically label neutrophils at an inflammatory site generated by tailfin transection. The locations of these neutrophils over time were observed and fitted using regression methods with two separate models: pure-diffusion and drift-diffusion equations. While a model hypothesis test (theF-test) suggested that the datapoints could be fitted by the drift-diffusion model, implying a fugetaxis process, dynamic simulation of the models suggested that migration of neutrophils away from a wound is better described by a zero-drift, “diffusion” process. This has implications for understanding the mechanisms of reverse migration and, by extension, neutrophil retention at inflammatory sites.

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Bellouquid, Abdel, Juanjo Nieto, and Luis Urrutia. "About the kinetic description of fractional diffusion equations modeling chemotaxis." Mathematical Models and Methods in Applied Sciences 26, no. 02 (November 19, 2015): 249–68. http://dx.doi.org/10.1142/s0218202516400029.

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In this paper, we are interested in the microscopic description of fractional diffusion chemotactic models. We will use the kinetic framework of collisional equations having a heavy-tailed distribution as equilibrium state and take an adequate hydrodynamic scaling to deduce the fractional Keller–Segel system for the cell dynamics. In addition, we use this frame to deduce some models for chemotaxis with fractional diffusion including biological effects and non-standard drift terms.

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Freitas, Frederico Campos, Angelica Nakagawa Lima, Vinícius de Godoi Contessoto, Paul C. Whitford, and Ronaldo Junio de Oliveira. "Drift-diffusion (DrDiff) framework determines kinetics and thermodynamics of two-state folding trajectory and tunes diffusion models." Journal of Chemical Physics 151, no. 11 (September 21, 2019): 114106. http://dx.doi.org/10.1063/1.5113499.

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Kerswill, Paul, Eivind Nessa Torgersen, and Susan Fox. "Reversing “drift”: Innovation and diffusion in the London diphthong system." Language Variation and Change 20, no. 3 (October 2008): 451–91. http://dx.doi.org/10.1017/s0954394508000148.

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AbstractThis study contributes to innovation and diffusion models by examining phonetic changes in London English. It evaluates Sapir's notion of “drift,” which involves “natural,” unconscious change, in relation to these changes. Investigating parallel developments in two related varieties of English enables drift to be tested in terms of the effect of extralinguistic factors. The diphthongs ofprice,mouth,face, andgoatin both London and New Zealand English are characterized by “Diphthong Shift,” a process that continued unabated in New Zealand. A new, large data set of London speech shows Diphthong Shift reversal, providing counterevidence for drift. We discuss Diphthong Shift and its “reversal” in relation to innovation, diffusion, leveling, and supralocalization, arguing that sociolinguistic factors and dialect contact override natural Diphthong Shift. Studying dialect change in a metropolis, with its large and linguistically innovative minority ethnic population, is of the utmost importance in understanding the dynamics of change.

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Kumar, Sunil, and Vimal Kumar Agrawal. "DESIGN AND SIMULATION OF DRIFT-DIFFUSION AND HYDRODYNAMIC MODELS FOR AlGaN/GaN HEMTs." ICTACT Journal on Microelectronics 1, no. 4 (January 1, 2016): 137–40. http://dx.doi.org/10.21917/ijme.2016.0029.

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Zou, Jiayong. "Comment on ‘Improvements for drift-diffusion plasma fluid models with explicit time integration’." Plasma Sources Science and Technology 29, no. 9 (September 10, 2020): 098002. http://dx.doi.org/10.1088/1361-6595/aba984.

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de Falco, Carlo, Joseph W. Jerome, and Riccardo Sacco. "Quantum-corrected drift-diffusion models: Solution fixed point map and finite element approximation." Journal of Computational Physics 228, no. 5 (March 2009): 1770–89. http://dx.doi.org/10.1016/j.jcp.2008.11.010.

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Allen, E. J. "SDE models with exponential drift and diffusion for approximating fatigue crack growth dynamics." Engineering Fracture Mechanics 200 (September 2018): 75–85. http://dx.doi.org/10.1016/j.engfracmech.2018.07.013.

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Yu, Feng, and Yong Yin. "Oil Spill Visualization Based on the Numeric Simulation of Tidal Current." International Journal of Virtual Reality 8, no. 2 (January 1, 2009): 71–74. http://dx.doi.org/10.20870/ijvr.2009.8.2.2727.

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This paper proposes an approach to implement the 3D visualization of oil spill based on tidal hydrodynamic model. It simulates tidal current of M2 component tide in Jiaozhou Bay. The simulation results conform to the tidal theory and probably conform to the flow measurement report of crude oil pier Phase III at Qingdao Harbor. Based on tidal current and eye-point related adaptive ocean surface mesh model, by analyzing the drift and diffusion mathematical models of oil spill on the sea, the dynamic visualization of drift and diffusion course of oil on the sea were implemented, the visualization result is satisfactory.

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Journal articles on the topic 'Diffusion drift models'

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