Pricing turbo warrants under mixed-exponential jump diffusion model
NASA Astrophysics Data System (ADS)
Yu, Jianfeng; Xu, Weidong
2016-06-01
Turbo warrant is a special type of barrier options in which the rebate is calculated as another exotic option. In this paper, using Laplace transforms we obtain the valuation of turbo warrant under the mixed-exponential jump diffusion model, which is able to approximate any jump size distribution. The numerical Laplace inversion examples verify that the analytical solutions are accurate. The results of simulation confirm the argument that jump risk should not be ignored in the valuation of turbo warrants.
Pricing equity warrants with a promised lowest price in Merton's jump-diffusion model
NASA Astrophysics Data System (ADS)
Xiao, Weilin; Zhang, Xili
2016-09-01
Motivated by the empirical evidence of jumps in the dynamics of firm behavior, this paper considers the problem of pricing equity warrants in the presence of a promised lowest price when the price of the underlying asset follows the Merton's jump-diffusion process. Using the Martingale approach, we propose a valuation model of equity warrants based on the firm value, its volatility, and parameters of the jump component, which are not directly observable. To implement our pricing model empirically, this paper also provides a promising estimation method for obtaining these desired variables based on observable data, such as stock prices and the book value of total liability. We conduct an empirical study to ascertain the performance of our proposed model using the data of Changdian warrant collected from 25 May 2006 (the listing date) to 29 January 2007 (the expiration date). Furthermore, the comparison of traditional models (such as the Black-Scholes model, the Noreen-Wolfson model, the Lauterbach-Schultz model, and the Ukhov model) with our model is presented. From the empirical study, we can see that the mean absolute error of our pricing model is 16.75%. By contrast, the Black-Scholes model, the Noreen-Wolfson model, the Lauterbach-Schultz model, and the Ukhov model applied to the same warrant produce mean absolute errors of 92.24%, 45.38%, 87.34%, 76.12%, respectively. Thus both the dilution effect and the jump feature cannot be ignored in determining the valuation of equity warrants.
Simple jumping process with memory: Transport equation and diffusion
NASA Astrophysics Data System (ADS)
Kamińska, A.; Srokowski, T.
2004-06-01
We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple stationary limit. Its master equation is interpreted as the kinetic equation with variable collision rate. The process can be easily applied to model systems which relax to distributions other than Maxwellian. The case of a constant jumping rate corresponds to the diffusion process, either normal or ballistic.
Rates of diffusion in dynamical systems with random jumps
NASA Astrophysics Data System (ADS)
Kobre, Elisha J.
2005-12-01
This dissertation explores the diffusion properties of a large class of measures under a dynamical system on bigcup i=0infinity S1i with randomly occurring jumps that behave according to a particular probability distribution. The drift rate for the center of mass of the system is then defined and is shown to be well defined Lebesgue almost everywhere. Properties of the drift rate are then explored. In particular the drift rate is shown to be continuous as a function of the probability "jump" distribution and, in a special case, it is shown that the drift rate increases with the probability of jumping. Finally, a central limit theorem for fluctuations about the drift rate is proved. The results are obtained by modeling the system as a random map on a compact space, and using the ergodic properties of the random map.
Implementation of jump-diffusion algorithms for understanding FLIR scenes
NASA Astrophysics Data System (ADS)
Lanterman, Aaron D.; Miller, Michael I.; Snyder, Donald L.
1995-07-01
Our pattern theoretic approach to the automated understanding of forward-looking infrared (FLIR) images brings the traditionally separate endeavors of detection, tracking, and recognition together into a unified jump-diffusion process. New objects are detected and object types are recognized through discrete jump moves. Between jumps, the location and orientation of objects are estimated via continuous diffusions. An hypothesized scene, simulated from the emissive characteristics of the hypothesized scene elements, is compared with the collected data by a likelihood function based on sensor statistics. This likelihood is combined with a prior distribution defined over the set of possible scenes to form a posterior distribution. The jump-diffusion process empirically generates the posterior distribution. Both the diffusion and jump operations involve the simulation of a scene produced by a hypothesized configuration. Scene simulation is most effectively accomplished by pipelined rendering engines such as silicon graphics. We demonstrate the execution of our algorithm on a silicon graphics onyx/reality engine.
Model for polygonal hydraulic jumps.
Martens, Erik A; Watanabe, Shinya; Bohr, Tomas
2012-03-01
We propose a phenomenological model for the polygonal hydraulic jumps discovered by Ellegaard and co-workers [Nature (London) 392, 767 (1998); Nonlinearity 12, 1 (1999); Physica B 228, 1 (1996)], based on the known flow structure for the type-II hydraulic jumps with a "roller" (separation eddy) near the free surface in the jump region. The model consists of mass conservation and radial force balance between hydrostatic pressure and viscous stresses on the roller surface. In addition, we consider the azimuthal force balance, primarily between pressure and viscosity, but also including nonhydrostatic pressure contributions from surface tension in light of recent observations by Bush and co-workers [J. Fluid Mech. 558, 33 (2006); Phys. Fluids 16, S4 (2004)]. The model can be analyzed by linearization around the circular state, resulting in a parameter relationship for nearly circular polygonal states. A truncated but fully nonlinear version of the model can be solved analytically. This simpler model gives rise to polygonal shapes that are very similar to those observed in experiments, even though surface tension is neglected, and the condition for the existence of a polygon with N corners depends only on a single dimensionless number φ. Finally, we include time-dependent terms in the model and study linear stability of the circular state. Instability occurs for sufficiently small Bond number and the most unstable wavelength is expected to be roughly proportional to the width of the roller as in the Rayleigh-Plateau instability.
Jump rates for surface diffusion of large molecules from first principles
Shea, Patrick Kreuzer, Hans Jürgen
2015-04-21
We apply a recently developed stochastic model for the surface diffusion of large molecules to calculate jump rates for 9,10-dithioanthracene on a Cu(111) surface. The necessary input parameters for the stochastic model are calculated from first principles using density functional theory (DFT). We find that the inclusion of van der Waals corrections to the DFT energies is critical to obtain good agreement with experimental results for the adsorption geometry and energy barrier for diffusion. The predictions for jump rates in our model are in excellent agreement with measured values and show a marked improvement over transition state theory (TST). We find that the jump rate prefactor is reduced by an order of magnitude from the TST estimate due to frictional damping resulting from energy exchange with surface phonons, as well as a rotational mode of the diffusing molecule.
Anomalous diffusion for a correlated process with long jumps
NASA Astrophysics Data System (ADS)
Srokowski, Tomasz
2011-09-01
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable Lévy distribution; it is assumed as a jumping process (the kangaroo process) with a variable jumping rate. Both the exponential and the algebraic form of the covariance-defined for the truncated distribution-are considered. It is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power-law correlations decays with time, but a simple modification of the process makes the tails stable. The main result of the paper is a finding that-in contrast to the velocity fluctuations-the position variance may be finite. It rises with time faster than linearly: the diffusion is anomalously enhanced. On the other hand, a process which follows from a superposition of the Ornstein-Uhlenbeck-Lévy processes always leads to position distributions with a divergent variance which means accelerated diffusion.
Multiscale integration schemes for jump-diffusion systems
Givon, D.; Kevrekidis, I.G.
2008-12-09
We study a two-time-scale system of jump-diffusion stochastic differential equations. We analyze a class of multiscale integration methods for these systems, which, in the spirit of [1], consist of a hybridization between a standard solver for the slow components and short runs for the fast dynamics, which are used to estimate the effect that the fast components have on the slow ones. We obtain explicit bounds for the discrepancy between the results of the multiscale integration method and the slow components of the original system.
NASA Astrophysics Data System (ADS)
Shi, Jingtao
2014-04-01
This paper is concerned with the relationship between maximum principle and dynamic programming for zero-sum stochastic differential games of jump diffusions. Under the assumption that the value function is smooth enough, relations among the adjoint processes, the generalised Hamiltonian function and the value function are given. A portfolio optimisation problem under model uncertainty in an incomplete financial market is discussed to show the applications of our result.
A jump persistent turning walker to model zebrafish locomotion
Mwaffo, Violet; Anderson, Ross P.; Butail, Sachit; Porfiri, Maurizio
2015-01-01
Zebrafish are gaining momentum as a laboratory animal species for the investigation of several functional and dysfunctional biological processes. Mathematical models of zebrafish behaviour are expected to considerably aid in the design of hypothesis-driven studies by enabling preliminary in silico tests that can be used to infer possible experimental outcomes without the use of zebrafish. This study is motivated by observations of sudden, drastic changes in zebrafish locomotion in the form of large deviations in turn rate. We demonstrate that such deviations can be captured through a stochastic mean reverting jump diffusion model, a process that is commonly used in financial engineering to describe large changes in the price of an asset. The jump process-based model is validated on trajectory data of adult subjects swimming in a shallow circular tank obtained from an overhead camera. Through statistical comparison of the empirical distribution of the turn rate against theoretical predictions, we demonstrate the feasibility of describing zebrafish as a jump persistent turning walker. The critical role of the jump term is assessed through comparison with a simplified mean reversion diffusion model, which does not allow for describing the heavy-tailed distributions observed in the fish turn rate. PMID:25392396
Understanding Vertical Jump Potentiation: A Deterministic Model.
Suchomel, Timothy J; Lamont, Hugh S; Moir, Gavin L
2016-06-01
This review article discusses previous postactivation potentiation (PAP) literature and provides a deterministic model for vertical jump (i.e., squat jump, countermovement jump, and drop/depth jump) potentiation. There are a number of factors that must be considered when designing an effective strength-power potentiation complex (SPPC) focused on vertical jump potentiation. Sport scientists and practitioners must consider the characteristics of the subject being tested and the design of the SPPC itself. Subject characteristics that must be considered when designing an SPPC focused on vertical jump potentiation include the individual's relative strength, sex, muscle characteristics, neuromuscular characteristics, current fatigue state, and training background. Aspects of the SPPC that must be considered for vertical jump potentiation include the potentiating exercise, level and rate of muscle activation, volume load completed, the ballistic or non-ballistic nature of the potentiating exercise, and the rest interval(s) used following the potentiating exercise. Sport scientists and practitioners should design and seek SPPCs that are practical in nature regarding the equipment needed and the rest interval required for a potentiated performance. If practitioners would like to incorporate PAP as a training tool, they must take the athlete training time restrictions into account as a number of previous SPPCs have been shown to require long rest periods before potentiation can be realized. Thus, practitioners should seek SPPCs that may be effectively implemented in training and that do not require excessive rest intervals that may take away from valuable training time. Practitioners may decrease the necessary time needed to realize potentiation by improving their subject's relative strength. PMID:26712510
Stochastic approach to modelling of near-periodic jumping loads
NASA Astrophysics Data System (ADS)
Racic, V.; Pavic, A.
2010-11-01
A mathematical model has been developed to generate stochastic synthetic vertical force signals induced by a single person jumping. The model is based on a unique database of experimentally measured individual jumping loads which has the most extensive range of possible jumping frequencies. The ability to replicate many of the temporal and spectral features of real jumping loads gives this model a definite advantage over the conventional half-sine models coupled with Fourier series analysis. This includes modelling of the omnipresent lack of symmetry of individual jumping pulses and jump-by-jump variations in amplitudes and timing. The model therefore belongs to a new generation of synthetic narrow band jumping loads which simulate reality better. The proposed mathematical concept for characterisation of near-periodic jumping pulses may be utilised in vibration serviceability assessment of civil engineering assembly structures, such as grandstands, spectator galleries, footbridges and concert or gym floors, to estimate more realistically dynamic structural response due to people jumping.
General Metropolis-Hastings jump diffusions for automatic target recognition in infrared scenes
NASA Astrophysics Data System (ADS)
Lanterman, Aaron D.; Miller, Michael I.; Snyder, Donald L.
1997-04-01
To locate and recognize ground-based targets in forward- looking IR (FLIR) images, 3D faceted models with associated pose parameters are formulated to accommodate the variability found in FLIR imagery. Taking a Bayesian approach, scenes are simulated from the emissive characteristics of the CAD models and compared with the collected data by a likelihood function based on sensor statistics. This likelihood is combined with a prior distribution defined over the set of possible scenes to form a posterior distribution. To accommodate scenes with variable numbers of targets, the posterior distribution is defined over parameter vectors of varying dimension. An inference algorithm based on Metropolis-Hastings jump- diffusion processes empirically samples from the posterior distribution, generating configurations of templates and transformations that match the collected sensor data with high probability. The jumps accommodate the addition and deletion of targets and the estimation of target identities; diffusions refine the hypotheses by drifting along the gradient of the posterior distribution with respect to the orientation and position parameters. Previous results on jumps strategies analogous to the Metropolis acceptance/rejection algorithm, with proposals drawn from the prior and accepted based on the likelihood, are extended to encompass general Metropolis-Hastings proposal densities. In particular, the algorithm proposes moves by drawing from the posterior distribution over computationally tractible subsets of the parameter space. The algorithm is illustrated by an implementation on a Silicon Graphics Onyx/Reality Engine.
Universal Earthquake-Occurrence Jumps, Correlations with Time, and Anomalous Diffusion
Corral, Alvaro
2006-10-27
Spatiotemporal properties of seismicity are investigated for a worldwide (WW) catalog and for southern California in the stationary case (SC), showing a nearly universal scaling behavior. Distributions of distances between consecutive earthquakes (jumps) are magnitude independent and show two power-law regimes, separated by jump values about 200 (WW) and 15 km (SC). Distributions of waiting times conditioned to the value of jumps show that both variables are correlated, in general, but turn out to be independent when only short or long jumps are considered. Finally, diffusion profiles are found to be independent on the magnitude, contrary to what the waiting-time distributions suggest.
A General Optimality Conditions for Stochastic Control Problems of Jump Diffusions
Bahlali, Seid; Chala, Adel
2012-02-15
We consider a stochastic control problem where the system is governed by a non linear stochastic differential equation with jumps. The control is allowed to enter into both diffusion and jump terms. By only using the first order expansion and the associated adjoint equation, we establish necessary as well as sufficient optimality conditions of controls for relaxed controls, who are a measure-valued processes.
Control Improvement for Jump-Diffusion Processes with Applications to Finance
Baeuerle, Nicole; Rieder, Ulrich
2012-02-15
We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.
The diffusion coefficient of vacancies and jump length of electrons in zinc doped manganese ferrite
NASA Astrophysics Data System (ADS)
Tawfik, A.; Olofa, S. A.
1997-10-01
Samples of mixed ferrite Mn 1- xZn xFe 2O 4 ( x = 0.0, 0.1, 0.3, 0.5 and 0.7) have been prepared by the usual ceramic technique. X-ray diffraction patterns confirmed the spinel cubic structure for the samples. The jump length of electrons in the octahedral sites and electrical conductivity were studied as a function of zinc concentration. The increase of the jump length with Zn concentration is attributed to the substitution of Fe 3+ for Zn 2+ at the A sites which increase the B-B interaction. The increase of the diffusion coefficient and jump rate of vacancies with increasing Zn concentration expedite densification of the samples during sintering.
NASA Astrophysics Data System (ADS)
Kulkarni, Nagraj Sheshgiri
A multicomponent, single-phase, diffusion simulation based on Darken's treatment of intrinsic diffusion has been developed, which provides all the information available from an intrinsic diffusion experiment, including composition profiles and diffusion paths, lattice shifts and velocities, intrinsic and interdiffusion fluxes, as well as fluxes and mean velocities in different frames of reference. The various steps involved in the simulation are discussed and the self-consistency of the simulation is tested with the aid of model systems having constant and variable molar volumes. After an examination of the historical development of the Darken-Manning theories and a brief discussion of previous tests in the literature, a systematic procedure for the comprehensive assessment of these theories is proposed in which the intrinsic diffusion simulation developed in this work occupies a central role. This procedure is then utilized to perform an assessment of the Darken-Manning relations for four binary systems: Ag-Cd, Au-Ni, Cu-Zn and Cu-Ni. It is shown that the Darken-Manning relations that provide the connection between the tracer, intrinsic and interdiffusion coefficients, are unsatisfactory. Hence, it is suggested that the development of multicomponent diffusion databases, which often use the Darken relations for the evaluation of the phenomenological coefficients, may be compromised. As an alternative to the traditional phenomenological formalism of multicomponent diffusion, a kinetic formalism based on atom jump frequencies is proposed. An expression for the intrinsic flux in terms of an unbiased and a biased component is derived. It is demonstrated with the aid of the simulation for the Cu-Zn system, that the biased flux may be evaluated from the experimental intrinsic flux and the unbiased flux (obtained from the tracer jump frequency). An unbiased jump frequency formalism that utilizes effective rather than tracer jump frequencies and avoids the complexities
Updating applied diffusion models
Weil, J.C.
1985-11-01
Most diffusion models currently used in air quality applications are substantially out of date with understanding of turbulence and diffusion in the planetary boundary layer. Under a Cooperative Agreement with the Environmental Protection Agency, the American Meteorological Society organized a workshop to help improve the basis of such models, their physics and hopefuly their performance. Reviews and recommendations were made on models in three areas: diffusion in the convective boundary layer (CBL), diffusion in the stabe boundary layer (SBL), and model uncertainty.
Non-Markovian jump processes in lasers
Levine, A.M. ); Kofman, A.G.; Zaibel, R.; Prior, Y. )
1989-10-20
A new model for stochastic fluctuations in lasers is introduced where successive phase jumps are correlated to previous jumps. The model is applicable in the generalized phase diffusion limit, the generalized Kubo oscillator limit, and the generalized telegraph noise limit.
Analysis and Model Tests of Autogiro Jump Take-off
NASA Technical Reports Server (NTRS)
Wheatley, John B; Bioletti, Carlton
1936-01-01
An analysis is made of the autogiro jump take-off, in which the kinetic energy of the rotor turning at excess speed is used to effect a vertical take-off. By the use of suitable approximations, the differential equation of motion of the rotor during this maneuver is reduced to a form that can be solved. Only the vertical jump was studied; the effect of a forward motion during the jump is discussed briefly. The results of model tests of the jump take-off have been incorporated in the paper and used to establish the relative accuracy of the results predicted from the analysis. Good agreement between calculation and experiment was obtained by making justifiable allowances.
Updating applied diffusion models
Weil, J.C.
1985-01-01
Most diffusion models currently used in air-quality applications are substantially out of date with understanding of turbulence and diffusion in the planetary boundary layer. Under a Cooperative Agreement with the Environmental Protection Agency, the American Meteorological Society organized a workshop to help improve the basis of such models, their physics and hopefully their performance. Reviews and recommendations were made on models in three areas: diffusion in the convective boundary layer (CBL), diffusion in the stable boundary layer (SBL), and model uncertainty. Progress has been made in all areas, but it is most significant and ready for application to practical models in the case of the CBL. This has resulted from a clear understanding of the vertical structure and diffusion in the CBL, as demonstrated by laboratory experiments, numerical simulations, and field observations. Understanding of turbulence structure and diffusion in the SBL is less complete and not yet ready for general use in applications.
Hard-sphere interactions in velocity-jump models
NASA Astrophysics Data System (ADS)
Franz, Benjamin; Taylor-King, Jake P.; Yates, Christian; Erban, Radek
2016-07-01
Group-level behavior of particles undergoing a velocity-jump process with hard-sphere interactions is investigated. We derive N -particle transport equations that include the possibility of collisions between particles and apply different approximation techniques to get expressions for the dependence of the collective diffusion coefficient on the number of particles and their diameter. The derived approximations are compared with numerical results obtained from individual-based simulations. The theoretical results compare well with Monte Carlo simulations providing the excluded-volume fraction is small.
Hard-sphere interactions in velocity-jump models.
Franz, Benjamin; Taylor-King, Jake P; Yates, Christian; Erban, Radek
2016-07-01
Group-level behavior of particles undergoing a velocity-jump process with hard-sphere interactions is investigated. We derive N-particle transport equations that include the possibility of collisions between particles and apply different approximation techniques to get expressions for the dependence of the collective diffusion coefficient on the number of particles and their diameter. The derived approximations are compared with numerical results obtained from individual-based simulations. The theoretical results compare well with Monte Carlo simulations providing the excluded-volume fraction is small. PMID:27575098
Effect of particle-hole symmetry on the behavior of tracer and jump diffusion coefficients.
Torrez Herrera, J J; Ranzuglia, G A; Manzi, S J; Pereyra, V D
2013-05-01
This paper analyzes the effect of particle-hole symmetry on the behavior of the tracer diffusion coefficient as well as the jump diffusion coefficient. The coefficients are obtained by performing a random walk of individual atoms in a two-dimensional square lattice at monolayer, using the n-fold way Monte Carlo simulation. Different hopping mechanisms have been introduced to study the effect of particle-hole symmetry. For hopping kinetics where the initial-state interactions are involved, the diffusion coefficient at high coverage falls several orders of magnitude due to the effect of particle-hole symmetry. For hopping kinetics where the final-state interactions are present, the effect is the opposite. For those involving both initial- and final-state interactions, like the so-called interaction kinetics, the effect of particle-hole symmetry is also discussed. This effect seems to be critical for repulsive lateral interactions, for which the behavior of the diffusion coefficients is modified by introducing the particle-hole symmetry condition. PMID:23767481
Jump-diffusion unravelling of a non-Markovian generalized Lindblad master equation
Barchielli, A.; Pellegrini, C.
2010-11-15
The ''correlated-projection technique'' has been successfully applied to derive a large class of highly non-Markovian dynamics, the so called non-Markovian generalized Lindblad-type equations or Lindblad rate equations. In this article, general unravelings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unraveling can be interpreted in terms of measurements continuous in time but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not; such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory.
Pricing American put option on zero-coupon bond in a jump-extended CIR model
NASA Astrophysics Data System (ADS)
Deng, Guohe
2015-05-01
This paper presents a jump extension to the CIR model of the short interest rate with exponential distribution jumps. We derive an approximated price of an American put option on a defaultable-free, zero-coupon bond using the two-GJ approach based on combining an European put option and a Bermudan option with two possible exercise dates. Closed-form solutions for both the European put option and the Bermudan option are obtained by using multivariate Fourier transforms and characteristic functions. The accuracy and efficiency of the approximation are examined using the least-square Monte Carlo simulation as the benchmarks. Finally several numerical examples illustrating the results have been presented and the prices have been compared to the corresponding prices for American option in the pure diffusion model.
Mathematical model to generate near-periodic human jumping force signals
NASA Astrophysics Data System (ADS)
Racic, V.; Pavic, A.
2010-01-01
A mathematical modelling procedure has been developed to generate synthetic vertical force signals induced by a single person jumping. The ability to replicate much of the temporal and spectral features of real jumping loads give this model a definite advantage over the conventional half-sine models coupled with Fourier series analysis. This includes modelling of the omnipresent lack of symmetry of individual jumping pulses and jump-by-jump variations in amplitudes and timing. The model therefore belongs to a new generation of synthetic narrowband jumping loads that simulate reality better. The proposed mathematical concept for characterisation of irregular jumping pulses may be utilised in vibration serviceability assessment of civil engineering assembly structures, such as grandstands, footbridges and concert or gym floors, to estimate realistic dynamic structural response due to people jumping.
Diffusing Diffusivity: A Model for Anomalous, yet Brownian, Diffusion
NASA Astrophysics Data System (ADS)
Chubynsky, Mykyta V.; Slater, Gary W.
2014-08-01
Wang et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 15160 (2009)] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian displacement distribution G(x ,t), with roughly exponential tails at short times, a situation they termed "anomalous yet Brownian" diffusion. The diversity of systems in which this is observed calls for a generic model. We present such a model where there is diffusivity memory but no direction memory in the particle trajectory, and we show that it leads to both a linear MSD and a non-Gaussian G(x ,t) at short times. In our model, the diffusivity is undergoing a (perhaps biased) random walk, hence the expression "diffusing diffusivity". G(x ,t) is predicted to be exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit for a variety of diffusivity distributions. Moreover, our generic model can be modified to produce subdiffusion.
Modelling of monovacancy diffusion in W over wide temperature range
Bukonte, L. Ahlgren, T.; Heinola, K.
2014-03-28
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{sup 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{sub 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.
A memory diffusion model for molecular anisotropic diffusion in siliceous β-zeolite.
Ji, Xiangfei; An, Zhuanzhuan; Yang, Xiaofeng
2016-01-01
A memory diffusion model of molecules on β-zeolite is proposed. In the model, molecular diffusion in β-zeolites is treated as jumping from one adsorption site to its neighbors and the jumping probability is a compound probability which includes that provided by the transitional state theory as well as that derived from the information about which direction the target molecule comes from. The proposed approach reveals that the diffusivities along two crystal axes on β-zeolite are correlated. The model is tested by molecular dynamics simulations on diffusion of benzene and other simple molecules in β-zeolites. The results show that the molecules with larger diameters fit the prediction much better and that the "memory effects" are important in all cases.
The naked toy model of a jumping ring
NASA Astrophysics Data System (ADS)
Donoso, Guillermo; Ladera, Celso L.
2014-01-01
We present a comprehensive analytical model of the well-known jumping ring—in fact an improved version of that system--as well as the experimental results that validate the model. Particular attention is paid to the magnetic driving force, whose explicit dependences upon the phase, amplitude and frequency of the exciting current we manage to separate experimentally and plot, so that it becomes evident how the magnetic force on the ring actually arises and evolves in time. We are able to measure not only the large Foucault currents that arise in the ring, but also the magnetic field generated by the ring itself in spite of the presence of the comparable magnetic field in which the ring moves.
Mazenko, Gene F
2008-09-01
We study the random diffusion model. This is a continuum model for a conserved scalar density field varphi driven by diffusive dynamics. The interesting feature of the dynamics is that the bare diffusion coefficient D is density dependent. In the simplest case, D=D[over ]+D_{1}deltavarphi , where D[over ] is the constant average diffusion constant. In the case where the driving effective Hamiltonian is quadratic, the model can be treated using perturbation theory in terms of the single nonlinear coupling D1 . We develop perturbation theory to fourth order in D1 . The are two ways of analyzing this perturbation theory. In one approach, developed by Kawasaki, at one-loop order one finds mode-coupling theory with an ergodic-nonergodic transition. An alternative more direct interpretation at one-loop order leads to a slowing down as the nonlinear coupling increases. Eventually one hits a critical coupling where the time decay becomes algebraic. Near this critical coupling a weak peak develops at a wave number well above the peak at q=0 associated with the conservation law. The width of this peak in Fourier space decreases with time and can be identified with a characteristic kinetic length which grows with a power law in time. For stronger coupling the system becomes metastable and then unstable. At two-loop order it is shown that the ergodic-nonergodic transition is not supported. It is demonstrated that the critical properties of the direct approach survive, going to higher order in perturbation theory.
Phase-field elasticity model based on mechanical jump conditions
NASA Astrophysics Data System (ADS)
Schneider, Daniel; Tschukin, Oleg; Choudhury, Abhik; Selzer, Michael; Böhlke, Thomas; Nestler, Britta
2015-05-01
Computational models based on the phase-field method typically operate on a mesoscopic length scale and resolve structural changes of the material and furthermore provide valuable information about microstructure and mechanical property relations. An accurate calculation of the stresses and mechanical energy at the transition region is therefore indispensable. We derive a quantitative phase-field elasticity model based on force balance and Hadamard jump conditions at the interface. Comparing the simulated stress profiles calculated with Voigt/Taylor (Annalen der Physik 274(12):573, 1889), Reuss/Sachs (Z Angew Math Mech 9:49, 1929) and the proposed model with the theoretically predicted stress fields in a plate with a round inclusion under hydrostatic tension, we show the quantitative characteristics of the model. In order to validate the elastic contribution to the driving force for phase transition, we demonstrate the absence of excess energy, calculated by Durga et al. (Model Simul Mater Sci Eng 21(5):055018, 2013), in a one-dimensional equilibrium condition of serial and parallel material chains. To validate the driving force for systems with curved transition regions, we relate simulations to the Gibbs-Thompson equilibrium condition (Johnson and Alexander, J Appl Phys 59(8):2735, 1986).
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
A New Model for Temperature Jump at a Fluid-Solid Interface
Shu, Jian-Jun; Teo, Ji Bin Melvin; Chan, Weng Kong
2016-01-01
The problem presented involves the development of a new analytical model for the general fluid-solid temperature jump. To the best of our knowledge, there are no analytical models that provide the accurate predictions of the temperature jump for both gas and liquid systems. In this paper, a unified model for the fluid-solid temperature jump has been developed based on our adsorption model of the interfacial interactions. Results obtained from this model are validated with available results from the literature. PMID:27764230
A jumping profile Hidden Markov Model and applications to recombination sites in HIV and HCV genomes
Schultz, Anne-Kathrin; Zhang, Ming; Leitner, Thomas; Kuiken, Carla; Korber, Bette; Morgenstern, Burkhard; Stanke, Mario
2006-01-01
Background Jumping alignments have recently been proposed as a strategy to search a given multiple sequence alignment A against a database. Instead of comparing a database sequence S to the multiple alignment or profile as a whole, S is compared and aligned to individual sequences from A. Within this alignment, S can jump between different sequences from A, so different parts of S can be aligned to different sequences from the input multiple alignment. This approach is particularly useful for dealing with recombination events. Results We developed a jumping profile Hidden Markov Model (jpHMM), a probabilistic generalization of the jumping-alignment approach. Given a partition of the aligned input sequence family into known sequence subtypes, our model can jump between states corresponding to these different subtypes, depending on which subtype is locally most similar to a database sequence. Jumps between different subtypes are indicative of intersubtype recombinations. We applied our method to a large set of genome sequences from human immunodeficiency virus (HIV) and hepatitis C virus (HCV) as well as to simulated recombined genome sequences. Conclusion Our results demonstrate that jumps in our jumping profile HMM often correspond to recombination breakpoints; our approach can therefore be used to detect recombinations in genomic sequences. The recombination breakpoints identified by jpHMM were found to be significantly more accurate than breakpoints defined by traditional methods based on comparing single representative sequences. PMID:16716226
Multispecies diffusion models: A study of uranyl species diffusion
Liu, Chongxuan; Shang, Jianying; Zachara, John M.
2011-12-14
Rigorous numerical description of multi-species diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication for imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multi-species diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multi-species diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multi-species U(VI) diffusion under steady-state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that a fully coupled diffusion model can be well approximated by a component-based diffusion model, which considers difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be rigorously enforced, if necessary, by adding an artificial kinetic reaction term induced by the charge separation. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from US Department of Energy's Hanford 300A where intragrain diffusion is a rate-limiting process controlling U(VI) adsorption and desorption. The grain-scale reactive diffusion model was able to describe U(VI) adsorption/desorption kinetics that has been described using a semi-empirical, multi-rate model
NASA Astrophysics Data System (ADS)
Yang, Eunjin; Kim, Ho-Young
2012-01-01
We investigate the dynamics of an elastic hoop as a model of the jumps of small insects. During a jump the initial elastic strain energy is converted to translational, gravitational, and vibrational energy, and is dissipated by interaction with the floor and the ambient air. We show that the strain energy is initially divided into translational, vibrational, and dissipation energies with a ratio that is constant regardless of the dimension, initial deflection, and the properties of a hoop. This novel result enables us to accurately predict the maximum jump height of a hoop with known initial conditions and drag coefficient without resorting to a numerical computation. Our model reduces the optimization of the hoop geometry for maximizing the jump height to a simple algebraic problem.
NASA Astrophysics Data System (ADS)
Holzapfel, C.; Chakraborty, S.; Rubie, D. C.; Frost, D. J.
2009-01-01
The limited stability range of wadsleyite seriously impedes our ability to constrain kinetic parameters (e.g. activation energy, activation volume) using experiments carried out over a wide range of temperature and pressure. We have carried out a new measurement to extend the experimental temperature range of the dataset of Chakraborty et al. [Chakraborty, S., Knoche, R., Schulze, H., Rubie, D.C., Dobson, D., Ross, N.L., Angel, R.J., 1999. Enhancement of cation diffusion rates across the 410-kilometer discontinuity in Earth's mantle. Science 283, 362-365] to the maximum possible limit for that experimental setup. This result allows us to (i) obtain a better constrained value for activation energy for Fe-Mg diffusion in wadsleyite at 15 GPa (˜230 kJ/mol), and (ii) characterize the compositional dependence of Fe-Mg diffusion in wadsleyite. Evaluation of all data available in the literature [i.e. this study; Chakraborty et al., 1999; Farber, D.L., Williams, Q., Ryerson, F.J., 2000. Divalent cation diffusion in Mg 2SiO 4 spinel (ringwoodite), β-phase (wadsleyite), and olivine: implications for the electrical conductivity of the mantle. J. Geophys. Res. 105, 513-529; Kubo, T., Shimojuko, A., Ohtani, E., 2004. Fe-Mg interdiffusion rates in wadsleyite and the diffusivity jump at the 410 km discontinuity. Phys. Chem. Miner. 31, 456-464] reveals that there is a strong pressure dependence of the diffusion coefficient (activation volume ≈14 cm 3/mol). The expression D (m/s)=1.24×10-6 exp[11.8(0.86-X)] exp{-[]229,000+(P-15)×13.9×10 J/mol}/{RT} is an excellent description of all experimentally measured diffusion coefficients in wadsleyite and points to consistency between the various studies from different laboratories that used different methods. This expression should provide a robust basis for extrapolation of diffusion data for wadsleyite to conditions removed from the experimental ones, e.g. for modeling processes in the interiors of cold subducting slabs. Moreover
Multispecies diffusion models: A study of uranyl species diffusion
NASA Astrophysics Data System (ADS)
Liu, Chongxuan; Shang, Jianying; Zachara, John M.
2011-12-01
Rigorous numerical description of multispecies diffusion requires coupling of species, charge, and aqueous and surface complexation reactions that collectively affect diffusive fluxes. The applicability of a fully coupled diffusion model is, however, often constrained by the availability of species self-diffusion coefficients, as well as by computational complication in imposing charge conservation. In this study, several diffusion models with variable complexity in charge and species coupling were formulated and compared to describe reactive multispecies diffusion in groundwater. Diffusion of uranyl [U(VI)] species was used as an example in demonstrating the effectiveness of the models in describing multispecies diffusion. Numerical simulations found that a diffusion model with a single, common diffusion coefficient for all species was sufficient to describe multispecies U(VI) diffusion under a steady state condition of major chemical composition, but not under transient chemical conditions. Simulations revealed that for multispecies U(VI) diffusion under transient chemical conditions, a fully coupled diffusion model could be well approximated by a component-based diffusion model when the diffusion coefficient for each chemical component was properly selected. The component-based diffusion model considers the difference in diffusion coefficients between chemical components, but not between the species within each chemical component. This treatment significantly enhanced computational efficiency at the expense of minor charge conservation. The charge balance in the component-based diffusion model can be enforced, if necessary, by adding a secondary migration term resulting from model simplification. The effect of ion activity coefficient gradients on multispecies diffusion is also discussed. The diffusion models were applied to describe U(VI) diffusive mass transfer in intragranular domains in two sediments collected from U.S. Department of Energy's Hanford 300A
The hydraulic jump in radially spreading flow: A new model and new experimental data
NASA Astrophysics Data System (ADS)
Blackford, B. L.
1996-02-01
A new model for the hydraulic jump in radially spreading flow is presented. The equation of motion for a liquid annulus spreading out under the influence of hydrostatic pressure gradient and Frictional drag is developed. The resulting nonlinear differential equation for the liquid depth, h(r), is solved by computer simulation. The jump is assumed to begin when the laminar flow is engulfed by the underlying boundary layer liquid, as suggested recently in the literature. This complicated mixing process is crudely modeled by a drag term which slows the flow and initiates a positive feedback mechanism culminating at a new critical depth, beyond which the depth increases asymptotically to a final value. The model predicts a new relationship between the laminar flow depth just before the jump and the final depth. An experimental apparatus was built to make detailed measurements of the depth h(r), both in the region before the jump and beyond the jump. The theoretical predictions were compared to the experimental data, and gave surprisingly good agreement by suitable adjustment of the two parameters k and C of the model. The parameter k determines the growth rate of the boundary layer thickness, and C determines the drag force. The results suggest that the usual textbook assumption of zero momentum loss across the jump is not appropriate for this type of hydraulic jump. The case of a hydraulic jump in the absence of gravity is considered also and a much different behavior is predicted, which could be tested by experiment in a microgravity environment.
Modelling of liquid flow after a hydraulic jump on a rotating disk prior to centrifugal atomization
NASA Astrophysics Data System (ADS)
Zhao, Y. Y.; Dowson, A. L.; Jacobs, M. H.
2000-01-01
This paper describes a simplified numerical model which is used to calculate the height distribution, and the radial and tangential velocities of a liquid on a rotating disk after a hydraulic jump and prior to centrifugal atomization. The results obtained from this numerical model are compared with predictions made using previously derived `hydraulic jump' and `analytical' models. Calculations, in conjunction with experimental measurements relating to the trajectory of liquid flow on the atomizing disk, have shown that the numerical model can not only give a reasonable prediction of the hydraulic jump location, but also yields more accurate information regarding the variations in liquid height, and radial and tangential velocities. The model is ideally suited for engineering applications.
NASA Technical Reports Server (NTRS)
Schultz, Christopher J.; Carey, Lawerence D.; Schultz, Elise V.; Stano, Geoffery T.; Kozlowski, Danielle M.; Goodman, Steven
2012-01-01
Key points that this analysis will begin to address are: 1)What physically is going on in the cloud when there is a jump in lightning? - Updraft variations, ice fluxes. 2)How do these processes fit in with severe storm conceptual models? 3)What would this information provide an end user (i.e., the forecaster)? - Relate LJA to radar observations, like changes in reflectivity, MESH, VIL, etc. based multi-Doppler derived physical relationships 4) How do we best transistionthis algorithm into the warning decision process. The known relationship between lightning updraft strength/volume and precipitation ice mass production can be extended to the concept of the lightning jump. Examination of the first lightning jump times from 329 storms in Schultz et al. shows an increase in the mean reflectivity profile and mixed phase echo volume during the 10 minutes prior to the lightning jump. Limited dual-Doppler results show that the largest lightning jumps are well correlated in time with increases in updraft strength/volume and precipitation ice mass production; however, the smaller magnitude lightning jumps appear to have more subtle relationships to updraft and ice mass characteristics.
Lagrangian model of copepod dynamics: Clustering by escape jumps in turbulence.
Ardeshiri, H; Benkeddad, I; Schmitt, F G; Souissi, S; Toschi, F; Calzavarini, E
2016-04-01
Planktonic copepods are small crustaceans that have the ability to swim by quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow perturbations, produced by a large predator (i.e., fish larvae), or by the inherent highly turbulent dynamics of the ocean. Through a combined experimental and numerical study, we investigate the impact of jumping behavior on the small-scale patchiness of copepods in a turbulent environment. Recorded velocity tracks of copepods displaying escape response jumps in still water are here used to define and tune a Lagrangian copepod (LC) model. The model is further employed to simulate the behavior of thousands of copepods in a fully developed hydrodynamic turbulent flow obtained by direct numerical simulation of the Navier-Stokes equations. First, we show that the LC velocity statistics is in qualitative agreement with available experimental observations of copepods in turbulence. Second, we quantify the clustering of LC, via the fractal dimension D_{2}. We show that D_{2} can be as low as ∼2.3 and that it critically depends on the shear-rate sensitivity of the proposed LC model, in particular it exhibits a minimum in a narrow range of shear-rate values. We further investigate the effect of jump intensity, jump orientation, and geometrical aspect ratio of the copepods on the small-scale spatial distribution. At last, possible ecological implications of the observed clustering on encounter rates and mating success are discussed. PMID:27176400
Lagrangian model of copepod dynamics: Clustering by escape jumps in turbulence
NASA Astrophysics Data System (ADS)
Ardeshiri, H.; Benkeddad, I.; Schmitt, F. G.; Souissi, S.; Toschi, F.; Calzavarini, E.
2016-04-01
Planktonic copepods are small crustaceans that have the ability to swim by quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow perturbations, produced by a large predator (i.e., fish larvae), or by the inherent highly turbulent dynamics of the ocean. Through a combined experimental and numerical study, we investigate the impact of jumping behavior on the small-scale patchiness of copepods in a turbulent environment. Recorded velocity tracks of copepods displaying escape response jumps in still water are here used to define and tune a Lagrangian copepod (LC) model. The model is further employed to simulate the behavior of thousands of copepods in a fully developed hydrodynamic turbulent flow obtained by direct numerical simulation of the Navier-Stokes equations. First, we show that the LC velocity statistics is in qualitative agreement with available experimental observations of copepods in turbulence. Second, we quantify the clustering of LC, via the fractal dimension D2. We show that D2 can be as low as ˜2.3 and that it critically depends on the shear-rate sensitivity of the proposed LC model, in particular it exhibits a minimum in a narrow range of shear-rate values. We further investigate the effect of jump intensity, jump orientation, and geometrical aspect ratio of the copepods on the small-scale spatial distribution. At last, possible ecological implications of the observed clustering on encounter rates and mating success are discussed.
Regression models of sprint, vertical jump, and change of direction performance.
Swinton, Paul A; Lloyd, Ray; Keogh, Justin W L; Agouris, Ioannis; Stewart, Arthur D
2014-07-01
It was the aim of the present study to expand on previous correlation analyses that have attempted to identify factors that influence performance of jumping, sprinting, and changing direction. This was achieved by using a regression approach to obtain linear models that combined anthropometric, strength, and other biomechanical variables. Thirty rugby union players participated in the study (age: 24.2 ± 3.9 years; stature: 181.2 ± 6.6 cm; mass: 94.2 ± 11.1 kg). The athletes' ability to sprint, jump, and change direction was assessed using a 30-m sprint, vertical jump, and 505 agility test, respectively. Regression variables were collected during maximum strength tests (1 repetition maximum [1RM] deadlift and squat) and performance of fast velocity resistance exercises (deadlift and jump squat) using submaximum loads (10-70% 1RM). Force, velocity, power, and rate of force development (RFD) values were measured during fast velocity exercises with the greatest values produced across loads selected for further analysis. Anthropometric data, including lengths, widths, and girths were collected using a 3-dimensional body scanner. Potential regression variables were first identified using correlation analyses. Suitable variables were then regressed using a best subsets approach. Three factor models generally provided the most appropriate balance between explained variance and model complexity. Adjusted R values of 0.86, 0.82, and 0.67 were obtained for sprint, jump, and change of direction performance, respectively. Anthropometric measurements did not feature in any of the top models because of their strong association with body mass. For each performance measure, variance was best explained by relative maximum strength. Improvements in models were then obtained by including velocity and power values for jumping and sprinting performance, and by including RFD values for change of direction performance. PMID:24345969
NASA Technical Reports Server (NTRS)
Schultz, C. J.; Carey, L. D.; Schultz, E. V.; Stano, G. T.; Blakeslee, R.; Goodman, S. J.
2014-01-01
The purpose of the total lightning jump algorithm (LJA) is to provide forecasters with an additional tool to identify potentially hazardous thunderstorms, yielding increased confidence in decisions within the operational warning environment. The LJA was first developed to objectively indentify rapid increases in total lightning (also termed "lightning jumps") that occur prior to the observance of severe and hazardous weather (Williams et al. 1999, Schultz et al. 2009, Gatlin and Goodman 2010, Schultz et al. 2011). However, a physical and framework leading up to and through the time of a lightning jump is still lacking within the literature. Many studies infer that there is a large increase in the updraft prior to or during the jump, but are not specific on what properties of the updraft are indeed increasing (e.g., maximum updraft speed vs volume or both) likely because these properties were not specifically observed. Therefore, the purpose of this work is to physically associate lightning jump occurrence to polarimetric and multi-Doppler radar measured thunderstorm intensity metrics and severe weather occurrence, thus providing a conceptual model that can be used to adapt the LJA to current operations.
NASA Technical Reports Server (NTRS)
Shultz, Christopher J.; Carey, Lawrence D.; Schultz, Elise V.; Stano, Geoffrey T.; Blakeslee, Richard J.; Goodman, Steven J.
2014-01-01
The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; AMS 10th Satellite Symposium) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014; this conference) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end to end physical and dynamical basis for relating lightning rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relation to updraft strength, updraft volume, precipitation-sized ice mass, etc.; however, relation specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler techniques to
Physical and Dynamical Linkages between Lightning Jumps and Storm Conceptual Models
NASA Technical Reports Server (NTRS)
Schultz, Christopher J.; Carey, Lawrence D.; Schultz, Elise V.; Blakeslee, Richard J.; Goodman, Steven J.
2014-01-01
The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; this conference) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014; this conference) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end-to-end physical and dynamical basis for coupling total lightning flash rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relationship to updraft strength, updraft volume, precipitation-sized ice mass, etc.; however, their relationship specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler and
Physical and Dynamical Linkages Between Lightning Jumps and Storm Conceptual Models
NASA Technical Reports Server (NTRS)
Schultz, Christopher J.; Carey, Lawrence D.; Schultz, Elise V.; Blakeslee, Richard J.; Goodman, Steven J.
2014-01-01
The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. Currently, the lightning jump algorithm is being tested in two separate but important efforts. Schultz et al. (2014; this conference) is exploring the transition of the algorithm from its research based formulation to a fully objective algorithm that includes storm tracking, Geostationary Lightning Mapper (GLM) Proxy data and the lightning jump algorithm. Chronis et al. (2014) provides context for the transition to current operational forecasting using lightning mapping array based products. However, what remains is an end-to-end physical and dynamical basis for coupling total lightning flash rates to severe storm manifestation, so the forecaster has a reason beyond simple correlation to utilize the lightning jump algorithm within their severe storm conceptual models. Therefore, the physical basis for the lightning jump algorithm in relation to severe storm dynamics and microphysics is a key component that must be further explored. Many radar studies have examined flash rates and their relationship to updraft strength, updraft volume, precipitation-sized ice mass, etc.; however, their relationship specifically to lightning jumps is fragmented within the literature. Thus the goal of this study is to use multiple Doppler and polarimetric
Framework for non-coherent interface models at finite displacement jumps and finite strains
NASA Astrophysics Data System (ADS)
Ottosen, Niels Saabye; Ristinmaa, Matti; Mosler, Jörn
2016-05-01
This paper deals with a novel constitutive framework suitable for non-coherent interfaces, such as cracks, undergoing large deformations in a geometrically exact setting. For this type of interface, the displacement field shows a jump across the interface. Within the engineering community, so-called cohesive zone models are frequently applied in order to describe non-coherent interfaces. However, for existing models to comply with the restrictions imposed by (a) thermodynamical consistency (e.g., the second law of thermodynamics), (b) balance equations (in particular, balance of angular momentum) and (c) material frame indifference, these models are essentially fiber models, i.e. models where the traction vector is collinear with the displacement jump. This constraints the ability to model shear and, in addition, anisotropic effects are excluded. A novel, extended constitutive framework which is consistent with the above mentioned fundamental physical principles is elaborated in this paper. In addition to the classical tractions associated with a cohesive zone model, the main idea is to consider additional tractions related to membrane-like forces and out-of-plane shear forces acting within the interface. For zero displacement jump, i.e. coherent interfaces, this framework degenerates to existing formulations presented in the literature. For hyperelasticity, the Helmholtz energy of the proposed novel framework depends on the displacement jump as well as on the tangent vectors of the interface with respect to the current configuration - or equivalently - the Helmholtz energy depends on the displacement jump and the surface deformation gradient. It turns out that by defining the Helmholtz energy in terms of the invariants of these variables, all above-mentioned fundamental physical principles are automatically fulfilled. Extensions of the novel framework necessary for material degradation (damage) and plasticity are also covered.
Birbarah, Patrick; Li, Zhaoer; Pauls, Alexander; Miljkovic, Nenad
2015-07-21
Superhydrophobic micro/nanostructured surfaces for dropwise condensation have recently received significant attention due to their potential to enhance heat transfer performance by shedding positively charged water droplets via coalescence-induced droplet jumping at length scales below the capillary length and allowing the use of external electric fields to enhance droplet removal and heat transfer, in what has been termed electric-field-enhanced (EFE) jumping-droplet condensation. However, achieving optimal EFE conditions for enhanced heat transfer requires capturing the details of transport processes that is currently lacking. While a comprehensive model has been developed for condensation on micro/nanostructured surfaces, it cannot be applied for EFE condensation due to the dynamic droplet-vapor-electric field interactions. In this work, we developed a comprehensive physical model for EFE condensation on superhydrophobic surfaces by incorporating individual droplet motion, electrode geometry, jumping frequency, field strength, and condensate vapor-flow dynamics. As a first step toward our model, we simulated jumping droplet motion with no external electric field and validated our theoretical droplet trajectories to experimentally obtained trajectories, showing excellent temporal and spatial agreement. We then incorporated the external electric field into our model and considered the effects of jumping droplet size, electrode size and geometry, condensation heat flux, and droplet jumping direction. Our model suggests that smaller jumping droplet sizes and condensation heat fluxes require less work input to be removed by the external fields. Furthermore, the results suggest that EFE electrodes can be optimized such that the work input is minimized depending on the condensation heat flux. To analyze overall efficiency, we defined an incremental coefficient of performance and showed that it is very high (∼10(6)) for EFE condensation. We finally proposed mechanisms
Cosmic ray anisotropy in fractional differential models of anomalous diffusion
Uchaikin, V. V.
2013-06-15
The problem of galactic cosmic ray anisotropy is considered in two versions of the fractional differential model for anomalous diffusion. The simplest problem of cosmic ray propagation from a point instantaneous source in an unbounded medium is used as an example to show that the transition from the standard diffusion model to the Lagutin-Uchaikin fractional differential model (with characteristic exponent {alpha} = 3/5 and a finite velocity of free particle motion), which gives rise to a knee in the energy spectrum at 10{sup 6} GeV, increases the anisotropy coefficient only by 20%, while the anisotropy coefficient in the Lagutin-Tyumentsev model (with exponents {alpha} = 0.3 and {beta} = 0.8, a long stay of particles in traps, and an infinite velocity of their jumps) is close to one. This is because the parameters of the Lagutin-Tyumentsev model have been chosen improperly.
Option pricing for stochastic volatility model with infinite activity Lévy jumps
NASA Astrophysics Data System (ADS)
Gong, Xiaoli; Zhuang, Xintian
2016-08-01
The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.
NASA Technical Reports Server (NTRS)
Schultz, Christopher J.; Carey, Lawrence D.; Schultz, Elise V.; Stano, Geoffrey T.; Gatlin, Patrick N.
2013-01-01
The presence and rates of total lightning are both correlated to and physically dependent upon storm updraft strength, mixed phase precipitation volume and the size of the charging zone. The updraft modulates the ingredients necessary for electrification within a thunderstorm, while the updraft also plays a critical role in the development of severe and hazardous weather. Therefore utilizing this relationship, the monitoring of lightning rates and jumps provides an additional piece of information on the evolution of a thunderstorm, more often than not, at higher temporal resolution than current operational radar systems. This correlation is the basis for the total lightning jump algorithm that has been developed in recent years. In order to become a viable option for operational forecasters to incorporate into their severe storm monitoring process, the total lightning jump must be placed into the framework of several severe storm conceptual models (e.g., radar evolution, storm morphology) which forecasters have built through training and experience. Thus, one of the goals of this study is to examine and relate the lightning jump concept to often used radar parameters (e.g., dBZ vertical structure, VIL, MESH, MESO/shear) in the warning environment. Tying lightning trends and lightning jump occurrences to these radar based parameters will provide forecasters with an additional tool that they can use to build an accurate realtime depiction as to what is going on in a given environment. Furthermore, relating the lightning jump concept to these parameters could also increase confidence in a warning decision they have already made, help tip the scales on whether or not to warn on a given storm, or to draw the forecaster s attention to a particular storm that is rapidly developing. Furthermore the lightning information will add vital storm scale information in regions that are not well covered by radar, or when radar failures occur. The physical basis for the lightning
Building reliable lattice Monte Carlo models for real drift and diffusion problems
NASA Astrophysics Data System (ADS)
Gauthier, Michel G.; Slater, Gary W.
2004-07-01
We revisit the well-known issue of representing an overdamped drift-and-diffusion system by an equivalent lattice random-walk model. We demonstrate that commonly used Monte Carlo algorithms do not conserve the diffusion coefficient when a driving field of arbitrary amplitude is present, and that such algorithms would actually require fluctuating jumping times and one clock per Cartesian direction to work properly. Although it is in principle possible to construct valid algorithms with fixed time steps, we show that no such algorithm can be used in more than two dimensions if the jumps are made along only one axis at each time step.
NASA Astrophysics Data System (ADS)
Mascia, Corrado
2016-01-01
This paper examines a class of linear hyperbolic systems which generalizes the Goldstein-Kac model to an arbitrary finite number of speeds vi with transition rates μij. Under the basic assumptions that the transition matrix is symmetric and irreducible, and the differences vi -vj generate all the space, the system exhibits a large-time behavior described by a parabolic advection-diffusion equation. The main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters vi and μij, establishing a complete connection between microscopic and macroscopic coefficients. It is shown that the drift speed is the arithmetic mean of the velocities vi. The diffusion matrix has a more complicate representation, based on the graph with vertices the velocities vi and arcs weighted by the transition rates μij. The approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the Kirchoff's matrix tree Theorem from graph theory.
Two-channel emission model for collective quantum jumps in Rydberg atoms
NASA Astrophysics Data System (ADS)
Cayayan, Lyndon; Clemens, James
2016-05-01
We consider a system of driven, damped Rydberg atoms with dipole-dipole energy shifts which can give rise to a Rydberg blockade when the atoms are driven on resonance and collective quantum jumps when the atoms are driven off resonance. For the damping we consider a two-channel emission model with competition between fully independent and fully collective spontaneous emission. For independent emission a quasiclassical model predicts a bistable steady state and quantum fluctuations drive collective jumps between the two bistable branches. We show that the collective emission is enhanced, relative to the independent emission, which shifts the total effective spontaneous emission rate and impacts the presence or absence of bistability predicted by the quasiclassical model.
NASA Technical Reports Server (NTRS)
Schultz, Chris; Carey, Larry; Schultz, Elise V.; Stano, Geoffrey; Gatlin, Patrick N.; Kozlowski, Danielle M.; Blakeslee, Rich J.; Goodman, Steve
2013-01-01
Key points this analysis will address: 1) What physically is going on in the cloud when there is a jump in lightning? -- Updraft variations, Ice fluxes 2) How do these processes fit in with severe storm conceptual models? 3) What would this information provide an end user? --Relate LJA to radar observations, like changes in reflectivity, MESH, VIL, etc. based multi -Doppler derived physical relationships
Optimizing Thomson's jumping ring
NASA Astrophysics Data System (ADS)
Tjossem, Paul J. H.; Brost, Elizabeth C.
2011-04-01
The height to which rings will jump in a Thomson jumping ring apparatus is the central question posed by this popular lecture demonstration. We develop a simple time-averaged inductive-phase-lag model for the dependence of the jump height on the ring material, its mass, and temperature and apply it to measurements of the jump height for a set of rings made by slicing copper and aluminum alloy pipe into varying lengths. The data confirm a peak jump height that grows, narrows, and shifts to smaller optimal mass when the rings are cooled to 77 K. The model explains the ratio of the cooled/warm jump heights for a given ring, the reduction in optimal mass as the ring is cooled, and the shape of the mass resonance. The ring that jumps the highest is found to have a characteristic resistance equal to the inductive reactance of the set of rings.
A new experimental model to study force depression: the Drosophila jump muscle
Koppes, Ryan A.; Swank, Douglas M.
2014-01-01
Force depression (FD) is a decrease in isometric force following active muscle shortening. Despite being well characterized experimentally, its underlying mechanism remains unknown. To develop a new, genetically manipulatable experimental model that would greatly improve our ability to study the underlying mechanism(s) of FD, we tested the Drosophila jump muscle for classical FD behavior. Steady-state force generation following active shortening decreased by 2, 8, and 11% of maximum isometric force with increasing shortening amplitudes of 5, 10, and 20% of optimal fiber length, and decreased by 11, 8, and 5% with increasing shortening velocities of 4, 20, and 200% of optimal fiber length per second. These steady-state FD (FDSS) characteristics of Drosophila jump muscle mimic those observed in mammalian skeletal muscle. A double exponential fit of transient force recovery following shortening identified two separate phases of force recovery: a rapid initial force redevelopment, and a slower recovery toward steady state. This analysis showed the slower rate of force redevelopment to be inversely proportional to the amount of FDSS, while the faster rate did not correlate with FDSS. This suggests that the mechanism behind the slower, most likely cross-bridge cycling rate, influences the amount of FDSS. Thus the jump muscle, when coupled with the genetic mutability of its sarcomere proteins, offers a unique and powerful experimental model to explore the underlying mechanism behind FD. PMID:24790016
Diffusion in silicate melts: III. Empirical models for multicomponent diffusion
NASA Astrophysics Data System (ADS)
Yan, Liang; Richter, Frank M.; Chamberlin, Laurinda
1997-12-01
Empirical models for multicomponent diffusion in an isotropic fluid were derived by splitting the component's dispersion velocity into two parts: (a) an intrinsic velocity which is proportional to each component's electrochemical potential gradient and independent of reference frame and (b) a net interaction velocity which is both model and reference frame dependent. Simple molecules (e.g., M pO q) were chosen as endmember components. The interaction velocity is assumed to be either the same for each component (leading to a common relaxation velocity U) or proportional to a common interaction force ( F). U or F is constrained by requiring no local buildup in either volume or charge. The most general form of the model-derived diffusion matrix [ D] can be written as a product of a model-dependent kinetic matrix [ L] and a model independent thermodynamic matrix [ G], [ D] = [ L] · [ G]. The elements of [ G] are functions of derivatives of chemical potential with respect to concentration. The elements of [ L] are functions of concentration and partial molar volume of the endmember components, Cio and Vio, and self diffusivity Di, and charge number zi of individual diffusing species. When component n is taken as the dependent variable they can be written in a common form L ij = D jδ ij + C io[V noD n - V joD j)A i + (p nz nD n - p jz jD j)B i] where the functional forms of the scaling factors Ai and Bi depend on the model considered. The off-diagonal element Lij ( i ≠ j) is directly proportional to the concentration of component i, and thus negligible when i is a dilute component. The salient feature of kinetic interaction or relaxation is to slow down larger (volume or charge) and faster diffusing components and to speed up smaller (volume or charge) and slower moving species, in order to prevent local volume or charge buildup. Empirical models for multicomponent diffusion were tested in the ternary system CaOAl 2O 3SiO 2 at 1500°C and 1 GPa over a large
Quantum jump model for a system with a finite-size environment
NASA Astrophysics Data System (ADS)
Suomela, S.; Kutvonen, A.; Ala-Nissila, T.
2016-06-01
Measuring the thermodynamic properties of open quantum systems poses a major challenge. A calorimetric detection has been proposed as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finite-size environment. We use the method to study the common fluctuation relations and prove that they are satisfied.
Quantum jump model for a system with a finite-size environment.
Suomela, S; Kutvonen, A; Ala-Nissila, T
2016-06-01
Measuring the thermodynamic properties of open quantum systems poses a major challenge. A calorimetric detection has been proposed as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finite-size environment. We use the method to study the common fluctuation relations and prove that they are satisfied. PMID:27415207
Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps
NASA Astrophysics Data System (ADS)
Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin
2016-11-01
In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 < 1, the disease may die out, and when R¯0 > 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.
Optimal harvesting of a stochastic delay logistic model with Lévy jumps
NASA Astrophysics Data System (ADS)
Qiu, Hong; Deng, Wenmin
2016-10-01
The optimal harvesting problem of a stochastic time delay logistic model with Lévy jumps is considered in this article. We first show that the model has a unique global positive solution and discuss the uniform boundedness of its pth moment with harvesting. Then we prove that the system is globally attractive and asymptotically stable in distribution under our assumptions. Furthermore, we obtain the existence of the optimal harvesting effort by the ergodic method, and then we give the explicit expression of the optimal harvesting policy and maximum yield.
Field-induced magnetization jumps and quantum criticality in the 2D J-Q model
NASA Astrophysics Data System (ADS)
Iaizzi, Adam; Sandvik, Anders
The J-Q model is a `designer hamiltonian' formed by adding a four spin `Q' term to the standard antiferromagnetic S = 1 / 2 Heisenberg model. The Q term drives a quantum phase transition to a valence-bond solid (VBS) state: a non-magnetic state with a pattern of local singlets which breaks lattice symmetries. The elementary excitations of the VBS are triplons, i.e. gapped S=1 quasiparticles. There is considerable interest in the quantum phase transition between the Néel and VBS states as an example of deconfined quantum criticality. Near the phase boundary, triplons deconfine into pairs of bosonic spin-1/2 excitations known as spinons. Using exact diagonalization and the stochastic series expansion quantum monte carlo method, we study the 2D J-Q model in the presence of an external magnetic field. We use the field to force a nonzero density of magnetic excitations at T=0 and look for signatures of Bose-Einstein condensation of spinons. At higher magnetic fields, there is a jump in the induced magnetization caused by the onset of an effective attractive interaction between magnons on a ferromagnetic background. We characterize the first order quantum phase transition and determine the minimum value of the coupling ratio q ≡ Q / J required to produce this jump. Funded by NSF DMR-1410126.
Computational modeling of diffusion in the cerebellum.
Marinov, Toma M; Santamaria, Fidel
2014-01-01
Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.
Hill, A A; Dewé, T; Kosmider, R; Von Dobschuetz, S; Munoz, O; Hanna, A; Fusaro, A; De Nardi, M; Howard, W; Stevens, K; Kelly, L; Havelaar, A; Stärk, K
2015-09-01
The scientific understanding of the driving factors behind zoonotic and pandemic influenzas is hampered by complex interactions between viruses, animal hosts and humans. This complexity makes identifying influenza viruses of high zoonotic or pandemic risk, before they emerge from animal populations, extremely difficult and uncertain. As a first step towards assessing zoonotic risk of influenza, we demonstrate a risk assessment framework to assess the relative likelihood of influenza A viruses, circulating in animal populations, making the species jump into humans. The intention is that such a risk assessment framework could assist decision-makers to compare multiple influenza viruses for zoonotic potential and hence to develop appropriate strain-specific control measures. It also provides a first step towards showing proof of principle for an eventual pandemic risk model. We show that the spatial and temporal epidemiology is as important in assessing the risk of an influenza A species jump as understanding the innate molecular capability of the virus. We also demonstrate data deficiencies that need to be addressed in order to consistently combine both epidemiological and molecular virology data into a risk assessment framework. PMID:26473042
Random diffusion model with structure corrections
NASA Astrophysics Data System (ADS)
McCowan, David D.; Mazenko, Gene F.
2010-05-01
The random diffusion model is a continuum model for a conserved scalar density field ϕ driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wave-number cutoff to one with a more natural large wave-number cutoff. We investigate whether the features seen previously—namely, a slowing down of the system and the development of a prepeak in the dynamic structure factor at a wave number below the first structure peak—survive in this model. A method for extracting information about a hidden prepeak in experimental data is presented.
Connectionist and diffusion models of reaction time.
Ratcliff, R; Van Zandt, T; McKoon, G
1999-04-01
Two connectionist frameworks, GRAIN (J. L. McClelland, 1993) and brain-state-in-a-box (J. A. Anderson, 1991), and R. Ratcliff's (1978) diffusion model were evaluated using data from a signal detection task. Dependent variables included response probabilities, reaction times for correct and error responses, and shapes of reaction-time distributions. The diffusion model accounted for all aspects of the data, including error reaction times that had previously been a problem for all response-time models. The connectionist models accounted for many aspects of the data adequately, but each failed to a greater or lesser degree in important ways except for one model that was similar to the diffusion model. The findings advance the development of the diffusion model and show that the long tradition of reaction-time research and theory is a fertile domain for development and testing of connectionist assumptions about how decisions are generated over time.
Achard de Leluardière, F; Hajri, L N; Lacouture, P; Duboy, J; Frelut, M L; Peres, G
2006-02-01
There may be concerns about the validity of kinetic models when studying locomotion in obese subjects (OS). The aim of the present study was to improve and validate a relevant representation of obese subject from four kinetic models. Fourteen teenagers with severe primary obesity (BMI = 40 +/- 5.2 kg/m(2)), were studied during jumping. The jumps were filmed by six cameras (synchronized, 50 Hz), associated with a force-plate (1,000 Hz). All the tested models were valid; the linear mechanical analysis of the jumps gave similar results (p > 0.05); but there were significantly different segment inertias when considering the subjects' abdomen (p < 0.01), which was associated with a significantly higher mechanical internal energy expenditure (p < 0.01) than that estimated from Dempster's and Hanavan's model, by about 40 and 30%. The validation of a modelling specifically for obese subjects will enable a better understanding of their locomotion. PMID:16399510
A model of the human triceps surae muscle-tendon complex applied to jumping.
Bobbert, M F; Huijing, P A; van Ingen Schenau, G J
1986-01-01
The purpose of this study was to gain more insight into the behavior of the muscle-tendon complex of human m. triceps surae in jumping. During one-legged vertical jumps of ten subjects ground reaction forces as well as cinematographic data were registered, and electromyograms were recorded from m. soleus and m. gastrocnemius. A model was developed of m. triceps surae, incorporating assumptions concerning dimensions, architecture, force-length and force-velocity relationships of muscle fibers, as well as assumptions concerning dimensions and elastic behavior of tendinous tissue in series with the muscle fibers. The velocity with which origin approaches insertion (V OI) was calculated for m. soleus and m. gastrocnemius using cine film data, and served as input of the model. During the last part of the push-off phase EMG-levels were found to be more or less constant, V OI of m. soleus and m. gastrocnemius rapidly increased, and the plantar flexing moment obtained by solving equations concerning a free body diagram of the foot rapidly declined. A similar decline was observed in the plantar flexing moment obtained by multiplying force calculated with help of the model by estimated moment arm at the ankle. As a result of the decline of exerted force tendon length decreases. According to the model the shortening velocity of tendon reaches higher values than that of muscle fibers. The results of a kinetic analysis demonstrate that during the last part of the push-off phase a combination of high angular velocities with relatively large plantar flexing moments is required. It is concluded that without a compliant tendon m. triceps surae would not be able to satisfy this requirement. PMID:3793737
Birth-jump processes and application to forest fire spotting.
Hillen, T; Greese, B; Martin, J; de Vries, G
2015-01-01
Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.
Fedorovich, E.
1995-09-01
The paper presents an extended theoretical background for applied modeling of the atmospheric convective boundary layer within the so-called zero-order jump approach, which implies vertical homogeneity of meteorological fields in the bulk of convective boundary layer (CBL) and zero-order discontinuities of variables at the interfaces of the layer. The zero-order jump model equations for the most typical cases of CBL are derived. The models of nonsteady, horizontally homogeneous CBL with and without shear, extensively studied in the past with the aid of zero-order jump models, are shown to be particular cases of the general zero-order jump theoretical framework. The integral budgets of momentum and heat are considered for different types of dry CBL. The profiles of vertical turbulent fluxes are presented and analyzed. The general version of the equation of CBL depth growth rate (entrainment rate equation) is obtained by the integration of the turbulence kinetic energy balance equation, invoking basic assumptions of the zero-order parameterizations of the CBL vertical structure. The problems of parameterizing the turbulence vertical structure and closure of the entrainment rate equation for specific cases of CBL are discussed. A parameterization scheme for the horizontal turbulent exchange in zero-order jump models of CBL is proposed. The developed theory is generalized for the case of CBL over irregular terrain. 28 refs., 2 figs.
THE EVOLUTION OF ASTEROIDS IN THE JUMPING-JUPITER MIGRATION MODEL
Roig, Fernando; Nesvorný, David E-mail: davidn@boulder.swri.edu
2015-12-15
In this work, we investigate the evolution of a primordial belt of asteroids, represented by a large number of massless test particles, under the gravitational effect of migrating Jovian planets in the framework of the jumping-Jupiter model. We perform several simulations considering test particles distributed in the Main Belt, as well as in the Hilda and Trojan groups. The simulations start with Jupiter and Saturn locked in the mutual 3:2 mean motion resonance plus three Neptune-mass planets in a compact orbital configuration. Mutual planetary interactions during migration led one of the Neptunes to be ejected in less than 10 Myr of evolution, causing Jupiter to jump by about 0.3 AU in semimajor axis. This introduces a large-scale instability in the studied populations of small bodies. After the migration phase, the simulations are extended over 4 Gyr, and we compare the final orbital structure of the simulated test particles to the current Main Belt of asteroids with absolute magnitude H < 9.7. The results indicate that, in order to reproduce the present Main Belt, the primordial belt should have had a distribution peaked at ∼10° in inclination and at ∼0.1 in eccentricity. We discuss the implications of this for the Grand Tack model. The results also indicate that neither primordial Hildas, nor Trojans, survive the instability, confirming the idea that such populations must have been implanted from other sources. In particular, we address the possibility of implantation of Hildas and Trojans from the Main Belt population, but find that this contribution should be minor.
Modeling diffusion in foamed polymer nanocomposites.
Ippalapalli, Sandeep; Ranaprathapan, A Dileep; Singh, Sachchida N; Harikrishnan, G
2013-04-15
Two-way multicomponent diffusion processes in polymeric nanocomposite foams, where the condensed phase is nanoscopically reinforced with impermeable fillers, are investigated. The diffusion process involves simultaneous outward permeation of the components of the dispersed gas phase and inward diffusion of atmospheric air. The transient variation in thermal conductivity of foam is used as the macroscopic property to track the compositional variations of the dispersed gases due to the diffusion process. In the continuum approach adopted, the unsteady-state diffusion process is combined with tortuosity theory. The simulations conducted at ambient temperature reveal distinct regimes of diffusion processes in the nanocomposite foams owing to the reduction in the gas-transport rate induced by nanofillers. Simulations at a higher temperature are also conducted and the predictions are compared with experimentally determined thermal conductivities under accelerated diffusion conditions for polyurethane foams reinforced with clay nanoplatelets of varying individual lamellar dimensions. Intermittent measurements of foam thermal conductivity are performed while the accelerated diffusion proceeded. The predictions under accelerated diffusion conditions show good agreement with experimentally measured thermal conductivities for nanocomposite foams reinforced with low and medium aspect-ratios fillers. The model shows higher deviations for foams with fillers that have a high aspect ratio.
Numerical modelling of microdroplet self-propelled jumping on micro-textured surface
NASA Astrophysics Data System (ADS)
Attarzadeh, S. M. Reza; Dolatabadi, Ali; Chun Kim, Kyung
2015-11-01
Understanding various stages of single and multiple droplet impact on a super-hydrophobic surface is of interest for many industrial applications such as aerospace industry. In this study, the phenomenon of coalescence induced droplets self-propelled jumping on a micro-textured super-hydrophobic surface is numerically simulated using Volume of Fluid (VOF) method. This model mimics the scenario of coalescing cloud-sized particles over the surface structure of an aircraft. The VOF coupled with a dynamic contact angle model is used to simulate the coalescence of two equal size droplets, that are initially placed very closed to each other with their interface overlapping with each other's which triggers the incipience of their coalescence. The textured surface is modeled as a series of equally spaced squared pillars, with 111° as the intrinsic contact angle all over the solid contact area. It is shown that the radial velocity of coalescing liquid bridge is reverted to upward direction due to the counter action of the surface to the basal area of droplet in contact. The presence of air beneath the droplet inside micro grooves which aimed at repelling water droplet is also captured in this model. The simulated results are found in good agreement with experimental observations. The authors gratefully acknowledge the financial support from Natural Sciences and Engineering Research Council of Canada (NSERC), Consortium de Recherche et d'innovation en Aerospatiale au Quebec (CRIAQ), Bombardier Aerospace, Pratt Whitney Canada.
Wang, Yuan; Zhou, Xiaobo; Wang, Honghui; Li, King; Yao, Lixiu; Wong, Stephen T C
2008-07-01
Mass spectrometry (MS) has shown great potential in detecting disease-related biomarkers for early diagnosis of stroke. To discover potential biomarkers from large volume of noisy MS data, peak detection must be performed first. This article proposes a novel automatic peak detection method for the stroke MS data. In this method, a mixture model is proposed to model the spectrum. Bayesian approach is used to estimate parameters of the mixture model, and Markov chain Monte Carlo method is employed to perform Bayesian inference. By introducing a reversible jump method, we can automatically estimate the number of peaks in the model. Instead of separating peak detection into substeps, the proposed peak detection method can do baseline correction, denoising and peak identification simultaneously. Therefore, it minimizes the risk of introducing irrecoverable bias and errors from each substep. In addition, this peak detection method does not require a manually selected denoising threshold. Experimental results on both simulated dataset and stroke MS dataset show that the proposed peak detection method not only has the ability to detect small signal-to-noise ratio peaks, but also greatly reduces false detection rate while maintaining the same sensitivity. PMID:18586741
Stochastic models for surface diffusion of molecules
Shea, Patrick Kreuzer, Hans Jürgen
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.
Evaluation of Dynamics of the West African Monsoon Jump Simulated by the MIT Regional Climate Model
NASA Astrophysics Data System (ADS)
Eltahir, Elfatih A. B.; Im, Eun-Soon
2015-04-01
The seasonal advance and retreat of the West African monsoon behaves abrupt northward jump of maximum rainfall from the Guinean coast to the Sahel region. Both global and regional climate models have difficulties in accurately reproducing such a behavior due to its complexity combined the dynamical and physical processes. In this study, we evaluate the performance of the MIT Regional Climate Model (MRCM) in simulating the West African monsoon. For this, 20-year long-term simulation (1989-2008) is performed using the ERAInterim reanalysis as the initial and boundary condition, and the analysis primarily focuses on the dynamics associated with abrupt phase transitions of the monsoon rainfall. We first examine detailed characteristics in terms of the onset, maximum, and retreat of the monsoon rainfall using daily precipitation. We then present the dynamical explanation behind rainfall variability from the analysis of the absolute vorticity near the tropopause and the meridional gradient of boundary-layer entropy within the dynamical theory proposed by Eltahir and Gong (1996). Acknowledgements : This research was supported by the National Research Foundation Singapore through the Singapore MIT Alliance for Research and Technology's Center for Environmental Sensing and Modeling interdisciplinary research program.
Flux-mediated diffuse mismatch model
NASA Astrophysics Data System (ADS)
Loh, G. C.; Tay, B. K.; Teo, E. H. T.
2010-09-01
The diffuse mismatch model (DMM) is modified to account for the effect of thermal flux on phonon transmission at interfaces. This new model, the flux-mediated diffuse mismatch model (FMDMM) takes a slightly different approach in its formulation, and does not employ the principle of detailed balance. Two competing processes—an increase in the flux coefficient, and a decrease in the rest of the transmission term, may result in either a rise or fall in thermal boundary resistance when thermal flux is increased. This might partially explain the large disparities between experimental, theoretical, and simulated results of thermal boundary resistance.
NASA Astrophysics Data System (ADS)
Zhu, Yanzheng; Zhang, Lixian; Sreeram, Victor; Shammakh, Wafa; Ahmad, Bashir
2016-10-01
In this paper, the resilient model approximation problem for a class of discrete-time Markov jump time-delay systems with input sector-bounded nonlinearities is investigated. A linearised reduced-order model is determined with mode changes subject to domination by a hierarchical Markov chain containing two different nonhomogeneous Markov chains. Hence, the reduced-order model obtained not only reflects the dependence of the original systems but also model external influence that is related to the mode changes of the original system. Sufficient conditions formulated in terms of bilinear matrix inequalities for the existence of such models are established, such that the resulting error system is stochastically stable and has a guaranteed l2-l∞ error performance. A linear matrix inequalities optimisation coupled with line search is exploited to solve for the corresponding reduced-order systems. The potential and effectiveness of the developed theoretical results are demonstrated via a numerical example.
A model of oceanic development by ridge jumping: Opening of the Scotia Sea
NASA Astrophysics Data System (ADS)
Maldonado, Andrés; Bohoyo, Fernando; Galindo-Zaldívar, Jesús; Hernández-Molina, Fº. Javier; Lobo, Francisco J.; Lodolo, Emanuele; Martos, Yasmina M.; Pérez, Lara F.; Schreider, Anatoly A.; Somoza, Luis
2014-12-01
, where an accretionary prism is identified. Such tectonics, locally affecting up to the most recent deposits, imply that a portion of the primitive oceanic crust is absent. Based on the stratigraphy of the deposits and the magnetic anomalies, an age of 44 Ma is postulated for the initiation of oceanic spreading in the eastern Ona basin, while spreading in the western Ona Basin would have occurred during the early Oligocene. The tectonics, depositional units and the age of the oceanic crust provide additional evidence regarding the Eocene opening of Drake Passage. The initial tectonic fragmentation of the South America-Antarctic Bridge, followed by oceanic spreading, was characterized by jumping of the spreading centers. An Eocene spreading center in the eastern Ona Basin was the precursor of the Scotia Sea. A model comprising four tectonic evolutionary phases is proposed: Phase I, Pacific subduction - Paleocene to middle Eocene; Phase II, eastern Ona back-arc spreading - middle to late Eocene; Phase III, ridge jumping and western Ona back-arc spreading - early Oligocene; and Phase IV, ridge jumping and West Scotia Ridge spreading - early Oligocene to late Miocene. The development of shallow gateways allowed for an initial connection between the Pacific and Atlantic oceans and, hence, initiated the thermal isolation of Antarctica during the middle and late Eocene. Deep gateways that enhanced the full isolation of Antarctica developed in Drake Passage from the Eocene/Oligocene transition onward. A significant correlation is observed between the tectonics, stratigraphic units and major climate events, thereby indicating the influence of the local tectonic and paleoceanographic events of the Southern Ocean on global evolution.
Persistent search in single and multiple confined domains: a velocity-jump process model
NASA Astrophysics Data System (ADS)
Poll, Daniel B.; Kilpatrick, Zachary P.
2016-05-01
We analyze velocity-jump process models of persistent search for a single target on a bounded domain. The searcher proceeds along ballistic trajectories and is absorbed upon collision with the target boundary. When reaching the domain boundary, the searcher chooses a random direction for its new trajectory. For circular domains and targets, we can approximate the mean first passage time (MFPT) using a Markov chain approximation of the search process. Our analysis and numerical simulations reveal that the time to find the target decreases for targets closer to the domain boundary. When there is a small probability of direction-switching within the domain, we find the time to find the target decreases slightly with the turning probability. We also extend our exit time analysis to the case of partitioned domains, where there is a single target within one of multiple disjoint subdomains. Given an average time of transition between domains < T> , we find that the optimal rate of transition that minimizes the time to find the target obeys {β\\text{min}}\\propto 1/\\sqrt< T> .
Mathematical modeling of molecular diffusion through mucus
Cu, Yen; Saltzman, W. Mark
2008-01-01
The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488
Guin, J.A.; Tarrer, A.R.
1992-01-01
The objective of this research is to determine the relationship between the size and shape of coal and petroleum macromolecules and their diffusion rates i.e., effective diffusivities, in catalyst pore structures. That is, how do the effective intrapore diffusivities depend on molecule configuration and pore geometry. This quarter we made a more comprehensive literature survey concerning configurational diffusion in porous catalysts or catalyst supports. A detailed literature review is reported. Also, a mathematical configurational diffusion model was developed. By using this model, the effective diffusivity for model compounds diffusing in porous media and a linear adsorption constant can be determined by fitting experimental data.
NASA Astrophysics Data System (ADS)
Petrov, Blagovest; Vink, Jorick S.; Gräfener, Götz
2016-05-01
Luminous blue variables (LBVs) have been suggested to be the direct progenitors of supernova Types IIb and IIn, with enhanced mass loss prior to explosion. However, the mechanism of this mass loss is not yet known. Here, we investigate the qualitative behaviour of theoretical stellar wind mass loss as a function of Teff across two bi-stability jumps in blue supergiant regime and also in proximity to the Eddington limit, relevant for LBVs. To investigate the physical ingredients that play a role in the radiative acceleration we calculate blue supergiant wind models with the CMFGEN non-local thermodynamic equilibrium model atmosphere code over an effective temperature range between 30 000 and 8800 K. Although our aim is not to provide new mass-loss rates for BA supergiants, we study and confirm the existence of two bi-stability jumps in mass-loss rates predicted by Vink et al. However, they are found to occur at somewhat lower Teff (20 000 and 9000 K, respectively) than found previously, which would imply that stars may evolve towards lower Teff before strong mass loss is induced by the bi-stability jumps. When the combined effects of the second bi-stability jump and the proximity to Eddington limit are accounted for, we find a dramatic increase in the mass-loss rate by up to a factor of 30. Further investigation of both bi-stability jumps is expected to lead to a better understanding of discrepancies between empirical modelling and theoretical mass-loss rates reported in the literature, and to provide key inputs for the evolution of both normal AB supergiants and LBVs, as well as their subsequent supernova Type II explosions.
Hickox, Lauren J; Ashby, Blake M; Alderink, Gordon J
2016-05-01
Most previous standing long jump studies have been based on the assumption of two-dimensional sagittal plane motion with bilateral symmetry. The purpose of this study was to investigate the validity of this assumption. Standing long jump trials were collected using six adult male participants. Each participant stood with a foot on each of two force plates and performed eight standing long jumps for maximal distance. Inverse dynamics analyses were performed for two-dimensional (2D) and three-dimensional (3D) models, and joint moments, powers, and work values were compared. The differences between these models with respect to the validity of the common planar jumping assumption were analyzed. Good agreement was observed between 2D and 3D methods for the lower body, with minimal differences in sagittal plane moments, power, and work for the ankle, knee, and lower back. There were significant, but relatively small differences in the sagittal plane kinematics and kinetics at the hip. For the upper body, the results contradicted the sagittal plane assumption in that significant moments and power were generated about the abduction/adduction axis of the shoulder and a similar amount of work was performed about both abduction/adduction and flexion/extension axes of the shoulder. The elbow also showed significant differences in power and work. These results indicate that an assumption of planar motion should be sufficient for many studies of the standing long jump that only examine lower body movement. However, for studies that include upper body motion, diagnosing injury risk, or investigating gender differences, a 3D model may be more appropriate. PMID:26949101
MODIS Solar Diffuser: Modelled and Actual Performance
NASA Technical Reports Server (NTRS)
Waluschka, Eugene; Xiong, Xiao-Xiong; Esposito, Joe; Wang, Xin-Dong; Krebs, Carolyn (Technical Monitor)
2001-01-01
The Moderate Resolution Imaging Spectroradiometer (MODIS) instrument's solar diffuser is used in its radiometric calibration for the reflective solar bands (VIS, NTR, and SWIR) ranging from 0.41 to 2.1 micron. The sun illuminates the solar diffuser either directly or through a attenuation screen. The attenuation screen consists of a regular array of pin holes. The attenuated illumination pattern on the solar diffuser is not uniform, but consists of a multitude of pin-hole images of the sun. This non-uniform illumination produces small, but noticeable radiometric effects. A description of the computer model used to simulate the effects of the attenuation screen is given and the predictions of the model are compared with actual, on-orbit, calibration measurements.
ERIC Educational Resources Information Center
Muller, Andreas
2013-01-01
On October 14,2012, Felix Baumgartner, an Austrian sky-diver, set some new world records for his discipline. Jumping from a height of about 39 km, he reached a top speed of 1342 km/h, becoming the first human being to break the sound barrier in free fall. In order to understand some essential physics aspects of this remarkable feat, we wonder why…
NASA Astrophysics Data System (ADS)
Shahraki, Meysam; Schmeling, Harro; Haas, Peter
2016-04-01
Isostatic equilibrium is a good approximation for passive continental margins. In these regions, geoid anomalies are proportional to the local dipole moment of density-depth distributions, which can be used to constrain the thickness of lithospheric jumps and corresponding tectonic stress. We analysed satellite derived geoid data and, after filtering, extracted typical averaged profiles across the Western and Eastern passive margins of the South Atlantic. They show geoid jumps of 8.1 m and 7.0 m for the Argentinian and African sides, respectively. Together with topography data and reasonable assumptions about densities these jumps are interpreted as isostatic geoid anomalies and yield best-fitting crustal and lithospheric thicknesses. They reveal a small asymmetry between the African and S-American crusts and lithospheres by a few kilometers. On both sides, the continental lithosphere is about 15 - 30km thicker than the oceanic lithosphere. To keep such geoid jumps stable over O(100Ma) fully dynamic models show that lithospheric viscosities must be of the order of 1e23 Pa s.
NASA Astrophysics Data System (ADS)
Teakles, Andrew; Mo, Ruping; Dierking, Carl F.; Emond, Chris; Smith, Trevor; McLennan, Neil; Joe, Paul I.
2014-01-01
As was the case for most other Olympic competitions, providing weather guidance for the ski jump and Nordic combined events involved its own set of unique challenges. The extent of these challenges was brought to light before the Vancouver 2010 Winter Olympics during a series of outflow wind events in the 2008/2009 winter season. The interactions with the race officials during the difficult race conditions brought on by the outflows provided a new perspective on the service delivery requirements for the upcoming Olympic Games. In particular, the turbulent nature of the winds and its impact on the ski jump practice events that season highlighted the need of race officials for nowcasting advice at very short time scales (from 2 min to 1 h) and forecast products tailored to their decision-making process. These realizations resulted in last minute modifications to the monitoring strategy leading up to the Olympic Games and required forecasters' conceptual models for flow within the Callaghan Valley to be downscaled further to reflect the evolution of turbulence at the ski jump site. The SNOW-V10 (Science of Nowcasting Olympic Weather for Vancouver 2010) team provided support for these efforts by supplying diagnostic case analyses of important events using numerical weather data and by enhancing the real-time monitoring capabilities at the ski jump venue.
Modelling Diffusion of a Personalized Learning Framework
ERIC Educational Resources Information Center
Karmeshu; Raman, Raghu; Nedungadi, Prema
2012-01-01
A new modelling approach for diffusion of personalized learning as an educational process innovation in social group comprising adopter-teachers is proposed. An empirical analysis regarding the perception of 261 adopter-teachers from 18 schools in India about a particular personalized learning framework has been made. Based on this analysis,…
NASA Astrophysics Data System (ADS)
Wu, Qiong; Li, Shu-Suo; Ma, Yue; Gong, Sheng-Kai
2012-10-01
The diffusion coefficients of several alloying elements (Al, Mo, Co, Ta, Ru, W, Cr, Re) in Ni are directly calculated using the five-frequency model and the first principles density functional theory. The correlation factors provided by the five-frequency model are explicitly calculated. The calculated diffusion coefficients show their excellent agreement with the available experimental data. Both the diffusion pre-factor (D0) and the activation energy (Q) of impurity diffusion are obtained. The diffusion coefficients above 700 K are sorted in the following order: DAl > DCr > DCo > DTa > DMo > DRu > DW > DRe. It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair (E1). The value of E2-E1 (E2 is the solute diffusion energy) and the correlation factor each also show a positive correlation. The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.
Generalized Drift-Diffusion Model In Semiconductors
Mesbah, S.; Bendib-Kalache, K.; Bendib, A.
2008-09-23
A new drift-diffusion model is proposed based on the computation of the stationary nonlocal current density. The semi classical Boltzmann equation is solved keeping all the anisotropies of the distribution function with the use of the continued fractions. The conductivity is calculated in the linear approximation and for arbitrary collision frequency with respect to Kv{sub t} where K{sup -1} is the characteristic length scale of the system and V{sub t} is the thermal velocity. The nonlocal conductivity can be used to close the generalized drift-diffusion equations valid for arbitrary collisionality.
Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes
NASA Astrophysics Data System (ADS)
Żaba, Mariusz; Garbaczewski, Piotr; Stephanovich, Vladimir
2014-03-01
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of Lévy-stable type and admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function ρ(x, t). Our main goal is to demonstrate a compatibility of a direct solution method (an explicit, albeit numerically assisted, integration of the master equation) with an indirect pathwise procedure, recently proposed in [Physica A 392, 3485, (2013)] as a valid tool for a dynamical analysis of non-Langevin jump-type processes. The path-wise method heavily relies on an accumulation of large sample path data, that are generated by means of a properly tailored Gillespie's algorithm. Their statistical analysis in turn allows to infer the dynamics of ρ(x, t). However, no consistency check has been completed so far to demonstrate that both methods are fully compatible and indeed provide a solution of the same dynamical problem. Presently we remove this gap, with a focus on potential deficiencies (various cutoffs, including those upon the jump size) of approximations involved in simulation routines and solutions protocols.
Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes
NASA Astrophysics Data System (ADS)
Żaba, Mariusz; Garbaczewski, Piotr; Stephanovich, Vladimir A.
2014-03-01
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of Lévy-stable type and admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function ρ( x, t). Our main goal is to demonstrate a compatibility of a direct solution method (an explicit, albeit numerically assisted, integration of the master equation) with an indirect pathwise procedure, recently proposed in [Physica A 392, 3485, (2013)] as a valid tool for a dynamical analysis of non-Langevin jump-type processes. The path-wise method heavily relies on an accumulation of large sample path data, that are generated by means of a properly tailored Gillespie's algorithm. Their statistical analysis in turn allows to infer the dynamics of ρ( x, t). However, no consistency check has been completed so far to demonstrate that both methods are fully compatible and indeed provide a solution of the same dynamical problem. Presently we remove this gap, with a focus on potential deficiencies (various cutoffs, including those upon the jump size) of approximations involved in simulation routines and solutions protocols.
Modeling Demic and Cultural Diffusion: An Introduction.
Fort, Joaquim; Crema, Enrico R; Madella, Marco
2015-07-01
Identifying the processes by which human cultures spread across different populations is one of the most topical objectives shared among different fields of study. Seminal works have analyzed a variety of data and attempted to determine whether empirically observed patterns are the result of demic and/or cultural diffusion. This special issue collects articles exploring several themes (from modes of cultural transmission to drivers of dispersal mechanisms) and contexts (from the Neolithic in Europe to the spread of computer programming languages), which offer new insights that will augment the theoretical and empirical basis for the study of demic and cultural diffusion. In this introduction we outline the state of art in the modeling of these processes, briefly discuss the pros and cons of two of the most commonly used frameworks (equation-based models and agent-based models), and summarize the significance of each article in this special issue.
Modeling Demic and Cultural Diffusion: An Introduction.
Fort, Joaquim; Crema, Enrico R; Madella, Marco
2015-07-01
Identifying the processes by which human cultures spread across different populations is one of the most topical objectives shared among different fields of study. Seminal works have analyzed a variety of data and attempted to determine whether empirically observed patterns are the result of demic and/or cultural diffusion. This special issue collects articles exploring several themes (from modes of cultural transmission to drivers of dispersal mechanisms) and contexts (from the Neolithic in Europe to the spread of computer programming languages), which offer new insights that will augment the theoretical and empirical basis for the study of demic and cultural diffusion. In this introduction we outline the state of art in the modeling of these processes, briefly discuss the pros and cons of two of the most commonly used frameworks (equation-based models and agent-based models), and summarize the significance of each article in this special issue. PMID:26932566
Relativistic diffusion processes and random walk models
Dunkel, Joern; Talkner, Peter; Haenggi, Peter
2007-02-15
The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (noncontinuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the nonrelativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.
Analytic modeling of a spray diffusion flame
NASA Technical Reports Server (NTRS)
Harsha, P. T.; Edelman, R. B.
1984-01-01
A detailed model for a spray diffusion flame is described. The model is based on the boundary layer form of the equations of motion, with droplet transport accounted for using a discretized droplet size distribution function. Interphase transport of mass and energy are accounted for, with a flame-sheet model used to describe the combustion process on a droplet scale. Near dynamic equilibrium is assumed for the description of droplet transport; droplets can diffuse relative to the gas phase. Gas-phase mixing is accounted for using a two-equation turbulence model; buoyancy effects are included, with a temperature fluctuation equation used to account for buoyancy effects on turbulence structure. Thermal radiation from gas-phase CO2 and H2O is included. Gas-phase chemical kinetics are modeled using a 20-reaction, 10-species version of the advanced quasi-global chemical kinetics formulation. Results are compared with data for a vaporizing Freon spray and a pentane spray flame. It is shown that the computational approach provides a reasonably valid picture of the overall development of a spray diffusion flame, and, furthermore, provides a useful tool for the parametric examination of the spray combustion process.
Modeling diffuse pollution with a distributed approach.
León, L F; Soulis, E D; Kouwen, N; Farquhar, G J
2002-01-01
The transferability of parameters for non-point source pollution models to other watersheds, especially those in remote areas without enough data for calibration, is a major problem in diffuse pollution modeling. A water quality component was developed for WATFLOOD (a flood forecast hydrological model) to deal with sediment and nutrient transport. The model uses a distributed group response unit approach for water quantity and quality modeling. Runoff, sediment yield and soluble nutrient concentrations are calculated separately for each land cover class, weighted by area and then routed downstream. The distributed approach for the water quality model for diffuse pollution in agricultural watersheds is described in this paper. Integrating the model with data extracted using GIS technology (Geographical Information Systems) for a local watershed, the model is calibrated for the hydrologic response and validated for the water quality component. With the connection to GIS and the group response unit approach used in this paper, model portability increases substantially, which will improve non-point source modeling at the watershed scale level.
NASA Astrophysics Data System (ADS)
Wollman, Andrew; Snyder, Trevor; Weislogel, Mark
2014-11-01
Rebounding droplets from superhydrophobic surfaces have attracted significant public and scientific attention because they are both enjoyable as well as industrially relevant. Demonstrations of bouncing droplets with volumes between 0.003 and 0.03 ml are common in the literature and limited primarily by gravity. In this presentation we demonstrate large droplet ``rebounds'' made possible by low-gravity testing in a drop tower. The up to 300 ml drops are best described as puddles that launch in a nearly identical manner to rebounding drops 4 orders of magnitude smaller in volume. A variety of jumping liquid and gas puddles are shown including puddles of highly specified and unusual initial geometry. The large length sales of the capillary fluidic surfaces ~ O (10 cm) enable 3D printing of all superhydrophobic surface topologies demonstrated. In addition, we demonstrate such puddle jumping as a passive drop-on-demand technique for large low-gravity drop dynamics investigations; such as collisions, rebounds, heat and mass transfer, and containerless possessing.
Dispersing V-type asteroids during the planetary instability in the jumping Jupiter model
NASA Astrophysics Data System (ADS)
Brasil, P. I.
2015-12-01
V-type asteroids are a particular class of asteroids whose surface mineralogy is associated to a basaltic composition. Currently, the only known source of these asteroids in the Main Belt is (4) Vesta. This asteroid is located in the inner belt (2.1 < a < 2.5 AU), and has associated a dynamical family formed by the impact ejecta of two large craters excavated on its basaltic surface some 2 and 1 Gyr ago, respectively. Thus, many V-type asteroids belong to the Vesta family. However, an increasing number of V-type asteroids is found outside the limits of the family. Some of these asteroids, especially those located in the inner belt, are explained as dynamical fugitives from the family. Others cannot be linked to the Vesta family nor to (4) Vesta, neither dynamically nor mineralogically. The most paradoxal cases are the V-type asteroids found beyond 2.5 AU, in the central (2.5 < a < 2.8 AU) and outer (2.8 < a < 3.2 AU) parts of the Main Belt, where no local source of basaltic material is recognized. In this work, we propose a coherent dynamical mechanism to explain the delivery of V-type asteroids originated in the inner belt to the central and outer belt. This mechanism involves the planetary instability during the epoch when the outer planets were migrating due to their interaction with a disk of planetesimals, some 4 Gyr ago. The instability is caused by mutual planetary encounters in the framework of the jumping Jupiter model with initially five outer planets: Jupiter, Saturn and three ice giants. As a consequence of this instability, an ice giant is temporarily scattered into the asteroid belt and helps to disperse the asteroids in semimajor axis by up to ~0.5 AU. The V-type asteroids dispersed by this mechanism could have originated either in an older cratering event on the surface of (4) Vesta, or in the fragmentation of another basaltic asteroid in the inner belt that likely have existed during the epoch of planetary migration. We tested several
Koppes, Ryan A; Swank, Douglas M; Corr, David T
2015-10-15
The increase in steady-state force after active lengthening in skeletal muscle, termed force enhancement (FE), has been observed for nearly one century. Although demonstrated experimentally at various structural levels, the underlying mechanism(s) remain unknown. We recently showed that the Drosophila jump muscle is an ideal model for investigating mechanisms behind muscle physiological properties, because its mechanical characteristics, tested thus far, duplicate those of fast mammalian skeletal muscles, and Drosophila has the advantage that it can be more easily genetically modified. To determine if Drosophila would be appropriate to investigate FE, we performed classic FE experiments on this muscle. Steady-state FE (FESS), following active lengthening, increased by 3, 7, and 12% of maximum isometric force, with increasing stretch amplitudes of 5, 10, and 20% of optimal fiber length (FLOPT), yet was similar for stretches across increasing stretch velocities of 4, 20, and 200% FLOPT/s. These FESS characteristics of the Drosophila jump muscle closely mimic those observed previously. Jump muscles also displayed typical transient FE characteristics. The transient force relaxation following active stretch was fit with a double exponential, yielding two phases of force relaxation: a fast initial relaxation of force, followed by a slower recovery toward steady state. Our analyses identified a negative correlation between the slow relaxation rate and FESS, indicating that there is likely an active component contributing to FE, in addition to a passive component. Herein, we have established the Drosophila jump muscle as a new and genetically powerful experimental model to investigate the underlying mechanism(s) of FE.
Koppes, Ryan A.; Swank, Douglas M.
2015-01-01
The increase in steady-state force after active lengthening in skeletal muscle, termed force enhancement (FE), has been observed for nearly one century. Although demonstrated experimentally at various structural levels, the underlying mechanism(s) remain unknown. We recently showed that the Drosophila jump muscle is an ideal model for investigating mechanisms behind muscle physiological properties, because its mechanical characteristics, tested thus far, duplicate those of fast mammalian skeletal muscles, and Drosophila has the advantage that it can be more easily genetically modified. To determine if Drosophila would be appropriate to investigate FE, we performed classic FE experiments on this muscle. Steady-state FE (FESS), following active lengthening, increased by 3, 7, and 12% of maximum isometric force, with increasing stretch amplitudes of 5, 10, and 20% of optimal fiber length (FLOPT), yet was similar for stretches across increasing stretch velocities of 4, 20, and 200% FLOPT/s. These FESS characteristics of the Drosophila jump muscle closely mimic those observed previously. Jump muscles also displayed typical transient FE characteristics. The transient force relaxation following active stretch was fit with a double exponential, yielding two phases of force relaxation: a fast initial relaxation of force, followed by a slower recovery toward steady state. Our analyses identified a negative correlation between the slow relaxation rate and FESS, indicating that there is likely an active component contributing to FE, in addition to a passive component. Herein, we have established the Drosophila jump muscle as a new and genetically powerful experimental model to investigate the underlying mechanism(s) of FE. PMID:26289752
NASA Astrophysics Data System (ADS)
Müller, Andreas
2013-01-01
On October 14,2012, Felix Baumgartner, an Austrian sky-diver, set some new world records for his discipline. Jumping from a height of about 39 km, he reached a top speed of 1342 km/h, becoming the first human being to break the sound barrier in free fall. In order to understand some essential physics aspects of this remarkable feat, we wonder why his start height had to be that high (when the tremendous effort that was necessary for leaping from such a height required 50 million, as reported in the press). More precisely, can you give an estimate for the minimal start height—which we will call the Baumgartner limit, zB—of a sky diver who wants to break the sound barrier in free fall?
A Diffuse Interface Model with Immiscibility Preservation
Tiwari, Arpit; Freund, Jonathan B.; Pantano, Carlos
2013-01-01
A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results. PMID:24058207
Anomalous diffusion in generalized Dykhne model
Dvoretskaya, O. A.; Kondratenko, P. S. Matveev, L. V.
2010-01-15
Contaminant transport is investigated in the generalized Dykhne model differing from the original Dykhne model by the presence of advection in the high-permeability medium. An analysis is presented of transport regimes and concentration tail behavior in the high-permeability medium. It is found that the transport regimes include anomalous ones: subdiffusion and quasi-diffusion. A difference is revealed between longitudinal and transverse transport. Regime change over time leads to multiple-regime long-distance asymptotic behavior of concentration distributions. An analogy is drawn between the problems examined here and transport through comb structures.
Distributed Energy Resources Market Diffusion Model
Maribu, Karl Magnus; Firestone, Ryan; Marnay, Chris; Siddiqui,Afzal S.
2006-06-16
Distributed generation (DG) technologies, such as gas-fired reciprocating engines and microturbines, have been found to be economically beneficial in meeting commercial-sector electrical, heating, and cooling loads. Even though the electric-only efficiency of DG is lower than that offered by traditional central stations, combined heat and power (CHP) applications using recovered heat can make the overall system energy efficiency of distributed energy resources (DER) greater. From a policy perspective, however, it would be useful to have good estimates of penetration rates of DER under various economic and regulatory scenarios. In order to examine the extent to which DER systems may be adopted at a national level, we model the diffusion of DER in the US commercial building sector under different technical research and technology outreach scenarios. In this context, technology market diffusion is assumed to depend on the system's economic attractiveness and the developer's knowledge about the technology. The latter can be spread both by word-of-mouth and by public outreach programs. To account for regional differences in energy markets and climates, as well as the economic potential for different building types, optimal DER systems are found for several building types and regions. Technology diffusion is then predicted via two scenarios: a baseline scenario and a program scenario, in which more research improves DER performance and stronger technology outreach programs increase DER knowledge. The results depict a large and diverse market where both optimal installed capacity and profitability vary significantly across regions and building types. According to the technology diffusion model, the West region will take the lead in DER installations mainly due to high electricity prices, followed by a later adoption in the Northeast and Midwest regions. Since the DER market is in an early stage, both technology research and outreach programs have the potential to increase
Diffusion through thin membranes: Modeling across scales
NASA Astrophysics Data System (ADS)
Aho, Vesa; Mattila, Keijo; Kühn, Thomas; Kekäläinen, Pekka; Pulkkinen, Otto; Minussi, Roberta Brondani; Vihinen-Ranta, Maija; Timonen, Jussi
2016-04-01
From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.
Distributed Wind Diffusion Model Overview (Presentation)
Preus, R.; Drury, E.; Sigrin, B.; Gleason, M.
2014-07-01
Distributed wind market demand is driven by current and future wind price and performance, along with several non-price market factors like financing terms, retail electricity rates and rate structures, future wind incentives, and others. We developed a new distributed wind technology diffusion model for the contiguous United States that combines hourly wind speed data at 200m resolution with high resolution electricity load data for various consumer segments (e.g., residential, commercial, industrial), electricity rates and rate structures for utility service territories, incentive data, and high resolution tree cover. The model first calculates the economics of distributed wind at high spatial resolution for each market segment, and then uses a Bass diffusion framework to estimate the evolution of market demand over time. The model provides a fundamental new tool for characterizing how distributed wind market potential could be impacted by a range of future conditions, such as electricity price escalations, improvements in wind generator performance and installed cost, and new financing structures. This paper describes model methodology and presents sample results for distributed wind market potential in the contiguous U.S. through 2050.
Diffuse Interface Model for Microstructure Evolution
NASA Astrophysics Data System (ADS)
Nestler, Britta
A phase-field model for a general class of multi-phase metallic alloys is proposed which describes both, multi-phase solidification phenomena as well as polycrystalline grain structures. The model serves as a computational method to simulate the motion and kinetics of multiple phase boundaries and enables the visualization of the diffusion processes and of the phase transitions in multi-phase systems. Numerical simulations are presented which illustrate the capability of the phase-field model to recover a variety of complex experimental growth structures. In particular, the phase-field model can be used to simulate microstructure evolutions in eutectic, peritectic and monotectic alloys. In addition, polycrystalline grain structures with effects such as wetting, grain growth, symmetry properties of adjacent triple junctions in thin film samples and stability criteria at multiple junctions are described by phase-field simulations.
Johnston, Lucas A; Butler, Robert J; Sparling, Tawnee L; Queen, Robin M
2015-02-01
Vertical jump performance is related to high-level function in athletics. The purpose of this study was to determine whether a single set of biomechanical variables exist that can predict vertical jump height during multiple jumping strategies: single foot jump, drop jump, and countermovement jump. Three-dimensional mechanics were collected during the 3 different jumping tasks in 50 recreational male athletes. Three successful trials were analyzed for each jump type. Testing order was randomized to minimize fatigue effects, and the dominant limb was used for analysis. All discrete variables were correlated to jump height and the 10 variables that had the strongest correlation were inserted into a linear regression model to identify what variables predicted maximum jump height. No single set of variables that predicted jump height existed across all 3 jumping tasks. One foot jump height was predicted by peak knee power, peak hip extension moment, peak knee extension velocity, and the percentage of the trial when peak knee flexion velocity occurred (r = 0.58). Countermovement jump height was predicted by peak hip power, ankle range of motion, and knee range of motion (r = 0.65). Drop jump height was predicted by the peak vertical ground reaction force and the percentage of the trial when the peak hip velocity occurred (r = 0.37). A single set of variables was not identified that could predict jump performance across different types of jumping tasks; therefore, additional interventional investigations are needed to better understand how to alter and improve jump performance.
Gorb, Stanislav N
2004-07-01
In Auchenorrhyncha, jumping is achieved by metathoracic muscles which are inserted into the trochanter of the hind leg. The synchronisation of movements of the hind legs is a difficult problem, as the leg extension that produces the jump occurs in less than 1 ms. Even slight asynchrony could potentially result in failure of a jump. Both the synchronisation of the movements of a pair of jumping legs, and their stabilisation during a jump, seem to be important problems for small jumping insects. The present study was performed in order to clarify some questions of the functional morphology of the leafhopper jumping mechanism. It is based on skeleton-muscle reconstruction, high-speed video recordings, transmission (TEM) and scanning electron microscopic (SEM) investigations of the cuticle, together with 3D inverse-kinematic modelling of angles and working zones of hind leg joints of cicada Cercopis vulnerata (Cercopidae). The complete extension of the hind leg takes less than 1 ms, which suggests that the jump is powered not only by the muscle system, but also by an elastic spring. Histological staining and fluorescence microscopy showed resilin-bearing structures, responsible for elastic energy storage, in the pleural area of the metathorax. Synchronisation of hind leg movements may be aided by microtrichia fields that are located on the medial surface of each hind coxa. In Auchenorrhyncha, hind coxae are rounded in their anterior and lateral parts, whereas medial parts are planar, and contact each other over a rather large area. The inverse-kinematic model of propulsive leg movements was used to draw the surface outlined by the medial surface of the coxa, during the jump movement. This is a cone surface, faced with its bulged-in side, medially. Surfaces outlined by the movements of both right and left coxae overlap in their anterior and posterior positions. In both extreme positions, coxae are presumably connected to each other by coupled microtrichia fields. Thus
Extended source model for diffusive coupling.
González-Ochoa, Héctor O; Flores-Moreno, Roberto; Reyes, Luz M; Femat, Ricardo
2016-01-01
Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources.
Extended source model for diffusive coupling.
González-Ochoa, Héctor O; Flores-Moreno, Roberto; Reyes, Luz M; Femat, Ricardo
2016-01-01
Motivated by the prevailing approach to diffusion coupling phenomena which considers point-like diffusing sources, we derived an analogous expression for the concentration rate of change of diffusively coupled extended containers. The proposed equation, together with expressions based on solutions to the diffusion equation, is intended to be applied to the numerical solution of systems exclusively composed of ordinary differential equations, however is able to account for effects due the finite size of the coupled sources. PMID:26802012
Recommendation Based on Trust Diffusion Model
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. PMID:25009827
A Void Diffusion Model of Granular Flow
NASA Astrophysics Data System (ADS)
Rudra, Jayanta; Vieth, Paul
2009-03-01
In an earlier paper^1 we derived a nonlinear diffusion equation to describe the dynamics in granular flow based on a Diffusion Void Model (DVM). The equation was successfully used to describe the flow of a homogeneous granular material through the hole of a container under gravity. It also properly described similar flow in the presence of a flat horizontal barrier placed above the hole. Recently, however, we have found out that the above nonlinear equation does not lead to correct static equilibrium. For example, the stability of the free surface of a granular aggregate cannot be described by the equation. The equation also fails to describe, say, how an unstable vertical column of a granular material will change to a stable λ-shaped pile at the angle of repose. In this paper work we derive an equation using an appropriate current density of voids that can explain all the observed dynamical characteristics of a simple granular state. ^1Jayanta K. Rudra and D. C. Hong, Phys. Rev. E47, R1459(1993).
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.
Circumnutation modeled by reaction-diffusion equations
Lubkin, S.R.
1992-01-01
In studies of biological oscillators, plants are only rarely examined. The authors study a common sub-diurnal oscillation of plants, called circumnutation. Based on experimental evidence that the oscillations consist of a turgor wave traveling around a growing plant part, circumnutation is modeled by a nonlinear reaction-diffusion system with cylindrical geometry. Because of its simplicity, and because biological oscillations are so common, an oscillatory [lambda]-[omega] reaction-diffusion system is chosen for the model. The authors study behavior of traveling waves in [lambda]-[omega] systems. The authors show the existence of Hopf bifurcations and the stability of the limit cycles born at the Hopf bifurcation for some parameter values. Using a Lindstedt-type perturbation scheme, the authors construct periodic solutions of the [lambda]-[omega] system near a Hopf bifurcation and show that the periodic solutions superimposed on the original traveling wave have the effect of altering its overall frequency and amplitude. Circumnutating plants generally display a strong directional preference to their oscillations, which is species-dependent. Circumnutation is modeled by a [lambda]-[omega] system on an annulus of variable width, which does not possess reflection symmetry about any axis. The annulus represents a region of high potassium concentration in the cross-section of the stem. The asymmetry of the annulus represents the anatomical asymmetry of the plant. Traveling waves are constructed on this variable-width annulus by a perturbation scheme, and perturbing the width of the annulus alters the amplitude and frequency of traveling waves on the domain by a small (order [epsilon][sup 2]) amount. The speed, frequency, and stability are unaffected by the direction of travel of the wave on the annulus. This indicates that the [lambda]-[omega] system on a variable-width domain cannot account for directional preferences of traveling waves in biological systems.
Peckmezian, Tina; Taylor, Phillip W
2015-04-01
Electric shock is used widely as an aversive stimulus in conditioning experiments, yet little attention has been given to its physiological effects and their consequences for bioassays. In the present study, we provide a detailed characterization of how electric shock affects the mobility and behaviour of Servaea incana, a jumping spider. We begin with four mobility assays and then narrow our focus to a single effective assay with which we assess performance and behaviour. Based on our findings, we suggest a voltage range that may be employed as an aversive stimulus while minimizing decrements in physical performance and other aspects of behaviour. Additionally, we outline a novel method for constructing electric shock platforms that overcome some of the constraints of traditional methods while being highly effective and easily modifiable to suit the study animal and experimental context. Finally, as a demonstration of the viability of our aversive stimulus in a passive avoidance conditioning task, we successfully train spiders to associate a dark compartment with electric shock. Future research using electric shock as an aversive stimulus with terrestrial invertebrates such as spiders and insects may benefit from the flexible and reliable methods outlined in the present study. PMID:25637868
NASA Astrophysics Data System (ADS)
Wang, Shifang; Wu, Tao; Deng, Yongju; Zheng, Qiusha; Zheng, Qian
2016-08-01
Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging-diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging-diverging effect included is in good agreement with reported experimental data.
NASA Astrophysics Data System (ADS)
Wang, Shifang; Wu, Tao; Deng, Yongju; Zheng, Qiusha; Zheng, Qian
2016-08-01
Gas diffusion in dry porous media has been a hot topic in several areas of technology for many years. In this paper, a diffusivity model for gas diffusion in dry porous media is developed based on fractal theory and Fick’s law, which incorporates the effects of converging-diverging pores and tortuous characteristics of capillaries as well as Knudsen diffusion. The effective gas diffusivity model is expressed as a function of the fluctuation amplitude of the capillary cross-section size variations, the porosity, the pore area fractal dimension and the tortuosity fractal dimension. The results show that the relative diffusivity decreases with the increase of the fluctuation amplitude and increases with the increase of pore area fractal dimension. To verify the validity of the present model, the relative diffusivity from the proposed fractal model is compared with the existing experimental data as well as two available models of Bruggeman and Shou. Our proposed diffusivity model with pore converging-diverging effect included is in good agreement with reported experimental data.
Modeling of hydrogen-air diffusion flame
NASA Technical Reports Server (NTRS)
Isaac, K. M.
1988-01-01
Work performed during the first six months of the project duration for NASA Grant (NAG-1-861) is reported. An analytical and computational study of opposed jet diffusion flame for the purpose of understanding the effects of contaminants in the reactants and thermal diffusion of light species on extinction and reignition of diffusion flames is in progress. The methodologies attempted so far are described.
Modeling of hydrogen-air diffusion flame
NASA Technical Reports Server (NTRS)
Isaac, K. M.
1989-01-01
An analytical and computational study of opposed jet diffusion flame for the purpose of understanding the effects of contaminants in the reactants and thermal diffusion of light species on extinction and reignition of diffusion flames is in progress. The methodologies that have been attempted so far are described. Results using a simple, one-step reaction for the hydrogen-air counterflow diffusion flame are presented. These results show the correct trends in the profiles of chemical species and temperature. The extinction limit can be clearly seen in the plot of temperature vs. Damkohler number.
A diffusion model of a neuron and neural nets.
Dabrowski, L
1993-01-01
In the paper a diffusion model of a neuron is treated. A new, less restrictive than usually, condition of applicability of a diffusion model is presented. As a result the point-process-to-point-process model of a neuron is obtained, which produces an output signal of the same kind as the accepted input signals.
Some Problems in Using Diffusion Models for New Products
ERIC Educational Resources Information Center
Bernhardt, Irwin; Mackenzie, Kenneth D.
1972-01-01
Analyzes some of the problems involved in using diffusion models to formulate marketing strategies for introducing new products. Six models, which remove some of the theoretical and methodological restrictions inherent in current models of the adoption and diffusion process, are presented. (Author/JH)
Sedimentary radioactive tracers and diffusive models.
Carroll, J; Lerche, I
2010-08-01
This paper examines the underlying assumptions and consequences of applying a steady-state equation to sediment profiles of radioactive tracers in order to deconvolute sedimentation from bioturbation processes modelled as a diffusive type process. Several factors follow immediately from this investigation: (i) if the observed radioactive concentration increases with depth over any finite depth range then the proposed steady-state, constant flux equation is not applicable. Any increase in radioactive concentration with depth implies a negative mixing coefficient which is a physical impossibility; (ii) when the radioactive concentration systematically decreases with increasing sedimentary depth then solutions to the steady-state conservation equation exist only when either the constant solid state flux to the sediment surface is small enough so that a positive mixing coefficient results or when the mixing coefficient is small enough so that a positive flux results. If the radioactive concentration, porosity and/or density of the solid phase are such that the proposed equation is inappropriate (because no physically acceptable solution exists) then one must abandon the proposed steady-state equation. Further: if the flux of solid sediment to the sediment surface varies with time then, of course, a steady-state conservation equation is also inappropriate. Simple examples illustrate that the assumption of steady-state restricts the applicability of this modelling approach to a relatively small sub-set of expected situations in the real world.
Approximation of epidemic models by diffusion processes and their statistical inference.
Guy, Romain; Larédo, Catherine; Vergu, Elisabeta
2015-02-01
Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an
Models to assess perfume diffusion from skin.
Schwarzenbach, R; Bertschi, L
2001-04-01
Temperature, fragrance concentration on the skin and power of ventilation have been determined as crucial parameters in fragrance diffusion from skin. A tool has been developed to simulate perfume diffusion from skin over time, allowing headspace analysis and fragrance profile assessments in a highly reproducible way.
An Ion Diffusion Model in Semi-Permeable Clay Materials
Liu, Chongxuan
2007-08-01
Ion diffusion in semi-impermeable clay materials dynamically interacts with electrostatic fields (or diffuse double layers) associated with clay particles. Current theory of ion transport in porous media containing fixed charges on solid materials, however, cannot explicitly account for the dynamic interactions. Here we proposed a model by coupling electrodynamics and nonequilibrium thermodynamics to describe ion diffusion in the clay materials. The developed model was validated by comparing the calculated and measured apparent ion diffusion coefficients in clay materials as a function of ionic strength, which affects the overlap extent of the electrostatic double layers associated with adjacent clay particles. The model shows that ion diffusion in clay materials is a complex function of factors including surface charge density, tortuosity, porosity, chemico-osmotic coefficient, and ion self-diffusivity. At transitional states, ion diffusive fluxes are dynamically related to the electrostatic fields, which shrink or expand as ion diffusion. At steady states, the electrostatic fields are time-invariant and ion diffusive fluxes conform to flux and concentration gradient relationships; and apparent diffusivity can be expressed by the ion diffusivity in bulk electrolytes corrected by a tortuosity factor and concentration gradient variations at the interfaces between clay materials and bulk solutions.
Enhanced Jumping-Droplet Departure.
Kim, Moon-Kyung; Cha, Hyeongyun; Birbarah, Patrick; Chavan, Shreyas; Zhong, Chen; Xu, Yuehan; Miljkovic, Nenad
2015-12-15
Water vapor condensation on superhydrophobic surfaces has received much attention in recent years because of its ability to shed water droplets at length scales 3 decades smaller than the capillary length (∼1 mm) via coalescence-induced droplet jumping. Jumping-droplet condensation has been demonstrated to enhance heat transfer, anti-icing, and self-cleaning efficiency and is governed by the theoretical inertial-capillary scaled jumping speed (U). When two droplets coalesce, the experimentally measured jumping speed (Uexp) is fundamentally limited by the internal fluid dynamics during the coalescence process (Uexp < 0.23U). Here, we theoretically and experimentally demonstrate multidroplet (>2) coalescence as an avenue to break the two-droplet speed limit. Using side-view and top-view high-speed imaging to study more than 1000 jumping events on a copper oxide nanostructured superhydrophobic surface, we verify that droplet jumping occurs as a result of three fundamentally different mechanisms: (1) coalescence between two droplets, (2) coalescence among more than two droplets (multidroplet), and (3) coalescence between one or more droplets on the surface and a returning droplet that has already departed (multihop). We measured droplet-jumping speeds for a wide range of droplet radii (5-50 μm) and demonstrated that while the two-droplet capillary-to-inertial energy conversion mechanism is not identical to that of multidroplet jumping, speeds above the theoretical two-droplet limit (>0.23U) can be achieved. However, we discovered that multihop coalescence resulted in drastically reduced jumping speeds (≪0.23U) due to adverse momentum contributions from returning droplets. To quantify the impact of enhanced jumping speed on heat-transfer performance, we developed a condensation critical heat flux model to show that modest jumping speed enhancements of 50% using multidroplet jumping can enhance performance by up to 40%. Our results provide a starting point for the
Diffusion model of the non-stoichiometric uranium dioxide
Moore, Emily; Guéneau, Christine; Crocombette, Jean-Paul
2013-07-15
Uranium dioxide (UO{sub 2}), which is used in light water reactors, exhibits a large range of non-stoichiometry over a wide temperature scale up to 2000 K. Understanding diffusion behavior of uranium oxides under such conditions is essential to ensure safe reactor operation. The current understanding of diffusion properties is largely limited by the stoichiometric deviations inherent to the fuel. The present DICTRA-based model considers diffusion across non-stoichiometric ranges described by experimentally available data. A vacancy and interstitial model of diffusion is applied to the U–O system as a function of its defect structure derived from CALPHAD-type thermodynamic descriptions. Oxygen and uranium self and tracer diffusion coefficients are assessed for the construction of a mobility database. Chemical diffusion coefficients of oxygen are derived with respect to the Darken relation and migration energies of defects are evaluated as a function of stoichiometric deviation. - Graphical abstract: Complete description of Oxygen–Uranium diffusion as a function of composition at various temperatures according to the developed Dictra model. - Highlights: • Assessment of a uranium–oxygen diffusion model with Dictra. • Complete description of U–O diffusion over wide temperature and composition range. • Oxygen model includes terms for interstitial and vacancy migration. • Interaction terms between defects help describe non-stoichiometric domain of UO{sub 2±x}. • Uranium model is separated into mobility terms for the cationic species.
Modeling diffusion in miscible polymer blend films.
Indrakanti, Ananth; Ramesh, Narayan; Duda, J Larry; Kumar, Sanat K
2004-07-01
Recent experiments designed to probe polymer transport in the bulk and in the vicinity of surfaces have examined the interdiffusion of multilayer sandwiches of isotopically labeled polymers. The measured time dependent concentration profiles normal to the surface are typically fit to Fick's law, with a single fitting parameter, the mutual binary diffusion coefficient (MBDC). The resulting MBDCs are found to vary over a broad range of film thicknesses and time, with the time dependence being viewed as a unique signature of the reptation mechanism of long chain motion, and the thickness dependence being attributed to the slowing down of chain dynamics near surfaces. Since the experiments are conducted at finite concentration, the MBDC, which is a product of the bare mobility and the concentration derivative of the chemical potential, could be dominated by the time and thickness dependence of this second term (which is ignored in Fick's law). To quantify this conjecture we consider the more rigorous Cahn formulation of the diffusion problem in terms of chemical potential gradients. We use square gradient theory to evaluate chemical potentials, and fit the resulting time dependent concentration profiles to the analytical solution of Fick's law. By thus mimicking the experimental analysis we find that the apparent MBDCs vary with time as t(-1/2) at short times, in good agreement with existing experiments. We show that this time dependence reflects the system's desire to minimize concentration gradients, a fact ignored in Fick's law. Since these arguments make no reference to the mechanism of chain motion, we argue that the time dependence of MBDC derived from interdiffusion experiments does not provide unequivocal support for the reptation mechanism of long chain transport. The MBDC values, which also vary with the degree of confinement, are predicted to increase with decreasing thickness for model parameters corresponding to experimental systems. In contrast, since the
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.
NASA Astrophysics Data System (ADS)
Yang, Eunjin; Kim, Ho-Young
2015-11-01
Small aquatic arthropods, such as water striders and fishing spiders, are able to jump off water to a height several times their body length. Inspired by the unique biological motility on water, we study a simple model using a flexible hoop to provide fundamental understanding and a mimicking principle of small jumpers on water. Behavior of a hoop on water, which is coated with superhydrophobic particles and initially bent into an ellipse from an equilibrium circular shape, is visualized with a high speed camera upon launching it into air by releasing its initial elastic strain energy. We observe that jumping of our hoops is dominated by the dynamic pressure of water rather than surface tension, and thus it corresponds to the dynamic condition experienced by fishing spiders. We calculate the reaction forces provided by water adopting the unsteady Bernoulli equation as well as the momentum loss into liquid inertia and viscous friction. Our analysis allows us to predict the jumping efficiency of the hoop on water in comparison to that on ground, and to discuss the evolutionary pressure rendering fishing spiders select such dynamic behavior.
A social diffusion model with an application on election simulation.
Lou, Jing-Kai; Wang, Fu-Min; Tsai, Chin-Hua; Hung, San-Chuan; Kung, Perng-Hwa; Lin, Shou-De; Chen, Kuan-Ta; Lei, Chin-Laung
2014-01-01
Issues about opinion diffusion have been studied for decades. It has so far no empirical approach to model the interflow and formation of crowd's opinion in elections due to two reasons. First, unlike the spread of information or flu, individuals have their intrinsic attitudes to election candidates in advance. Second, opinions are generally simply assumed as single values in most diffusion models. However, in this case, an opinion should represent preference toward multiple candidates. Previously done models thus may not intuitively interpret such scenario. This work is to design a diffusion model which is capable of managing the aforementioned scenario. To demonstrate the usefulness of our model, we simulate the diffusion on the network built based on a publicly available bibliography dataset. We compare the proposed model with other well-known models such as independent cascade. It turns out that our model consistently outperforms other models. We additionally investigate electoral issues with our model simulator.
A Social Diffusion Model with an Application on Election Simulation
Wang, Fu-Min; Hung, San-Chuan; Kung, Perng-Hwa; Lin, Shou-De
2014-01-01
Issues about opinion diffusion have been studied for decades. It has so far no empirical approach to model the interflow and formation of crowd's opinion in elections due to two reasons. First, unlike the spread of information or flu, individuals have their intrinsic attitudes to election candidates in advance. Second, opinions are generally simply assumed as single values in most diffusion models. However, in this case, an opinion should represent preference toward multiple candidates. Previously done models thus may not intuitively interpret such scenario. This work is to design a diffusion model which is capable of managing the aforementioned scenario. To demonstrate the usefulness of our model, we simulate the diffusion on the network built based on a publicly available bibliography dataset. We compare the proposed model with other well-known models such as independent cascade. It turns out that our model consistently outperforms other models. We additionally investigate electoral issues with our model simulator. PMID:24995351
Some Problems in Using Diffusion Models for New Products.
ERIC Educational Resources Information Center
Bernhardt, Irwin; Mackenzie, Kenneth D.
This paper analyzes some of the problems of using diffusion models to formulate marketing strategies for new products. Though future work in this area appears justified, many unresolved problems limit its application. There is no theory for adoption and diffusion processes; such a theory is outlined in this paper. The present models are too…
Parameter Variability and Distributional Assumptions in the Diffusion Model
ERIC Educational Resources Information Center
Ratcliff, Roger
2013-01-01
If the diffusion model (Ratcliff & McKoon, 2008) is to account for the relative speeds of correct responses and errors, it is necessary that the components of processing identified by the model vary across the trials of a task. In standard applications, the rate at which information is accumulated by the diffusion process is assumed to be normally…
A Comparison of Competing Models of the News Diffusion Process.
ERIC Educational Resources Information Center
Mayer, Michael E.; And Others
1990-01-01
Investigates the diffusion of information about the space shuttle Challenger explosion by comparing loglinear models of the diffusion process. Finds that the most parsimonious model with adequate goodness of fit was a linear one in which a person's location affected how the information was heard, which in turn affected when the information was…
Ab initio modeling of quasielastic neutron scattering of hydrogen pipe diffusion in palladium
NASA Astrophysics Data System (ADS)
Schiavone, Emily J.; Trinkle, Dallas R.
2016-08-01
A recent quasielastic neutron scattering (QENS) study of hydrogen in heavily deformed fcc palladium provided the first direct measurement of hydrogen pipe diffusion, which has a significantly higher diffusivity and lower activation barrier than in bulk. While ab initio estimates of hydrogen diffusion near a dislocation corroborated the experimental values, open questions remain from the Chudley-Elliott analysis of the QENS spectra, including significant nonmonotonic changes in jump distance with temperature. We calculate the spherically averaged incoherent scattering function at different temperatures using our ab initio data for the network of site energies, jump rates, and jump vectors to directly compare to experiment. Diffusivities and jump distances are sensitive to how a single Lorentzian is fit to the scattering function. Using a logarithmic least squares fit over the range of experimentally measured energies, our diffusivities and jump distances agree well with those measured by experiment. However, these calculated quantities do not reflect barriers or distances in our dislocation geometry. This computational approach allows for validation against experiment, along with a more detailed understanding of the QENS results.
Genomics Analogy Model for Educators (GAME): From Jumping Genes to Alternative Splicing
ERIC Educational Resources Information Center
Corn, Joanie; Pittendrigh, Barry R.; Orvis, Kathryn S.
2004-01-01
Studies have shown that there is usually a lack of understanding concerning the fields of genetics and genomics among high school students (Lewis and Wood-Robinson, 2000). A recent article (Kirkpatrick et al, 2002) introduced the GAME (Genomics Analogy Model for Educators) model and two of its components: (1) explaining sequencing technology with…
Dynamic hysteresis modeling including skin effect using diffusion equation model
NASA Astrophysics Data System (ADS)
Hamada, Souad; Louai, Fatima Zohra; Nait-Said, Nasreddine; Benabou, Abdelkader
2016-07-01
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Analysis of stochastic two-prey one-predator model with Lévy jumps
NASA Astrophysics Data System (ADS)
Liu, Meng; Bai, Chuanzhi; Deng, Meiling; Du, Bo
2016-03-01
Taking white noises and Lévy noises into account, a two-prey one-predator model in random environments is proposed and investigated. Under some simple assumptions, the critical value between persistence in the mean and extinction for each population is obtained. Then sufficient conditions for stability in distribution of the model are established. Finally, some numerical examples are introduced to validate the analytical findings.
Simulation of stochastic diffusion via first exit times
NASA Astrophysics Data System (ADS)
Lötstedt, Per; Meinecke, Lina
2015-11-01
In molecular biology it is of interest to simulate diffusion stochastically. In the mesoscopic model we partition a biological cell into unstructured subvolumes. In each subvolume the number of molecules is recorded at each time step and molecules can jump between neighboring subvolumes to model diffusion. The jump rates can be computed by discretizing the diffusion equation on that unstructured mesh. If the mesh is of poor quality, due to a complicated cell geometry, standard discretization methods can generate negative jump coefficients, which no longer allows the interpretation as the probability to jump between the subvolumes. We propose a method based on the mean first exit time of a molecule from a subvolume, which guarantees positive jump coefficients. Two approaches to exit times, a global and a local one, are presented and tested in simulations on meshes of different quality in two and three dimensions.
NASA Astrophysics Data System (ADS)
Liu, Qun
2015-09-01
In this paper, a stochastic n-species Gilpin-Ayala competitive model with Lévy jumps and Markovian switching is proposed and studied. Some asymptotic properties are investigated and sufficient conditions for extinction, non-persistence in the mean and weak persistence are established. The threshold between extinction and weak persistence is obtained. The results illustrate that the asymptotic properties of the considered system have close relationships with Lévy jumps and the stationary distribution of the Markovian chain. Moreover, some simulation figures are presented to confirm our main results.
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. PMID:26291782
A computational kinetic model of diffusion for molecular systems.
Teo, Ivan; Schulten, Klaus
2013-09-28
Regulation of biomolecular transport in cells involves intra-protein steps like gating and passage through channels, but these steps are preceded by extra-protein steps, namely, diffusive approach and admittance of solutes. The extra-protein steps develop over a 10-100 nm length scale typically in a highly particular environment, characterized through the protein's geometry, surrounding electrostatic field, and location. In order to account for solute energetics and mobility of solutes in this environment at a relevant resolution, we propose a particle-based kinetic model of diffusion based on a Markov State Model framework. Prerequisite input data consist of diffusion coefficient and potential of mean force maps generated from extensive molecular dynamics simulations of proteins and their environment that sample multi-nanosecond durations. The suggested diffusion model can describe transport processes beyond microsecond duration, relevant for biological function and beyond the realm of molecular dynamics simulation. For this purpose the systems are represented by a discrete set of states specified by the positions, volumes, and surface elements of Voronoi grid cells distributed according to a density function resolving the often intricate relevant diffusion space. Validation tests carried out for generic diffusion spaces show that the model and the associated Brownian motion algorithm are viable over a large range of parameter values such as time step, diffusion coefficient, and grid density. A concrete application of the method is demonstrated for ion diffusion around and through the Eschericia coli mechanosensitive channel of small conductance ecMscS.
Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models
NASA Technical Reports Server (NTRS)
Yoder, Dennis A.
2016-01-01
This paper will include a detailed comparison of heat transfer models that rely upon the thermal diffusivity. The goals are to inform users of the development history of the various models and the resulting differences in model formulations, as well as to evaluate the models on a variety of validation cases so that users might better understand which models are more broadly applicable.
Model calculations for diffuse molecular clouds. [interstellar hydrogen cloud model
NASA Technical Reports Server (NTRS)
Glassgold, A. E.; Langer, W. D.
1974-01-01
A steady state isobaric cloud model is developed. The pressure, thermal, electrical, and chemical balance equations are solved simultaneously with a simple one dimensional approximation to the equation of radiative transfer appropriate to diffuse clouds. Cooling is mainly by CII fine structure transitions, and a variety of heating mechanisms are considered. Particular attention is given to the abundance variation of H2. Inhomogeneous density distributions are obtained because of the attenuation of the interstellar UV field and the conversion from atomic to molecular hyrodgen. The effects of changing the model parameters are described and the applicability of the model to OAO-3 observations is discussed. Good qualitative agreement with the fractional H2 abundance determinations has been obtained. The observed kinetic temperatures near 80 K can also be achieved by grain photoelectron heating. The problem of the electron density is solved taking special account of the various hydrogen ions as well as heavier ones.
Nonequilibrium drift-diffusion model for organic semiconductor devices
NASA Astrophysics Data System (ADS)
Felekidis, Nikolaos; Melianas, Armantas; Kemerink, Martijn
2016-07-01
Two prevailing formalisms are currently used to model charge transport in organic semiconductor devices. Drift-diffusion calculations, on the one hand, are time effective but assume local thermodynamic equilibrium, which is not always realistic. Kinetic Monte Carlo models, on the other hand, do not require this assumption but are computationally expensive. Here, we present a nonequilibrium drift-diffusion model that bridges this gap by fusing the established multiple trap and release formalism with the drift-diffusion transport equation. For a prototypical photovoltaic system the model is shown to quantitatively describe, with a single set of parameters, experiments probing (1) temperature-dependent steady-state charge transport—space-charge limited currents, and (2) time-resolved charge transport and relaxation of nonequilibrated photocreated charges. Moreover, the outputs of the developed kinetic drift-diffusion model are an order of magnitude, or more, faster to compute and in good agreement with kinetic Monte Carlo calculations.
What can the diffusion model tell us about prospective memory?
Horn, Sebastian S; Bayen, Ute J; Smith, Rebekah E
2011-03-01
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 analyse 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 trade-offs. 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 was analysed 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 reaction time. PMID:21443332
Modeling Intragranular Diffusion in Low-Connectivity Granular Media
Ewing, Robert G.; Liu, Chongxuan; Hu, Qinhong
2012-03-20
Diffusive exchange of solutes between bulk water in an aquifer and water in the intragranular pores of the solid phase remains confusing after decades of study. In a previous paper, we reviewed some of the explanations, and suggested that the disparities between observation and theory were largely due to low connectivity of the intragranular pores. Low connectivity indicates that a useful conceptual framework is percolation theory, which guided our analysis. The present study was initiated to improve the finite difference (FD) model presented in the previous paper, and to test that new model rigorously against new random walk (RW) simulations of diffusion in low-connectivity porous spheres starting from non-equilibrium. The new FD model calculates diffusion separately in the infinite cluster and the finite clusters, and closely matches the new, more complex RW results. The percolation-theory based description of the new model is fairly simple, and can readily be incorporated into existing FD models. The simulations showed that the combination of low intragranular pore connectivity, and out-diffusion initiated at diffusive non-equilibrium, can produce diffusive behavior that appears as if the solute had undergone slow sorption, even in the absence of any sorption process. This mechanism may help explain some hitherto confusing aspects of intragranular diffusion.
Diffusion models for Jupiter's radiation belt
NASA Technical Reports Server (NTRS)
Jacques, S. A.; Davis, L., Jr.
1972-01-01
Solutions are given for the diffusion of trapped particles in a planetary magnetic field in which the first and second adiabatic invariants are preserved but the third is not, using as boundary conditions a fixed density at the outer boundary (the magnetopause) and a zero density at an inner boundary (the planetary surface). Losses to an orbiting natural satellite are included and an approximate evaluation is made of the effects of the synchrotron radiation on the energy of relativistic electrons. Choosing parameters appropriate to Jupiter, the electrons required to produce the observed synchrotron radiation are explained. If a speculative mechanism in which the diffusion is driven by ionospheric wind is the true explanation of the electrons producing the synchrotron emission it can be concluded that Jupiter's inner magnetosphere is occupied by an energetic proton flux that would be a serious hazard to spacecraft.
Pulmonary hemorrhage resulting from bungee jumping.
Manos, Daria; Hamer, Okka; Müller, Nestor L
2007-11-01
Pulmonary hemorrhage is a relatively common complication of blunt chest trauma. Occasionally, it may result from pulmonary barotrauma after scuba diving or from sports activities not associated with barotrauma such as long breath-hold diving. We report a case of symmetric diffuse upper lobe hemorrhage resulting from a bungee jump in a previously healthy man. Bungee jumping is an increasingly popular sport with relatively few reported injuries. To our knowledge pulmonary hemorrhage in this setting has not yet been described.
Addition of Diffusion Model to MELCOR and Comparison with Data
Brad Merrill; Richard Moore; Chang Oh
2004-06-01
A chemical diffusion model was incorporated into the thermal-hydraulics package of the MELCOR Severe Accident code (Reference 1) for analyzing air ingress events for a very high temperature gas-cooled reactor.
Modelling oxygen self-diffusion in UO2 under pressure
Cooper, Michael William D.; Grimes, R. W.; Fitzpatrick, M. E.; Chroneos, A.
2015-10-22
Access to values for oxygen self-diffusion over a range of temperatures and pressures in UO2 is important to nuclear fuel applications. Here, elastic and expansivity data are used in the framework of a thermodynamic model, the cBΩ model, to derive the oxygen self-diffusion coefficient in UO2 over a range of pressures (0–10 GPa) and temperatures (300–1900 K). Furthermore, the significant reduction in oxygen self-diffusion as a function of increasing hydrostatic pressure, and the associated increase in activation energy, is identified.
A model for diffusive systems: Beyond the Arrhenius mechanism
NASA Astrophysics Data System (ADS)
Rosa, A. C. P.; Vaveliuk, Pablo; Mundim, Kleber C.; Moret, M. A.
2016-05-01
Diffusivity in supercooled liquids was observed to exhibit a non-Arrhenius behavior near the glass-transition temperature. This process, which occurs where the activation energy depends on the temperature, suggests the possibility of a metastable equilibrium. This peculiar phenomenon cannot be explained using the usual Markovian stochastic models. Based on a non-linear Fokker-Planck equation, we propose a diffusion coefficient that is proportional to the supercooled-liquid concentration. The proposed model allows us to explain the anomalous behavior of the diffusivity robustly. We demonstrate that this new approach is consistent with experimental patterns. Besides, it could be applied to non-Arrhenius chemical kinetics.
Performance analysis of jump-gliding locomotion for miniature robotics.
Vidyasagar, A; Zufferey, Jean-Christohphe; Floreano, Dario; Kovač, M
2015-04-01
Recent work suggests that jumping locomotion in combination with a gliding phase can be used as an effective mobility principle in robotics. Compared to pure jumping without a gliding phase, the potential benefits of hybrid jump-gliding locomotion includes the ability to extend the distance travelled and reduce the potentially damaging impact forces upon landing. This publication evaluates the performance of jump-gliding locomotion and provides models for the analysis of the relevant dynamics of flight. It also defines a jump-gliding envelope that encompasses the range that can be achieved with jump-gliding robots and that can be used to evaluate the performance and improvement potential of jump-gliding robots. We present first a planar dynamic model and then a simplified closed form model, which allow for quantification of the distance travelled and the impact energy on landing. In order to validate the prediction of these models, we validate the model with experiments using a novel jump-gliding robot, named the 'EPFL jump-glider'. It has a mass of 16.5 g and is able to perform jumps from elevated positions, perform steered gliding flight, land safely and traverse on the ground by repetitive jumping. The experiments indicate that the developed jump-gliding model fits very well with the measured flight data using the EPFL jump-glider, confirming the benefits of jump-gliding locomotion to mobile robotics. The jump-glide envelope considerations indicate that the EPFL jump-glider, when traversing from a 2 m height, reaches 74.3% of optimal jump-gliding distance compared to pure jumping without a gliding phase which only reaches 33.4% of the optimal jump-gliding distance. Methods of further improving flight performance based on the models and inspiration from biological systems are presented providing mechanical design pathways to future jump-gliding robot designs. PMID:25811417
Performance analysis of jump-gliding locomotion for miniature robotics.
Vidyasagar, A; Zufferey, Jean-Christohphe; Floreano, Dario; Kovač, M
2015-03-26
Recent work suggests that jumping locomotion in combination with a gliding phase can be used as an effective mobility principle in robotics. Compared to pure jumping without a gliding phase, the potential benefits of hybrid jump-gliding locomotion includes the ability to extend the distance travelled and reduce the potentially damaging impact forces upon landing. This publication evaluates the performance of jump-gliding locomotion and provides models for the analysis of the relevant dynamics of flight. It also defines a jump-gliding envelope that encompasses the range that can be achieved with jump-gliding robots and that can be used to evaluate the performance and improvement potential of jump-gliding robots. We present first a planar dynamic model and then a simplified closed form model, which allow for quantification of the distance travelled and the impact energy on landing. In order to validate the prediction of these models, we validate the model with experiments using a novel jump-gliding robot, named the 'EPFL jump-glider'. It has a mass of 16.5 g and is able to perform jumps from elevated positions, perform steered gliding flight, land safely and traverse on the ground by repetitive jumping. The experiments indicate that the developed jump-gliding model fits very well with the measured flight data using the EPFL jump-glider, confirming the benefits of jump-gliding locomotion to mobile robotics. The jump-glide envelope considerations indicate that the EPFL jump-glider, when traversing from a 2 m height, reaches 74.3% of optimal jump-gliding distance compared to pure jumping without a gliding phase which only reaches 33.4% of the optimal jump-gliding distance. Methods of further improving flight performance based on the models and inspiration from biological systems are presented providing mechanical design pathways to future jump-gliding robot designs.
The diffusion and telegraph equations in diagenetic modeling
Boudreau, B.P. )
1989-08-01
This paper considers the practical aspects of differentiating between the solutions of the Diffusion and Telegraph Equations when they are used to model molecular diffusion in sediment pore waters and the diffusive bioturbation of solids. If molecular diffusion is the only transport mechanism in pore water, then the results from a simple random-walk model coupled to the hydrodynamic or kinetic theories of diffusion indicate that the solute profiles predicted by these two equations differ measurably only for periods up to 10{sup {minus}10} s after the introduction of a transient and for spatial scales less than 10{sup {minus}6} cm. In addition, the distinct propagating front predicted by the Telegraph Equation moves so fast and is so attenuated as to be unmeasurable. In this situation, the Telegraph Equation offers no practical advantage over the Diffusion Equation for the description of diagenetic pore water profiles. These findings also hold when advection due to burial and chemical reaction are included in the model. The time scales associated with bioturbation of solids are sufficiently long compared to normal sampling times that the profiles of some transients, both in deep-sea and near-shore sediments, should exhibit behavior characteristic of the Telegraph Equation if mixing is diffusive (local).
Scaling in the Diffusion Limited Aggregation Model
NASA Astrophysics Data System (ADS)
Menshutin, Anton
2012-01-01
We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/Rdep(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/Rdep) function on an ensemble with 1000 clusters of 5×107 particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.
Diffusive feed of reactants and Hopf bifurcations in an oscillatory reaction-diffusion model
NASA Astrophysics Data System (ADS)
von Haeften, B.; Izús, G. G.
1999-01-01
We study an oscillatory chemical model (the "Brusselator") with the aim of analyzing the effect of a controlled diffusive feed of reactants in the appearance of chemical oscillations. The reflectivities of the boundary, which adjust the external fluxes, act as control parameters capable to alter the attractive basin of the thermodynamic branch, leading to oscillatory behavior.
Innovation Diffusion Model in Higher Education: Case Study of E-Learning Diffusion
ERIC Educational Resources Information Center
Buc, Sanjana; Divjak, Blaženka
2015-01-01
The diffusion of innovation (DOI) is critical for any organization and especially nowadays for higher education institutions (HEIs) in the light of vast pressure of emerging educational technologies as well as of the demand of economy and society. DOI takes into account the initial and the implementation phase. The conceptual model of DOI in…
SOLVING THE TWO-DIMENSIONAL DIFFUSION FLOW MODEL.
Hromadka, T.V.; Lai, Chintu
1985-01-01
A simplification of the two-dimensional (2-D) continuity and momentum equations is the diffusion equation. To investigate its capability, the numerical model using the diffusion approach is applied to a hypothetical failure problem of a regional water reservoir. The model is based on an explicit, integrated finite-difference scheme, and the floodplain is simulated by a popular home computer which supports 64K FORTRAN. Though simple, the 2-D model can simulate some interesting flooding effects that a 1-D full dynamic model cannot.
Update on Advection-Diffusion Purge Flow Model
NASA Technical Reports Server (NTRS)
Brieda, Lubos
2015-01-01
Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.
James Biggs; Mary Mullen; Kathryn Bennett
1999-11-01
The New Mexico meadow jumping mouse (Zapus hudsonius luteus) is currently listed as a state threatened species in New Mexico and has been identified as potentially occurring within the Los Alamos National Laboratory (LANL) boundary. We describe the development of a model to identify and rank habitat at LANL that may be suitable for occupation by this species. The model calculates a habitat suitability ranking (HSR) based on total plant cover, plant species composition, total number of plant species, and plant height. Input data for the model is based on the measurement of these variables at known locations where this species has been found within the Jemez Mountains. Model development included the selection of habitat variables, developing a probability distribution for each variable, and applying weights to each variable based on their overall importance in defining the suitability of the habitat. The habitat variables (HV) include plant cover (HV1), grass/forb cover (HV2), plant height (HV3), number of forbs (HV4), number of grasses (HV5), and sedge/rush cover (HV6). Once the HVs were selected, probability values were calculated for each. Each variable was then assigned a ''weighting factor'' to reflect the variables' importance relative to one another with respect to contribution to quality of habitat. The least important variable, sedge/rush cover, was assigned a weight factor of ''1'' with increasing values assigned to each remaining variable as follows: number of forbs = 3, number of grasses = 3, plant height = 5, grass/forb cover = 6, and total plant cover = 7. Based on the probability values and weighting factors, a HSR is calculated as follows: HSR = (P{sub HV1}(7) + P{sub HV2}(6) + P{sub HV3}(5) + P{sub HV4}(3) + P{sub HV5}(3) + P{sub HV6}(1)). Once calculated, the HSR values are placed into one of four habitat categorical groupings by which management strategies are applied.
NASA Astrophysics Data System (ADS)
Cook, Richard J.
1988-01-01
This paper answers the title question by giving an operational definition of quantum jumps based on measurement theory. This definition forms the basis of a theory of quantum jumps which leads to a number of testable predictions. Experiments are proposed to test the theory. The suggested experiments also test the quantum Zeno paradox, i.e., they test the proposition that frequent observation of a quantum system inhibits quantum jumps in that system.
Picker, Mike; Colville, Jonathan F; Burrows, Malcolm
2012-06-23
We report on a newly discovered cockroach (Saltoblattella montistabularis) from South Africa, which jumps and therefore differs from all other extant cockroaches that have a scuttling locomotion. In its natural shrubland habitat, jumping and hopping accounted for 71 per cent of locomotory activity. Jumps are powered by rapid and synchronous extension of the hind legs that are twice the length of the other legs and make up 10 per cent of the body weight. In high-speed images of the best jumps the body was accelerated in 10 ms to a take-off velocity of 2.1 m s(-1) so that the cockroach experienced the equivalent of 23 times gravity while leaping a forward distance of 48 times its body length. Such jumps required 38 µJ of energy, a power output of 3.4 mW and exerted a ground reaction force through both hind legs of 4 mN. The large hind legs have grooved femora into which the tibiae engage fully in advance of a jump, and have resilin, an elastic protein, at the femoro-tibial joint. The extensor tibiae muscles contracted for 224 ms before the hind legs moved, indicating that energy must be stored and then released suddenly in a catapult action to propel a jump. Overall, the jumping mechanisms and anatomical features show remarkable convergence with those of grasshoppers with whom they share their habitat and which they rival in jumping performance.
NASA Astrophysics Data System (ADS)
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Diffusion tensor imaging of diffuse axonal injury in a rat brain trauma model.
van de Looij, Yohan; Mauconduit, Franck; Beaumont, Marine; Valable, Samuel; Farion, Régine; Francony, Gilles; Payen, Jean-François; Lahrech, Hana
2012-01-01
Diffusion tensor imaging (DTI) was used to study traumatic brain injury. The impact-acceleration trauma model was used in rats. Here, in addition to diffusivities (mean, axial and radial), fractional anisotropy (FA) was used, in particular, as a parameter to characterize the cerebral tissue early after trauma. DTI was implemented at 7 T using fast spiral k-space sampling and the twice-refocused spin echo radiofrequency sequence for eddy current minimization. The method was carefully validated on different phantom measurements. DTI of a trauma group (n = 5), as well as a sham group (n = 5), was performed at different time points during 6 h following traumatic brain injury. Two cerebral regions, the cortex and corpus callosum, were analyzed carefully. A significant decrease in diffusivity in the trauma group versus the sham group was observed, suggesting the predominance of cellular edema in both cerebral regions. No significant FA change was detected in the cortex. In the corpus callosum of the trauma group, the FA indices were significantly lower. A net discontinuity in fiber reconstructions in the corpus callosum was observed by fiber tracking using DTI. Histological analysis using Hoechst, myelin basic protein and Bielschowsky staining showed fiber disorganization in the corpus callosum in the brains of the trauma group. On the basis of our histology results and the characteristics of the impact-acceleration model responsible for the presence of diffuse axonal injury, the detection of low FA caused by a drastic reduction in axial diffusivity and the presence of fiber disconnections of the DTI track in the corpus callosum were considered to be related to the presence of diffuse axonal injury. PMID:21618304
Scaling in the diffusion limited aggregation model.
Menshutin, Anton
2012-01-01
We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/R{dep}(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/R{dep}) function on an ensemble with 1000 clusters of 5×10{7} particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10 000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA. PMID:22304265
A model for restricted diffusion in complex fluids
NASA Astrophysics Data System (ADS)
de Bruyn, John; Wylie, Jonathan
2014-03-01
We use a model originally due to Tanner to study the diffusion of tracer particles in complex fluids both analytically and through Monte-Carlo simulations. The model consists of regions through which the particles diffuse freely, separated by membranes with a specified low permeability. The mean squared displacement of the particles calculated from the model agrees well with experimental data on the diffusion of particles in a concentrated colloidal suspension when the membrane permeability is used as an adjustable parameter. Data on a micro-phase-separated polymer system can be well modeled by considering two populations of particles constrained by membranes with different permeabilites. Supported by the Hong Kong Research Grants Council and the Natural Sciences and Engineering Research Council of Canada.
A Novel Restricted Diffusion Model of Evoked Dopamine
2015-01-01
In vivo fast-scan cyclic voltammetry provides high-fidelity recordings of electrically evoked dopamine release in the rat striatum. The evoked responses are suitable targets for numerical modeling because the frequency and duration of the stimulus are exactly known. Responses recorded in the dorsal and ventral striatum of the rat do not bear out the predictions of a numerical model that assumes the presence of a diffusion gap interposed between the recording electrode and nearby dopamine terminals. Recent findings, however, suggest that dopamine may be subject to restricted diffusion processes in brain extracellular space. A numerical model cast to account for restricted diffusion produces excellent agreement between simulated and observed responses recorded under a broad range of anatomical, stimulus, and pharmacological conditions. The numerical model requires four, and in some cases only three, adjustable parameters and produces meaningful kinetic parameter values. PMID:24983330
Cohabitation reaction-diffusion model for virus focal infections
NASA Astrophysics Data System (ADS)
Amor, Daniel R.; Fort, Joaquim
2014-12-01
The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction-diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction-diffusion equations may lead to unrealistic descriptions. We argue that previous virus infection models also have this limitation, because they assume that a virion can simultaneously reproduce inside a cell and diffuse away from it. For this reason, we build a several-species cohabitation model that does not have this limitation. Furthermore, we perform a sensitivity analysis for the most relevant parameters of the model, and we compare the predicted infection speed with observed data for two different strains of the T7 virus.
NASA Astrophysics Data System (ADS)
Matte, D.; Laprise, R.; Theriault, J. M.; Lucas-Picher, P.
2015-12-01
Many studies have shown the importance of choosing the domain size adequately for dynamical downscaling with nested regional climate models. It is well known that domain should not be too large to avoid large departure from the driving data, and not be too small to provide sufficient distance from the lateral inflow to allow a full development of the small-scale features resolved by the increase resolution. Although practitioners of dynamical downscaling are well aware that the jump of resolution between the driving data and the nested regional climate model impacts the simulated climate, the issue has never been properly study. Larger is the jump of resolution, larger is the distance from the lateral inflow to fully develop the small-scale features permitted by the increase resolution. Our investigation compares direct nesting to achieve a grid mesh of 0.15o from driving data at 3.6°, 1.8o, 0.45° and 0.15° using the perfect-prognostic approach of the Big-Brother protocol. The results show that the small-scale transient-eddy component struggles to be fully developed with reduced resolution of the driving data. Overall, this study suggests that domain location (i.e. domain of interest or subsequent nested domains) must be chosen carefully according to the jump of resolution to allow the optimal development of small-scale features allowed by the increase resolution of the nested model.
Langevin equation with fluctuating diffusivity: A two-state model.
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool. PMID:27575079
Langevin equation with fluctuating diffusivity: A two-state model
NASA Astrophysics Data System (ADS)
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
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. PMID:23555677
An Urban Diffusion Simulation Model for Carbon Monoxide
ERIC Educational Resources Information Center
Johnson, W. B.; And Others
1973-01-01
A relatively simple Gaussian-type diffusion simulation model for calculating urban carbon (CO) concentrations as a function of local meteorology and the distribution of traffic is described. The model can be used in two ways: in the synoptic mode and in the climatological mode. (Author/BL)
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 Diffusion Model Account of the Lexical Decision Task
ERIC Educational Resources Information Center
Ratcliff, Roger; Gomez, Pablo; McKoon, Gail
2004-01-01
The diffusion model for 2-choice decisions (R. Ratcliff, 1978) was applied to data from lexical decision experiments in which word frequency, proportion of high- versus low-frequency words, and type of nonword were manipulated. The model gave a good account of all of the dependent variables--accuracy, correct and error response times, and their…
Modeling Copper Diffusion in Polycrystalline CdTe Solar Cells
Akis, Richard; Brinkman, Daniel; Sankin, Igor; Fang, Tian; Guo, Da; Vasileska, Dragica; Ringhofer, Christain
2014-06-06
It is well known that Cu plays an important role in CdTe solar cell performance as a dopant. In this work, a finite-difference method is developed and used to simulate Cu diffusion in CdTe solar cells. In the simulations, which are done on a two-dimensional (2D) domain, the CdTe is assumed to be polycrystalline, with the individual grains separated by grain boundaries. When used to fit experimental Cu concentration data, bulk and grain boundary diffusion coefficients and activation energies for CdTe can be extracted. In the past, diffusion coefficients have been typically obtained by fitting data to simple functional forms of limited validity. By doing full simulations, the simplifying assumptions used in those analytical models are avoided and diffusion parameters can thus be determined more accurately
A three-dimensional spin-diffusion model for micromagnetics
NASA Astrophysics Data System (ADS)
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter
2015-10-01
We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation.
A three-dimensional spin-diffusion model for micromagnetics
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Hrkac, Gino; Praetorius, Dirk; Suess, Dieter
2015-01-01
We solve a time-dependent three-dimensional spin-diffusion model coupled to the Landau-Lifshitz-Gilbert equation numerically. The presented model is validated by comparison to two established spin-torque models: The model of Slonzewski that describes spin-torque in multi-layer structures in the presence of a fixed layer and the model of Zhang and Li that describes current driven domain-wall motion. It is shown that both models are incorporated by the spin-diffusion description, i.e., the nonlocal effects of the Slonzewski model are captured as well as the spin-accumulation due to magnetization gradients as described by the model of Zhang and Li. Moreover, the presented method is able to resolve the time dependency of the spin-accumulation. PMID:26442796
ERIC Educational Resources Information Center
Nye, Susan B.
2010-01-01
Jumping rope is an activity that can be fun and enjoyable for all students. It requires minimal activity space, can be performed individually or in small groups, and is an inexpensive way to engage students in a lifelong physical activity. Jumping rope is commonly used by coaches and athletes for training purposes to improve aerobic endurance,…
ERIC Educational Resources Information Center
Rebilas, Krzysztof
2013-01-01
Consider a skier who goes down a takeoff ramp, attains a speed "V", and jumps, attempting to land as far as possible down the hill below (Fig. 1). At the moment of takeoff the angle between the skier's velocity and the horizontal is [alpha]. What is the optimal angle [alpha] that makes the jump the longest possible for the fixed magnitude of the…
Numerical modelling of swirling diffusive flames
NASA Astrophysics Data System (ADS)
Parra-Santos, Teresa; Perez, Ruben; Szasz, Robert Z.; Gutkowski, Artur N.; Castro, Francisco
2016-03-01
Computational Fluid Dynamics has been used to study the mixing and combustion of two confined jets whose setup and operating conditions are those of the benchmark of Roback and Johnson. Numerical model solves 3D transient Navier Stokes for turbulent and reactive flows. Averaged velocity profiles using RNG swirl dominated k-epsilon model have been validated with experimental measurements from other sources for the non reactive case. The combustion model is Probability Density Function. Bearing in mind the annular jet has swirl number over 0.5, a vortex breakdown appears in the axis of the burner. Besides, the sudden expansion with a ratio of 2 in diameter between nozzle exits and the test chamber produces the boundary layer separation with the corresponding torus shape recirculation. Contrasting the mixing and combustion models, the last one produces the reduction of the vortex breakdown.
Modelling on cavitation in a diffuser with vortex generator
NASA Astrophysics Data System (ADS)
Jablonská, J.
2013-04-01
Based on cavitation modelling in Laval nozzle results and experience, problem with the diffuser with vortex generator was defined. The problem describes unsteady multiphase flow of water. Different cavitation models were used when modelling in Fluent, flow condition is inlet and pressure condition is outlet. Boundary conditions were specified by Energy Institute, Victor Kaplan's Department of Fluid Engineering, Faculty of Mechanical Engineering, Brno University of Technology. Numerical modelling is compared with experiment.
A diffuse interface Lox/hydrogen transcritical flame model
NASA Astrophysics Data System (ADS)
Gaillard, Pierre; Giovangigli, Vincent; Matuszewski, Lionel
2016-05-01
We present a diffuse-interface all-pressure flame model that transitions smoothly between subcritical and supercritical conditions. The model involves a non-equilibrium liquid/gas diffuse interface of van der Waals/Korteweg type embedded into a non-ideal multicomponent reactive fluid. The multicomponent transport fluxes are evaluated in their thermodynamic form in order to avoid singularities at thermodynamic mechanical stability limits. The model also takes into account condensing liquid water in order to avoid thermodynamic chemical instabilities. The resulting equations are used to investigate the interface between cold dense and hot light oxygen as well as the structure of diffusion flames between cold dense oxygen and gaseous-like hydrogen at all pressures, either subcritical or supercritical.
Diffusion Models for the Doping of Semiconductor Crystals.
NASA Astrophysics Data System (ADS)
Hearne, M. T.
Available from UMI in association with The British Library. Requires signed TDF. Discrete models, based on the physics of diffusion at the atomic level, are presented in the form of difference equations, thus providing explicit numerical techniques for evaluating concentration profiles. Models are developed for three diffusion mechanisms. All three of the models are used to study diffusion of dopant in semiconductor crystals during growth by the Czochralski technique. This study is motivated by previously published experimental data which showed dopant concentration profiles for grown gallium arsenide crystals. For these results the distribution of dopant, in this case chromium, was found to deviate significantly from the concentration profile which would be expected if no diffusion of dopant is assumed to take place. Four problems are modelled in one dimension. The first model to be developed is equivalent to Fick's first law of diffusion (the standard diffusion equation). Computed results are obtained for a given set of values of parameters, and the sensitivity of the model to variation of a number of these parameters is investigated. A more sophisticated model is then developed for which the dopant is assumed to diffuse substitutionally. The effect of the vacancy concentration is considered in a more rigorous manner than for the preceding model, and self-diffusion is taken into account. The corresponding partial differential equations are derived, although these are highly non-linear, and cannot be solved for the Czochralski growth problem. Results are again presented demonstrating the effect of varying certain parameters. For the third model, dopant is assumed to diffuse interstitially with effectively infinite diffusivity. Most of the dopant is, however, assumed to exist in the form of substitutionals which are "created" by interstitials occupying lattices. This model is applied, in one dimension, to two problems. The first application is not to Czochralski
Hierarchical set of models to estimate soil thermal diffusivity
NASA Astrophysics Data System (ADS)
Arkhangelskaya, Tatiana; Lukyashchenko, Ksenia
2016-04-01
Soil thermal properties significantly affect the land-atmosphere heat exchange rates. Intra-soil heat fluxes depend both on temperature gradients and soil thermal conductivity. Soil temperature changes due to energy fluxes are determined by soil specific heat. Thermal diffusivity is equal to thermal conductivity divided by volumetric specific heat and reflects both the soil ability to transfer heat and its ability to change temperature when heat is supplied or withdrawn. The higher soil thermal diffusivity is, the thicker is the soil/ground layer in which diurnal and seasonal temperature fluctuations are registered and the smaller are the temperature fluctuations at the soil surface. Thermal diffusivity vs. moisture dependencies for loams, sands and clays of the East European Plain were obtained using the unsteady-state method. Thermal diffusivity of different soils differed greatly, and for a given soil it could vary by 2, 3 or even 5 times depending on soil moisture. The shapes of thermal diffusivity vs. moisture dependencies were different: peak curves were typical for sandy soils and sigmoid curves were typical for loamy and especially for compacted soils. The lowest thermal diffusivities and the smallest range of their variability with soil moisture were obtained for clays with high humus content. Hierarchical set of models will be presented, allowing an estimate of soil thermal diffusivity from available data on soil texture, moisture, bulk density and organic carbon. When developing these models the first step was to parameterize the experimental thermal diffusivity vs. moisture dependencies with a 4-parameter function; the next step was to obtain regression formulas to estimate the function parameters from available data on basic soil properties; the last step was to evaluate the accuracy of suggested models using independent data on soil thermal diffusivity. The simplest models were based on soil bulk density and organic carbon data and provided different
Groundwater transport modeling with nonlinear sorption and intraparticle diffusion
NASA Astrophysics Data System (ADS)
Singh, Anshuman; Allen-King, Richelle M.; Rabideau, Alan J.
2014-08-01
Despite recent advances in the mechanistic understanding of sorption in groundwater systems, most contaminant transport models provide limited support for nonideal sorption processes such as nonlinear isotherms and/or diffusion-limited sorption. However, recent developments in the conceptualization of "dual mode" sorption for hydrophobic organic contaminants have provided more realistic and mechanistically sound alternatives to the commonly used Langmuir and Freundlich models. To support the inclusion of both nonlinear and diffusion-limited sorption processes in groundwater transport models, this paper presents two numerical algorithms based on the split operator approach. For the nonlinear equilibrium scenario, the commonly used two-step split operator algorithm has been modified to provide a more robust treatment of complex multi-parameter isotherms such as the Polanyi-partitioning model. For diffusion-limited sorption, a flexible three step split-operator procedure is presented to simulate intraparticle diffusion in multiple spherical particles with different sizes and nonlinear isotherms. Numerical experiments confirmed the accuracy of both algorithms for several candidate isotherms. However, the primary advantages of the algorithms are: (1) flexibility to accommodate any isotherm equation including "dual mode" and similar expressions, and (2) ease of adapting existing grid-based transport models of any dimensionality to include nonlinear sorption and/or intraparticle diffusion. Comparisons are developed for one-dimensional transport scenarios with different isotherms and particle configurations. Illustrative results highlight (1) the potential influence of isotherm model selection on solute transport predictions, and (2) the combined effects of intraparticle diffusion and nonlinear sorption on the plume transport and flushing for both single-particle and multi-particle scenarios.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
A multiple mapping conditioning model for differential diffusion
NASA Astrophysics Data System (ADS)
Dialameh, L.; Cleary, M. J.; Klimenko, A. Y.
2014-02-01
This work introduces modeling of differential diffusion within the multiple mapping conditioning (MMC) turbulent mixing and combustion framework. The effect of differential diffusion on scalar variance decay is analyzed and, following a number of publications, is found to scale as Re-1/2. The ability to model the differential decay rates is the most important aim of practical differential diffusion models, and here this is achieved in MMC by introducing what is called the side-stepping method. The approach is practical and, as it does not involve an increase in the number of MMC reference variables, economical. In addition we also investigate the modeling of a more refined and difficult to reproduce differential diffusion effect - the loss of correlation between the different scalars. For this we develop an alternative MMC model with two reference variables but which also makes use of the side-stepping method. The new models are successfully validated against DNS results available in literature for homogenous, isotropic two scalar mixing.
Coupled chemical and diffusion model for compacted bentonite
Olin, M.; Lehikoinen, J.; Muurinen, A.
1995-12-31
A chemical equilibrium model has been developed for ion-exchange and to a limited extent for other reactions, such as precipitation or dissolution of calcite or gypsum, in compacted bentonite water systems. The model was successfully applied to some bentonite experiments, especially as far as monovalent ions were concerned. The fitted log-binding constants for the exchange of sodium for potassium, magnesium, and calcium were 0.27, 1.50, and 2.10, respectively. In addition, a coupled chemical and diffusion model has been developed to take account of diffusion in pore water, surface diffusion and ion-exchange.d the model was applied to the same experiments as the chemical equilibrium model, and its validation was found partly successful. The above values for binding constants were used also in the coupled model. The apparent (both for anions and cations) and surface diffusion (only for cations) constants yielding the best agreement between calculated and experimental data were 3.0 {times} 10{sup {minus}11} m{sup 2}/s and 6.0 {times} 10{sup {minus}12} m{sup 2}/s, respectively. These values are questionable, however, as experimental results good enough for fitting are currently not available.
Models of geochemical systems from mixture theory: diffusion
Kirwan, A.D. Jr; Kump, L.R.
1987-05-01
The problem of diffusion of a geochemical component in a natural environment is investigated from the standpoint of mixture theory. The approach here differs from previous diffusion studies in that both the conservation of mass and momentum for the component is considered. This approach avoids parameterizing the diffusive flux in the mass equation by Fick's law. It is shown that when the momentum equation is included with the mass equation, the linear approximation for the space-time distribution of a solute in a binary system is the telegraph equation, well known from electrodynamics. This contrasts with the diffusion equation, which relies on introducing the Fick's law assumption into the conservation of mass equation for the solute. Solutions for both the diffusion and telegraph equation models are obtained and compared for the case of migration of a minor component into the sea bed when the sediment-water interface concentration is a prescribed function of time. Although the stationary, steady state solutions of the telegraph and diffusion equations are identical, the former has a transient solution in which fluctuations propagate at finite speed. The Fickian assumption, in contrast, requires an infinite speed of propagation.
NASA Technical Reports Server (NTRS)
Srinivasan, R. Srini; Gerth, Wayne A.; Powell, Michael R.; Paloski, William H. (Technical Monitor)
2000-01-01
A three-region mathematical model of gas bubble dynamics has been shown suitable for describing diffusion-limited dynamics of more than one bubble in a given volume of extravascular tissue. The model is based on the dynamics of gas exchange between a bubble and a well-stirred tissue region through an intervening unperfused diffusion region previously assumed to have constant thickness and uniform gas diffusivity. As a result, the gas content of the diffusion region remains constant as the volume of the region increases with bubble growth, causing dissolved gas in the region to violate Henry's law. Earlier work also neglected the relationship between the varying diffusion region volume and the fixed total tissue volume, because only cases in which the diffusion region volume is a small fraction of the overall tissue volume were considered. We herein extend the three-region model to correct these theoretical inconsistencies by allowing both the thickness and gas content of the diffusion region to vary during bubble evolution. A postulated difference in gas diffusivity between an infinitesimally thin layer at the bubble surface and the remainder of the diffusion region leads to variation in diffusion region gas content and thickness during bubble growth and resolution. This variable thickness, differential diffusivity (VTDD) model can yield bubble lifetimes considerably longer than those yielded by earlier three-region models for given model and decompression parameters, and meets a need for theoretically consistent but relatively simple bubble dynamics models for use in studies of decompression sickness (DCS) in human subjects, Keywords: decompression sickness, gas diffusion in tissue, diffusivity
MESOI: an interactive Lagrangian trajectory puff diffusion model
Ramsdell, J.V.; Athey, G.F.
1981-12-01
MESOI is an interactive Lagrangian trajectory puff diffusion model based on an earlier model by Start and Wendell at the Air Resources Laboratory Field Office at Idaho Falls, Idaho. Puff trajectories are determined using spatially and temporally varying wind fields. Diffusion in the puffs is computed as a function of distance traveled and atmospheric stability. Exposures are computed at nodes of a 31 by 31 grid. There is also provision for interpolation of short term exposures at off-grid locations. This report discusses: the theoretical bases of the model, the numerical approach used in the model, and the sensitivity and accuracy of the model. It contains a description of the computer program and a listing of the code. MESOI is written in FORTRAN. A companion report (Athey, Allwine and Ramsdell, 1981) contains a user's guide to MESOI and documents utility programs that maintain the data files needed by the model.
Nonlinear diffusion model for Rayleigh-Taylor mixing.
Boffetta, G; De Lillo, F; Musacchio, S
2010-01-22
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusivity models for the mean temperature profile. It is found that a nonlinear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows us to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Computer modelling of nanoscale diffusion phenomena at epitaxial interfaces
NASA Astrophysics Data System (ADS)
Michailov, M.; Ranguelov, B.
2014-05-01
The present study outlines an important area in the application of computer modelling to interface phenomena. Being relevant to the fundamental physical problem of competing atomic interactions in systems with reduced dimensionality, these phenomena attract special academic attention. On the other hand, from a technological point of view, detailed knowledge of the fine atomic structure of surfaces and interfaces correlates with a large number of practical problems in materials science. Typical examples are formation of nanoscale surface patterns, two-dimensional superlattices, atomic intermixing at an epitaxial interface, atomic transport phenomena, structure and stability of quantum wires on surfaces. We discuss here a variety of diffusion mechanisms that control surface-confined atomic exchange, formation of alloyed atomic stripes and islands, relaxation of pure and alloyed atomic terraces, diffusion of clusters and their stability in an external field. The computational model refines important details of diffusion of adatoms and clusters accounting for the energy barriers at specific atomic sites: smooth domains, terraces, steps and kinks. The diffusion kinetics, integrity and decomposition of atomic islands in an external field are considered in detail and assigned to specific energy regions depending on the cluster stability in mass transport processes. The presented ensemble of diffusion scenarios opens a way for nanoscale surface design towards regular atomic interface patterns with exotic physical features.
GIS-BASED 1-D DIFFUSIVE WAVE OVERLAND FLOW MODEL
KALYANAPU, ALFRED; MCPHERSON, TIMOTHY N.; BURIAN, STEVEN J.
2007-01-17
This paper presents a GIS-based 1-d distributed overland flow model and summarizes an application to simulate a flood event. The model estimates infiltration using the Green-Ampt approach and routes excess rainfall using the 1-d diffusive wave approximation. The model was designed to use readily available topographic, soils, and land use/land cover data and rainfall predictions from a meteorological model. An assessment of model performance was performed for a small catchment and a large watershed, both in urban environments. Simulated runoff hydrographs were compared to observations for a selected set of validation events. Results confirmed the model provides reasonable predictions in a short period of time.
Turing instability in reaction-diffusion models on complex networks
NASA Astrophysics Data System (ADS)
Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya
2016-09-01
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.
Mathematical modeling of clearing liquid drop diffusion after intradermal injection
NASA Astrophysics Data System (ADS)
Stolnitz, Mikhail M.; Bashkatov, Alexey N.; Genina, Elina A.; Tuchin, Valery V.
2007-05-01
The mathematical model of clearing agent diffusion after intradermal injection has been developed. Skin was presented as multilayer medium, but one layer with proper boundary conditions is considered. Analytical solution of the boundary problem for small and large time intervals is obtained.
Modeling development of inhibition zones in an agar diffusion bioassay
Chandrasekar, Vaishnavi; Knabel, Stephen J; Anantheswaran, Ramaswamy C
2015-01-01
A two-temperature agar diffusion bioassay is commonly used to quantify the concentration of nisin using Micrococcus luteus as the indicator microorganism. A finite element computational model based on Fick's second law of diffusion was used to predict the radius of the inhibition zone in this diffusion bioassay. The model developed was used to calculate nisin concentration profiles as a function of time and position within the agar. The minimum inhibitory concentration (MIC) of nisin against M. luteus was determined experimentally. The critical time (Tc) for growth of M. luteus within the agar diffusion bioassay was experimentally determined using incubation studies with nisin. The radius of the inhibition zone was predicted from the computational model as the location where the predicted nisin concentration at Tc was equal to MIC. The MIC was experimentally determined to be 0.156 μg mL−1, and Tc was determined to be 7 h. Good agreement (R2 = 0.984) was obtained between model-predicted and experimentally determined inhibition zone radii. PMID:26405525
Decomposing Task-Switching Costs with the Diffusion Model
ERIC Educational Resources Information Center
Schmitz, Florian; Voss, Andreas
2012-01-01
In four experiments, task-switching processes were investigated with variants of the alternating runs paradigm and the explicit cueing paradigm. The classical diffusion model for binary decisions (Ratcliff, 1978) was used to dissociate different components of task-switching costs. Findings can be reconciled with the view that task-switching…
A simple reaction-rate model for turbulent diffusion flames
NASA Technical Reports Server (NTRS)
Bangert, L. H.
1975-01-01
A simple reaction rate model is proposed for turbulent diffusion flames in which the reaction rate is proportional to the turbulence mixing rate. The reaction rate is also dependent on the mean mass fraction and the mean square fluctuation of mass fraction of each reactant. Calculations are compared with experimental data and are generally successful in predicting the measured quantities.
Reaction Diffusion Modeling of Calcium Dynamics with Realistic ER Geometry
Means, Shawn; Smith, Alexander J.; Shepherd, Jason; Shadid, John; Fowler, John; Wojcikiewicz, Richard J. H.; Mazel, Tomas; Smith, Gregory D.; Wilson, Bridget S.
2006-01-01
We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations. PMID:16617072
Modeling development of inhibition zones in an agar diffusion bioassay.
Chandrasekar, Vaishnavi; Knabel, Stephen J; Anantheswaran, Ramaswamy C
2015-09-01
A two-temperature agar diffusion bioassay is commonly used to quantify the concentration of nisin using Micrococcus luteus as the indicator microorganism. A finite element computational model based on Fick's second law of diffusion was used to predict the radius of the inhibition zone in this diffusion bioassay. The model developed was used to calculate nisin concentration profiles as a function of time and position within the agar. The minimum inhibitory concentration (MIC) of nisin against M. luteus was determined experimentally. The critical time (T c) for growth of M. luteus within the agar diffusion bioassay was experimentally determined using incubation studies with nisin. The radius of the inhibition zone was predicted from the computational model as the location where the predicted nisin concentration at T c was equal to MIC. The MIC was experimentally determined to be 0.156 μg mL(-1), and T c was determined to be 7 h. Good agreement (R (2) = 0.984) was obtained between model-predicted and experimentally determined inhibition zone radii.
A Mixed-Culture Biofilm Model with Cross-Diffusion.
Rahman, Kazi A; Sudarsan, Rangarajan; Eberl, Hermann J
2015-11-01
We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system. PMID:26582360
A Mixed-Culture Biofilm Model with Cross-Diffusion.
Rahman, Kazi A; Sudarsan, Rangarajan; Eberl, Hermann J
2015-11-01
We propose a deterministic continuum model for mixed-culture biofilms. A crucial aspect is that movement of one species is affected by the presence of the other. This leads to a degenerate cross-diffusion system that generalizes an earlier single-species biofilm model. Two derivations of this new model are given. One, like cellular automata biofilm models, starts from a discrete in space lattice differential equation where the spatial interaction is described by microscopic rules. The other one starts from the same continuous mass balances that are the basis of other deterministic biofilm models, but it gives up a simplifying assumption of these models that has recently been criticized as being too restrictive in terms of ecological structure. We show that both model derivations lead to the same PDE model, if corresponding closure assumptions are introduced. To investigate the role of cross-diffusion, we conduct numerical simulations of three biofilm systems: competition, allelopathy and a mixed system formed by an aerobic and an anaerobic species. In all cases, we find that accounting for cross-diffusion affects local distribution of biomass, but it does not affect overall lumped quantities such as the total amount of biomass in the system.
User's Manual for the APRAC-1A Urban Diffusion Model Computer Program.
ERIC Educational Resources Information Center
Mancuso, R. L.; And Others
The APRAC-1A diffusion model was developed as a versatile and practical model for computing the concentrations of pollutants at any point within a city. The model calculates pollutant contributions from diffusion on various scales, including: extra-urban diffusion, mainly from sources in upwind cities; intra-urban diffusion from freeway, arterial,…
Increase bone strength and improve heart and other muscle endurance by performing jump training with a rope, both while stationary and moving. The Train Like an Astronaut project uses the excitemen...
Enright, Ryan; Miljkovic, Nenad; Sprittles, James; Nolan, Kevin; Mitchell, Robert; Wang, Evelyn N
2014-10-28
Surface engineering at the nanoscale is a rapidly developing field that promises to impact a range of applications including energy production, water desalination, self-cleaning and anti-icing surfaces, thermal management of electronics, microfluidic platforms, and environmental pollution control. As the area advances, more detailed insights of dynamic wetting interactions on these surfaces are needed. In particular, the coalescence of two or more droplets on ultra-low adhesion surfaces leads to droplet jumping. Here we show, through detailed measurements of jumping droplets during water condensation coupled with numerical simulations of binary droplet coalescence, that this process is fundamentally inefficient with only a small fraction of the available excess surface energy (≲ 6%) convertible into translational kinetic energy. These findings clarify the role of internal fluid dynamics during the jumping droplet coalescence process and underpin the development of systems that can harness jumping droplets for a wide range of applications.
Modeling the diffusion of phosphorus in silicon in 3-D
Baker, K.R.
1994-12-31
The use of matrix preconditioning in semiconductor process simulation is examined. The simplified nonlinear single-species model for the diffusion of phosphorus into silicon is considered. The experimental three-dimensional simulator, PEPPER3, which uses finite differences and the numerical method of lines to implement the reaction-diffusion equation is modified to allow NSPCG to be called to solve the linear system in the inner Newton loop. Use of NSPCG allowed various accelerators such as Generalized Minimal Residual (GMRES) and Conjugate Gradient (CG) to be used in conjunction with preconditioners such as Richardson, Jacobi, and Incomplete Cholesky.
Reaction-diffusion modelling of bacterial colony patterns
NASA Astrophysics Data System (ADS)
Mimura, Masayasu; Sakaguchi, Hideo; Matsushita, Mitsugu
2000-07-01
It is well known from experiments that bacterial species Bacillus subtilis exhibit various colony patterns. These are essentially classified into five types in the morphological diagram, depending on the substrate softness and nutrient concentration. (A) diffusion-limited aggregation-like; (B) Eden-like; (C) concentric ring-like; (D) disk-like; and (E) dense branching morphology-like. There arises the naive question of whether the diversity of colony patterns observed in experiments is caused by different effects or governed by the same underlying principles. Our research has led us to propose reaction-diffusion models to describe the morphological diversity of colony patterns except for Eden-like ones.
A Diffusion Model Account of the Lexical Decision Task
Ratcliff, Roger; Gomez, Pablo; McKoon, Gail
2005-01-01
The diffusion model for 2-choice decisions (R. Ratcliff, 1978) was applied to data from lexical decision experiments in which word frequency, proportion of high- versus low-frequency words, and type of nonword were manipulated. The model gave a good account of all of the dependent variables—accuracy, correct and error response times, and their distributions—and provided a description of how the component processes involved in the lexical decision task were affected by experimental variables. All of the variables investigated affected the rate at which information was accumulated from the stimuli—called drift rate in the model. The different drift rates observed for the various classes of stimuli can all be explained by a 2-dimensional signal-detection representation of stimulus information. The authors discuss how this representation and the diffusion model’s decision process might be integrated with current models of lexical access. PMID:14756592
Fluid limit of the continuous-time random walk with general Levy jump distribution functions
Cartea, A.; Del-Castillo-Negrete, Diego B
2007-01-01
The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x). There are two well-known fluid limits of this model in the uncoupled case. For exponential decaying waiting times and Gaussian jump distribution functions the fluid limit leads to the diffusion equation. On the other hand, for algebraic decaying waiting times psi similar to t(-(1+beta)) and algebraic decaying jump distributions eta similar to x(-(1+alpha)) corresponding to Levy stable processes, the fluid limit leads to the fractional diffusion equation of order alpha in space and order beta in time. However, these are two special cases of a wider class of models. Here we consider the CTRW for the most general Levy stochastic processes in the Levy-Khintchine representation for the jump distribution function and obtain an integrodifferential equation describing the dynamics in the fluid limit. The resulting equation contains as special cases the regular and the fractional diffusion equations. As an application we consider the case of CTRWs with exponentially truncated Levy jump distribution functions. In this case the fluid limit leads to a transport equation with exponentially truncated fractional derivatives which describes the interplay between memory, long jumps, and truncation effects in the intermediate asymptotic regime. The dynamics exhibits a transition from superdiffusion to subdiffusion with the crossover time scaling as tau(c)similar to lambda(-alpha/beta), where 1/lambda is the truncation length scale. The asymptotic behavior of the propagator (Green's function) of the truncated fractional equation exhibits a transition from algebraic decay for t <
Gunnell, D; Nowers, M
1997-07-01
This review summarizes the published literature on suicide by jumping, in particular focusing on the social and psychological characteristics of people who have chosen this method of suicide, and the opportunities for prevention. Suicide by jumping accounts for 5% of suicides in England and Wales, and there are marked variations in the use of this method world-wide. A number of locations have gained notoriety as popular places from which to jump. Such sites include The Golden Gate Bridge and Niagara Falls in the USA, and Beachy Head and the Clifton Suspension Bridge in the UK. There is no consistent evidence that those who commit suicide by jumping differ sociodemographically or in their psychopathology from those who use other methods of suicide, although this method is more often used for in-patient suicides, possibly due to lack of access to other means. Survivors of suicidal jumps experience higher subsequent rates of suicide and mental ill health, but the majority do not go on to kill themselves, suggesting that preventive efforts may be worthwhile. This view is supported by other evidence that restricting access to the means of suicide may prevent some would-be suicides. Such measures may also reduce the emotional trauma suffered by those who witness these acts. Health authorities and coroners should consider reviewing local patterns of suicide by jumping, and if necessary institute preventive measures. PMID:9259217
Continuum modeling of diffusion and dispersion in dense granular flows
NASA Astrophysics Data System (ADS)
Christov, Ivan C.; Stone, Howard A.
2014-03-01
Continuum modeling of granular flows remains a challenge of modern statistical physics. Granular materials do not perform Brownian motion, yet diffusion and shear dispersion can be observed in such systems when agitation causes inelastic collisions between particles. In a number of canonical flow regimes (e.g., in a rotating container or down an incline), granular materials can behave like fluids. We formulate and solve the granular counterparts to two basic fluid mechanics problems: diffusion of a pulse and shear dispersion of a pulse for dense granular materials in rapid flow. We provide a theory to account for the concentration-dependent diffusivity of bidisperse granular mixtures, and we give an asymptotic argument for the self-similar behavior of such a diffusion process for which an exact self-similar analytical solution does not exist. For shear dispersion, we show that the effective dispersivity of the depth-averaged concentration of the dispersing powder varies as the Péclet number squared, as in classical Taylor-Aris dispersion of molecular solutes. The calculation is extended to generic shear profiles, showing a significant enhancement for convex profiles due to the shear-rate dependence of the diffusivity of granular materials. ICC was supported by NSF Grant DMS-1104047 and the U.S. DOE through the LANL/LDRD Program; HAS was supported by NSF Grant CBET-1234500.
Continuum modeling of diffusion and dispersion in dense granular flows
NASA Astrophysics Data System (ADS)
Christov, Ivan C.; Stone, Howard A.
2014-11-01
Continuum modeling of granular flows remains a challenge of modern statistical physics. Granular materials do not perform Brownian motion, yet diffusion and shear dispersion can be observed in such systems when agitation causes inelastic collisions between particles. In a number of canonical flow regimes (e.g., in a rotating container or down an incline), granular materials can behave like fluids. We formulate and solve the granular counterparts to two basic fluid mechanics problems: diffusion of a pulse and shear dispersion of a pulse for dense granular materials in rapid flow. We provide a theory to account for the concentration-dependent diffusivity of bidisperse granular mixtures, and we give an asymptotic argument for the self-similar behavior of such a diffusion process for which an exact self-similar analytical solution does not exist. For shear dispersion, we show that the effective dispersivity of the depth-averaged concentration of the dispersing powder varies as the Péclet number squared, as in classical Taylor-Aris dispersion of molecular solutes. The calculation is extended to generic shear profiles, showing a significant enhancement for convex profiles due to the shear-rate dependence of the diffusivity of granular materials. ICC was supported by NSF Grant DMS-1104047 and the U.S. DOE through the LANL/LDRD Program; HAS was supported by NSF Grant CBET-1234500.
Modeling and quality assessment of halftoning by error diffusion.
Kite, T D; Evans, B L; Bovik, A C
2000-01-01
Digital halftoning quantizes a graylevel image to one bit per pixel. Halftoning by error diffusion reduces local quantization error by filtering the quantization error in a feedback loop. In this paper, we linearize error diffusion algorithms by modeling the quantizer as a linear gain plus additive noise. We confirm the accuracy of the linear model in three independent ways. Using the linear model, we quantify the two primary effects of error diffusion: edge sharpening and noise shaping. For each effect, we develop an objective measure of its impact on the subjective quality of the halftone. Edge sharpening is proportional to the linear gain, and we give a formula to estimate the gain from a given error filter. In quantifying the noise, we modify the input image to compensate for the sharpening distortion and apply a perceptually weighted signal-to-noise ratio to the residual of the halftone and modified input image. We compute the correlation between the residual and the original image to show when the residual can be considered signal independent. We also compute a tonality measure similar to total harmonic distortion. We use the proposed measures for edge sharpening, noise shaping, and tonality to evaluate the quality of error diffusion algorithms. PMID:18255461
Predicting vulnerability to sleep deprivation using diffusion model parameters.
Patanaik, Amiya; Zagorodnov, Vitali; Kwoh, Chee Keong; Chee, Michael W L
2014-10-01
We used diffusion modelling to predict vulnerability to decline in psychomotor vigilance task (PVT) performance following a night of total sleep deprivation (SD). A total of 135 healthy young adults (69 women, age = 21.9 ± 1.7 years) participated in several within-subject cross-over design studies that incorporated the PVT. Participants were classified as vulnerable (lower tertile) or non-vulnerable (upper tertile) according to their change in lapse rate [lapse = reaction time (RT) ≥ 500 ms] between the evening before (ESD) and the morning after SD. RT data were fitted using Ratcliff's diffusion model. Although both groups showed significant change in RT during SD, there was no significant group difference in RT during the ESD session. In contrast, during ESD, the mean diffusion drift of vulnerable subjects was significantly lower than for non-vulnerable subjects. Mean drift and non-decision times were both adversely affected by sleep deprivation. Both mean drift and non-decision time showed significant state × vulnerability interaction. Diffusion modelling appears to have promise in predicting vulnerability to vigilance decline induced by a night of total sleep deprivation.
Fitting degradation of shoreline scarps by a nonlinear diffusion model
Andrews, D.J.; Buckna, R.C.
1987-01-01
The diffusion model of degradation of topographic features is a promising means by which vertical offsets on Holocene faults might be dated. In order to calibrate the method, we have examined present-day profiles of wave-cut shoreline scarps of late Pleistocene lakes Bonneville and Lahontan. A table is included that allows easy application of the model to scarps with simple initial shape. -from Authors
Internal hydraulic jumps with large upstream shear
NASA Astrophysics Data System (ADS)
Ogden, Kelly; Helfrich, Karl
2015-11-01
Internal hydraulic jumps in approximately two-layered flows with large upstream shear are investigated using numerical simulations. The simulations allow continuous density and velocity profiles, and a jump is forced to develop by downstream topography, similar to the experiments conducted by Wilkinson and Wood (1971). High shear jumps are found to exhibit significantly more entrainment than low shear jumps. Furthermore, the downstream structure of the flow has an important effect on the jump properties. Jumps with a slow upper (inactive) layer exhibit a velocity minimum downstream of the jump, resulting in a sub-critical downstream state, while flows with the same upstream vertical shear and a larger barotropic velocity remain super-critical downstream of the jump. A two-layer theory is modified to account for the vertical structure of the downstream density and velocity profiles and entrainment is allowed through a modification of the approach of Holland et al. (2002). The resulting theory can be matched reasonably well with the numerical simulations. However, the results are very sensitive to how the downstream vertical profiles of velocity and density are incorporated into the layered model, highlighting the difficulty of the two layer approximation when the shear is large.
A Diffusion Model for Two-sided Service Systems
NASA Astrophysics Data System (ADS)
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.
Modeling hydrogen diffusion for solar cell passivation and process optimization
NASA Astrophysics Data System (ADS)
Zhang, Yi
A diffusion model for hydrogen (H) in crystalline silicon was established which takes into account the charged state conversion, junction field, mobile traps, and complex formation and dissociation at dopant and trap sites. Carrier exchange among the various charged species is a "fast" process compared to the diffusion process. A numerical method was developed to solve the densities of various charged species from the Poisson's equation that involves shallow-level dopants and one "negative U" impurity, e.g., H. Time domain implicit method was adopted in finite difference scheme to solve the fully coupled equations. Limiting versions of the model were applied to the problems that are of interest to photovoltaics. Simplified trap-limited model was used to describe the low temperature diffusion profiles, assuming process-induced traps, a constant bulk trap level, and trapping/detrapping mechanisms. The results of the simulation agreed with those obtained from experiments. The best fit yielded a low surface free H concentration, Cs, (˜10 14 cm-3) from high temperature extrapolated diffusivity value. In the case of ion beam hydrogenation, mobile traps needed to be considered. PAS analysis showed the existence of vacancy-type defects in implanted Si substrates. Simulation of hydrogen diffusion in p-n junction was first attempted in this work. The order of magnitude of Cs (˜10 14 cm-3) was confirmed. Simulation results showed that the preferred charged state of H is H- (H +) in n- (p-) side of the junction. The accumulation of H- (H+) species on n+ (p+) side of the n+-p (p+-n) junction was observed, which could retard the diffusion in junction. The diffusion of hydrogen through heavily doped region in a junction is trap-limited. Several popular hydrogenation techniques were evaluated by means of modeling and experimental observations. In particular, PECVD followed by RTP hydrogenation was found to be two-step process: PECVD deposition serves as a predeposition step of H
Extended model of the channel diffusivity in the rutile structure
NASA Astrophysics Data System (ADS)
Ruebenbauer, K.; Wdowik, U. D.; Kwater, M.; Kowalik, J. T.
1996-11-01
A model describing the diffusivity of a highly diluted and randomly distributed substitutional cationic impurity via the open and almost empty <001> channels in the rutile structure has been developed recently. The above model is based upon the assumption that the insignificant fraction of the impurities resides in the channels. An extended model is developed that allows for a significant fraction of the impurities to stay within channels, and it is used to evaluate emission Mössbauer spectra originating from the diffusing impurities embedded in single-crystalline samples. Final results are shown for the 14.4-keV Mössbauer line in 57Co(Fe). It is shown that spectral line positions depend upon the wave-vector transfer to the system, and that the data are sensitive to the fraction of both parent and daughter impurities residing in the channels.
Numerical modelling and image reconstruction in diffuse optical tomography
Dehghani, Hamid; Srinivasan, Subhadra; Pogue, Brian W.; Gibson, Adam
2009-01-01
The development of diffuse optical tomography as a functional imaging modality has relied largely on the use of model-based image reconstruction. The recovery of optical parameters from boundary measurements of light propagation within tissue is inherently a difficult one, because the problem is nonlinear, ill-posed and ill-conditioned. Additionally, although the measured near-infrared signals of light transmission through tissue provide high imaging contrast, the reconstructed images suffer from poor spatial resolution due to the diffuse propagation of light in biological tissue. The application of model-based image reconstruction is reviewed in this paper, together with a numerical modelling approach to light propagation in tissue as well as generalized image reconstruction using boundary data. A comprehensive review and details of the basis for using spatial and structural prior information are also discussed, whereby the use of spectral and dual-modality systems can improve contrast and spatial resolution. PMID:19581256
A model of the diffuse galactic gamma ray emission
NASA Technical Reports Server (NTRS)
Sreekumar, Parameswaran
1990-01-01
The galaxy was observed to be a source of high energy gamma rays as shown by the two successful satellite experiments, SAS-2 and COS-B. It is generally understood that these diffuse gamma rays result from interactions between energetic cosmic rays and interstellar gas. This work makes use of the most recent data on the distribution of atomic and molecular hydrogen in the galaxy along with new estimates of gamma ray production functions to model the diffuse galactic gamma ray emission. The model allows various spatial distributions for cosmic rays in the Galaxy including non-axisymmetric ones. In the light of the expected data from EGRET (Energetic Gamma-Ray Experiment Telescope), an improved model of cosmic ray-matter-gamma ray interaction will provide new insights into the distribution of cosmic rays and the strength of its coupling to matter.
Assessment of a Molecular Diffusion Model in MELCOR
Chang OH; Richard Moore
2005-06-01
The MELCOR (version 1.8.5) [1] computer code with INEEL revisions is being improved for the analysis of very high temperature gas-cooled reactors [2]. Following a loss-of-coolant accident, flow through the reactor vessel may initially stagnate due to a non-uniform concentration of helium and air. However, molecular diffusion will eventually result in a uniform concentration of air and helium. The differences in fluid temperatures within the reactor vessel will then result in the establishment of a natural circulation flow that can supply significant amounts of air to the reactor core. The heat released by the resulting oxidation of graphite in the reactor core has the potential to increase the peak fuel temperature. In order to analyze the effects of oxidation on the response of the reactor during accidents, a molecular diffusion model was added to MELCOR. The model is based on Fick's Second Law for spatially uniform pressure and temperature. This paper describes equimolal counter diffusion experiments in a two bulb diffusion cell and the results of the assessment calculations.
Characterization and modeling of thermal diffusion and aggregation in nanofluids.
Gharagozloo, Patricia E.; Goodson, Kenneth E.
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.
Performance of turbulence models for transonic flows in a diffuser
NASA Astrophysics Data System (ADS)
Liu, Yangwei; Wu, Jianuo; Lu, Lipeng
2016-09-01
Eight turbulence models frequently used in aerodynamics have been employed in the detailed numerical investigations for transonic flows in the Sajben diffuser, to assess the predictive capabilities of the turbulence models for shock wave/turbulent boundary layer interactions (SWTBLI) in internal flows. The eight turbulence models include: the Spalart-Allmaras model, the standard k - 𝜀 model, the RNG k - 𝜀 model, the realizable k - 𝜀 model, the standard k - ω model, the SST k - ω model, the v2¯ - f model and the Reynolds stress model. The performance of the different turbulence models adopted has been systematically assessed by comparing the numerical results with the available experimental data. The comparisons show that the predictive performance becomes worse as the shock wave becomes stronger. The v2¯ - f model and the SST k - ω model perform much better than other models, and the SST k - ω model predicts a little better than the v2¯ - f model for pressure on walls and velocity profile, whereas the v2¯ - f model predicts a little better than the SST k - ω model for separation location, reattachment location and separation length for strong shock case.
Thermomechanics of damageable materials under diffusion: modelling and analysis
NASA Astrophysics Data System (ADS)
Roubíček, Tomáš; Tomassetti, Giuseppe
2015-12-01
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat generation/consumption/transfer is considered. Damage is modelled as rate-independent. The applications include metal-hydrogen systems with metal/hydride phase transformation, poroelastic rocks, structural and ferro/para-magnetic phase transformation, water and heat transport in concrete, and if diffusion is neglected, plasticity with damage and viscoelasticity, etc. For the ensuing system of partial differential equations and inclusions, we prove existence of solutions by a carefully devised semi-implicit approximation scheme of the fractional-step type.
Chaotic map models of soot fluctuations in turbulent diffusion flames
Mukerji, S.; McDonough, J.M.; Menguec, M.P.; Manickavasagam, S.; Chung, S.
1998-10-01
In this paper, the authors introduce a methodology to characterize time-dependent soot volume fraction fluctuations in turbulent diffusion flames via chaotic maps. The approach is based on the hypothesis that fluctuations of properties in turbulent flames are deterministic in nature, rather than statistical. The objective is to develop models of these fluctuations to be used in comprehensive algorithms to study the nature of turbulent flames and the interaction of turbulence with radiation. To this end the authors measured the time series of soot scattering coefficient in an ethylene diffusion flame from light scattering experiments and fit these data to linear combinations of chaotic maps of the unit interval. Both time series and power spectra can be modeled with reasonable accuracy in this way.
Model-free simulation approach to molecular diffusion tensors.
Chevrot, Guillaume; Hinsen, Konrad; Kneller, Gerald R
2013-10-21
In the present work, we propose a simple model-free approach for the computation of molecular diffusion tensors from molecular dynamics trajectories. The method uses a rigid body trajectory of the molecule under consideration, which is constructed a posteriori by an accumulation of quaternion-based superposition fits of consecutive conformations. From the rigid body trajectory, we compute the translational and angular velocities of the molecule and by integration of the latter also the corresponding angular trajectory. All quantities can be referred to the laboratory frame and a molecule-fixed frame. The 6 × 6 diffusion tensor is computed from the asymptotic slope of the tensorial mean square displacement and, for comparison, also from the Kubo integral of the velocity correlation tensor. The method is illustrated for two simple model systems - a water molecule and a lysozyme molecule in bulk water. We give estimations of the statistical accuracy of the calculations. PMID:24160503
Model-free simulation approach to molecular diffusion tensors
NASA Astrophysics Data System (ADS)
Chevrot, Guillaume; Hinsen, Konrad; Kneller, Gerald R.
2013-10-01
In the present work, we propose a simple model-free approach for the computation of molecular diffusion tensors from molecular dynamics trajectories. The method uses a rigid body trajectory of the molecule under consideration, which is constructed a posteriori by an accumulation of quaternion-based superposition fits of consecutive conformations. From the rigid body trajectory, we compute the translational and angular velocities of the molecule and by integration of the latter also the corresponding angular trajectory. All quantities can be referred to the laboratory frame and a molecule-fixed frame. The 6 × 6 diffusion tensor is computed from the asymptotic slope of the tensorial mean square displacement and, for comparison, also from the Kubo integral of the velocity correlation tensor. The method is illustrated for two simple model systems - a water molecule and a lysozyme molecule in bulk water. We give estimations of the statistical accuracy of the calculations.
A surface diffusion model for Dip Pen Nanolithography line writing
NASA Astrophysics Data System (ADS)
Saha, Sourabh K.; Culpepper, Martin L.
2010-06-01
Dip Pen Nanolithography is a direct write process that creates nanoscale dots and lines. Models typically predict dot and line size via assumption of constant ink flow rate from tip to substrate. This is appropriate for dot writing. It is however well-known, though models rarely reflect, that the ink flow rate depends upon writing speed during line writing. Herein, we explain the physical phenomenon that governs line writing and use this to model tip-substrate diffusion in line writing. We accurately predict (i) the increase in flow rate with writing speed and (ii) line width within 12.5%.
Forecasting Diffusion of Technology by using Bass Model
NASA Astrophysics Data System (ADS)
Kim, Do-Hoi; Shin, Young-Geun; Park, Sang-Sung; Jang, Dong-Sik
2009-08-01
Generally, researching method of technology forecasting has been depended on intuition of expert until now. So there were many defects like consuming much time and money and so on. In this paper, we forecast diffusion of technology by using Bass model that is one of the quantitative analysis methods. We applied this model at technology market. And for input data of experiment, we use patent data that is representing each technology in technology market. We expect this research will be suggest new possibility that patent data can be applied in Bass model.
Consistent flamelet modeling of differential molecular diffusion for turbulent non-premixed flames
NASA Astrophysics Data System (ADS)
Wang, Haifeng
2016-03-01
Treating differential molecular diffusion correctly and accurately remains as a great challenge to the modeling of turbulent non-premixed combustion. The aim of this paper is to develop consistent modeling strategies for differential molecular diffusion in flamelet models. Two types of differential molecular diffusion models are introduced, linear differential diffusion models and nonlinear differential diffusion models. A multi-component turbulent mixing layer problem is analyzed in detail to gain insights into differential molecular diffusion and its characteristics, particularly the dependence of differential molecular diffusion on the Reynolds number and the Lewis number. These characteristics are then used to validate the differential molecular diffusion models. Finally, the new models are applied to the modeling of a series of laboratory-scale turbulent non-premixed jet flames with different Reynolds number (Sandia Flames B, C, and D) to further assess the models' performance.
Most current electrostatic surface complexation models describing ionic binding at the particle/water interface rely on the use of Poisson - Boltzmann (PB) theory for relating diffuse layer charge densities to diffuse layer electrostatic potentials. PB theory is known to contain ...
Molecular Diffusive Motion in a Monolayer of a Model Lubricant
NASA Astrophysics Data System (ADS)
Diama, A.; Criswell, L.; Mo, H.; Taub, H.; Herwig, K. W.; Hansen, F. Y.; Volkmann, U. G.; Dimeo, R.; Neumann, D.
2003-03-01
Squalane (C_30H_62), a branched alkane of intermediate length consisting of a tetracosane backbone (n-C_24H_50 or C24) and six symmetrically placed methyl sidegroups, is frequently taken as a model lubricant. We have conducted quasielastic neutron scattering (QNS) experiments to investigate the diffusive motion on different time scales in a squalane monolayer adsorbed on the (0001) surfaces of an exfoliated graphite substrate. Unlike tetracosane, high-energy resolution spectra (time scale ˜0.1 - 4 ns) at temperatures of 215 K and 230 K show the energy width of the QNS to have a maximum near Q = 1.2 ÅThis nonmonotonic Q dependence suggests a more complicated diffusive motion than the simple rotation about the long molecular axis believed to occur in a C24 monolayer at this temperature. Lower-energy-resolution spectra (time scale ˜4 - 40 ps) show evidence of two types of diffusive motion whose rates have opposite temperature dependences. The rate of the faster motion decreases as the monolayer is heated, and we speculate that it is due to hindered rotation of the methyl groups. The rate of the slower motion increases with temperature and may involve both uniaxial rotation and translational diffusion. Our experimental results will be compared with molecular dynamics simulations.
Modeling diffusive transport with a fractional derivative without singular kernel
NASA Astrophysics Data System (ADS)
Gómez-Aguilar, J. F.; López-López, M. G.; Alvarado-Martínez, V. M.; Reyes-Reyes, J.; Adam-Medina, M.
2016-04-01
In this paper we present an alternative representation of the diffusion equation and the diffusion-advection equation using the fractional calculus approach, the spatial-time derivatives are approximated using the fractional definition recently introduced by Caputo and Fabrizio in the range β , γ ∈(0 ; 2 ] for the space and time domain respectively. In this representation two auxiliary parameters σx and σt are introduced, these parameters related to equation results in a fractal space-time geometry provide an entire new family of solutions for the diffusion processes. The numerical results showed different behaviors when compared with classical model solutions. In the range β , γ ∈(0 ; 1) , the concentration exhibits the non-Markovian Lévy flights and the subdiffusion phenomena; when β = γ = 1 the classical case is recovered; when β , γ ∈(1 ; 2 ] the concentration exhibits the Markovian Lévy flights and the superdiffusion phenomena; finally when β = γ = 2 the concentration is anomalous dispersive and we found ballistic diffusion.
Reaction-diffusion processes and metapopulation models on duplex networks
NASA Astrophysics Data System (ADS)
Xuan, Qi; Du, Fang; Yu, Li; Chen, Guanrong
2013-03-01
Reaction-diffusion processes, used to model various spatially distributed dynamics such as epidemics, have been studied mostly on regular lattices or complex networks with simplex links that are identical and invariant in transferring different kinds of particles. However, in many self-organized systems, different particles may have their own private channels to keep their purities. Such division of links often significantly influences the underlying reaction-diffusion dynamics and thus needs to be carefully investigated. This article studies a special reaction-diffusion process, named susceptible-infected-susceptible (SIS) dynamics, given by the reaction steps β→α and α+β→2β, on duplex networks where links are classified into two groups: α and β links used to transfer α and β particles, which, along with the corresponding nodes, consist of an α subnetwork and a β subnetwork, respectively. It is found that the critical point of particle density to sustain reaction activity is independent of the network topology if there is no correlation between the degree sequences of the two subnetworks, and this critical value is suppressed or extended if the two degree sequences are positively or negatively correlated, respectively. Based on the obtained results, it is predicted that epidemic spreading may be promoted on positive correlated traffic networks but may be suppressed on networks with modules composed of different types of diffusion links.
Diffuse interface modeling of a radial vapor bubble collapse
NASA Astrophysics Data System (ADS)
Magaletti, Francesco; Marino, Luca; Massimo Casciola, Carlo
2015-12-01
A diffuse interface model is exploited to study in details the dynamics of a cavitation vapor bubble, by including phase change, transition to supercritical conditions, shock wave propagation and thermal conduction. The numerical experiments show that the actual dynamic is a sequence of collapses and rebounds demonstrating the importance of nonequilibrium phase changes. In particular the transition to supercritical conditions avoids the full condensation and leads to shockwave emission after the collapse and to successive bubble rebound.
Modeling of Diffusion in Liquid Ge and Its Alloys
NASA Technical Reports Server (NTRS)
Stroud, David G.
1998-01-01
This report summarizes progress made on NASA Grant NAG3-1437, Modeling of diffusion in Liquid Ge and Its Alloys, which was in effect from January 15, 1993 through July 10, 1997. It briefly describes the purpose of the grant, and the work accomplished in simulations and other studies of thermophysical properties of liquid semiconductors and related materials. A list of publications completed with the support of the grant is also given.
Lattice Boltzmann model for the convection-diffusion equation.
Chai, Zhenhua; Zhao, T S
2013-06-01
We propose a lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.
An epidemic model of rumor diffusion in online social networks
NASA Astrophysics Data System (ADS)
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.
Reaction-diffusion processes and metapopulation models in heterogeneous networks
NASA Astrophysics Data System (ADS)
Colizza, Vittoria; Pastor-Satorras, Romualdo; Vespignani, Alessandro
2007-04-01
Dynamical reaction-diffusion processes and metapopulation models are standard modelling approaches for a wide array of phenomena in which local quantities-such as density, potentials and particles-diffuse and interact according to the physical laws. Here, we study the behaviour of the basic reaction-diffusion process (given by the reaction steps B-->A and B+A-->2B) defined on networks with heterogeneous topology and no limit on the nodes' occupation number. We investigate the effect of network topology on the basic properties of the system's phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density-driven phase transitions, whereas phase transition and critical points independent of the particle density are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic metapopulation and agent-based models that include the complex features of real-world networks.
Kar, Julia; Quesada, Peter M
2013-02-01
The central goal of this study was to contribute to the advancements being made in determining the underlying causes of anterior cruciate ligament (ACL) injuries. ACL injuries are frequently incurred by recreational and professional young female athletes during non-contact impact activities in sports like volleyball and basketball. This musculoskeletal-neuromuscular study investigated stop-jumps and factors related to ACL injury like knee valgus and internal-external moment loads, knee anterior-posterior (AP) shear forces, ACL strains and internal forces. Motion capture data was obtained from the landing phase of stop-jumps performed by eleven young recreational female athletes and electromyography (EMG) data collected from quadriceps, hamstring and gastrocnimius muscles which were then compared to numerically estimated activations. Numerical simulation tools used were Inverse Kinematics, Computed Muscle Control and Forward Dynamics and the knee modeled as a six degree of freedom joint. Results showed averaged peak strains of 12.2 ± 4.1% in the right and 11.9 ± 3.0% in the left ACL. Averaged peak knee AP shear forces were 482.3 ± 65.7 N for the right and 430.0 ± 52.4 N for the left knees, approximately equal to 0.7-0.8 times body weight across both knees. A lack of symmetry was observed between the knees for valgus angles (p < 0.04), valgus moments (p < 0.001) and muscle activations (p < 0.001), all of which can be detrimental to ACL stability during impact activities. Comparisons between recorded EMG data and estimated muscle activations show the relation between electrical signal and muscle depolarization. In summary, this study outlines a musculoskeletal simulation approach that provides numerical estimations for a number of variables associated with ACL injuries in female athletes performing stop-jumps.
Impact Acceleration Model of Diffuse Traumatic Brain Injury.
Hellewell, Sarah C; Ziebell, Jenna M; Lifshitz, Jonathan; Morganti-Kossmann, M Cristina
2016-01-01
The impact acceleration (I/A) model of traumatic brain injury (TBI) was developed to reliably induce diffuse traumatic axonal injury in rats in the absence of skull fractures and parenchymal focal lesions. This model replicates a pathophysiology that is commonly observed in humans with diffuse axonal injury (DAI) caused by acceleration-deceleration forces. Such injuries are typical consequences of motor vehicle accidents and falls, which do not necessarily require a direct impact to the closed skull. There are several desirable characteristics of the I/A model, including the extensive axonal injury produced in the absence of a focal contusion, the suitability for secondary insult modeling, and the adaptability for mild/moderate injury through alteration of height and/or weight. Furthermore, the trauma device is inexpensive and readily manufactured in any laboratory, and the induction of injury is rapid (~45 min per animal from weighing to post-injury recovery) allowing multiple animal experiments per day. In this chapter, we describe in detail the methodology and materials required to produce the rat model of I/A in the laboratory. We also review current adaptations to the model to alter injury severity, discuss frequent complications and technical issues encountered using this model, and provide recommendations to ensure technically sound injury induction. PMID:27604723
THE LOS ALAMOS NATIONAL LABORATORY ATMOSPHERIC TRANSPORT AND DIFFUSION MODELS
M. WILLIAMS
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.
Jun, K S; Kang, J W; Lee, K S
2007-01-01
Diffuse pollution sources along a stream reach are very difficult to both monitor and estimate. In this paper, a systematic method using an optimal estimation algorithm is presented for simultaneous estimation of diffuse pollution and model parameters in a stream water quality model. It was applied with the QUAL2E model to the South Han River in South Korea for optimal estimation of kinetic constants and diffuse loads along the river. Initial calibration results for kinetic constants selected from a sensitivity analysis reveal that diffuse source inputs for nitrogen and phosphorus are essential to satisfy the system mass balance. Diffuse loads for total nitrogen and total phosphorus were estimated by solving the expanded inverse problem. Comparison of kinetic constants estimated simultaneously with diffuse sources to those estimated without diffuse loads, suggests that diffuse sources must be included in the optimization not only for its own estimation but also for adequate estimation of the model parameters. Application of the optimization method to river water quality modeling is discussed in terms of the sensitivity coefficient matrix structure.
Reaction-diffusion models of within-feather pigmentation patterning.
Prum, Richard O; Williamson, Scott
2002-04-22
Feathers are complex, branched keratin structures that exhibit a diversity of pigmentation patterns. Feather pigments are transferred into developing feather keratinocytes from pigment cells that migrate into the tubular feather germ from the dermis. Within-feather pigment patterns are determined by differential pigmentation of keratinocytes within independent barb ridges during feather development. Little is known about the molecular mechanisms that determine which keratinocytes receive pigment. We apply reaction-diffusion models to the growth of within-feather pigment patterns based on a realistic model of feather growth. These models accurately simulate the growth of a diversity of the within-feather pigmentation patterns found in real feathers, including a central patch, a 'hollow' central patch, concentric central patches, bars, chevrons, a central circular spot, rows of paired spots, and arrays of offset dots. The models can also simulate the complex transitions between distinct pigmentation patterns among feathers observed in real avian plumages, including transitions from bars to chevrons, bars to paired dots, and bars to arrays of dots. The congruence between the developmental dynamics of the simulated and observed feather patterns indicates that the reaction-diffusion models provide a realistic and accurate description of the determination of pigment pattern within avian feather follicles. The models support the hypothesis that within-feather pigmentation patterning is determined by antagonistic interactions among molecular expression gradients within the tubular follicle and feather germ.
A Temporal Model of Technology Diffusion into Small Firms in Wales.
ERIC Educational Resources Information Center
Thomas, Brychan; Packham, Gary; Miller, Chris
2001-01-01
Discusses technology diffusion through formal and informal networks. Develops a model that includes channels and mechanisms involved in transferring technology into innovative small businesses. The model depicts influences that increase or slow the rate of diffusion. (SK)
Super-resolution image reconstruction using diffuse source models.
Ellis, Michael A; Viola, Francesco; Walker, William F
2010-06-01
Image reconstruction is central to many scientific fields, from medical ultrasound and sonar to computed tomography and computer vision. Although lenses play a critical reconstruction role in these fields, digital sensors enable more sophisticated computational approaches. A variety of computational methods have thus been developed, with the common goal of increasing contrast and resolution to extract the greatest possible information from raw data. This paper describes a new image reconstruction method named the Diffuse Time-domain Optimized Near-field Estimator (dTONE). dTONE represents each hypothetical target in the system model as a diffuse region of targets rather than a single discrete target, which more accurately represents the experimental data that arise from signal sources in continuous space, with no additional computational requirements at the time of image reconstruction. Simulation and experimental ultrasound images of animal tissues show that dTONE achieves image resolution and contrast far superior to those of conventional image reconstruction methods. We also demonstrate the increased robustness of the diffuse target model to major sources of image degradation through the addition of electronic noise, phase aberration and magnitude aberration to ultrasound simulations. Using experimental ultrasound data from a tissue-mimicking phantom containing a 3-mm-diameter anechoic cyst, the conventionally reconstructed image has a cystic contrast of -6.3 dB, whereas the dTONE image has a cystic contrast of -14.4 dB.
Measurements and modeling of explosive vapor diffusion in snow
NASA Astrophysics Data System (ADS)
Albert, Mary R.; Cragin, James H.; Leggett, Daniel C.
2000-08-01
The detection of buried mines is important to both for humanitarian and military strategic de-mining both at home and abroad, and recent efforts in chemical detection show promise for definitive identification of buried miens. The impact of weather has a large effect on the fate and transport of the explosives vapor that these systems sense. In many areas of military conflict, and at Army military training grounds in cold regions, winter weather affects military operations for many months of the year. In cold regions, the presence of freezing ground or a snow cover may provide increased temporary storage of the explosive, potentially leading to opportunities for more optimal sensing conditions later. This paper discusses the result of a controlled laboratory experiment to investigate explosives diffusion through snow, quantitative microscopy measurements of snow microstructure including specific surface, and verifications of our transport model using this data. In experiments measuring 1,3-DNB, 2,4-DNT and 2,4,6-TNT we determined an effective diffusion coefficient of 1.5 X 10-6 cm2/s from measurements through isothermal sieved snow with equivalent sphere radius of 0.11 mm. Adsorption is a major factor in diffusive transport of these explosives through snow. The data was used to verify our finite element mole of explosives transport. Measurements and model results show close agreement.
Cosmic ray diffusion: Detailed investigation of a recent model
Lerche, Ian; Tautz, R. C.
2011-08-15
A recently proposed model [A. Shalchi, Astrophys. J. 720, L127 (2010)] of perpendicular cosmic ray scattering is investigated in detail, with special emphasis to the relevant diffusion coefficients. Solution of a pair of critical equations, as well as a fundamental integral needed to describe the particle transport, are represented via a mathematically correct expansion procedure, thus modifying the previously available approximations. It is hoped that these significant improvements will aid in allowing a clearer understanding of precisely what the model is capable of evaluating.
Affinity based information diffusion model in social networks
NASA Astrophysics Data System (ADS)
Liu, Hongli; Xie, Yun; Hu, Haibo; Chen, Zhigao
2014-12-01
There is a widespread intuitive sense that people prefer participating in spreading the information in which they are interested. The affinity of people with information disseminated can affect the information propagation in social networks. In this paper, we propose an information diffusion model incorporating the mechanism of affinity of people with information which considers the fitness of affinity values of people with affinity threshold of the information. We find that the final size of information diffusion is affected by affinity threshold of the information, average degree of the network and the probability of people's losing their interest in the information. We also explore the effects of other factors on information spreading by numerical simulations and find that the probabilities of people's questioning and confirming the information can affect the propagation speed, but not the final scope.
Time Fractional Diffusion Equations and Analytical Solvable Models
NASA Astrophysics Data System (ADS)
Bakalis, Evangelos; Zerbetto, Francesco
2016-08-01
The anomalous diffusion of a particle that moves in complex environments is analytically studied by means of the time fractional diffusion equation. The influence on the dynamics of a random moving particle caused by a uniform external field is taken into account. We extract analytical solutions in terms either of the Mittag-Leffler functions or of the M- Wright function for the probability distribution, for the velocity autocorrelation function as well as for the mean and the mean square displacement. Discussion of the applicability of the model to real systems is made in order to provide new insight of the medium from the analysis of the motion of a particle embedded in it.
ERIC Educational Resources Information Center
Ball, Stephen; Cohen, Ann; Meyer, Margaret
2012-01-01
Jump Into Action (JIA) is a school-based team-taught program to help fifth-grade students make healthy food choices and be more active. The JIA team (physical education teacher, classroom teacher, school nurse, and parent) work together to provide a supportive environment as students set goals to improve food choices and increase activity.…
ERIC Educational Resources Information Center
Baylie, M.; Ford, P. J.; Mathlin, G. P.; Palmer, C.
2009-01-01
The jumping ring experiment has become central to liquid nitrogen shows given as part of the outreach and open day activities carried out within the University of Bath. The basic principles of the experiment are described as well as the effect of changing the geometry of the rings and their metallurgical state. In general, aluminium rings are…
ERIC Educational Resources Information Center
Tretter, Thomas
2005-01-01
In the spirit of the National Science Education Standards (NRC 1996), many teachers attempt to have their students experience science in a constructivist, inquiry-oriented manner. The egg bungee jump activity will certainly support that mode of teaching, and has the added benefit of providing a concrete context within which students can explore…
ERIC Educational Resources Information Center
Fitzgerald, Mike; Brand, Lance
2004-01-01
In this article, the authors present an egg bungee jumping activity. This activity introduces students to ways that engineers might apply calculations of failure to meet a challenge. Students are required to use common, everyday materials such as rubber bands, string, plastic bags, and eggs. They will apply technological problem solving, material…
Srinivasan, R S; Gerth, W A; Powell, M R
2000-10-01
The three-region model of gas bubble dynamics consists of a bubble and a well-stirred tissue region with an intervening unperfused diffusion region previously assumed to have constant thickness and uniform gas diffusivity. As a result, the diffusion region gas content remains unchanged as its volume increases with bubble growth, causing dissolved gas in the region to violate Henry's law. Earlier work also neglected the relationship between the varying diffusion region volume and the fixed total tissue volume. The present work corrects these theoretical inconsistencies by postulating a difference in gas diffusivity between an infinitesimally thin layer at the bubble surface and the remainder of the diffusion region, thus allowing both thickness and gas content of the diffusion region to vary during bubble evolution. The corrected model can yield bubble lifetimes considerably longer than those yielded by earlier three-region models, and meets a need for theoretically consistent but relatively simple bubble dynamics models for use in studies of decompression sickness (DCS) in human subjects.
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. PMID:21804911
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.
NASA Astrophysics Data System (ADS)
Musho, Matthew K.; Kozak, John J.
1984-10-01
A method is presented for calculating exactly the relative width (σ2)1/2/
Subgrid models for mass and thermal diffusion in turbulent mixing
NASA Astrophysics Data System (ADS)
Lim, H.; Yu, Y.; Glimm, J.; Li, X.-L.; Sharp, D. H.
2010-12-01
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.
A multiphase solute diffusion model for dendritic alloy solidification
Wang, C.Y.; Beckermann, C.
1993-12-01
A solute diffusion model, aimed at predicting microstructure formation in metal castings, is proposed for dendritic solidification of alloys. The model accounts for the different length scales existing in a dendritic structure. This is accomplished by utilizing a multiphase approach, in which not only the various physical phases but also phases associated with different length scales are considered separately. The macroscopic conservation equations are derived for each phase using the volume averaging technique, with constitutive relations developed for the interfacial transfer terms. It is shown that the multiphase model can rigorously incorporate the growth of dendrite tips and coarsening of dendrite arms. In addition, the distinction of different length scales enables the inclusion of realistic descriptions of the dendrite topology and relations to key metallurgical parameters. Another novel aspect of the model is that a single set of conservation equations for solute diffusion is developed for both equiaxed and columnar dendritic solidification. Finally, illustrative calculations for equiaxed, columnar, and mixed columnar-equiaxed solidification are carried out to provide quantitative comparisons with previous studies, and a variety of fundamental phenomena such as recalescence, dendrite tip undercooling, and columnar-to-equiaxed transition (CET) are predicted.
A Reaction-Diffusion Model of Cholinergic Retinal Waves
Lansdell, Benjamin; Ford, Kevin; Kutz, J. Nathan
2014-01-01
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability. PMID:25474327
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.
Anomalous diffusion in neutral evolution of model proteins
NASA Astrophysics Data System (ADS)
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.
Xu, Zuwei; Zhao, Haibo Zheng, Chuguang
2015-01-15
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
NASA Astrophysics Data System (ADS)
Xu, Zuwei; Zhao, Haibo; Zheng, Chuguang
2015-01-01
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance-rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
Moldrup, P.; Olesen, T.; Yamaguchi, T.; Schjoenning, P.; Rolston, D.E.
1999-08-01
Accurate description of gas diffusivity (ratio of gas diffusion coefficients in soil and free air, D{sub s}/D{sub 0}) in undisturbed soils is a prerequisite for predicting in situ transport and fate of volatile organic chemicals and greenhouse gases. Reference point gas diffusivities (R{sub p}) in completely dry soil were estimated for 20 undisturbed soils by assuming a power function relation between gas diffusivity and air-filled porosity ({epsilon}). Among the classical gas diffusivity models, the Buckingham (1904) expression, equal to the soil total porosity squared, best described R{sub p}. Inasmuch, as their previous works implied a soil-type dependency of D{sub s}/D{sub 0}({epsilon}) in undisturbed soils, the Buckingham R{sub p} expression was inserted in two soil-type-dependent D{sub s}/D{sub 0}({epsilon}) models. One D{sub s}/D{sub 0}({epsilon}) model is a function of pore-size distribution (the Campbell water retention parameter used in a modified Burdine capillary tube model), and the other is a calibrated, empirical function of soil texture (silt + sand fraction). Both the Buckingham-Burdine-Campbell (BBC) and the Buckingham/soil texture-based D{sub s}/D{sub 0}({epsilon}) models described well the observed soil type effects on gas diffusivity and gave improved predictions compared with soil type independent models when tested against an independent data set for six undisturbed surface soils. This study emphasizes that simple but soil-type-dependent power function D{sub s}/D{sub 0}({epsilon}) models can adequately describe and predict gas diffusivity in undisturbed soil. The authors recommend the new BBC model as basis for modeling gas transport and reactions in undisturbed soil systems.
Modeling Diffusion Induced Stresses for Lithium-Ion Battery Materials
NASA Astrophysics Data System (ADS)
Chiu Huang, Cheng-Kai
Advancing lithium-ion battery technology is of paramount importance for satisfying the energy storage needs in the U.S., especially for the application in the electric vehicle industry. To provide a better acceleration for electric vehicles, a fast and repeatable discharging rate is required. However, particle fractures and capacity loss have been reported under high current rate (C-rate) during charging/discharging and after a period of cycling. During charging and discharging, lithium ions extract from and intercalate into electrode materials accompanied with the volume change and phase transition between Li-rich phase and Li-poor phase. It is suggested that the diffusion-induced-stress is one of the main reasons causing capacity loss due to the mechanical degradation of electrode particles. Therefore, there is a fundamental need to provide a mechanistic understanding by considering the structure-mechanics-property interactions in lithium-ion battery materials. Among many cathode materials, the olivine-based lithium-iron-phosphate (LiFePO4) with an orthorhombic crystal structure is one of the promising cathode materials for the application in electric vehicles. In this research we first use a multiphysic approach to investigate the stress evolution, especially on the phase boundary during lithiation in single LiFePO4 particles. A diffusion-controlled finite element model accompanied with the experimentally observed phase boundary propagation is developed via a finite element package, ANSYS, in which lithium ion concentration-dependent anisotropic material properties and volume misfits are incorporated. The stress components on the phase boundary are used to explain the Mode I, Mode II, and Mode III fracture propensities in LiFePO4 particles. The elastic strain energy evolution is also discussed to explain why a layer-by-layer lithium insertion mechanism (i.e. first-order phase transformation) is energetically preferred. Another importation issue is how current
Parametric Pattern Selection in a Reaction-Diffusion Model
Stich, Michael; Ghoshal, Gourab; Pérez-Mercader, Juan
2013-01-01
We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways. PMID:24204813
Reading and a diffusion model analysis of reaction time.
Naples, Adam; Katz, Leonard; Grigorenko, Elena L
2012-01-01
Processing speed is associated with reading performance. However, the literature is not clear either on the definition of processing speed or on why and how it contributes to reading performance. In this study we demonstrated that processing speed, as measured by reaction time, is not a unitary construct. Using the diffusion model of two-choice reaction time, we assessed processing speed in a series of same-different reaction time tasks for letter and number strings. We demonstrated that the association between reaction time and reading performance is driven by processing speed for reading-related information, but not motor or sensory encoding speed.
Reading and a Diffusion Model Analysis of Reaction Time
Naples, Adam; Katz, Leonard; Grigorenko, Elena L.
2012-01-01
Processing speed is associated with reading performance. However, the literature is not clear either on the definition of processing speed or on why and how it contributes to reading performance. In this study we demonstrated that processing speed, as measured by reaction time, is not a unitary construct. Using the diffusion model of two-choice reaction time, we assessed processing speed in a series of same-different reaction time tasks for letter and number strings. We demonstrated that the association between reaction time and reading performance is driven by processing speed for reading-related information, but not motor or sensory encoding speed. PMID:22612543
A study of hydrogen diffusion flames using PDF turbulence model
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1991-01-01
The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.
A study of hydrogen diffusion flames using PDF turbulence model
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1991-01-01
The application of probability density function (pdf) turbulence models is addressed. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional computational fluid dynamic (CFD) flow solver with the Monte Carlo simulation of the pdf evolution equation was developed. The algorithm was validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames was carried out using this algorithm. Numerical results compared favorably with experimental data. The computations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.
SHIR competitive information diffusion model for online social media
NASA Astrophysics Data System (ADS)
Liu, Yun; Diao, Su-Meng; Zhu, Yi-Xiang; Liu, Qing
2016-11-01
In online social media, opinion divergences and differentiations generally exist as a result of individuals' extensive participation and personalization. In this paper, a Susceptible-Hesitated-Infected-Removed (SHIR) model is proposed to study the dynamics of competitive dual information diffusion. The proposed model extends the classical SIR model by adding hesitators as a neutralized state of dual information competition. It is both hesitators and stable spreaders that facilitate information dissemination. Researching on the impacts of diffusion parameters, it is found that the final density of stiflers increases monotonically as infection rate increases and removal rate decreases. And the advantage information with larger stable transition rate takes control of whole influence of dual information. The density of disadvantage information spreaders slightly grows with the increase of its stable transition rate, while whole spreaders of dual information and the relaxation time remain almost unchanged. Moreover, simulations imply that the final result of competition is closely related to the ratio of stable transition rates of dual information. If the stable transition rates of dual information are nearly the same, a slightly reduction of the smaller one brings out a significant disadvantage in its propagation coverage. Additionally, the relationship of the ratio of final stiflers versus the ratio of stable transition rates presents power characteristic.
A chaotic model for advertising diffusion problem with competition
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Rebilas, Krzysztof
2013-02-01
Consider a skier who goes down a takeoff ramp, attains a speed V, and jumps, attempting to land as far as possible down the hill below (Fig. 1). At the moment of takeoff the angle between the skier's velocity and the horizontal is α. What is the optimal angle α that makes the jump the longest possible for the fixed magnitude of the velocity V? Of course, in practice, this is a very sophisticated problem; the skier's range depends on a variety of complex factors in addition to V and α. However, if we ignore these and assume the jumper is in free fall between the takeoff ramp and the landing point below, the problem becomes an exercise in kinematics that is suitable for introductory-level students. The solution is presented here.
Kohfahl, Claus; Graupner, Torsten; Fetzer, Christian; Holzbecher, Ekkehard; Pekdeger, Asaf
2011-08-01
This study reports column tests and modelling results to assess the impact of hardpans and cemented layers on oxygen supply in mine waste sediments. The analysed sediment samples were obtained from a low-sulphide and low-carbonate polymetallic mine waste tailings impoundment located in the Freiberg mining district in Germany. The three samples were characterised by different degrees and types of cementation. After physical and mineralogical properties of the samples had been determined, breakthrough curves of oxygen were measured in column studies at different degrees of water saturation, and the diffusivities were assessed using a numerical modelling approach. Results demonstrate that cemented layers and hardpans in undisturbed sediments associated with fine-grained material operate as preferential pathways for diffusive gas transport during rewetting, leading to higher oxygen diffusivities compared to disturbed sediments. Under air-dry conditions, the disturbed samples show higher diffusivities than the undisturbed sample, indicating clogging of the porosity by precipitation of secondary minerals such as trivalent Fe oxyhydroxides acting as a barrier and thereby decreasing the diffusivity of the undisturbed sample. In contrast to sediments without cementation, diffusion experiments of sediments with cemented layers used in this study yield similar tortuosities in spite of their different grain size distributions, pointing to the important role of these heterogeneities for gas diffusion.
Modeling the Determinants Influencing the Diffusion of Mobile Internet
NASA Astrophysics Data System (ADS)
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.
A polarizable continuum model for molecules at spherical diffuse interfaces
NASA Astrophysics Data System (ADS)
Di Remigio, Roberto; Mozgawa, Krzysztof; Cao, Hui; Weijo, Ville; Frediani, Luca
2016-03-01
We present an extension of the Polarizable Continuum Model (PCM) to simulate solvent effects at diffuse interfaces with spherical symmetry, such as nanodroplets and micelles. We derive the form of the Green's function for a spatially varying dielectric permittivity with spherical symmetry and exploit the integral equation formalism of the PCM for general dielectric environments to recast the solvation problem into a continuum solvation framework. This allows the investigation of the solvation of ions and molecules in nonuniform dielectric environments, such as liquid droplets, micelles or membranes, while maintaining the computationally appealing characteristics of continuum solvation models. We describe in detail our implementation, both for the calculation of the Green's function and for its subsequent use in the PCM electrostatic problem. The model is then applied on a few test systems, mainly to analyze the effect of interface curvature on solvation energetics.
A polarizable continuum model for molecules at spherical diffuse interfaces.
Di Remigio, Roberto; Mozgawa, Krzysztof; Cao, Hui; Weijo, Ville; Frediani, Luca
2016-03-28
We present an extension of the Polarizable Continuum Model (PCM) to simulate solvent effects at diffuse interfaces with spherical symmetry, such as nanodroplets and micelles. We derive the form of the Green's function for a spatially varying dielectric permittivity with spherical symmetry and exploit the integral equation formalism of the PCM for general dielectric environments to recast the solvation problem into a continuum solvation framework. This allows the investigation of the solvation of ions and molecules in nonuniform dielectric environments, such as liquid droplets, micelles or membranes, while maintaining the computationally appealing characteristics of continuum solvation models. We describe in detail our implementation, both for the calculation of the Green's function and for its subsequent use in the PCM electrostatic problem. The model is then applied on a few test systems, mainly to analyze the effect of interface curvature on solvation energetics. PMID:27036423
Soot oxidation and agglomeration modeling in a microgravity diffusion flame
Ezekoye, O.A.; Zhang, Z.
1997-07-01
The global evolution of a microgravity diffusion flame is detailed. Gas species evolution is computed using a reduced finite rate chemical mechanism. Soot evolution is computed using various combinations of existing soot mechanisms. Radiative transfer is coupled to the soot and gas phase chemistry processes using a P1 spherical harmonics radiation model. The soot agglomeration model was examined to note the dependence of soot growth and oxidation processes on soot surface area predictions. For limiting cases where agglomeration was excluded from the soot evolution model, soot primary particle sizes and number concentrations were calculated, and the number of primary particles per aggregate was inferred. These computations are compared with experimental results for microgravity and nonbuoyant flame conditions.
ERIC Educational Resources Information Center
Henderson, Nancy
2010-01-01
This article profiles Jill Jayne, who was working as a registered nutritionist in the New York City public school system when she was assigned to a group of 25 urban students in an after-school program in East Harlem. In the spring of 2006, Jayne took her "Jump With Jill" show to the streets outside Central Park, collected tips in a tin pot and,…
Clustered continuous-time random walks: diffusion and relaxation consequences
Weron, Karina; Stanislavsky, Aleksander; Jurlewicz, Agnieszka; Meerschaert, Mark M.; Scheffler, Hans-Peter
2012-01-01
We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies. PMID:22792038
Data on the Velocity Slip and Temperature Jump on a Gas-Solid Interface
NASA Astrophysics Data System (ADS)
Sharipov, Felix
2011-06-01
The present review is dedicated to the velocity slip and temperature jump coefficients applied to modeling of gas flows. Such coefficients are used when a moderate gas rarefaction must be taken into account. In this case, calculations of gas flows can be performed on the basis of continuum mechanics equations applying the velocity slip and temperature jump boundary conditions. Thus, the velocity slip and temperature jump coefficients have the same importance in gas dynamics as the transport coefficients such as viscosity, thermal conductivity, and diffusion coefficients. A critical analysis of theoretical and experimental data on the slip and jump coefficients available in the open literature is presented in an accessible form so that it can be easily understandable for nonspecialists in rarefied gas dynamics. The most reliable results are selected and tabulated. The results cover a single gas with the complete and noncomplete accommodation on a solid surface, gaseous mixtures, and polyatomic gases. Many examples of applications of the slip and jump boundary conditions are given. The review will be useful as a reference for mathematicians, physicists, and engineers dealing with flows of moderately rarefied gases.
Modeling diffusion-induced stress in nanowire electrode structures
NASA Astrophysics Data System (ADS)
Deshpande, Rutooj; Cheng, Yang-Tse; Verbrugge, Mark W.
There is an intense, worldwide effort to develop durable lithium ion batteries with high energy and power densities for a wide range of applications, including electric and hybrid electric vehicles. One of the critical challenges in advancing lithium ion battery technologies is fracture and decrepitation of the electrodes as a result of lithium diffusion during charging and discharging operations. When lithium is inserted in either the positive or negative electrode, a large volume change on the order of a few to several hundred percent, can occur. Diffusion-induced stresses (DISs) can therefore cause the nucleation and growth of cracks, leading to mechanical degradation of the active electrode materials. Our work is aimed at developing a mathematical model relating surface energy with diffusion-induced stresses in nanowire electrodes. With decreasing size of the electrode, the ratio of surface area to volume increases. Thus, surface energy and surface stress can play an important role in mitigating DISs in nanostructured electrodes. In this work, we establish relationships between the surface energy, surface stress, and the magnitude of DISs in nanowires. We find that DISs, especially the tensile stresses, can decrease significantly due to the surface effects. Our model also establishes a relationship between stress and the nanowire radius. We show that, with decreasing size, the electrode material will be less prone to mechanical degradation, leading to an increase in the life of lithium ion batteries, provided other phenomena are unaffected by increased surface area (e.g., chemical degradation reactions). Also we show that, in the case of nanostructures, surface strain energy is significant in magnitude comparing with bulk strain energy. A mathematical tool to calculate total strain energy is developed that can be used to compare strain energy with the fracture energy of that material in electrode system.
Innovation Diffusion: A Deterministic Model of Space-Time Integration with Physical Analog
ERIC Educational Resources Information Center
Haynes, Kingsley E.; And Others
1977-01-01
Extends a fundamental temporal diffusion model to integrate space and time dimensions of innovation diffusion. Compares analogous developments in the physical sciences and argues that the proposed model may help link the concepts of catalysts in physical science diffusion processes to the role of change agents in social science systems. (Author/JG)
A Microscopic Multiphase Diffusion Model of Viable Epidermis Permeability
Nitsche, Johannes M.; Kasting, Gerald B.
2013-01-01
A microscopic model of passive transverse mass transport of small solutes in the viable epidermal layer of human skin is formulated on the basis of a hexagonal array of cells (i.e., keratinocytes) bounded by 4-nm-thick, anisotropic lipid bilayers and separated by 1-μm layers of extracellular fluid. Gap junctions and tight junctions with adjustable permeabilities are included to modulate the transport of solutes with low membrane permeabilities. Two keratinocyte aspect ratios are considered to represent basal and spinous cells (longer) and granular cells (more flattened). The diffusion problem is solved in a unit cell using a coordinate system conforming to the hexagonal cross section, and an efficient two-dimensional treatment is applied to describe transport in both the cell membranes and intercellular spaces, given their thinness. Results are presented in terms of an effective diffusion coefficient, D¯epi, and partition coefficient, K¯epi/w, for a homogenized representation of the microtransport problem. Representative calculations are carried out for three small solutes—water, L-glucose, and hydrocortisone—covering a wide range of membrane permeability. The effective transport parameters and their microscopic interpretation can be employed within the context of existing three-layer models of skin transport to provide more realistic estimates of the epidermal concentrations of topically applied solutes. PMID:23708370
Diffusion dynamics in the disordered Bose Hubbard model
NASA Astrophysics Data System (ADS)
Wadleigh, Laura; Russ, Philip; Demarco, Brian
2016-05-01
We explore the dynamics of diffusion for out-of-equilibrium superfluid, Mott insulator, and Bose glass states using an atomic realization of the disordered Bose Hubbard (DBH) model. Dynamics in strongly correlated systems, especially far from equilibrium, are not well understood. The introduction of disorder further complicates these systems. We realize the DBH model--which has been central to our understanding of quantum phase transitions in disordered systems--using ultracold Rubidium-87 atoms trapped in a cubic disordered optical lattice. By tightly focusing a beam into the center of the gas, we create a hole in the atomic density profile. We achieve Mott insulator, superfluid, or Bose glass states by varying the interaction and disorder strength, and measure the time evolution of the density profile after removing the central barrier. This allows us to infer diffusion rates from the velocities at the edge of the hole and to look for signatures of superfluid puddles in the Bose glass state. We acknowledge funding from NSF Grant PHY 15-05468, NSF Grant DGE-1144245, and ARO Grant W911NF-12-1-0462.
The Approximate Number System Acuity Redefined: A Diffusion Model Approach
Park, Joonkoo; Starns, Jeffrey J.
2015-01-01
While all humans are capable of non-verbally representing numerical quantity using so-called the approximate number system (ANS), there exist considerable individual differences in its acuity. For example, in a non-symbolic number comparison task, some people find it easy to discriminate brief presentations of 14 dots from 16 dots while others do not. Quantifying individual ANS acuity from such a task has become an essential practice in the field, as individual differences in such a primitive number sense is thought to provide insights into individual differences in learned symbolic math abilities. However, the dominant method of characterizing ANS acuity—computing the Weber fraction (w)—only utilizes the accuracy data while ignoring response times (RT). Here, we offer a novel approach of quantifying ANS acuity by using the diffusion model, which accounts both accuracy and RT distributions. Specifically, the drift rate in the diffusion model, which indexes the quality of the stimulus information, is used to capture the precision of the internal quantity representation. Analysis of behavioral data shows that w is contaminated by speed-accuracy tradeoff, making it problematic as a measure of ANS acuity, while drift rate provides a measure more independent from speed-accuracy criterion settings. Furthermore, drift rate is a better predictor of symbolic math ability than w, suggesting a practical utility of the measure. These findings demonstrate critical limitations of the use of w and suggest clear advantages of using drift rate as a measure of primitive numerical competence. PMID:26733929
A microscopic multiphase diffusion model of viable epidermis permeability.
Nitsche, Johannes M; Kasting, Gerald B
2013-05-21
A microscopic model of passive transverse mass transport of small solutes in the viable epidermal layer of human skin is formulated on the basis of a hexagonal array of cells (i.e., keratinocytes) bounded by 4-nm-thick, anisotropic lipid bilayers and separated by 1-μm layers of extracellular fluid. Gap junctions and tight junctions with adjustable permeabilities are included to modulate the transport of solutes with low membrane permeabilities. Two keratinocyte aspect ratios are considered to represent basal and spinous cells (longer) and granular cells (more flattened). The diffusion problem is solved in a unit cell using a coordinate system conforming to the hexagonal cross section, and an efficient two-dimensional treatment is applied to describe transport in both the cell membranes and intercellular spaces, given their thinness. Results are presented in terms of an effective diffusion coefficient, D¯(epi), and partition coefficient, K¯(epi/w), for a homogenized representation of the microtransport problem. Representative calculations are carried out for three small solutes-water, L-glucose, and hydrocortisone-covering a wide range of membrane permeability. The effective transport parameters and their microscopic interpretation can be employed within the context of existing three-layer models of skin transport to provide more realistic estimates of the epidermal concentrations of topically applied solutes.
ERIC Educational Resources Information Center
Jeffery, Rondo N.; Farhang, Amiri
2016-01-01
The classroom jumping ring demonstration is nearly always performed using alternating current (AC), in which the ring jumps or flies off the extended iron core when the switch is closed. The ring jumps higher when cooled with liquid nitrogen (LN2). We have performed experiments using DC to power the solenoid and find similarities and significant…
Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models
NASA Technical Reports Server (NTRS)
Yoder, Dennis A.
2016-01-01
In this study, several variable turbulent Prandtl number formulations are examined for boundary layers, pipe flow, and axisymmetric jets. The model formulations include simple algebraic relations between the thermal diffusivity and turbulent viscosity as well as more complex models that solve transport equations for the thermal variance and its dissipation rate. Results are compared with available data for wall heat transfer and profile measurements of mean temperature, the root-mean-square (RMS) fluctuating temperature, turbulent heat flux and turbulent Prandtl number. For wall-bounded problems, the algebraic models are found to best predict the rise in turbulent Prandtl number near the wall as well as the log-layer temperature profile, while the thermal variance models provide a good representation of the RMS temperature fluctuations. In jet flows, the algebraic models provide no benefit over a constant turbulent Prandtl number approach. Application of the thermal variance models finds that some significantly overpredict the temperature variance in the plume and most underpredict the thermal growth rate of the jet. The models yield very similar fluctuating temperature intensities in jets from straight pipes and smooth contraction nozzles, in contrast to data that indicate the latter should have noticeably higher values. For the particular low subsonic heated jet cases examined, changes in the turbulent Prandtl number had no effect on the centerline velocity decay.
Pre-Clinical Models of Diffuse Intrinsic Pontine Glioma
Misuraca, Katherine L.; Cordero, Francisco J.; Becher, Oren J.
2015-01-01
Diffuse intrinsic pontine glioma (DIPG) is a rare and incurable brain tumor that arises in the brainstem of children predominantly between the ages of 6 and 8. 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 and to potentially treat them in the clinic. This review will detail the initial strides toward 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. Finally, 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. PMID:26258075
Molecular Modeling of Diffusion on a Crystalline PETN Surface
Lin, P; Khare, R; Gee, R H; Weeks, B L
2007-07-13
Surface diffusion on a PETN crystal was investigated by treating the surface diffusion as an activated process in the formalism of transition state theory. In particular, surface diffusion on the (110) and (101) facets, as well as diffusion between these facets, were considered. We successfully obtained the potential energy barriers required for PETN surface diffusion. Our results show that the (110) surface is more thermally active than the (101) surface and PETN molecules mainly diffuses from the (110) to (101) facet. These results are in good agreement with experimental observations and previous simulations.
NASA Astrophysics Data System (ADS)
Yolcu, Cem; Memiç, Muhammet; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren
2016-05-01
We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems.
Yolcu, Cem; Memiç, Muhammet; Şimşek, Kadir; Westin, Carl-Fredrik; Özarslan, Evren
2016-05-01
We study the influence of diffusion on NMR experiments when the molecules undergo random motion under the influence of a force field and place special emphasis on parabolic (Hookean) potentials. To this end, the problem is studied using path integral methods. Explicit relationships are derived for commonly employed gradient waveforms involving pulsed and oscillating gradients. The Bloch-Torrey equation, describing the temporal evolution of magnetization, is modified by incorporating potentials. A general solution to this equation is obtained for the case of parabolic potential by adopting the multiple correlation function (MCF) formalism, which has been used in the past to quantify the effects of restricted diffusion. Both analytical and MCF results were found to be in agreement with random walk simulations. A multidimensional formulation of the problem is introduced that leads to a new characterization of diffusion anisotropy. Unlike the case of traditional methods that employ a diffusion tensor, anisotropy originates from the tensorial force constant, and bulk diffusivity is retained in the formulation. Our findings suggest that some features of the NMR signal that have traditionally been attributed to restricted diffusion are accommodated by the Hookean model. Under certain conditions, the formalism can be envisioned to provide a viable approximation to the mathematically more challenging restricted diffusion problems. PMID:27300946
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
NASA Astrophysics Data System (ADS)
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
Modeling realistic breast lesions using diffusion limited aggregation
NASA Astrophysics Data System (ADS)
Rashidnasab, Alaleh; Elangovan, Premkumar; Dance, David R.; Young, Kenneth C.; Diaz, Oliver; Wells, Kevin
2012-03-01
Synthesizing the appearance of malignant masses and inserting these into digital mammograms can be used as part of a wider framework for investigating the radiological detection task in X-ray mammography. However, the randomness associated with cell division within cancerous masses and the associated complex morphology challenges the realism of the modeling process. In this paper, Diffusion Limited Aggregation (DLA), a type of fractal growth process is proposed and utilized for modeling breast lesions. Masses of different sizes, shapes and densities were grown by controlling DLA growth parameters either prior to growth, or dynamically updating these during growth. A validation study was conducted by presenting 30 real and 30 simulated masses in a random order to a team of radiologists. The results from the validation study suggest that the observers found it difficult to differentiate between the real and simulated lesions.
On Modeling Viral Diffusion in Heterogeneous Wireless Networks
NASA Astrophysics Data System (ADS)
Nguyen, Hoai-Nam; Shinoda, Yoichi
Smart phones and computers now are able to co-work in a wireless environment where malware can propagate. Although many investigations have modeled the spread of malware, little has been done to take into account different characteristics of items to see how they affect disease diffusion in an ad hoc network. We have therefore developed a novel framework, consisting of two models, which consider diversity of objects as well as interactions between their different classes. Our framework is able to produce a huge result space thus makes it appropriate to describe many viral proliferating scenarios. Additionally, we have developed a formula to calculate the possible average number of newly infected devices in the considered system. An important contribution of our work is the comprehension of item diversity, which states that a mixture of device types causes a bigger malware spread as the number of device types in the network increases.
NASA Astrophysics Data System (ADS)
Yoshida, Masayuki; Morooka, Masami; Takahashi, Manabu; Tomokage, Hajime
2000-05-01
Based on the pair diffusion models of vacancy and interstitial (V and I) mechanisms, the V and I components of effective P diffusion coefficient, DP^+,Veff and DP^+,Ieff, and the controlling process of P diffusion in Si are obtained. Assuming that the I mechanism is dominant, not only the I- concentration, CI^-, but also its gradient, d CI^-/d λ , is effective on DP^+,Ieff at high CP^+. DP^+,Ieff is large at d CI^-/d λ <0 and small at d CI^-/d λ >0. P+ and I- are generated by the dissociation of P-I pair. When excess I- thus generated is removed, d CI^-/d λ <0 is obtained. d CI^-/d λ <0 is also obtained by the decrease in quasi self-interstitial formation energy. Several diffusion models simulate the P diffusion profile well under an inert atmosphere. Applying the controlling process to them, the reason why they simulate the P profile well is investigated. Because all of them simulate the P profile well, it is difficult to conclude which model is correct. It is suggested that it is possible to conclude which model is correct from the P profile under oxidation at CP^+s >1× 1020 cm-3 (s: surface).
The Diffusion Model Is Not a Deterministic Growth Model: Comment on Jones and Dzhafarov (2014)
Smith, Philip L.; Ratcliff, Roger; McKoon, Gail
2015-01-01
Jones and Dzhafarov (2014) claim that several current models of speeded decision making in cognitive tasks, including the diffusion model, can be viewed as special cases of other general models or model classes. The general models can be made to match any set of response time (RT) distribution and accuracy data exactly by a suitable choice of parameters and so are unfalsifiable. The implication of their claim is that models like the diffusion model are empirically testable only by artificially restricting them to exclude unfalsifiable instances of the general model. We show that Jones and Dzhafarov’s argument depends on enlarging the class of “diffusion” models to include models in which there is little or no diffusion. The unfalsifiable models are deterministic or near-deterministic growth models, from which the effects of within-trial variability have been removed or in which they are constrained to be negligible. These models attribute most or all of the variability in RT and accuracy to across-trial variability in the rate of evidence growth, which is permitted to be distributed arbitrarily and to vary freely across experimental conditions. In contrast, in the standard diffusion model, within-trial variability in evidence is the primary determinant of variability in RT. Across-trial variability, which determines the relative speed of correct responses and errors, is theoretically and empirically constrained. Jones and Dzhafarov’s attempt to include the diffusion model in a class of models that also includes deterministic growth models misrepresents and trivializes it and conveys a misleading picture of cognitive decision-making research. PMID:25347314
Drop jumping as a training method for jumping ability.
Bobbert, M F
1990-01-01
Vertical jumping ability is of importance for good performance in sports such as basketball and volleyball. Coaches are in need of exercises that consume only little time and still help to improve their players' jumping ability, without involving a high risk of injury. Drop jumping is assumed to satisfy these requirements. This assumption is supported by a review of results of training studies. However, it appears that regular jumping exercises can be just as helpful. The same holds for exercises with weights, provided the subjects have no weight-training history. In fact, for unskilled jumpers who have no weight-training history, the effects of training programmes utilising these different exercises are additive. The most effective, efficient and safe way for a coach to improve the jumping achievement of his athletes may well be to submit them first to a training programme utilising regular jumps, then to a weight-training programme and finally to a drop jump training programme. In drop jump training programmes themselves, the improvement in jumping height varies greatly among studies. This variation cannot be explained satisfactorily with the information available on subjects and training programmes. Given the current state of knowledge, coaches seem to have no other option than to strictly copy a programme which has proved to be very effective. Obviously there is a need for more systematic research of the relationship between design and effect of drop jump training programmes. The most important variable to be controlled is drop jumping technique. From a review of biomechanical studies of drop jumping, it becomes clear that jumping technique strongly affects the mechanical output of muscles. The biomechanics of 2 techniques are discussed. In the bounce drop jump the downward movement after the drop is reversed as soon as possible into an upward push-off, while in the countermovement drop jump this is done more gradually by increasing the amplitude of the
Drop jumping as a training method for jumping ability.
Bobbert, M F
1990-01-01
Vertical jumping ability is of importance for good performance in sports such as basketball and volleyball. Coaches are in need of exercises that consume only little time and still help to improve their players' jumping ability, without involving a high risk of injury. Drop jumping is assumed to satisfy these requirements. This assumption is supported by a review of results of training studies. However, it appears that regular jumping exercises can be just as helpful. The same holds for exercises with weights, provided the subjects have no weight-training history. In fact, for unskilled jumpers who have no weight-training history, the effects of training programmes utilising these different exercises are additive. The most effective, efficient and safe way for a coach to improve the jumping achievement of his athletes may well be to submit them first to a training programme utilising regular jumps, then to a weight-training programme and finally to a drop jump training programme. In drop jump training programmes themselves, the improvement in jumping height varies greatly among studies. This variation cannot be explained satisfactorily with the information available on subjects and training programmes. Given the current state of knowledge, coaches seem to have no other option than to strictly copy a programme which has proved to be very effective. Obviously there is a need for more systematic research of the relationship between design and effect of drop jump training programmes. The most important variable to be controlled is drop jumping technique. From a review of biomechanical studies of drop jumping, it becomes clear that jumping technique strongly affects the mechanical output of muscles. The biomechanics of 2 techniques are discussed. In the bounce drop jump the downward movement after the drop is reversed as soon as possible into an upward push-off, while in the countermovement drop jump this is done more gradually by increasing the amplitude of the
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
An intravoxel oriented flow model for diffusion-weighted imaging of the kidney.
Hilbert, Fabian; Bock, Maximilian; Neubauer, Henning; Veldhoen, Simon; Wech, Tobias; Bley, Thorsten Alexander; Köstler, Herbert
2016-10-01
By combining intravoxel incoherent motion (IVIM) and diffusion tensor imaging (DTI) we introduce a new diffusion model called intravoxel oriented flow (IVOF) that accounts for anisotropy of diffusion and the flow-related signal. An IVOF model using a simplified apparent flow fraction tensor (IVOFf ) is applied to diffusion-weighted imaging of human kidneys. The kidneys of 13 healthy volunteers were examined on a 3 T scanner. Diffusion-weighted images were acquired with six b values between 0 and 800 s/mm(2) and 30 diffusion directions. Diffusivity and flow fraction were calculated for different diffusion models. The Akaike information criterion was used to compare the model fit of the proposed IVOFf model to IVIM and DTI. In the majority of voxels the proposed IVOFf model with a simplified apparent flow fraction tensor performs better than IVIM and DTI. Mean diffusivity is significantly higher in DTI compared with models that account for the flow-related signal. The fractional anisotropy of diffusion is significantly reduced when flow fraction is considered to be anisotropic. Anisotropy of the apparent flow fraction tensor is significantly higher in the renal medulla than in the cortex region. The IVOFf model describes diffusion-weighted data in the human kidney more accurately than IVIM or DTI. The apparent flow fraction in the kidney proved to be anisotropic. PMID:27488570
Modelling interactions between soil evolution and diffusive surface processes
NASA Astrophysics Data System (ADS)
Kirkby, Mike; Johnson, Michelle; Gloor, Emanual
2014-05-01
Bioturbation, combined with settlement under gravity, generates profiles of bulk density, porosity and hydraulic conductivity (Ksat). Rates of bioturbation are linked to rates of diffusive downslope sediment transport (creep) and rates can be compared via the increase in OSL ages of soil aggregate grains with depth. Some primary porosity is also produced by weathering of rock to saprolite, often with little reduction in bulk density but some dilation of joints. Downward percolation of rain water near the surface is controlled by the diffusion-induced decrease in porosity and Ksat, driving lateral subsurface flow in the zone of fluctuating water table, and leaving progressively less water for downward percolation. As the depth to the weathering front is varied, progressively less water is therefore available for weathering, producing the observed decrease in weathering rate with increasing soil depth. These processes are modelled by repeatedly applying a stochastic realisation of daily rainfalls for an area until the annual hydrological cycle stabilises, providing the average partition of rainfall into its components of evapotranspiration, lateral flow and downward percolation, with depth in the soil. The average hydrology is then applied to drive evolution of the weathering profile over longer time spans.
Magnetic field diffusion modeling of a small enclosed firing system
Warne, L.K.; Merewether, K.O.
1996-01-01
Intense magnetic fields exist in the immediate vicinity of a lightning strike (and near power lines). Conducting barriers increase the rise time (and thus decrease the rise rate) interior to the barrier, but typically do not prevent penetration of the magnetic field, since the lightning current fall time may be larger than the barrier diffusion time. Thus, substantial energy is present in the interior field, although the degradation of rise rate makes it more difficult to couple into electrical circuits. This report assesses the threat posed by the diffusive magnetic field to interior components and wire loops (where voltages are induced). Analytical and numerical bounding analyses are carried out on a pill box shaped conducting barrier to develop estimates for the worst case magnetic field threats inside the system. Worst case induced voltages and energies are estimated and compared with threshold charge voltages and energies on the output capacitor of the system. Variability of these quantities with respect to design parameters are indicated. The interior magnetic field and induced voltage estimates given in this report can be used as excitations for more detailed interior and component models.
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S A; Kugeiko, M M; Firago, V A; Sobchuk, A N
2014-01-31
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)
Analytical model of diffuse reflectance spectrum of skin tissue
NASA Astrophysics Data System (ADS)
Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.
2014-01-01
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.
Postural control model interpretation of stabilogram diffusion analysis
NASA Technical Reports Server (NTRS)
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.
BF{sub 3} PIII modeling: Implantation, amorphisation and diffusion
Essa, Z.; Cristiano, F.; Spiegel, Y.; Boulenc, P.; Qiu, Y.; Quillec, M.; Taleb, N.; Burenkov, A.; Hackenberg, M.; Bedel-Pereira, E.; Mortet, V.; Torregrosa, Frank; Tavernier, C.
2012-11-06
In the race for highly doped ultra-shallow junctions (USJs) in complementary metal oxide semi-conductor (CMOS) technologies, plasma immersion ion implantation (PIII) is a promising alternative to traditional beamline implantation. Currently, no commercial technology computer aided design (TCAD) process simulator allows modeling the complete USJ fabrication process by PIII, including as-implanted dopant profiles, damage formation, dopant diffusion and activation. In this work, a full simulation of a p-type BF{sub 3} PIII USJ has been carried out. In order to investigate the various physical phenomena mentioned above, process conditions included a high energy/high dose case (10 kV, 5 Multiplication-Sign 10{sup 15} cm{sup -2}), specifically designed to increase damage formation, as well as more technology relevant implant conditions (0.5 kV) for comparison. All implanted samples were annealed at different temperatures and times. As implanted profiles for both boron and fluorine in BF{sub 3} implants were modeled and compared to Secondary Ion Mass Spectrometry (SIMS) measurements. Amorphous/crystalline (a/c) interface depths were measured by transmission electron microscopy (TEM) and successfully simulated. Diffused profiles simulations agreed with SIMS data at low thermal budgets. A boron peak behind the a/c interface was observed in all annealed SIMS profiles for the 10 kV case, indicating boron trapping from EOR defects in this region even after high thermal budgets. TEM measurements on the annealed samples showed an end of range (EOR) defects survival behind the a/c interface, including large dislocation loops (DLs) lying on (001) plane parallel to the surface. In the last part of this work, activation simulations were compared to Hall measurements and confirmed the need to develop a (001) large BICs model.
A seed-diffusion model for tropical tree diversity patterns
NASA Astrophysics Data System (ADS)
Derzsi, A.; Néda, Z.
2012-10-01
Diversity patterns of tree species in a tropical forest community are approached by a simple lattice model and investigated by Monte Carlo simulations using a backtracking method. Our spatially explicit neutral model is based on a simple statistical physics process, namely the diffusion of seeds. The model has three parameters: the speciation rate, the size of the meta-community in which the studied tree-community is embedded, and the average surviving time of the seeds. By extensive computer simulations we aim towards the reproduction of relevant statistical measures derived from the experimental data of the Barro Colorado Island tree census in 1995. The first two parameters of the model are fixed to known values, characteristic of the studied community, thus obtaining a model with only one freely adjustable parameter. As a result of this, the average number of species in the considered territory, the relative species abundance distribution, the species-area relationship and the spatial auto-correlation function of the individuals in abundant species are simultaneously fitted with only one parameter which is the average surviving time of the seeds.
Reactor-Diffusion Models For Cartilage Pattern Formation
NASA Astrophysics Data System (ADS)
Glimm, Tilmann; Hentschel, H. G. E.
2004-03-01
In the early stages of the development of the embryonic chick limb, the sites of future skeletal elements are marked by a prepattern formed by condensations of precartilage cells. A number of different theories have been proposed as to what mechanism determines the characteristic size, shape and number of these condensations. Nevertheless, there is still little definite knowledge on this question. In this talk, we present a model of the limb based on recent experiments and additional hypotheses. In this model, it is a ``reactor-diffusion'' mechanism which gives rise to precartilage condensation. The model consists of a system of nonlinear partial differential equations which govern the spatiotemporal distribution of various types of mesenchymal cells and relevant biomolecules. These biomolecules include Fibroblast growth factors (FGFs), transforming growth factor-betas (TGF-βs), the extracellular matrix protein Fibronectin, as well as a laterally-acting inhibitor. We present the results of numerical simulations for the system of PDEs. Also addressed are preliminary results on how this PDE model can be tied in with more biologically realistic cellular automata based models.
A reaction-diffusion model of human brain development.
Lefèvre, Julien; Mangin, Jean-François
2010-04-01
Cortical folding exhibits both reproducibility and variability in the geometry and topology of its patterns. These two properties are obviously the result of the brain development that goes through local cellular and molecular interactions which have important consequences on the global shape of the cortex. Hypotheses to explain the convoluted aspect of the brain are still intensively debated and do not focus necessarily on the variability of folds. Here we propose a phenomenological model based on reaction-diffusion mechanisms involving Turing morphogens that are responsible for the differential growth of two types of areas, sulci (bottom of folds) and gyri (top of folds). We use a finite element approach of our model that is able to compute the evolution of morphogens on any kind of surface and to deform it through an iterative process. Our model mimics the progressive folding of the cortical surface along foetal development. Moreover it reveals patterns of reproducibility when we look at several realizations of the model from a noisy initial condition. However this reproducibility must be tempered by the fact that a same fold engendered by the model can have different topological properties, in one or several parts. These two results on the reproducibility and variability of the model echo the sulcal roots theory that postulates the existence of anatomical entities around which the folding organizes itself. These sulcal roots would correspond to initial conditions in our model. Last but not least, the parameters of our model are able to produce different kinds of patterns that can be linked to developmental pathologies such as polymicrogyria and lissencephaly. The main significance of our model is that it proposes a first approach to the issue of reproducibility and variability of the cortical folding. PMID:20421989
Hall, Matt G; Bongers, Andre; Sved, Paul; Watson, Geoffrey; Bourne, Roger M
2015-04-01
Non-Gaussian diffusion dynamics was investigated in the two distinct water populations identified by a biexponential model of diffusion in prostate tissue. Diffusion-weighted MRI (DWI) signal attenuation was measured ex vivo in two formalin-fixed prostates at 9.4 T with diffusion times Δ = 10, 20 and 40 ms, and b values in the range 0.017-8.2 ms/µm(2) . A conventional biexponential model was compared with models in which either the lower diffusivity component or both of the components of the biexponential were stretched. Models were compared using Akaike's Information Criterion (AIC) and a leave-one-out (LOO) test of model prediction accuracy. The doubly stretched (SS) model had the highest LOO prediction accuracy and lowest AIC (highest information content) in the majority of voxels at Δ = 10 and 20 ms. The lower diffusivity stretching factor (α2 ) of the SS model was consistently lower (range ~0.3-0.9) than the higher diffusivity stretching factor (α1 , range ~0.7-1.1), indicating a high degree of diffusion heterogeneity in the lower diffusivity environment, and nearly Gaussian diffusion in the higher diffusivity environment. Stretched biexponential models demonstrate that, in prostate tissue, the two distinct water populations identified by the simple biexponential model individually exhibit non-Gaussian diffusion dynamics.
The small ice cap instability in diffusive climate models
NASA Technical Reports Server (NTRS)
North, G. R.
1984-01-01
Simple climate models which invoke diffusive heat transport and ice cap albedo feedback have equilibrium solutions with no stable ice cap smaller than a radius of about 20 deg on a great circle. Attention is presently given to a solution of this phenomenon which is physically appealing. The ice-free solution has a thermal minimum, and if the minimum temperature is just above the critical value for ice formation, then the artificial addition of a patch of ice leads to a widespread depression of the temperature below the critical freezing temperature. A second stable solution will then exist whose spatial extent is determined by the range of the influence function of a point sink of heat, due to the albedo shift in the patch.
Energy efficient engine diffuser/combustor model technology
NASA Technical Reports Server (NTRS)
Gardner, W.
1980-01-01
A full scale, full annular diffuser/combustor model test rig was tested to investigate how configurational changes affect pressure loss and flow separation characteristics. The rig was characterized by five major modules: inlet; prediffuser; strut; simulated combustor; and full combustor. The prediffuser featured a short, curved wall dump design. Performance goals included: (1) a separation-free prediffuser flow field; (2) total pressure loss limited to 3.0 percent in the prediffuser and shrouds; and (3) an overall section pressure loss of 5.5 percent P sub T3 at the design airflow distribution. The results indicated that the prediffuser configurations operate well within the program goals for pressure loss and demonstrate separation free operation over a wide range of inlet conditions.
Exploring Lightning Jump Characteristics
NASA Technical Reports Server (NTRS)
Chronis, Themis; Carey, Larry D.; Schultz, Christopher J.; Schultz, Elise; Calhoun, Kristin; Goodman, Steven J.
2014-01-01
This study is concerned with the characteristics of storms exhibiting an abrupt temporal increase in the total lightning flash rate (i.e., lightning jump, LJ). An automated storm tracking method is used to identify storm "clusters" and total lightning activity from three different lightning detection systems over Oklahoma, northern Alabama and Washington, D.C. On average and for different employed thresholds, the clusters that encompass at least one LJ (LJ1) last longer, relate to higher Maximum Expected Size of Hail, Vertical Integrated Liquid and lightning flash rates (area-normalized) than the clusters that did not exhibit any LJ (LJ0). The respective mean values for LJ1 (LJ0) clusters are 80 min (35 min), 14 mm (8 mm), 25 kg per square meter (18 kg per square meter) and 0.05 flash per min per square kilometer (0.01 flash per min per square kilometer). Furthermore, the LJ1 clusters are also characterized by slower decaying autocorrelation functions, a result that implies a less "random" behavior in the temporal flash rate evolution. In addition, the temporal occurrence of the last LJ provides an estimate of the time remaining to the storm's dissipation. Depending of the LJ strength (i.e., varying thresholds), these values typically range between 20-60 min, with stronger jumps indicating more time until storm decay. This study's results support the hypothesis that the LJ is a proxy for the storm's kinematic and microphysical state rather than a coincidental value.
NASA Astrophysics Data System (ADS)
Ferry, D. K.
2014-09-01
Generally, one thinks of a “quantum jump” as the process in which an electron “jumps” between a pair of quantum states, even as the process is treated within perturbation theory. This jump of an electron has remained a key point of conservative (i.e., traditional) quantum mechanics. But, the question of the time dependence of such a transition, e.g. the time for an atom to be ionized by radiation, is somewhat different than this view. A detailed approach in which an incoming wave first polarizes the quantum states and then completes the transition has allowed for a detailed discussion of the smooth transition of the electron from one state to the next. Here, we will discuss the history of the process, and illustrate the approach with the question of “how long does it take for an electron to emit a phonon?” The entire process arises from the proper application of wave mechanics and obviates the need to even consider a discussion of quantum jumps.
Stochastic fire-diffuse-fire model with realistic cluster dynamics
NASA Astrophysics Data System (ADS)
Calabrese, Ana; Fraiman, Daniel; Zysman, Daniel; Ponce Dawson, Silvina
2010-09-01
Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R ’s that replicates the experimental observations reported in [D. Fraiman , Biophys. J. 90, 3897 (2006)10.1529/biophysj.105.075911]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.
A reaction-diffusion model of cytosolic hydrogen peroxide.
Lim, Joseph B; Langford, Troy F; Huang, Beijing K; Deen, William M; Sikes, Hadley D
2016-01-01
As a signaling molecule in mammalian cells, hydrogen peroxide (H2O2) determines the thiol/disulfide oxidation state of several key proteins in the cytosol. Localization is a key concept in redox signaling; the concentrations of signaling molecules within the cell are expected to vary in time and in space in manner that is essential for function. However, as a simplification, all theoretical studies of intracellular hydrogen peroxide and many experimental studies to date have treated the cytosol as a well-mixed compartment. In this work, we incorporate our previously reported reduced kinetic model of the network of reactions that metabolize hydrogen peroxide in the cytosol into a model that explicitly treats diffusion along with reaction. We modeled a bolus addition experiment, solved the model analytically, and used the resulting equations to quantify the spatiotemporal variations in intracellular H2O2 that result from this kind of perturbation to the extracellular H2O2 concentration. We predict that micromolar bolus additions of H2O2 to suspensions of HeLa cells (0.8 × 10(9)cells/l) result in increases in the intracellular concentration that are localized near the membrane. These findings challenge the assumption that intracellular concentrations of H2O2 are increased uniformly throughout the cell during bolus addition experiments and provide a theoretical basis for differing phenotypic responses of cells to intracellular versus extracellular perturbations to H2O2 levels.
The Defect Diffusion Model of Glass-Forming Liquids
NASA Astrophysics Data System (ADS)
Fontanella, John; Bendler, John; Wintersgill, Mary; Shlesinger, Michael
2013-03-01
The defect diffusion model (DDM) provides an explanation of many properties of glass-forming liquids. For example, it has been used to interpret dielectric relaxation (alpha and beta relaxations and the boson peak), viscosity, ionic conductivity, (including the effects of temperature and pressure) positron annihilation lifetime spectroscopy data, the physical basis of fragility, scaling, the ratio of the apparent isochoric activation energy to the isobaric activation enthalpy and its relationship to monomer volume, and correlation lengths. In the model, the glass transition, Tg, occurs because of rigidity percolation. In addition the transition at TB (or TLL) is associated with mobility percolation. In the simplest form of the DDM, a supercooled liquid contains mobile single defects (MSDs) and immobile, clustered single defects (ICSDs). Consequently, dynamic heterogeneity is a natural feature of the model. If the glass transition did not intervene, all MSDs would disappear at a critical temperature Tc. In the present talk, the model will be used to comment on the change of heat capacity, thermal expansion coefficient and compressibility at Tg. Work supported in part by the Office of Naval Research
A diffuse interface model of grain boundary faceting
NASA Astrophysics Data System (ADS)
Abdeljawad, F.; Medlin, D. L.; Zimmerman, J. A.; Hattar, K.; Foiles, S. M.
2016-06-01
Interfaces, free or internal, greatly influence the physical properties and stability of materials microstructures. Of particular interest are the processes that occur due to anisotropic interfacial properties. In the case of grain boundaries (GBs) in metals, several experimental observations revealed that an initially flat GB may facet into hill-and-valley structures with well defined planes and corners/edges connecting them. Herein, we present a diffuse interface model that is capable of accounting for strongly anisotropic GB properties and capturing the formation of hill-and-valley morphologies. The hallmark of our approach is the ability to independently examine the various factors affecting GB faceting and subsequent facet coarsening. More specifically, our formulation incorporates higher order expansions to account for the excess energy due to facet junctions and their non-local interactions. As a demonstration of the modeling capability, we consider the Σ5 <001 > tilt GB in body-centered-cubic iron, where faceting along the {210} and {310} planes was experimentally observed. Atomistic calculations were utilized to determine the inclination-dependent GB energy, which was then used as an input in our model. Linear stability analysis and simulation results highlight the role of junction energy and associated non-local interactions on the resulting facet length scales. Broadly speaking, our modeling approach provides a general framework to examine the microstructural stability of polycrystalline systems with highly anisotropic GBs.
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. PMID:26172648
Multiple-to-dominant path collapse of linked-flux model for diffusion-limited nucleation
NASA Astrophysics Data System (ADS)
Lau, Y. H.; Wu, D. T.
2013-01-01
While capable of estimating diffusion-limited nucleation rates, Kelton's linked-flux model has no simple solution. To increase the model's usability, we simplify the model by retaining only the dominant nucleation path to obtain a series solution. The solution agrees well with the Kelton's model's predictions of the nucleation rate, and thus provides a simple estimate of diffusion-limited nucleation rates.
Modelling thermal radiation in buoyant turbulent diffusion flames
NASA Astrophysics Data System (ADS)
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.
NASA/MSFC multilayer diffusion models and computer programs, version 5
NASA Technical Reports Server (NTRS)
Dumbauld, R. K.; Bjorklund, J. R.
1975-01-01
The transport and diffusion models and algorithms developed for use by NASA in predicting concentrations and dosages downwind from normal and abnormal launches of rocket vehicles are described along with the associated computer programs for use in performing the calculations. Topics discussed include: the mathematical specifications and procedures used in the Preprocessor Program to calculate rocket exhaust cloud rise, cloud dimensions, and other input parameters to the transport and diffusion models; the revised mathematical specifications for the Multilayer Diffusion Models; users' instructions for implementing the Preprocessor and Multilayer Diffusion Models Programs; and worked example problems illustrating the use of the models and computer programs.
Protein folding dynamics: the diffusion-collision model and experimental data.
Karplus, M.; Weaver, D. L.
1994-01-01
The diffusion-collision model of protein folding is assessed. A description is given of the qualitative aspects and quantitative results of the diffusion-collision model and their relation to available experimental data. We consider alternative mechanisms for folding and point out their relationship to the diffusion-collision model. We show that the diffusion-collision model is supported by a growing body of experimental and theoretical evidence, and we outline future directions for developing the model and its applications. PMID:8003983
Photodynamic therapy: computer modeling of diffusion and reaction phenomena
NASA Astrophysics Data System (ADS)
Hampton, James A.; Mahama, Patricia A.; Fournier, Ronald L.; Henning, Jeffery P.
1996-04-01
We have developed a transient, one-dimensional mathematical model for the reaction and diffusion phenomena that occurs during photodynamic therapy (PDT). This model is referred to as the PDTmodem program. The model is solved by the Crank-Nicholson finite difference technique and can be used to predict the fates of important molecular species within the intercapillary tissue undergoing PDT. The following factors govern molecular oxygen consumption and singlet oxygen generation within a tumor: (1) photosensitizer concentration; (2) fluence rate; and (3) intercapillary spacing. In an effort to maximize direct tumor cell killing, the model allows educated decisions to be made to insure the uniform generation and exposure of singlet oxygen to tumor cells across the intercapillary space. Based on predictions made by the model, we have determined that the singlet oxygen concentration profile within the intercapillary space is controlled by the product of the drug concentration, and light fluence rate. The model predicts that at high levels of this product, within seconds singlet oxygen generation is limited to a small core of cells immediately surrounding the capillary. The remainder of the tumor tissue in the intercapillary space is anoxic and protected from the generation and toxic effects of singlet oxygen. However, at lower values of this product, the PDT-induced anoxic regions are not observed. An important finding is that an optimal value of this product can be defined that maintains the singlet oxygen concentration throughout the intercapillary space at a near constant level. Direct tumor cell killing is therefore postulated to depend on the singlet oxygen exposure, defined as the product of the uniform singlet oxygen concentration and the time of exposure, and not on the total light dose.
Collective Diffusion Model for Ion Conduction through Microscopic Channels
Liu, Yingting; Zhu, Fangqiang
2013-01-01
Ion conduction through microscopic channels is of central importance in both biology and nanotechnology. To better understand the current-voltage (I-V) dependence of ion channels, here we describe and prove a collective diffusion model that quantitatively relates the spontaneous ion permeation at equilibrium to the stationary ionic fluxes driven by small voltages. The model makes it possible to determine the channel conductance in the linear I-V range from equilibrium simulations without the application of a voltage. To validate the theory, we perform molecular-dynamics simulations on two channels—a conical-shaped nanopore and the transmembrane pore of an α-hemolysin—under both equilibrium and nonequilibrium conditions. The simulations reveal substantial couplings between the motions of cations and anions, which are effectively captured by the collective coordinate in the model. Although the two channels exhibit very different linear ranges in the I-V curves, in both cases the channel conductance at small voltages is in reasonable agreement with the prediction from the equilibrium simulation. The simulations also suggest that channel charges, rather than geometric asymmetry, play a more prominent role in current rectification. PMID:23442858
Reaction–diffusion model of hair-bundle morphogenesis
Jacobo, Adrian; Hudspeth, A. J.
2014-01-01
The hair bundle, an apical specialization of the hair cell composed of several rows of regularly organized stereocilia and a kinocilium, is essential for mechanotransduction in the ear. Its precise organization allows the hair bundle to convert mechanical stimuli to electrical signals; mutations that alter the bundle’s morphology often cause deafness. However, little is known about the proteins involved in the process of morphogenesis and how the structure of the bundle arises through interactions between these molecules. We present a mathematical model based on simple reaction–diffusion mechanisms that can reproduce the shape and organization of the hair bundle. This model suggests that the boundary of the cell and the kinocilium act as signaling centers that establish the bundle’s shape. The interaction of two proteins forms a hexagonal Turing pattern—a periodic modulation of the concentrations of the morphogens, sustained by local activation and long-range inhibition of the reactants—that sets a blueprint for the location of the stereocilia. Finally we use this model to predict how different alterations to the system might impact the shape and organization of the hair bundle. PMID:25313064
Jump into a New Fold—A Homology Based Model for the ABCG2/BCRP Multidrug Transporter
László, Laura; Sarkadi, Balázs
2016-01-01
ABCG2/BCRP is a membrane protein, involved in xenobiotic and endobiotic transport in key pharmacological barriers and drug metabolizing organs, in the protection of stem cells, and in multidrug resistance of cancer. Pharmacogenetic studies implicated the role of ABCG2 in response to widely used medicines and anticancer agents, as well as in gout. Its Q141K variant exhibits decreased functional expression thus increased drug accumulation and decreased urate secretion. Still, there has been no reliable molecular model available for this protein, as the published structures of other ABC transporters could not be properly fitted to the ABCG2 topology and experimental data. The recently published high resolution structure of a close homologue, the ABCG5-ABCG8 heterodimer, revealed a new ABC transporter fold, unique for ABCG proteins. Here we present a structural model of the ABCG2 homodimer based on this fold and detail the experimental results supporting this model. In order to describe the effect of mutations on structure and dynamics, and characterize substrate recognition and cholesterol regulation we performed molecular dynamics simulations using full length ABCG2 protein embedded in a membrane bilayer and in silico docking simulations. Our results show that in the Q141K variant the introduced positive charge diminishes the interaction between the nucleotide binding and transmembrane domains and the R482G variation alters the orientation of transmembrane helices. Moreover, the R482 position, which plays a role the substrate specificity of the transporter, is located in one of the substrate binding pockets identified by the in silico docking calculations. In summary, the ABCG2 model and in silico simulations presented here may have significant impact on understanding drug distribution and toxicity, as well as drug development against cancer chemotherapy resistance or gout. PMID:27741279
Vivot, Alexandre; Power, Melinda C; Glymour, M Maria; Mayeda, Elizabeth R; Benitez, Andreana; Spiro, Avron; Manly, Jennifer J; Proust-Lima, Cécile; Dufouil, Carole; Gross, Alden L
2016-02-15
Improvements in cognitive test scores upon repeated assessment due to practice effects (PEs) are well documented, but there is no empirical evidence on whether alternative specifications of PEs result in different estimated associations between exposure and rate of cognitive change. If alternative PE specifications produce different estimates of association between an exposure and rate of cognitive change, this would be a challenge for nearly all longitudinal research on determinants of cognitive aging. Using data from 3 cohort studies-the Three-City Study-Dijon (Dijon, France, 1999-2010), the Normative Aging Study (Greater Boston, Massachusetts, 1993-2007), and the Washington Heights-Inwood Community Aging Project (New York, New York, 1999-2012)-for 2 exposures (diabetes and depression) and 3 cognitive outcomes, we compared results from longitudinal models using alternative PE specifications: no PEs; use of an indicator for the first cognitive visit; number of prior testing occasions; and square root of the number of prior testing occasions. Alternative specifications led to large differences in the estimated rates of cognitive change but minimal differences in estimated associations of exposure with cognitive level or change. Based on model fit, using an indicator for the first visit was often (but not always) the preferred model. PE specification can lead to substantial differences in estimated rates of cognitive change, but in these diverse examples and study samples it did not substantively affect estimated associations of risk factors with change.
NASA Astrophysics Data System (ADS)
Stachelhaus, Scott L.; Moran, S. Bradley
2012-03-01
A series of 223Ra (t1/2 = 11.4 d) and 224Ra (t1/2 = 3.66 d) measurements made in the Mid-Atlantic Bight yield eddy diffusivity (K) estimates of 1.2 ± 0.3 × 102 m2 s-1 and 1.4 ± 0.2 × 102 m2 s-1, respectively. These results fall in line with previous studies from multiple locations throughout the ocean, in which 224Ra-based eddy diffusivities invariably exceed those determined using 223Ra. Such a pattern conflicts with the Fickian model for eddy diffusivity, in which K is constant. Moreover, this trend runs counter to the length scale-dependent view of eddy diffusion, which suggests that K values estimated using 223Ra should exceed those of 224Ra, because the length scale of the former is greater than that of the latter. A finite mixing-length model based on the concept of differential diffusion is used to provide an explanation for this discrepancy.
Distributed-order diffusion equations and multifractality: Models and solutions
NASA Astrophysics Data System (ADS)
Sandev, Trifce; Chechkin, Aleksei V.; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M.; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Distributed-order diffusion equations and multifractality: Models and solutions.
Sandev, Trifce; Chechkin, Aleksei V; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided. PMID:26565178
A locust-inspired miniature jumping robot.
Zaitsev, Valentin; Gvirsman, Omer; Ben Hanan, Uri; Weiss, Avi; Ayali, Amir; Kosa, Gabor
2015-12-01
Unmanned ground vehicles are mostly wheeled, tracked, or legged. These locomotion mechanisms have a limited ability to traverse rough terrain and obstacles that are higher than the robot's center of mass. In order to improve the mobility of small robots it is necessary to expand the variety of their motion gaits. Jumping is one of nature's solutions to the challenge of mobility in difficult terrain. The desert locust is the model for the presented bio-inspired design of a jumping mechanism for a small mobile robot. The basic mechanism is similar to that of the semilunar process in the hind legs of the locust, and is based on the cocking of a torsional spring by wrapping a tendon-like wire around the shaft of a miniature motor. In this study we present the jumping mechanism design, and the manufacturing and performance analysis of two demonstrator prototypes. The most advanced jumping robot demonstrator is power autonomous, weighs 23 gr, and is capable of jumping to a height of 3.35 m, covering a distance of 1.37 m. PMID:26602094
A locust-inspired miniature jumping robot.
Zaitsev, Valentin; Gvirsman, Omer; Ben Hanan, Uri; Weiss, Avi; Ayali, Amir; Kosa, Gabor
2015-11-25
Unmanned ground vehicles are mostly wheeled, tracked, or legged. These locomotion mechanisms have a limited ability to traverse rough terrain and obstacles that are higher than the robot's center of mass. In order to improve the mobility of small robots it is necessary to expand the variety of their motion gaits. Jumping is one of nature's solutions to the challenge of mobility in difficult terrain. The desert locust is the model for the presented bio-inspired design of a jumping mechanism for a small mobile robot. The basic mechanism is similar to that of the semilunar process in the hind legs of the locust, and is based on the cocking of a torsional spring by wrapping a tendon-like wire around the shaft of a miniature motor. In this study we present the jumping mechanism design, and the manufacturing and performance analysis of two demonstrator prototypes. The most advanced jumping robot demonstrator is power autonomous, weighs 23 gr, and is capable of jumping to a height of 3.35 m, covering a distance of 1.37 m.
Diffusion Models of the Flanker Task: Discrete versus Gradual Attentional Selection
ERIC Educational Resources Information Center
White, Corey N.; Ratcliff, Roger; Starns, Jeffrey J.
2011-01-01
The present study tested diffusion models of processing in the flanker task, in which participants identify a target that is flanked by items that indicate the same (congruent) or opposite response (incongruent). Single- and dual-process flanker models were implemented in a diffusion-model framework and tested against data from experiments that…
Applicability of an Adoption-Diffusion Model to Resource Conservation: A Supporting View.
ERIC Educational Resources Information Center
Nowak, Peter J.
At issue is the extent to which one can employ an adoption and diffusion of innovations model(s) to explain and predict the use of soil and water conservation practices. Much, however, can be gained from using models in this area. Four dimensions that should be present in any research design if it is to account for adoption and diffusion of…
A diffuse interface model of grain boundary faceting
NASA Astrophysics Data System (ADS)
Abdeljawad, Fadi; Medlin, Douglas; Zimmerman, Jonathan; Hattar, Khalid; Foiles, Stephen
Incorporating anisotropy into thermodynamic treatments of interfaces dates back to over a century ago. For a given orientation of two abutting grains in a pure metal, depressions in the grain boundary (GB) energy may exist as a function of GB inclination, defined by the plane normal. Therefore, an initially flat GB may facet resulting in a hill-and-valley structure. Herein, we present a diffuse interface model of GB faceting that is capable of capturing anisotropic GB energies and mobilities, and accounting for the excess energy due to facet junctions and their non-local interactions. The hallmark of our approach is the ability to independently examine the role of each of the interface properties on the faceting behavior. As a demonstration, we consider the Σ 5 < 001 > tilt GB in iron, where faceting along the { 310 } and { 210 } planes was experimentally observed. Linear stability analysis and numerical examples highlight the role of junction energy and associated non-local interactions on the resulting facet length scales. On the whole, our modeling approach provides a general framework to examine the spatio-temporal evolution of highly anisotropic GBs in polycrystalline metals. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
Antideuteron fluxes from dark matter annihilation in diffusion models
Donato, F.; Fornengo, N.; Maurin, D.
2008-08-15
Antideuterons are among the most promising galactic cosmic-ray-related targets for dark matter indirect detection. Currently only upper limits exist on the flux, but the development of new experiments, such as GAPS and AMS-02, provides exciting perspectives for a positive measurement in the near future. In this paper, we present a novel and updated calculation of both the secondary and primary d fluxes. We employ a two-zone diffusion model which successfully reproduces cosmic-ray nuclear data and the observed antiproton flux. We review the nuclear and astrophysical uncertainties and provide an up to date secondary (i.e. background) antideuteron flux. The primary (i.e. signal) contribution is calculated for generic weakly interactive massive particles (WIMPs) annihilating in the galactic halo: we explicitly consider and quantify the various sources of uncertainty in the theoretical evaluations. Propagation uncertainties, as is the case of antiprotons, are sizeable. Nevertheless, antideuterons offer an exciting target for indirect dark matter detection for low and intermediate mass WIMP dark matter. We then show the reaching capabilities of the future experiments for neutralino dark matter in a variety of supersymmetric models.
Perceptual decision making: drift-diffusion model is equivalent to a Bayesian model
Bitzer, Sebastian; Park, Hame; Blankenburg, Felix; Kiebel, Stefan J.
2014-01-01
Behavioral data obtained with perceptual decision making experiments are typically analyzed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence toward a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses. PMID:24616689
Subgrid models for mass and thermal diffusion in turbulent mixing
Sharp, David H; Lim, Hyunkyung; Li, Xiao - Lin; Gilmm, James G
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 resolving the
Model Complexity in Diffusion Modeling: Benefits of Making the Model More Parsimonious
Lerche, Veronika; Voss, Andreas
2016-01-01
The diffusion model (Ratcliff, 1978) takes into account the reaction time distributions of both correct and erroneous responses from binary decision tasks. This high degree of information usage allows the estimation of different parameters mapping cognitive components such as speed of information accumulation or decision bias. For three of the four main parameters (drift rate, starting point, and non-decision time) trial-to-trial variability is allowed. We investigated the influence of these variability parameters both drawing on simulation studies and on data from an empirical test-retest study using different optimization criteria and different trial numbers. Our results suggest that less complex models (fixing intertrial variabilities of the drift rate and the starting point at zero) can improve the estimation of the psychologically most interesting parameters (drift rate, threshold separation, starting point, and non-decision time). PMID:27679585
Model Complexity in Diffusion Modeling: Benefits of Making the Model More Parsimonious.
Lerche, Veronika; Voss, Andreas
2016-01-01
The diffusion model (Ratcliff, 1978) takes into account the reaction time distributions of both correct and erroneous responses from binary decision tasks. This high degree of information usage allows the estimation of different parameters mapping cognitive components such as speed of information accumulation or decision bias. For three of the four main parameters (drift rate, starting point, and non-decision time) trial-to-trial variability is allowed. We investigated the influence of these variability parameters both drawing on simulation studies and on data from an empirical test-retest study using different optimization criteria and different trial numbers. Our results suggest that less complex models (fixing intertrial variabilities of the drift rate and the starting point at zero) can improve the estimation of the psychologically most interesting parameters (drift rate, threshold separation, starting point, and non-decision time). PMID:27679585
Model Complexity in Diffusion Modeling: Benefits of Making the Model More Parsimonious
Lerche, Veronika; Voss, Andreas
2016-01-01
The diffusion model (Ratcliff, 1978) takes into account the reaction time distributions of both correct and erroneous responses from binary decision tasks. This high degree of information usage allows the estimation of different parameters mapping cognitive components such as speed of information accumulation or decision bias. For three of the four main parameters (drift rate, starting point, and non-decision time) trial-to-trial variability is allowed. We investigated the influence of these variability parameters both drawing on simulation studies and on data from an empirical test-retest study using different optimization criteria and different trial numbers. Our results suggest that less complex models (fixing intertrial variabilities of the drift rate and the starting point at zero) can improve the estimation of the psychologically most interesting parameters (drift rate, threshold separation, starting point, and non-decision time).
Farr, W M; Mandel, I; Stevens, D
2015-06-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient 'global' proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580
Farr, W M; Mandel, I; Stevens, D
2015-06-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient 'global' proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently.
Farr, W. M.; Mandel, I.; Stevens, D.
2015-01-01
Selection among alternative theoretical models given an observed dataset is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing Bayesian model selection, but it suffers from a fundamental difficulty and it requires jumps between model parameter spaces, but cannot efficiently explore both parameter spaces at once. Thus, a naive jump between parameter spaces is unlikely to be accepted in the Markov chain Monte Carlo (MCMC) algorithm and convergence is correspondingly slow. Here, we demonstrate an interpolation technique that uses samples from single-model MCMCs to propose intermodel jumps from an approximation to the single-model posterior of the target parameter space. The interpolation technique, based on a kD-tree data structure, is adaptive and efficient in modest dimensionality. We show that our technique leads to improved convergence over naive jumps in an RJMCMC, and compare it to other proposals in the literature to improve the convergence of RJMCMCs. We also demonstrate the use of the same interpolation technique as a way to construct efficient ‘global’ proposal distributions for single-model MCMCs without prior knowledge of the structure of the posterior distribution, and discuss improvements that permit the method to be used in higher dimensional spaces efficiently. PMID:26543580
Monte Carlo Modeling of Diffuse Scattering from Single Crystals: The Program ZMC
Goossens, D.J.; Heerdegen, A.P.; Chan, E.J.; Welberry, T.R.
2012-04-30
Diffuse scattering probes the local ordering in a crystal, whereas Bragg peaks are descriptive of the average long-range ordering. The population of local configurations can be explored by modeling the three-dimensional distribution of diffuse scattering. Local configurations are not constrained by the average crystallographic symmetry, so one way of modeling diffuse scattering is by modeling a disordered (short-range-ordered) structure and then calculating its diffuse scattering. The structure must contain enough unit cells to give a statistically valid model of the populations of local configurations, and so requirements for a program to model this ordering are very different from programs that model average crystal structures (used to fit the Bragg diffraction). ZMC is a program that has been developed to model diffuse scattering, particularly from molecular crystals. The strategies used to tackle the problem and the way in which they are implemented will be discussed.
NASA Astrophysics Data System (ADS)
Verdecchia, K.; Diop, M.; St. Lawrence, K.
2015-03-01
Diffuse correlation spectroscopy (DCS) is a non-invasive optical technique capable of monitoring tissue perfusion changes, particularly in the brain. The normalized temporal intensity autocorrelation function generated by DCS is typically characterized by assuming that the movement of erythrocytes can be modeled as a Brownian diffusion-like process instead of the expected random flow model. Carp et al. [Biomedical Optics Express, 2011] proposed a hybrid model, referred to as the hydrodynamic diffusion model, to capture both the random ballistic and diffusive nature of erythrocyte motion. The purpose of this study was to compare how well the Brownian diffusion and the hydrodynamic diffusion models characterized DCS data acquired directly on the brain, avoiding the confounding effects of scalp and skull. Data were acquired from seven pigs during normocapnia (39.9 +/- 0.7 mmHg) and hypocapnia (22.1 +/- 1.6 mmHg) with the DCS fibers placed 7 mm apart, directly on the cerebral cortex. The hydrodynamic diffusion model was found to provide a consistently better fit to the autocorrelation functions compared to the Brownian diffusion model and was less sensitive to the chosen start and end time points used in the fitting. However, the decrease in cerebral blood flow from normocapnia to hypocapnia determined was similar for the two models (-42.6 +/- 8.6 % for the Brownian model and -42.2 +/- 10.2 % for the hydrodynamic model), suggesting that the latter is reasonable for monitoring flow changes.
Developing A Laser Shockwave Model For Characterizing Diffusion Bonded Interfaces
James A. Smith; Jeffrey M. Lacy; Barry H. Rabin
2014-07-01
12. Other advances in QNDE and related topics: Preferred Session Laser-ultrasonics Developing A Laser Shockwave Model For Characterizing Diffusion Bonded Interfaces 41st Annual Review of Progress in Quantitative Nondestructive Evaluation Conference QNDE Conference July 20-25, 2014 Boise Centre 850 West Front Street Boise, Idaho 83702 James A. Smith, Jeffrey M. Lacy, Barry H. Rabin, Idaho National Laboratory, Idaho Falls, ID ABSTRACT: The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) which is assigned with reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU. The new LEU fuel is based on a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to complete the fuel qualification process, the laser shock technique is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. The Laser Shockwave Technique (LST) is being investigated to characterize interface strength in fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However the deposition of laser energy into the containment layer on specimen’s surface is intractably complex. The shock wave energy is inferred from the velocity on the backside and the depth of the impression left on the surface from the high pressure plasma pulse created by the shock laser. To help quantify the stresses and strengths at the interface, a finite element model is being developed and validated by comparing numerical and experimental results for back face velocities and front face depressions with experimental results. This paper will report on initial efforts to develop a finite element model for laser
Reaction time in ankle movements: a diffusion model analysis
Michmizos, Konstantinos P.; Krebs, Hermano Igo
2015-01-01
Reaction time (RT) is one of the most commonly used measures of neurological function and dysfunction. Despite the extensive studies on it, no study has ever examined the RT in the ankle. Twenty-two subjects were recruited to perform simple, 2- and 4-choice RT tasks by visually guiding a cursor inside a rectangular target with their ankle. RT did not change with spatial accuracy constraints imposed by different target widths in the direction of the movement. RT increased as a linear function of potential target stimuli, as would be predicted by Hick–Hyman law. Although the slopes of the regressions were similar, the intercept in dorsal–plantar (DP) direction was significantly smaller than the intercept in inversion–eversion (IE) direction. To explain this difference, we used a hierarchical Bayesian estimation of the Ratcliff's (Psychol Rev 85:59, 1978) diffusion model parameters and divided processing time into cognitive components. The model gave a good account of RTs, their distribution and accuracy values, and hence provided a testimony that the non-decision processing time (overlap of posterior distributions between DP and IE < 0.045), the boundary separation (overlap of the posterior distributions < 0.1) and the evidence accumulation rate (overlap of the posterior distributions < 0.01) components of the RT accounted for the intercept difference between DP and IE. The model also proposed that there was no systematic change in non-decision processing time or drift rate when spatial accuracy constraints were altered. The results were in agreement with the memory drum hypothesis and could be further justified neurophysiologically by the larger innervation of the muscles controlling DP movements. This study might contribute to assessing deficits in sensorimotor control of the ankle and enlighten a possible target for correction in the framework of our on-going effort to develop robotic therapeutic interventions to the ankle of children with cerebral palsy
Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment
Stauffer, Dietrich; Schulze, Christian
2008-01-01
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in a percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times but anomalous diffusion at intermediate times. The effective exponents for square distance vs time usually are below one at these intermediate times, but they can also be larger than one for high barrier concentrations. Thus, we observe sub- and superdiffusion in a crowded environment. PMID:19669520
Optimization of a Free Water Elimination Two-Compartment Model for Diffusion Tensor Imaging
Hoy, Andrew R.; Koay, Cheng Guan; Kecskemeti, Steven R.; Alexander, Andrew L.
2014-01-01
Diffusion tensor imaging is used to measure the diffusion of water in tissue. The diffusion properties carry information about the relative organization and structure of the underlying tissue. In the case of a single voxel containing both tissue and a fast diffusing component such as free water, a single diffusion tensor is no longer appropriate. A two-tensor free water elimination model has previously been proposed to correct for the case of volume mixing. Here, this model was implemented in a straightforward but novel manner without the use of spatial constraints. The optimal acquisition parameters were investigated through Monte Carlo simulations and human brain imaging studies. At a signal-to-noise ratio of 40 with 64 diffusion-weighted encoding images, the most accurate estimates of fast diffusion signal were obtained with two diffusion-weighted shells (b-value in s/mm^2 x number of directions) of 500×32 and 1500×32. The potential bias in fractional anisotropy induced by this two-compartment model was more than an order of magnitude less than the error of using the single diffusion tensor model in the presence of partial volume effects with free water. This strategy may be useful for characterizing the diffusion of tissues adjacent to cerebral spinal fluid (CSF), tissues affected by edema, and removing artifacts from blurring and ghosting of the CSF signal. PMID:25271843
Suarez, Andrew V.; Holway, David A.; Case, Ted J.
2001-01-01
Invading organisms may spread through local movements (giving rise to a diffusion-like process) and by long-distance jumps, which are often human-mediated. The local spread of invading organisms has been fit with varying success to models that couple local population growth with diffusive spread, but to date no quantitative estimates exist for the relative importance of local dispersal relative to human-mediated long-distance jumps. Using a combination of literature review, museum records, and personal surveys, we reconstruct the invasion history of the Argentine ant (Linepithema humile), a widespread invasive species, at three spatial scales. Although the inherent dispersal abilities of Argentine ants are limited, in the last century, human-mediated dispersal has resulted in the establishment of this species on six continents and on many oceanic islands. Human-mediated jump dispersal has also been the primary mode of spread at a continental scale within the United States. The spread of the Argentine ant involves two discrete modes. Maximum distances spread by colonies undergoing budding reproduction averaged 150 m/year, whereas annual jump-dispersal distances averaged three orders of magnitude higher. Invasions that involve multiple dispersal processes, such as those documented here, are undoubtedly common. Detailed data on invasion dynamics are necessary to improve the predictive power of future modeling efforts. PMID:11158600
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.
ERIC Educational Resources Information Center
Offenbacher, Elmer L.
1970-01-01
The physics of vertical jumping is described as an interesting illustration for motivating students in a general physics course to master the kinematics and dynamics of one dimensional motion. The author suggests that mastery of the physical principles of the jump may promote understanding of certain biological phenomena, aspects of physical…
NASA Astrophysics Data System (ADS)
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-01
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch-Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients.
NASA Astrophysics Data System (ADS)
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-01
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch–Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients.
Mekkaoui, Imen; Moulin, Kevin; Croisille, Pierre; Pousin, Jerome; Viallon, Magalie
2016-08-01
Cardiac motion presents a major challenge in diffusion weighted MRI, often leading to large signal losses that necessitate repeated measurements. The diffusion process in the myocardium is difficult to investigate because of the unqualified sensitivity of diffusion measurements to cardiac motion. A rigorous mathematical formalism is introduced to quantify the effect of tissue motion in diffusion imaging. The presented mathematical model, based on the Bloch-Torrey equations, takes into account deformations according to the laws of continuum mechanics. Approximating this mathematical model by using finite elements method, numerical simulations can predict the sensitivity of the diffusion signal to cardiac motion. Different diffusion encoding schemes are considered and the diffusion weighted MR signals, computed numerically, are compared to available results in literature. Our numerical model can identify the existence of two time points in the cardiac cycle, at which the diffusion is unaffected by myocardial strain and cardiac motion. Of course, these time points depend on the type of diffusion encoding scheme. Our numerical results also show that the motion sensitivity of the diffusion sequence can be reduced by using either spin echo technique with acceleration motion compensation diffusion gradients or stimulated echo acquisition mode with unipolar and bipolar diffusion gradients. PMID:27385441
Hydraulic jumps in one dimension
NASA Astrophysics Data System (ADS)
Bohr, Tomas; Andersen, Anders; Bonn, Daniel; Bouramrirene, Farid
2006-11-01
We present a study of hydraulic jumps in thin fluid layers with flow predominantly in one direction, created either by confining the flow to a narrow channel or by providing an inflow in the form of a narrow sheet. In all cases we find that the (normal) velocity of the flow at the low side of the jump has a particular critical value, larger than the wave speed. In the channel flow we clearly demonstrate the linear height profile predicted by Watson (1964), although turbulent fluctuations change the apparent viscosity. We show how to calculate the flow structure through the jump, where separation occurs. In the sheet case we find that the jump has the shape of a lozenge with sharply defined, oblique shocks. The variation of the angle of the lozenge with flux is determined by the condition that the normal velocity at the jump remains at the critical value.
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
Moustafa, Ahmed A; Kéri, Szabolcs; Somlai, Zsuzsanna; Balsdon, Tarryn; Frydecka, Dorota; Misiak, Blazej; White, Corey
2015-09-15
In this study, we tested reward- and punishment learning performance using a probabilistic classification learning task in patients with schizophrenia (n=37) and healthy controls (n=48). We also fit subjects' data using a Drift Diffusion Model (DDM) of simple decisions to investigate which components of the decision process differ between patients and controls. Modeling results show between-group differences in multiple components of the decision process. Specifically, patients had slower motor/encoding time, higher response caution (favoring accuracy over speed), and a deficit in classification learning for punishment, but not reward, trials. The results suggest that patients with schizophrenia adopt a compensatory strategy of favoring accuracy over speed to improve performance, yet still show signs of a deficit in learning based on negative feedback. Our data highlights the importance of applying fitting models (particularly drift diffusion models) to behavioral data. The implications of these findings are discussed relative to theories of schizophrenia and cognitive processing.
Moustafa, Ahmed A; Kéri, Szabolcs; Somlai, Zsuzsanna; Balsdon, Tarryn; Frydecka, Dorota; Misiak, Blazej; White, Corey
2015-09-15
In this study, we tested reward- and punishment learning performance using a probabilistic classification learning task in patients with schizophrenia (n=37) and healthy controls (n=48). We also fit subjects' data using a Drift Diffusion Model (DDM) of simple decisions to investigate which components of the decision process differ between patients and controls. Modeling results show between-group differences in multiple components of the decision process. Specifically, patients had slower motor/encoding time, higher response caution (favoring accuracy over speed), and a deficit in classification learning for punishment, but not reward, trials. The results suggest that patients with schizophrenia adopt a compensatory strategy of favoring accuracy over speed to improve performance, yet still show signs of a deficit in learning based on negative feedback. Our data highlights the importance of applying fitting models (particularly drift diffusion models) to behavioral data. The implications of these findings are discussed relative to theories of schizophrenia and cognitive processing. PMID:26005124
Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion
NASA Astrophysics Data System (ADS)
Li, Yan; Lankeit, Johannes
2016-05-01
This article deals with an initial-boundary value problem for the coupled chemotaxis-haptotaxis system with nonlinear diffusion under homogeneous Neumann boundary conditions in a bounded smooth domain Ω \\subset {{{R}}n} , n = 2, 3, 4, where χ,ξ and μ are given nonnegative parameters. The diffusivity D(u) is assumed to satisfy D(u)≥slant δ {{u}m-1} for all u > 0 with some δ >0 . It is proved that for sufficiently regular initial data global bounded solutions exist whenever m>2-\\frac{2}{n} . For the case of non-degenerate diffusion (i.e. D(0) > 0) the solutions are classical; for the case of possibly degenerate diffusion (D(0)≥slant 0 ), the existence of bounded weak solutions is shown.
Modeling bioluminescent photon transport in tissue based on Radiosity-diffusion model
NASA Astrophysics Data System (ADS)
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.
Lift-off dynamics in a simple jumping robot
NASA Astrophysics Data System (ADS)
Aguilar, Jeffrey; Lesov, Alex; Wiesenfeld, Kurt; Goldman, Daniel I.
2013-03-01
Jumping is an important behavior utilized by animals to escape predation, hunt, reach higher ground, and as a primary mode of locomotion. Many mathematical and physical robot models use numerous parameters and multi-link legs to accurately model jumping dynamics. However, a simple robot model can reveal important principles of high performance jumping. We study vertical jumping in a simple robot comprising an actuated mass-spring arrangement. The actuator frequency and phase are systematically varied to find optimal performance. Optimal jumps occur above and below (but not at) the robot's resonant frequency f0. Two distinct jumping modes emerge: a simple jump which is optimal above f0 is achievable with a squat maneuver, and a peculiar stutter jump which is optimal below f0 is generated with a counter-movement. A simple dynamical model reveals how optimal lift-off results from non-resonant transient dynamics. An expanded explanation of this work is provided at http://crablab.gatech.edu/pages/jumpingrobot/index.html This work was supported by the GEM Consortium, Burroughs Wellcome Fund, ARL MAST CTA, and NSF PoLS.
The development of a through-diffusion model with a parent-daughter decay chain.
Chen, Chin-Lung; Wang, Tsing-Hai; Lee, Ching-Hor; Teng, Shi-Ping
2012-09-01
A valid performance assessment of radioactive waste repositories strongly depends on the reliability of nuclide transport parameters, including distribution and diffusion coefficients. To reduce the waste produced and time spent conducting diffusion experiments, a robust model is required to accurately interpret the experiment results. Therefore, we developed a through-diffusion model with parent-daughter nuclide decay chain. We validated our model through comparisons with the Moridis model (Moridis, 1999) and Bharat model (Bharat et al., 2009), assessing our model and these two models using the distribution of parent nuclide concentrations. This strongly supports the rationality and functionality of extending our proposed model to daughter nuclides. In this study, we derived analytical solutions for the parent nuclides of the through-diffusion experiment using the multicompartment (MC) model. We also propose a simplified formula for estimating the apparent diffusion coefficient of parent nuclides based on the analytical solutions. Through numerical experiments, we verified the feasibility of the formula. Our models are useful for determining the apparent diffusion coefficient of daughter nuclides when conducting through-diffusion experiments with parent-daughter nuclide decay chains. Additionally, the proposed models offer the advantages of saving time and reducing experimental waste.
Diffusion-controlled reactions modeling in Geant4-DNA
Karamitros, M.; Luan, S.; Bernal, M.A.; Allison, J.; Baldacchino, G.; Davidkova, M.; Francis, Z.; Friedland, W.; Ivantchenko, V.; Ivantchenko, A.; Mantero, A.; Nieminem, P.; Santin, G.; Tran, H.N.; Stepan, V.; Incerti, S.
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-controlled reactions modeling in Geant4-DNA
NASA Astrophysics Data System (ADS)
Karamitros, M.; Luan, S.; Bernal, M. A.; Allison, J.; Baldacchino, G.; Davidkova, M.; Francis, Z.; Friedland, W.; Ivantchenko, V.; Ivantchenko, A.; Mantero, A.; Nieminem, P.; Santin, G.; Tran, H. N.; Stepan, V.; Incerti, S.
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
Detection of confinement and jumps in single-molecule membrane trajectories
NASA Astrophysics Data System (ADS)
Meilhac, N.; Le Guyader, L.; Salomé, L.; Destainville, N.
2006-01-01
We propose a variant of the algorithm by [R. Simson, E. D. Sheets, and K. Jacobson, Biophys. 69, 989 (1995)]. Their algorithm was developed to detect transient confinement zones in experimental single-particle tracking trajectories of diffusing membrane proteins or lipids. We show that our algorithm is able to detect confinement in a wider class of confining potential shapes than that of Simson Furthermore, it enables to detect not only temporary confinement but also jumps between confinement zones. Jumps are predicted by membrane skeleton fence and picket models. In the case of experimental trajectories of μ -opioid receptors, which belong to the family of G-protein-coupled receptors involved in a signal transduction pathway, this algorithm confirms that confinement cannot be explained solely by rigid fences.
Quantum-corrected drift-diffusion models for transport in semiconductor devices
De Falco, Carlo; Gatti, Emilio; Lacaita, Andrea L.; Sacco, Riccardo . E-mail: riccardo.sacco@mate.polimi.it
2005-04-10
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.
Model for radon diffusion through the lunar regolith.
NASA Technical Reports Server (NTRS)
Friesen, L. J.; Heymann, D.
1972-01-01
Description of a model for radon diffusion through the lunar regolith in which the atom migrates by random walk. The regolith is represented by a system of randomly oriented baffles in which the mean distance which the atom travels between two collisions takes on the role of a mean free path. The effective mean time between two collisions depends on two entities: the actual mean time-of-flight and the mean sticking time on grain surfaces for one collision. The latter depends strongly on the temperature and the heat of adsorption of radon on regolith materials. Both the mean free path as well as the heat of adsorption are either poorly known or unknown for the lunar regolith; hence these quantities are treated as free parameters. Because of the greatly different mean lifetimes against radioactive decay of Rn219, Rn220, and Rn222, the regolith acts as a powerful 'filter' for these species. Rn222 escape is significant (32%) even for a mean free path of 1 micron, a heat of adsorption of 7.0 kcal/mole and a regolith depth of 4 m. Calculations of radon escape from a 4 m thick regolith, using mean free paths of 1, 10, and 80 microns and heats of adsorption of 4.0, 5.2, and 7.0 kcal/mole show that the Rn222/Rn220 escape ratio can be as small as 7.7 and as large as, or larger than 47. The small value of 7.7 is of particular interest, because it is nearly equal to the escape ratio inferred by Turkevich et al. (1970) from their Surveyor 5 results.
Climate stability for a Sellers-type model. [atmospheric diffusive energy balance model
NASA Technical Reports Server (NTRS)
Ghil, M.
1976-01-01
We study a diffusive energy-balance climate model governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. We consider also models similar to the main one studied, and determine the number of their steady states. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. We investigate the stability under small perturbations of the main model's climates. A stability criterion is derived, and its application shows that the 'present climate' and the 'deep freeze' are stable, whereas the model's glacial is unstable. A variational principle is introduced to confirm the results of this stability analysis. For a sufficient decrease in solar radiation (about 2%) the glacial and interglacial solutions disappear, leaving the ice-covered earth as the only possible climate.
Bass-SIR model for diffusion of new products in social networks
NASA Astrophysics Data System (ADS)
Fibich, Gadi
2016-09-01
We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the susceptible-infected-recovered (SIR) model, but rather by a new model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from nonadopters to adopters is described by a nonstandard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Moreover, unlike the SIR model, there is no threshold value above which the diffusion will peter out. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.
Jumping mechanisms in jumping plant lice (Hemiptera, Sternorrhyncha, Psyllidae).
Burrows, M
2012-10-15
Jumping mechanisms and performance were analysed in three species of psyllids (Hemiptera, Sternorrhyncha) that ranged from 2 to 4 mm in body length and from 0.7 to 2.8 mg in mass. Jumping was propelled by rapid movements of the short hind legs, which were only 10-20% longer than the other legs and 61-77% of body length. Power was provided by large thoracic muscles that depressed the trochantera so that the two hind legs moved in parallel planes on either side of the body. These movements accelerated the body to take-off in 0.9 ms in the smallest psyllid and 1.7 ms in the largest, but in all species imparted a rapid forward rotation so that at take-off the head pointed downwards, subtending angles of approximately -60 deg relative to the ground. The front legs thus supported the body just before take-off and either lost contact with the ground at the same time as, or even after, the hind legs. In the best jumps from the horizontal, take-off velocity reached 2.7 m s(-1) and the trajectory was steep at 62-80 deg. Once airborne, the body spun rapidly at rates of up to 336 Hz in the pitch plane. In many jumps, the wings did not open to provide stabilisation, but some jumps led directly to sustained flight. In their best jumps, the smallest species experienced a force of 637 g. The largest species had an energy requirement of 13 μJ, a power output of 13 mW and exerted a force of nearly 10 mN. In a rare jumping strategy seen in only two of 211 jumps analysed, the femoro-tibial joints extended further and resulted in the head pointing upwards at take-off and the spin rate being greatly reduced.
Amphiphile diffusion in model membrane systems studied by pulsed NMR.
Lindblom, G; Wennerström, H
1977-01-01
The translational diffusion of the amphiphilic molecules in a number of lyotropic liquid crystalline phases has been measured with the pulsed NMR pulsed magnetic field gradient method. The amphiphiles studied were soaps, monoglycerids and lecithins. Measurements were performed both for oriented lamellar and for cubic phases. The order of magnitude of the diffusion coefficients was found to be the same as in neat liquids of analogous compounds. It was also found that the difussion coefficient depend markedly on the amphiphile end group in a way that parallels the area per polar head group as determined in X-ray studies. When corrections for geometrical factors has been made the diffusion rate is approximately equal in cubic and lamellar phases containing the same amphiphile.
The membrane skeleton of erythrocytes: models of its effect on lateral diffusion.
Saxton, M J
1990-01-01
The membrane skeleton, a network of structural proteins attached to the cytoplasmic surface of the plasma membrane, hinders lateral diffusion of integral proteins. 2. In some types of cells, such as epithelial cells and nerve cells, the obstruction of lateral diffusion by the membrane skeleton is one of the mechanisms by which proteins are localized to domains on the cell surface. 3. The effect of the membrane skeleton on lateral diffusion may involve steric hindrance, transient binding or both. Three pictures of the effect are reviewed, the discrete barrier model, the continuous barrier model and the transient binding model. 4. Experiments to distinguish the models are discussed.
Utrillas, María P; Marín, María J; Esteve, Anna R; Estellés, Victor; Tena, Fernando; Cañada, Javier; Martínez-Lozano, José A
2009-01-01
Values of measured and modeled diffuse UV erythemal irradiance (UVER) for all sky conditions are compared on planes inclined at 40 degrees and oriented north, south, east and west. The models used for simulating diffuse UVER are of the geometric-type, mainly the Isotropic, Klucher, Hay, Muneer, Reindl and Schauberger models. To analyze the precision of the models, some statistical estimators were used such as root mean square deviation, mean absolute deviation and mean bias deviation. It was seen that all the analyzed models reproduce adequately the diffuse UVER on the south-facing plane, with greater discrepancies for the other inclined planes. When the models are applied to cloud-free conditions, the errors obtained are higher because the anisotropy of the sky dome acquires more importance and the models do not provide the estimation of diffuse UVER accurately. PMID:19496991
Utrillas, María P; Marín, María J; Esteve, Anna R; Estellés, Victor; Tena, Fernando; Cañada, Javier; Martínez-Lozano, José A
2009-01-01
Values of measured and modeled diffuse UV erythemal irradiance (UVER) for all sky conditions are compared on planes inclined at 40 degrees and oriented north, south, east and west. The models used for simulating diffuse UVER are of the geometric-type, mainly the Isotropic, Klucher, Hay, Muneer, Reindl and Schauberger models. To analyze the precision of the models, some statistical estimators were used such as root mean square deviation, mean absolute deviation and mean bias deviation. It was seen that all the analyzed models reproduce adequately the diffuse UVER on the south-facing plane, with greater discrepancies for the other inclined planes. When the models are applied to cloud-free conditions, the errors obtained are higher because the anisotropy of the sky dome acquires more importance and the models do not provide the estimation of diffuse UVER accurately.
NASA Astrophysics Data System (ADS)
Wu, Yixiang; Zou, Xingfu
2016-10-01
Mass action and standard incidence are two major infection mechanisms in modelling spread of infectious diseases. Spatial heterogeneity plays an important role in spread of infectious diseases, and hence, motivates and advocates diffusive models for disease dynamics. By analyzing a diffusive SIS model with the standard incidence infection mechanism, some recent works [2,12] have investigated the asymptotical profiles of the endemic steady state for large and small diffusion rates, and the results show that controlling the diffusion rate of the susceptible individuals can help eradicate the infection, while controlling the diffusion rate of the infectious individuals cannot. This paper aims to reveal the difference between the two infection mechanisms in a spatially heterogeneous environment. To this end, we consider a diffusive SIS model of the same structure but with the mass action infection adopted, and explore the asymptotic profiles of the endemic steady state for small and large diffusion rates. It turns out that the new model poses some new challenges due to the nonlocal term in the equilibrium problem and the unboundedness of the nonlinear term. Our results on this new model reveal some fundamental differences between the two transmission mechanisms in such spatial models, which may provide some implications on disease modelling and controls.
A fractional Fokker-Planck model for anomalous diffusion
Anderson, Johan; Kim, Eun-jin; Moradi, Sara
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.
Diffusion Dynamics and Creative Destruction in a Simple Classical Model
2015-01-01
ABSTRACT The article explores the impact of the diffusion of new methods of production on output and employment growth and income distribution within a Classical one‐sector framework. Disequilibrium paths are studied analytically and in terms of simulations. Diffusion by differential growth affects aggregate dynamics through several channels. The analysis reveals the non‐steady nature of economic change and shows that the adaptation pattern depends both on the innovation's factor‐saving bias and on the extent of the bias, which determines the strength of the selection pressure on non‐innovators. The typology of different cases developed shows various aspects of Schumpeter's concept of creative destruction. PMID:27642192
Safety assessment of jumps in ski racing.
Schindelwig, K; Reichl, W; Kaps, P; Mössner, M; Nachbauer, W
2015-12-01
The influence of important parameters on the flight trajectory for jumps in downhill World Cup races was investigated. To quantify the impact injury risk at landing, the parameter equivalent landing height (ELH) was introduced, which considered a variable slope inclination during the landing movement. Altogether, 145 runs at four different jumps in World Cup races and trainings were recorded and analyzed. A simulation model was developed to predict the flight phase of the skier. Drag and lift areas were selected by parameter identification to fit the simulation trajectory to the two-dimensional data from the video analysis. The maximum values of the ELH which can be absorbed with muscle force was taken from the study of Minetti et al. for elite female and male ski racers. A sensitivity analysis based on the four jumps showed that ELH is mainly influenced by takeoff angle, takeoff speed, and the steepness of the landing surface. With the help of the developed simulation software, it should be possible to predict the ELH for jumps in advance. In case of an excessive ELH, improvements can be made by changing the takeoff inclination or the approach speed. PMID:25123506
An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes
Degond, Pierre; Gallego, Samy . E-mail: gallego@mip.ups-tlse.fr; Mehats, Florian
2007-01-20
We present an entropic quantum drift-diffusion model (eQDD) and show how it can be derived on a bounded domain as the diffusive approximation of the Quantum Liouville equation with a quantum BGK operator. Some links between this model and other existing models are exhibited, especially with the density gradient (DG) model and the Schroedinger-Poisson drift-diffusion model (SPDD). Then a finite difference scheme is proposed to discretize the eQDD model coupled to the Poisson equation and we show how this scheme can be slightly modified to discretize the other models. Numerical results show that the properties listed for the eQDD model are checked, as well as the model captures important features concerning the modeling of a resonant tunneling diode. To finish, some comparisons between the models stated above are realized.
Modeling of the magnetic free energy of self-diffusion in bcc Fe
NASA Astrophysics Data System (ADS)
Sandberg, N.; Chang, Z.; Messina, L.; Olsson, P.; Korzhavyi, P.
2015-11-01
A first-principles based approach to calculating self-diffusion rates in bcc Fe is discussed with particular focus on the magnetic free energy associated with diffusion activation. First, the enthalpies and entropies of vacancy formation and migration in ferromagnetic bcc Fe are calculated from standard density functional theory methods in combination with transition state theory. Next, the shift in diffusion activation energy when going from the ferromagnetic to the paramagnetic state is estimated by averaging over random spin states. Classical and quantum mechanical Monte Carlo simulations within the Heisenberg model are used to study the effect of spin disordering on the vacancy formation and migration free energy. Finally, a quasiempirical model of the magnetic contribution to the diffusion activation free energy is applied in order to connect the current first-principles results to experimental data. The importance of the zero-point magnon energy in modeling of diffusion in bcc Fe is stressed.
Cooperative jump motions of jammed particles in a one-dimensional periodic potential.
Sakaguchi, Hidetsugu
2009-12-01
Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated and it is compared with theoretical estimates. We find that the size distribution of the cooperative jump motions obeys an exponential law in a large system.
Diffusion versus network models as descriptions for the spread of prion diseases in the brain.
Matthäus, Franziska
2006-05-01
In this paper we will discuss different modeling approaches for the spread of prion diseases in the brain. Firstly, we will compare reaction-diffusion models with models of epidemic diseases on networks. The solutions of the resulting reaction-diffusion equations exhibit traveling wave behavior on a one-dimensional domain, and the wave speed can be estimated. The models can be tested for diffusion-driven (Turing) instability, which could present a possible mechanism for the formation of plaques. We also show that the reaction-diffusion systems are capable of reproducing experimental data on prion spread in the mouse visual system. Secondly, we study classical epidemic models on networks, and use these models to study the influence of the network topology on the disease progression. PMID:16219329
Employing a Modified Diffuser Momentum Model to Simulate Ventilation of the Orion CEV
NASA Technical Reports Server (NTRS)
Straus, John; Lewis, John F.
2011-01-01
The Ansys CFX CFD modeling tool was used to support the design efforts of the ventilation system for the Orion CEV. CFD modeling was used to establish the flow field within the cabin for several supply configurations. A mesh and turbulence model sensitivity study was performed before the design studies. Results were post-processed for comparison with performance requirements. Most configurations employed straight vaned diffusers to direct and throw the flow. To manage the size of the models, the diffuser vanes were not resolved. Instead, a momentum model was employed to account for the effect of the diffusers. The momentum model was tested against a separate, vane-resolved side study. Results are presented for a single diffuser configuration for a low supply flow case.
Kee, Kerk F; Sparks, Lisa; Struppa, Daniele C; Mannucci, Mirco A; Damiano, Alberto
2016-01-01
By integrating the simplicial model of social aggregation with existing research on opinion leadership and diffusion networks, this article introduces the constructs of simplicial diffusers (mathematically defined as nodes embedded in simplexes; a simplex is a socially bonded cluster) and simplicial diffusing sets (mathematically defined as minimal covers of a simplicial complex; a simplicial complex is a social aggregation in which socially bonded clusters are embedded) to propose a strategic approach for information diffusion of cancer screenings as a health intervention on Facebook for community cancer prevention and control. This approach is novel in its incorporation of interpersonally bonded clusters, culturally distinct subgroups, and different united social entities that coexist within a larger community into a computational simulation to select sets of simplicial diffusers with the highest degree of information diffusion for health intervention dissemination. The unique contributions of the article also include seven propositions and five algorithmic steps for computationally modeling the simplicial model with Facebook data.
Ho, C.K.; Webb, S.W.
1996-05-01
A review of mechanisms, models, and data relevant to the postulated phenomenon of enhanced vapor-phase diffusion in porous media is presented. Information is obtained from literature spanning two different disciplines (soil science and engineering) to gain a diverse perspective on this topic. Findings indicate that while enhanced vapor diffusion tends to correct the discrepancies observed between past theory and experiments, no direct evidence exists to support the postulated processes causing enhanced vapor diffusion. Numerical modeling analyses of experiments representative of the two disciplines are presented in this paper to assess the sensitivity of different systems to enhanced vapor diffusion. Pore-scale modeling is also performed to evaluate the relative significance of enhanced vapor diffusion mechanisms when compared to Fickian diffusion. The results demonstrate the need for additional experiments so that more discerning analyses can be performed.
NASA Astrophysics Data System (ADS)
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
Rook Jumping Maze Design Considerations
NASA Astrophysics Data System (ADS)
Neller, Todd W.; Fisher, Adrian; Choga, Munyaradzi T.; Lalvani, Samir M.; McCarty, Kyle D.
We define the Rook Jumping Maze, provide historical perspective, and describe a generation method for such mazes. When applying stochastic local search algorithms to maze design, most creative effort concerns the definition of an objective function that rates maze quality. We define and discuss several maze features to consider in such a function definition. Finally, we share our preferred design choices, make design process observations, and note the applicability of these techniques to variations of the Rook Jumping Maze.
Effects of Isometric Scaling on Vertical Jumping Performance
Bobbert, Maarten F.
2013-01-01
Jump height, defined as vertical displacement in the airborne phase, depends on vertical takeoff velocity. For centuries, researchers have speculated on how jump height is affected by body size and many have adhered to what has come to be known as Borelli’s law, which states that jump height does not depend on body size per se. The underlying assumption is that the amount of work produced per kg body mass during the push-off is independent of size. However, if a big body is isometrically downscaled to a small body, the latter requires higher joint angular velocities to achieve a given takeoff velocity and work production will be more impaired by the force-velocity relationship of muscle. In the present study, the effects of pure isometric scaling on vertical jumping performance were investigated using a biologically realistic model of the human musculoskeletal system. The input of the model, muscle stimulation over time, was optimized using jump height as criterion. It was found that when the human model was miniaturized to the size of a mouse lemur, with a mass of about one-thousandth that of a human, jump height dropped from 40 cm to only 6 cm, mainly because of the force-velocity relationship. In reality, mouse lemurs achieve jump heights of about 33 cm. By implication, the unfavourable effects of the small body size of mouse lemurs on jumping performance must be counteracted by favourable effects of morphological and physiological adaptations. The same holds true for other small jumping animals. The simulations for the first time expose and explain the sheer magnitude of the isolated effects of isometric downscaling on jumping performance, to be counteracted by morphological and physiological adaptations. PMID:23936494
Hindered diffusion in agarose gels: test of effective medium model.
Johnson, E M; Berk, D A; Jain, R K; Deen, W M
1996-01-01
The diffusivities of uncharged macromolecules in gels (D) are typically lower than in free solution (D infinity), because of a combination of hydrodynamic and steric factors. To examine these factors, we measured D and D infinity for dilute solutions of several fluorescein-labeled macromolecules, using an image-based fluorescence recovery after photobleaching technique. Test macromolecules with Stokes-Einstein radii (rs) of 2.1-6.2 nm, including three globular proteins (bovine serum albumin, ovalbumin, lactalbumin) and four narrow fractions of Ficoll, were studied in agarose gels with agarose volume fractions (phi) of 0.038-0.073. The gels were characterized by measuring the hydraulic permeability of supported agarose membranes, allowing calculation of the Darcy permeability (kappa) for each gel sample. It was found that kappa, which is a measure of the intrinsic hydraulic conductance of the gel, decreased by an order of magnitude as phi was increased over the range indicated. The diffusivity ratio D/D infinity, which varied from 0.20 to 0.63, decreased with increases in rs or phi. Thus as expected, diffusional hindrances were the most severe for large macromolecules and/or relatively concentrated gels. According to a recently proposed theory for hindered diffusion through fibrous media, the diffusivity ratio is given by the product of a hydrodynamic factor (F) and a steric factor (S). The functional form is D/D infinity = F(rs/k1/2) S(f), where f = [(rs+rf)/rf]2 phi and rf is the fiber radius. Values of D/D infinity calculated from this effective medium theory, without use of adjustable parameters, were in much better agreement with the measured values than were predictions based on other approaches. The strengths and limitations of the effective medium theory for predicting diffusivities in gels are discussed. PMID:8789119
Diffusion on a hypersphere: application to the Wright-Fisher model
NASA Astrophysics Data System (ADS)
Maruyama, Kishiko; Itoh, Yoshiaki
2016-04-01
The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a hypersphere is transformed into the diffusion for the Wright-Fisher model with a particular mutation rate. We use the Ito calculus considering stochastic differential equations. The expansion gives a simple interpretation of the Griffiths eigenfunction expansion for the Wright-Fisher model. Our representation is useful to simulate the Wright-Fisher model as well as Brownian motion on a hypersphere.
An efficient wavelet analysis method to film-pore diffusion model arising in mathematical chemistry.
Hariharan, G
2014-04-01
In this paper, we have established an efficient Legendre wavelet based approximation method to solve film-pore diffusion model arising in engineering. Film-pore diffusion model is widely used to determine study the kinetics of adsorption systems. The use of Legendre wavelet based approximation method is found to be accurate, simple, fast, flexible, convenient, and computationally attractive. It is shown that film-pore diffusion model satisfactorily describe kinetics of methylene blue adsorption onto the three low-cost adsorbents, Guava, teak and gulmohar plant leaf powders, used in this study. PMID:24562792
Nonstandard jump functions for radially symmetric shock waves
Baty, Roy S.; Tucker, Don H.; Stanescu, Dan
2008-10-01
Nonstandard analysis is applied to derive generalized jump functions for radially symmetric, one-dimensional, magnetogasdynamic shock waves. It is assumed that the shock wave jumps occur on infinitesimal intervals, and the jump functions for the physical parameters occur smoothly across these intervals. Locally integrable predistributions of the Heaviside function are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the physical parameters for two families of self-similar flows. It is shown that the microstructures for these families of radially symmetric, magnetogasdynamic shock waves coincide in a nonstandard sense for a specified density jump function
Nonstandard jump functions for radically symmetric shock waves
Baty, Roy S; Tucker, Don H; Stanescu, Dan
2008-01-01
Nonstandard analysis is applied to derive generalized jump functions for radially symmetric, one-dimensional, magnetogasdynamic shock waves. It is assumed that the shock wave jumps occur on infinitesimal intervals and the jump functions for the physical parameters occur smoothly across these intervals. Locally integrable predistributions of the Heaviside function are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the physical parameters for two families of self-similar flows. It is shown that the microstructures for these families of radially symmetric, magnetogasdynamic shock waves coincide in a nonstandard sense for a specified density jump function.
Hierarchical Bass model: a product diffusion model considering a diversity of sensitivity to fashion
NASA Astrophysics Data System (ADS)
Tashiro, Tohru
2016-11-01
We propose a new product diffusion model including the number of how many adopters or advertisements a non-adopter met until he/she adopts the product, where (non-)adopters mean people (not) possessing it. By this effect not considered in the Bass model, we can depict a diversity of sensitivity to fashion. As an application, we utilize the model to fit the iPod and the iPhone unit sales data, and so the better agreement is obtained than the Bass model for the iPod data. We also present a new method to estimate the number of advertisements in a society from fitting parameters of the Bass model and this new model.
Biphasic activity of a jumping spider.
Okuyama, Toshinori
2011-01-01
Individual variation is a ubiquitous and important factor that affects ecological dynamics. This study examined individual variation in the nest-use pattern of the jumping spider Phidippus audax. Although the jumping spider is a diurnal species, field observations in this study revealed that the majority of individuals remained in their nests during the day. An accompanying examination of the hunger level of the spiders revealed that spiders that remained in nests were more starved than those observed outside nests. If spiders actively forage when they are starved, as has been suggested by previous studies, one would expect to see the opposite trend (i.e., spiders that remained in nests are more satiated). Thus, the pattern observed in the field contradicts the known behavioral pattern of the spiders. An individual-based model was used to investigate the behavioral mechanism of the spider and the discrepancy found in the observations. A basic assumption of the model is that spiders possess distinct inactive and active phases (biphasic activity pattern), and transitions between the two phases are regulated by the hunger level of the spider. Data from a laboratory experiment were used to examine the assumptions of the model partially. The model was able to capture patterns observed in the data, suggesting that the pattern of transitions in biphasic activity is an important trait of the foraging behavior of the jumping spider. PMID:21085925
Biphasic activity of a jumping spider
NASA Astrophysics Data System (ADS)
Okuyama, Toshinori
2011-01-01
Individual variation is a ubiquitous and important factor that affects ecological dynamics. This study examined individual variation in the nest-use pattern of the jumping spider Phidippus audax. Although the jumping spider is a diurnal species, field observations in this study revealed that the majority of individuals remained in their nests during the day. An accompanying examination of the hunger level of the spiders revealed that spiders that remained in nests were more starved than those observed outside nests. If spiders actively forage when they are starved, as has been suggested by previous studies, one would expect to see the opposite trend (i.e., spiders that remained in nests are more satiated). Thus, the pattern observed in the field contradicts the known behavioral pattern of the spiders. An individual-based model was used to investigate the behavioral mechanism of the spider and the discrepancy found in the observations. A basic assumption of the model is that spiders possess distinct inactive and active phases (biphasic activity pattern), and transitions between the two phases are regulated by the hunger level of the spider. Data from a laboratory experiment were used to examine the assumptions of the model partially. The model was able to capture patterns observed in the data, suggesting that the pattern of transitions in biphasic activity is an important trait of the foraging behavior of the jumping spider.
Monte Carlo simulation with fixed steplength for diffusion processes in nonhomogeneous media
NASA Astrophysics Data System (ADS)
Ruiz Barlett, V.; Hoyuelos, M.; Mártin, H. O.
2013-04-01
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared with integration of the diffusion equation. It is important to notice that the same method is completely erroneous when applied to non-homogeneous diffusion coefficients. A simple alternative, jumping at fixed steplengths with appropriate transition probabilities, produces correct results. Here, a model for diffusion of calcium ions in the neuromuscular junction of the crayfish is used as a test to compare Monte Carlo simulation with fixed and Gaussian steplength.
Diffusive flux in a model of stochastically gated oxygen transport in insect respiration
NASA Astrophysics Data System (ADS)
Berezhkovskii, Alexander M.; Shvartsman, Stanislav Y.
2016-05-01
Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.
Radiative diffusivity factors in cirrus and stratocumulus clouds: Application to two-stream models
NASA Technical Reports Server (NTRS)
Stephens, Graeme L.; Flatau, P. J.; Tsay, S.-C.; Hein, Paul F.
1990-01-01
A diffusion-like description of radiative transfer in clouds and the free atmosphere is often used. The two stream model is probably the best known example of such a description. The main idea behind the approach is that only the first few moments of radiance are needed to describe the radiative field correctly. Integration smooths details of the angular distribution of specific intensity and it is assumed that the closure parameters of the theory (diffusivity factors) are only weakly dependent on the distribution. The diffusivity factors are investigated using the results obtained from both Stratocumulus and Cirrus phases of FIRE experiment. A new theoretical framework is described in which two (upwards and downwards) diffusivity factors are used and a detailed multistream model is used to provide further insight about both the diffusivity factors and their dependence on scattering properties of clouds.
Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.
Bendahmane, Mostafa; Ruiz-Baier, Ricardo; Tian, Canrong
2016-05-01
In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis.
Numerical study of a cylinder model of the diffusion MRI signal for neuronal dendrite trees.
Van Nguyen, Dang; Grebenkov, Denis; Le Bihan, Denis; Li, Jing-Rebecca
2015-03-01
We study numerically how the neuronal dendrite tree structure can affect the diffusion magnetic resonance imaging (dMRI) signal in brain tissue. For a large set of randomly generated dendrite trees, synthetic dMRI signals are computed and fitted to a cylinder model to estimate the effective longitudinal diffusivity D(L) in the direction of neurites. When the dendrite branches are short compared to the diffusion length, D(L) depends significantly on the ratio between the average branch length and the diffusion length. In turn, D(L) has very weak dependence on the distribution of branch lengths and orientations of a dendrite tree, and the number of branches per node. We conclude that the cylinder model which ignores the connectivity of the dendrite tree, can still be adapted to describe the apparent diffusion coefficient in brain tissue. PMID:25681802
Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.
Berezhkovskii, Alexander M; Shvartsman, Stanislav Y
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.
Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.
Bendahmane, Mostafa; Ruiz-Baier, Ricardo; Tian, Canrong
2016-05-01
In this paper we analyze the effects of introducing the fractional-in-space operator into a Lotka-Volterra competitive model describing population super-diffusion. First, we study how cross super-diffusion influences the formation of spatial patterns: a linear stability analysis is carried out, showing that cross super-diffusion triggers Turing instabilities, whereas classical (self) super-diffusion does not. In addition we perform a weakly nonlinear analysis yielding a system of amplitude equations, whose study shows the stability of Turing steady states. A second goal of this contribution is to propose a fully adaptive multiresolution finite volume method that employs shifted Grünwald gradient approximations, and which is tailored for a larger class of systems involving fractional diffusion operators. The scheme is aimed at efficient dynamic mesh adaptation and substantial savings in computational burden. A numerical simulation of the model was performed near the instability boundaries, confirming the behavior predicted by our analysis. PMID:26219250
Modeling of TCE diffusion to the atmosphere and distribution in plant stems.
Ma, Xingmao; Burken, Joel
2004-09-01
Fate of chlorinated solvents in phytoremediation has been delineated by many discoveries made in recent years. Plant uptake, metabolism, rhizosphere degradation, accumulation, and volatilization were shown to occur to differing degrees for many organic contaminants including chlorinated solvents. Among these mechanistic findings, recent research confirmed that volatile organic compounds (VOCs) volatilize from stems and that the resulting diffusive flux to the atmosphere is related to exposure concentration and to height up the stem. A comprehensive model was developed based upon all identified fate and transport mechanisms for VOCs, including translocation in the xylem flow and diffusion. The dispersion and diffusion in the radial direction were considered as one process (effective diffusion) as the two could not be investigated individually. The mechanism-based model mathematically indicates an exponential decrease of concentrations with height. While an analytic solution for the comprehensive model was not attained, it can serve as a starting point for other modeling efforts. The comprehensive model was simplified in this work for practical application to experimentally obtained data on trichloroethylene (TCE) fate. Model output correlated well with experimental results, and effective diffusivities for TCE in plant tissues were obtained through the model calibrations. The simplified model approximated TCE concentrations in the transpiration stream as well as TCE volatilization to the atmosphere. Xylem transport, including advection, dispersion, and diffusion through cell walls with subsequent volatilization to the atmosphere, is a major fate for VOCs in phytoremediation. PMID:15461166
Ages estimated from a diffusion equation model for scarp degradation
Colman, Steven M.; Watson, K.E.N.
1983-01-01
The diffusion equation derived from the continuity equation for hillslopes is applied to scarp erosion in unconsolidated materials. Solutions to this equation allow direct calculation of the product of the rate coefficient and the age of the scarp from measurements of scarp morphology. Where the rate coefficient can be estimated or can be derived from scarps of known age, this method allows direct calculation of unknown ages of scarps.
Delayed-exponential approximation of a linear homogeneous diffusion model of neuron.
Pacut, A; Dabrowski, L
1988-01-01
The diffusion models of neuronal activity are general yet conceptually simple and flexible enough to be useful in a variety of modeling problems. Unfortunately, even simple diffusion models lead to tedious numerical calculations. Consequently, the existing neural net models use characteristics of a single neuron taken from the "pre-diffusion" era of neural modeling. Simplistic elements of neural nets forbid to incorporate a single learning neuron structure into the net model. The above drawback cannot be overcome without the use of the adequate structure of the single neuron as an element of a net. A linear (not necessarily homogeneous) diffusion model of a single neuron is a good candidate for such a structure, it must, however, be simplified. In the paper the structure of the diffusion model of neuron is discussed and a linear homogeneous model with reflection is analyzed. For this model an approximation is presented, which is based on the approximation of the first passage time distribution of the Ornstein-Uhlenbeck process by the delayed (shifted) exponential distribution. The resulting model has a simple structure and has a prospective application in neural modeling and in analysis of neural nets.
Optimal prediction for moment models: crescendo diffusion and reordered equations
NASA Astrophysics Data System (ADS)
Seibold, Benjamin; Frank, Martin
2009-12-01
A direct numerical solution of the radiative transfer equation or any kinetic equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We want to generally study the moment closure within the framework of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system, for radiation moment systems. We apply this strategy to radiative transfer and show that several closures can be re-derived within this framework, such as P N , diffusion, and diffusion correction closures. In addition, the formalism gives rise to new parabolic systems, the reordered P N equations, that are similar to the simplified P N equations. Furthermore, we propose a modification to existing closures. Although simple and with no extra cost, this newly derived crescendo diffusion yields better approximations in numerical tests.
Measuring and modeling diffuse scattering in protein X-ray crystallography
Van Benschoten, Andrew H.; Liu, Lin; Gonzalez, Ana; Brewster, Aaron S.; Sauter, Nicholas K.; Wall, Michael E.
2016-01-01
X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practices for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation–libration–screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. These results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering. PMID:27035972
Measuring and modeling diffuse scattering in protein X-ray crystallography
Van Benschoten, Andrew H.; Liu, Lin; Gonzalez, Ana; Brewster, Aaron S.; Sauter, Nicholas K.; Fraser, James S.; Wall, Michael E.
2016-03-28
X-ray diffraction has the potential to provide rich information about the structural dynamics of macromolecules. To realize this potential, both Bragg scattering, which is currently used to derive macromolecular structures, and diffuse scattering, which reports on correlations in charge density variations, must be measured. Until now, measurement of diffuse scattering from protein crystals has been scarce because of the extra effort of collecting diffuse data. Here, we present 3D measurements of diffuse intensity collected from crystals of the enzymes cyclophilin A and trypsin. The measurements were obtained from the same X-ray diffraction images as the Bragg data, using best practicesmore » for standard data collection. To model the underlying dynamics in a practical way that could be used during structure refinement, we tested translation–libration–screw (TLS), liquid-like motions (LLM), and coarse-grained normal-modes (NM) models of protein motions. The LLM model provides a global picture of motions and was refined against the diffuse data, whereas the TLS and NM models provide more detailed and distinct descriptions of atom displacements, and only used information from the Bragg data. Whereas different TLS groupings yielded similar Bragg intensities, they yielded different diffuse intensities, none of which agreed well with the data. In contrast, both the LLM and NM models agreed substantially with the diffuse data. In conclusion, these results demonstrate a realistic path to increase the number of diffuse datasets available to the wider biosciences community and indicate that dynamics-inspired NM structural models can simultaneously agree with both Bragg and diffuse scattering.« less
Anisotropy-resolving models for predicting separation in 3--D asymmetric diffusers
NASA Astrophysics Data System (ADS)
Jeyapaul, Elbert; Durbin, Paul
2011-11-01
All linear eddy-viscosity models are qualitatively incorrect in predicting separation in 3-D asymmetric diffusers. The failure to predict normal stress and shear stress anisotropy at high production-dissipation ratios is the cause. The Explicit algebraic Reynolds stress model (Wallin and Johansson, 2000) predicts the mean flow field in the diffuser accurately, but not the wall pressure and Reynolds stresses. Recalibrating the coefficients of the rapid part of pressure-strain model improves the wall pressure prediction. Including the convective, diffusive, streamline curvature effects on anisotropy has not been beneficial. The model has been tested using a family of diffusers having the same nominal streamwise pressure gradient, LES data is used as a reference. Professor
Wang, Zhiwu; Hamilton-Brehm, Scott; Lochner, Adriane; Elkins, James G; Morrell-Falvey, Jennifer L
2011-01-01
Abstract: The morphological and structural properties of microbial biofilms are influenced by internal substrate diffusion and utilization processes. In the case of microbial hydrolysis of plant cell walls, only thin and uniform biofilm structures are typically formed by cellulolytic microorganisms. In this study, we develop a hydrolysate diffusion and utilization model system to examine factors influencing cellulolytic biofilm formation. Model simulations using Caldicellulosiruptor obsidiansis as a representative organism, reveal that the growth of the cellulolytic biofilm is limited by hydrolysate utilization but not diffusion. As a consequence, the cellulolytic biofilm has a uniform growth rate, and there is a hydrolysate surplus that diffuses through the cellulolytic biofilm into the bulk solution where it is consumed by planktonic cells. Predictions based on the model were tested in a cellulose fermentation study and the results are consistent with the model and previously reported experimental data. The factors determining the rate-limiting step of biofilm growth are also analyzed.
A Functional Model for Teaching Osmosis-Diffusion to Biology Students
ERIC Educational Resources Information Center
Olsen, Richard W.; Petry, Douglas E.
1976-01-01
Described is a maternal-fetal model, operated by the student, to teach osmosis-diffusion to biology students. Included are materials needed, assembly instructions, and student operating procedures. (SL)
Degenerate mobilities in phase field models are insufficient to capture surface diffusion
NASA Astrophysics Data System (ADS)
Lee, Alpha A.; Münch, Andreas; Süli, Endre
2015-08-01
Phase field models frequently provide insight into phase transitions and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via surface diffusion is the long-time, sharp interface limit of microscopic phase field models such as the Cahn-Hilliard equation with a degenerate mobility function. Contrary to this conventional wisdom, we show that the long-time behaviour of degenerate Cahn-Hilliard equation with a polynomial free energy undergoes coarsening, reflecting the presence of bulk diffusion, rather than pure surface diffusion. This reveals an important limitation of phase field models that are frequently used to model surface diffusion.
Woo, Jiyoung; Chen, Hsinchun
2016-01-01
As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums.
Woo, Jiyoung; Chen, Hsinchun
2016-01-01
As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums. PMID:26839759
Models of diffusion-limited uptake of trace elements in fossils and rates of fossilization
NASA Astrophysics Data System (ADS)
Kohn, Matthew J.
2008-08-01
Many fossils are assumed to take up trace elements by a process of combined diffusion plus adsorption (DA), yet in principle composition profiles can be explained by several different diffusion-limited processes, including diffusion plus reaction or recrystallization (DR) and double-medium diffusion (DMD). The DA and DMD models are supported by REE and U composition profiles across fossil teeth, measured by laser-ablation ICP-MS, that show error-function - like diffusion profiles into enamel from the dentine-enamel interface and concentrations in the interior of enamel that are at original biogenic levels or higher. Published composition and age profiles in some Pleistocene bones may be better explained by a DR model. All three diffusion models imply linear behavior between age and distance squared, vastly simplifying U-series dating methods for Pleistocene fossils. Modeled uptake rates for fossil teeth yield a strict minimum bound on durations of about one decade to one century. The similarity of diffusion profiles in teeth, irrespective of depositional ages ranging from ˜30 ka to >30 Ma, implies that uptake occurred quickly, with a maximum duration of a few tens of kyr for typical fossil enamel; faster uptake is implied for typical fossil bone and dentine. Disparities in these uptake estimates compared to some archeological bone may reflect sampling and preservation bias for paleontological vs. archeological materials.
NASA Astrophysics Data System (ADS)
McMillen, Laura; Vavylonis, Dimitrios; Vavylonis Group Team
It is debated whether transport of actin across the cell by diffusion alone is sufficiently fast to account for the rapid reorganization of actin filaments at the leading edge of motile cells. In order to investigate this question, we created a 3D model of the whole cell that includes reaction and diffusion of actin using a particle Monte Carlo method. For the lamellipodium of the simulated cell we use the model by Smith et al. Biophys. J 104:247 (2013), which includes two diffuse pools of actin, one which is slowly diffusing and the other which diffuses more quickly, as well as a pool of filamentous actin undergoing retrograde flow towards the cell center. We adjusted this model to fit a circular geometry around the whole cell. We also consider actin in the cell center which is either diffusing or in stationary filamentous form, representing cortical actin or actin in stress fibers. The local rates of polymerization and the lifetime distributions of polymerized actin were estimated from single molecule speckle microscopy experiments by the group of N. Watanabe. With this model we are able to simulate prior experiments that monitored the redistribution of actin after photoactivation or fluorescence recovery after photobleaching in various parts of the cell. We find that transport by diffusion is sufficient to fit these data, without the need for an active transport mechanism, however significant concentration gradients may develop at steady state.
Application of a diffusion-desorption rate equation model in astrochemistry.
He, Jiao; Vidali, Gianfranco
2014-01-01
Desorption and diffusion are two of the most important processes on interstellar grain surfaces; knowledge of them is critical for the understanding of chemical reaction networks in the interstellar medium (ISM). However, a lack of information on desorption and diffusion is preventing further progress in astrochemistry. To obtain desorption energy distributions of molecules from the surfaces of ISM-related materials, one usually carries out adsorption-desorption temperature programmed desorption (TPD) experiments, and uses rate equation models to extract desorption energy distributions. However, the often-used rate equation models fail to adequately take into account diffusion processes and thus are only valid in situations where adsorption is strongly localized. As adsorption-desorption experiments show that adsorbate molecules tend to occupy deep adsorption sites before occupying shallow ones, a diffusion process must be involved. Thus, it is necessary to include a diffusion term in the model that takes into account the morphology of the surface as obtained from analyses of TPD experiments. We take the experimental data of CO desorption from the MgO(100) surface and of D2 desorption from amorphous solid water ice as examples to show how a diffusion-desorption rate equation model explains the redistribution of adsorbate molecules among different adsorption sites. We extract distributions of desorption energies and diffusion energy barriers from TPD profiles. These examples are contrasted with a system where adsorption is strongly localized--HD from an amorphous silicate surface. Suggestions for experimental investigations are provided.
Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks
NASA Astrophysics Data System (ADS)
Powell, Sean K.; Momot, Konstantin I.
2012-09-01
In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0∘ to 90∘. The corresponding diffusion ellipsoids are prolate for θ<θMA, spherical for θ≈θMA, and oblate for θ>θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.
Optimizing the Distribution of Leg Muscles for Vertical Jumping.
Wong, Jeremy D; Bobbert, Maarten F; van Soest, Arthur J; Gribble, Paul L; Kistemaker, Dinant A
2016-01-01
A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas-which determine the maximum force deliverable by the muscles-constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal
Optimizing the Distribution of Leg Muscles for Vertical Jumping
Wong, Jeremy D.; Bobbert, Maarten F.; van Soest, Arthur J.; Gribble, Paul L.; Kistemaker, Dinant A.
2016-01-01
A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas—which determine the maximum force deliverable by the muscles—constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal
Optimizing the Distribution of Leg Muscles for Vertical Jumping.
Wong, Jeremy D; Bobbert, Maarten F; van Soest, Arthur J; Gribble, Paul L; Kistemaker, Dinant A
2016-01-01
A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas-which determine the maximum force deliverable by the muscles-constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal
Modelling oxygen self-diffusion in UO_{2} under pressure
Cooper, Michael William D.; Grimes, R. W.; Fitzpatrick, M. E.; Chroneos, A.
2015-10-22
Access to values for oxygen self-diffusion over a range of temperatures and pressures in UO_{2} is important to nuclear fuel applications. Here, elastic and expansivity data are used in the framework of a thermodynamic model, the cBΩ model, to derive the oxygen self-diffusion coefficient in UO_{2} over a range of pressures (0–10 GPa) and temperatures (300–1900 K). Furthermore, the significant reduction in oxygen self-diffusion as a function of increasing hydrostatic pressure, and the associated increase in activation energy, is identified.
Reaction-diffusion processes and epidemic metapopulation models in complex networks
NASA Astrophysics Data System (ADS)
Vespignani, A.
2008-08-01
The correct description of reaction-diffusion phenomena requires a detailed knowledge of the contact networks defining the interactions between individuals and groups of individuals. For this reason, the study of reaction-diffusion processes has been recently widened with opportune models and methods dealing with the heterogeneity and large scale fluctuations observed in many real world networks. Here we present a brief overview of some recent results on reaction-diffusion processes in complex networks which provide useful insights into the dynamic behavior of epidemic metapopulation models.
A qualitative model for aggregation and diffusion of β-amyloid in Alzheimer's disease.
Achdou, Yves; Franchi, Bruno; Marcello, Norina; Tesi, Maria Carla
2013-12-01
In this paper we present a mathematical model for the aggregation and diffusion of Aβ amyloid in the brain affected by Alzheimer's disease, at the early stage of the disease. The model is based on a classical discrete Smoluchowski aggregation equation modified to take diffusion into account. We also describe a numerical scheme and discuss the results of the simulations in the light of the recent biomedical literature.
Efficient simulation of diffusion-based choice RT models on CPU and GPU.
Verdonck, Stijn; Meers, Kristof; Tuerlinckx, Francis
2016-03-01
In this paper, we present software for the efficient simulation of a broad class of linear and nonlinear diffusion models for choice RT, using either CPU or graphical processing unit (GPU) technology. The software is readily accessible from the popular scripting languages MATLAB and R (both 64-bit). The speed obtained on a single high-end GPU is comparable to that of a small CPU cluster, bringing standard statistical inference of complex diffusion models to the desktop platform.
Dynamics and stability of directional jumps in the desert locust
Gvirsman, Omer
2016-01-01
Locusts are known for their ability to jump large distances to avoid predation. The jump also serves to launch the adult locust into the air in order to initiate flight. Various aspects of this important behavior have been studied extensively, from muscle physiology and biomechanics, to the energy storage systems involved in powering the jump, and more. Less well understood are the mechanisms participating in control of the jump trajectory. Here we utilise video monitoring and careful analysis of experimental directional jumps by adult desert locusts, together with dynamic computer simulation, in order to understand how the locusts control the direction and elevation of the jump, the residual angular velocities resulting from the jump and the timing of flapping-flight initiation. Our study confirms and expands early findings regarding the instrumental role of the initial body position and orientation. Both real-jump video analysis and simulations based on our expanded dynamical model demonstrate that the initial body coordinates of position (relative to the hind-legs ground-contact points) are dominant in predicting the jumps’ azimuth and elevation angles. We also report a strong linear correlation between the jumps’ pitch-angular-velocity and flight initiation timing, such that head downwards rotations lead to earlier wing opening. In addition to offering important insights into the bio-mechanical principles of locust jumping and flight initiation, the findings from this study will be used in designing future prototypes of a bio-inspired miniature jumping robot that will be employed in animal behaviour studies and environmental monitoring applications. PMID:27703846
A diffuse plate boundary model for Indian Ocean tectonics
NASA Technical Reports Server (NTRS)
Wiens, D. A.; Demets, C.; Gordon, R. G.; Stein, S.; Argus, D.
1985-01-01
It is suggested that motion along the virtually aseismic Owen fracture zone is negligible, so that Arabia and India are contained within a single Indo-Arabian plate divided from the Australian plate by a diffuse boundary. The boundary is a zone of concentrated seismicity and deformation commonly characterized as 'intraplate'. The rotation vector of Australia relative to Indo-Arabia is consistent with the seismologically observed 2 cm/yr of left-lateral strike-slip along the Ninetyeast Ridge, north-south compression in the Central Indian Ocean, and the north-south extension near Chagos.
Estimating networks with jumps
Kolar, Mladen; Xing, Eric P.
2013-01-01
We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying data collected over a period of time, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to i.i.d. data from an invariant model widely considered in current literature of structural estimation. In particular, we consider the scenario in which the model evolves in a piece-wise constant fashion. We propose a procedure that estimates the structure of a graphical model by minimizing the temporally smoothed L1 penalized regression, which allows jointly estimating the partition boundaries of the VCVS model and the coefficient of the sparse precision matrix on each block of the partition. A highly scalable proximal gradient method is proposed to solve the resultant convex optimization problem; and the conditions for sparsistent estimation and the convergence rate of both the partition boundaries and the network structure are established for the first time for such estimators. PMID:25013533
Advances in modeling sorption and diffusion of moisture in porous reactive materials.
Harley, Stephen J; Glascoe, Elizabeth A; Lewicki, James P; Maxwell, Robert S
2014-06-23
Water-vapor-uptake experiments were performed on a silica-filled poly(dimethylsiloxane) (PDMS) network and modeled by using two different approaches. The data was modeled by using established methods and the model parameters were used to predict moisture uptake in a sample. The predictions are reasonably good, but not outstanding; many of the shortcomings of the modeling are discussed. A high-fidelity modeling approach is derived and used to improve the modeling of moisture uptake and diffusion. Our modeling approach captures the physics and kinetics of diffusion and adsorption/desorption, simultaneously. It predicts uptake better than the established method; more importantly, it is also able to predict outgassing. The material used for these studies is a filled-PDMS network; physical interpretations concerning the sorption and diffusion of moisture in this network are discussed.
Nilsson, Markus; van Westen, Danielle; Ståhlberg, Freddy; Sundgren, Pia C; Lätt, Jimmy
2013-08-01
Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange
Comparison and analysis of theoretical models for diffusion-controlled dissolution.
Wang, Yanxing; Abrahamsson, Bertil; Lindfors, Lennart; Brasseur, James G
2012-05-01
Dissolution models require, at their core, an accurate diffusion model. The accuracy of the model for diffusion-dominated dissolution is particularly important with the trend toward micro- and nanoscale drug particles. Often such models are based on the concept of a "diffusion layer." Here a framework is developed for diffusion-dominated dissolution models, and we discuss the inadequacy of classical models that are based on an unphysical constant diffusion layer thickness assumption, or do not correctly modify dissolution rate due to "confinement effects": (1) the increase in bulk concentration from confinement of the dissolution process, (2) the modification of the flux model (the Sherwood number) by confinement. We derive the exact mathematical solution for a spherical particle in a confined fluid with impermeable boundaries. Using this solution, we analyze the accuracy of a time-dependent "infinite domain model" (IDM) and "quasi steady-state model" (QSM), both formally derived for infinite domains but which can be applied in approximate fashion to confined dissolution with proper adjustment of a concentration parameter. We show that dissolution rate is sensitive to the degree of confinement or, equivalently, to the total concentration C(tot). The most practical model, the QSM, is shown to be very accurate for most applications and, consequently, can be used with confidence in design-level dissolution models so long as confinement is accurately treated. The QSM predicts the ratio of diffusion layer thickness to particle radius (the Sherwood number) as a constant plus a correction that depends on the degree of confinement. The QSM also predicts that the time required for complete saturation or dissolution in diffusion-controlled dissolution experiments is singular (i.e., infinite) when total concentration equals the solubility. Using the QSM, we show that measured differences in dissolution rate in a diffusion-controlled dissolution experiment are a result of
Measurement and modeling of CO2 diffusion coefficient in Saline Aquifer at reservoir conditions
NASA Astrophysics Data System (ADS)
Azin, Reza; Mahmoudy, Mohamad; Raad, Seyed Mostafa Jafari; Osfouri, Shahriar
2013-12-01
Storage of CO2 in deep saline aquifers is a promising techniques to mitigate global warming and reduce greenhouse gases (GHG). Correct measurement of diffusivity is essential for predicting rate of transfer and cumulative amount of trapped gas. Little information is available on diffusion of GHG in saline aquifers. In this study, diffusivity of CO2 into a saline aquifer taken from oil field was measured and modeled. Equilibrium concentration of CO2 at gas-liquid interface was determined using Henry's law. Experimental measurements were reported at temperature and pressure ranges of 32-50°C and 5900-6900 kPa, respectively. Results show that diffusivity of CO2 varies between 3.52-5.98×10-9 m2/s for 5900 kPa and 5.33-6.16×10-9 m2/s for 6900 kPa initial pressure. Also, it was found that both pressure and temperature have a positive impact on the measures of diffusion coefficient. Liquid swelling due to gas dissolution and variations in gas compressibility factor as a result of pressure decay was found negligible. Measured diffusivities were used model the physical model and develop concentration profile of dissolved gas in the liquid phase. Results of this study provide unique measures of CO2 diffusion coefficient in saline aquifer at high pressure and temperature conditions, which can be applied in full-field studies of carbon capture and sequestration projects.
The Diffuse Galactic Gamma-Ray Emission Model for GLAST LAT
Porter, T.A.; Digel, S.W.; Grenier, I.A.; Moskalenko, I.V.; Strong, A.W.; /Garching, Max Planck Inst., MPE
2007-06-13
Diffuse emission from the Milky Way dominates the gamma-ray sky. About 80% of the high-energy luminosity of the Milky Way comes from processes in the interstellar medium. The Galactic diffuse emission traces interactions of energetic particles, primarily protons and electrons, with the interstellar gas and radiation field, thus delivering information about cosmic-ray spectra and interstellar mass in distant locations. Additionally, the Galactic diffuse emission is the celestial foreground for the study of gamma-ray point sources and the extragalactic diffuse gamma-ray emission. We will report on the latest developments in the modeling of the Galactic diffuse emission, which will be used for the Gamma Ray Large Area Space Telescope (GLAST) investigations.
Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks
NASA Astrophysics Data System (ADS)
Rätz, Andreas; Röger, Matthias
2014-08-01
Signalling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term in the membrane equations. A specific model of this form was recently proposed by the authors for the GTPase cycle in cells. We investigate here a putative role of diffusive instabilities in cell polarization. By a linearized stability analysis, we identify two different mechanisms. The first resembles a classical Turing instability for the membrane subsystem and requires (unrealistically) large differences in the lateral diffusion of activator and substrate. On the other hand, the second possibility is induced by the difference in cytosolic and lateral diffusion and appears much more realistic. We complement our theoretical analysis by numerical simulations that confirm the new stability mechanism and allow us to investigate the evolution beyond the regime where the linearization applies.
Bellassai, Debora; Spinazzola, Antonio; Silvestri, Stefano
2015-01-01
In absence of results of environmental monitoring to proceed with the assessment of occupational exposure, it was developed a model that retraces the one of Pasquill and Gifford, currently used for the estimation of concentrations of pollutants at certain distances from the source in outdoor environment. Purpose of the study is the quantitative estimate of the diffusion of airborne asbestos fibers in function of the distance from the source in an factory where railway carriages were produced during the period when asbestos was sprayed as insulator of the body. The treatment was carried out in a large shed without separation from other operations. The application of the model, given the characteristics of the emitting source, has allowed us to estimate the diffusion of particles inside the shed with an expected decrease in concentration inversely proportional to the distance from the source. By appropriate calculations the concentration by weight has been converted into number offibers by volume, the unit of measure currently used for the definition of asbestos pollution. PMID:26193738
Sun, Jia; Zhang, Xiao-Peng; Li, Xiao-Ting; Tang, Lei; Cui, Yong; Zhang, Xiao-Yan; Sun, Ying-Shi
2014-01-01
In vivo imaging studies in animal models are hindered by variables that contribute to poor image quality and measurement reliability. As such we sought to improve the diffusion coefficient (ADC) of an orthotopic mouse model of gastric cancer in diffusion-weighted images (DWI) using alginate moulding and Ultrasonic coupling medium. BGC-823 human gastric cancer cells were subcutaneously injected into the abdomen of nude mice and 1 mm3 primary tumour was orthotopically transplanted. Alginate and coupling medium were applied to the mice and MRI (T2 and DWI) was performed for 6 weeks. Regions of interest (ROI) were drawn and liver and tumour ADC were evaluated. Using alginate moulding, the mean quality total score of DW imaging was 8.53; however, in control animals this value was 5.20 (p < 0.001). The coefficient of variation of ADC of liver in experimental and control groups were 0.071 and 0.270 (p < 0.001), respectively, suggesting this method may be helpful for DWI studies of important human diseases such as gastric cancer. PMID:25123166
Random variability in mesoscale wind observations and implications for diffusion models
Hanna, S.R.
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.
Quasilinear model for energetic particle diffusion in radial and velocity space
NASA Astrophysics Data System (ADS)
Waltz, R. E.; Bass, E. M.; Staebler, G. M.
2013-04-01
A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2×2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.
Quasilinear model for energetic particle diffusion in radial and velocity space
Waltz, R. E.; Staebler, G. M.; Bass, E. M.
2013-04-15
A quasilinear model for passive energetic particle (EP) turbulent diffusion in radial and velocity space is fitted and tested against nonlinear gyrokinetic tokamak simulations with the GYRO code [J. Candy and R. E. Waltz, Phys. Rev. Lett. 91, 045001 (2003)]. Off diagonal elements of a symmetric positive definite 2 Multiplication-Sign 2 EP diffusion matrix account for fluxes up radial (energy) gradients driven by energy (radial) gradients of the EP velocity space distribution function. The quasilinear ratio kernel of the model is provided by a simple analytic formula for the EP radial and velocity space EP diffusivity relative to radial thermal ion energy diffusivity at each linear mode of the turbulence driven by the thermal plasma. The TGLF [G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas 14, 0055909 (2007); ibid. 15, 0055908 (2008)] tokamak transport model provides the linear mode frequency and growth rates to the kernel as well as the nonlinear spectral weight for each mode.
NASA Astrophysics Data System (ADS)
Shima, Hiroyuki
2012-11-01
The tree-based rope swing is a popular recreational facility, often installed in outdoor areas. Hanging from a rope, users drop from a high platform and then swing at great speed like ‘Tarzan’, finally jumping ahead to land on the ground. The question naturally arises, how far can Tarzan jump using the swing? In this paper, I present an introductory analysis of the mechanics of the Tarzan swing, a large pendulum-like swing with Tarzan himself attached as weight. This enables determination of how much further forward Tarzan can jump using a given swing apparatus. The discussion is based on elementary mechanics and is, therefore, expected to provide rich opportunities for investigations using analytic and numerical methods.
Froghopper-inspired direction-changing concept for miniature jumping robots.
Jung, Gwang-Pil; Cho, Kyu-Jin
2016-09-14
To improve the maneuverability and agility of jumping robots, several researchers have studied steerable jumping mechanisms. This steering ability enables robots to reach a particular target by controlling their jumping direction. To this end, we propose a novel direction-changing concept for miniature jumping robots. The proposed concept allows robots to be steerable while exerting minimal effects on jumping performance. The key design principles were adopted from the froghopper's power-producing hind legs and the moment cancellation accomplished by synchronized leg operation. These principles were applied via a pair of symmetrically positioned legs and conventional gears, which were modeled on the froghopper's anatomy. Each leg has its own thrusting energy, which improves jumping performance by allowing the mechanism to thrust itself with both power-producing legs. Conventional gears were utilized to simultaneously operate the legs and cancel out the moments that they induce, which minimizes body spin. A prototype to verify the concept was built and tested by varying the initial jumping posture. Three jumping postures (synchronous, asynchronous, and single-legged) were tested to investigate how synchronization and moment cancelling affect jumping performance. The results show that synchronous jumping allows the mechanism to change direction from -40° to 40°, with an improved take-off speed. The proposed concept can only be steered in a limited range of directions, but it has potential for use in miniature jumping robots that can change jumping direction with a minimal drop in jumping performance.
Froghopper-inspired direction-changing concept for miniature jumping robots.
Jung, Gwang-Pil; Cho, Kyu-Jin
2016-01-01
To improve the maneuverability and agility of jumping robots, several researchers have studied steerable jumping mechanisms. This steering ability enables robots to reach a particular target by controlling their jumping direction. To this end, we propose a novel direction-changing concept for miniature jumping robots. The proposed concept allows robots to be steerable while exerting minimal effects on jumping performance. The key design principles were adopted from the froghopper's power-producing hind legs and the moment cancellation accomplished by synchronized leg operation. These principles were applied via a pair of symmetrically positioned legs and conventional gears, which were modeled on the froghopper's anatomy. Each leg has its own thrusting energy, which improves jumping performance by allowing the mechanism to thrust itself with both power-producing legs. Conventional gears were utilized to simultaneously operate the legs and cancel out the moments that they induce, which minimizes body spin. A prototype to verify the concept was built and tested by varying the initial jumping posture. Three jumping postures (synchronous, asynchronous, and single-legged) were tested to investigate how synchronization and moment cancelling affect jumping performance. The results show that synchronous jumping allows the mechanism to change direction from -40° to 40°, with an improved take-off speed. The proposed concept can only be steered in a limited range of directions, but it has potential for use in miniature jumping robots that can change jumping direction with a minimal drop in jumping performance. PMID:27625411
Modelling the effect of diffuse light on canopy photosynthesis in controlled environments.
Cavazzoni, James; Volk, Tyler; Tubiello, Francesco; Monje, Oscar
2002-01-01
A layered canopy model was used to analyze the effects of diffuse light on canopy gross photosynthesis in controlled environment plant growth chambers, where, in contrast to the field, highly diffuse light can occur at high irradiance. The model suggests that high diffuse light fractions (approximately 0.7) and irradiance (1400 micromoles m-2 s-1) may enhance crop life-cycle canopy gross photosynthesis for hydroponic wheat by about 20% compared to direct light at the same irradiance. Our simulations suggest that high accuracy is not needed in specifying diffuse light fractions in chambers between approximately 0.7 and 1, because simulated photosynthesis for closed canopies plateau in this range. We also examined the effect of leaf angle distribution on canopy photosynthesis under growth chamber conditions, as these distributions determine canopy extinction coefficients for direct and diffuse light. We show that the spherical leaf angle distribution is not suitable for modeling photosynthesis of planophile canopies (e.g., soybean and peanut) in growth chambers. Also, the absorption of the light reflected from the surface below the canopy should generally be included in model simulations, as the corresponding albedo values in the photosynthetically active range may be quite high in growth chambers (e.g., approximately 0.5). In addition to the modeling implications, our results suggest that diffuse light conditions should be considered when drawing conclusions from experiments in controlled environments.
Modeling cation diffusion in compacted water-saturatedNa-bentonite at low ionic strength
Bourg, Ian C.; Sposito, Garrison; Bourg, Alain C.M.
2007-08-28
Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the 'macropore/nanopore' model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the 'surface diffusion' model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm{sup -3} (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.2 kg dm{sup -3}.
Modelling the effect of diffuse light on canopy photosynthesis in controlled environments
NASA Technical Reports Server (NTRS)
Cavazzoni, James; Volk, Tyler; Tubiello, Francesco; Monje, Oscar; Janes, H. W. (Principal Investigator)
2002-01-01
A layered canopy model was used to analyze the effects of diffuse light on canopy gross photosynthesis in controlled environment plant growth chambers, where, in contrast to the field, highly diffuse light can occur at high irradiance. The model suggests that high diffuse light fractions (approximately 0.7) and irradiance (1400 micromoles m-2 s-1) may enhance crop life-cycle canopy gross photosynthesis for hydroponic wheat by about 20% compared to direct light at the same irradiance. Our simulations suggest that high accuracy is not needed in specifying diffuse light fractions in chambers between approximately 0.7 and 1, because simulated photosynthesis for closed canopies plateau in this range. We also examined the effect of leaf angle distribution on canopy photosynthesis under growth chamber conditions, as these distributions determine canopy extinction coefficients for direct and diffuse light. We show that the spherical leaf angle distribution is not suitable for modeling photosynthesis of planophile canopies (e.g., soybean and peanut) in growth chambers. Also, the absorption of the light reflected from the surface below the canopy should generally be included in model simulations, as the corresponding albedo values in the photosynthetically active range may be quite high in growth chambers (e.g., approximately 0.5). In addition to the modeling implications, our results suggest that diffuse light conditions should be considered when drawing conclusions from experiments in controlled environments.
Modeling cation diffusion in compacted water-saturated sodium bentonite at low ionic strength.
Bourg, Ian C; Sposito, Garrison; Bourg, Alain C M
2007-12-01
Sodium bentonites are used as barrier materials for the isolation of landfills and are under consideration for a similar use in the subsurface storage of high-level radioactive waste. The performance of these barriers is determined in large part by molecular diffusion in the bentonite pore space. We tested two current models of cation diffusion in bentonite against experimental data on the relative apparent diffusion coefficients of two representative cations, sodium and strontium. On the "macropore/nanopore" model, solute molecules are divided into two categories, with unequal pore-scale diffusion coefficients, based on location: in macropores or in interlayer nanopores. On the "surface diffusion" model, solute molecules are divided into categories based on chemical speciation: dissolved or adsorbed. The macropore/nanopore model agrees with all experimental data at partial montmorillonite dry densities ranging from 0.2 (a dilute bentonite gel) to 1.7 kg dm(-3) (a highly compacted bentonite with most of its pore space located in interlayer nanopores), whereas the surface diffusion model fails at partial montmorillonite dry densities greater than about 1.3 kg dm(-3). PMID:18186346
Modelling the effect of diffuse light on canopy photosynthesis in controlled environments.
Cavazzoni, James; Volk, Tyler; Tubiello, Francesco; Monje, Oscar
2002-01-01
A layered canopy model was used to analyze the effects of diffuse light on canopy gross photosynthesis in controlled environment plant growth chambers, where, in contrast to the field, highly diffuse light can occur at high irradiance. The model suggests that high diffuse light fractions (approximately 0.7) and irradiance (1400 micromoles m-2 s-1) may enhance crop life-cycle canopy gross photosynthesis for hydroponic wheat by about 20% compared to direct light at the same irradiance. Our simulations suggest that high accuracy is not needed in specifying diffuse light fractions in chambers between approximately 0.7 and 1, because simulated photosynthesis for closed canopies plateau in this range. We also examined the effect of leaf angle distribution on canopy photosynthesis under growth chamber conditions, as these distributions determine canopy extinction coefficients for direct and diffuse light. We show that the spherical leaf angle distribution is not suitable for modeling photosynthesis of planophile canopies (e.g., soybean and peanut) in growth chambers. Also, the absorption of the light reflected from the surface below the canopy should generally be included in model simulations, as the corresponding albedo values in the photosynthetically active range may be quite high in growth chambers (e.g., approximately 0.5). In addition to the modeling implications, our results suggest that diffuse light conditions should be considered when drawing conclusions from experiments in controlled environments. PMID:12882223
Nonstandard Analysis and Jump Conditions for Converging Shock Waves
NASA Technical Reports Server (NTRS)
Baty, Roy S.; Farassat, Fereidoun; Tucker, Don H.
2008-01-01
Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.
A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks
Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan
2015-01-01
Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. PMID:25491372
Diffusive to quasi-ballistic random laser: incoherent and coherent models
NASA Astrophysics Data System (ADS)
Guerin, W.; Chong, Y. D.; Baudouin, Q.; Liertzer, M.; Rotter, S.; Kaiser, R.
2016-09-01
We study the crossover between the diffusive and quasi-ballistic regimes of random lasers. In particular, we compare incoherent models based on the diffusion equation and the radiative transfer equation (RTE), which neglect all wave effects, with a coherent wave model for the random laser threshold. We show that both the incoherent and the coherent models predict qualitatively similar thresholds, with a smooth transition from a diffuse to a quasi-ballistic regime. The shape of the intensity distribution in the sample as predicted by the RTE model at threshold is also in good agreement with the coherent model. The approximate incoherent models thus provide useful analytical predictions for the threshold of random lasers as well as the shape of the random laser modes at threshold.
King, M.D.; Burkardt, N.; Clark, B.T.
2006-01-01
Recent literature on the diffusion of innovations concentrates either specifically on public adoption of policy, where social or environmental conditions are the dependent variables for adoption, or on private adoption of an innovation, where emphasis is placed on the characteristics of the innovation itself. This article uses both the policy diffusion literature and the diffusion of innovation literature to assess watershed management councils' decisions to adopt, or not adopt, scientific models. Watershed management councils are a relevant case study because they possess both public and private attributes. We report on a survey of councils in the United States that was conducted to determine the criteria used when selecting scientific models for studying watershed conditions. We found that specific variables from each body of literature play a role in explaining the choice to adopt scientific models by these quasi-public organizations. The diffusion of innovation literature contributes to an understanding of how organizations select models by confirming the importance of a model's ability to provide better data. Variables from the policy diffusion literature showed that watershed management councils that employ consultants are more likely to use scientific models. We found a gap between those who create scientific models and those who use these models. We recommend shrinking this gap through more communication between these actors and advancing the need for developers to provide more technical assistance.
The hydrogen diffusion in liquid aluminum alloys from ab initio molecular dynamics.
Jakse, N; Pasturel, A
2014-09-01
We study the hydrogen diffusion in liquid aluminum alloys through extensive ab initio molecular dynamics simulations. At the microscopic scale, we show that the hydrogen motion is characterized by a broad distribution of spatial jumps that does not correspond to a Brownian motion. To determine the self-diffusion coefficient of hydrogen in liquid aluminum alloys, we use a generalized continuous time random walk model recently developed to describe the hydrogen diffusion in pure aluminum. In particular, we show that the model successfully accounts the effects of alloying elements on the hydrogen diffusion in agreement with experimental features.
NASA Astrophysics Data System (ADS)
Rozel, A. B.; Golabek, G.; Thielmann, M.; Tackley, P.
2015-12-01
We present a semi analytical model of mantle convection able to predict the grain size profile of the present day Earth. Grain size evolution has been studied with increasing interest over the last decades but its behavior in both mantle and lithosphere remains largely misunderstood due to its non-linearity. Several recent studies suggest that it might play a fundamental role in localization of deformation in the lithosphere but we focus here on the mantle in which we also observe important processes.We propose a 1D compressible thermal convection model based on the equality of advective heat flux and the integral of viscous dissipation in the whole domain. Imposing mass conservation, our model is able to predict all rheological parameters able to produce both present day average surface velocity and lower mantle viscosity. Composite rheologies involving dislocation creep and grain size dependent diffusion creep are considered. The effect of phase transitions on the grain size is also explicitely taken into account. We present the family of solutions for the activation volume and the viscosity jump at the 660 discontinuity according to any initial choice of activation energy. The scaling laws for rheological parameters obtained are compared to self-consistent evolutionary simulations of mantle convection in 2D spherical annulus geometry considering composite rheologies. The transition between diffusion and dislocation creep due to the cooling of the Earth is illustrated in a set of numerical simulations starting from the physical conditions of the Archean.
Modelling of silica diffusion experiments with 32Si in Boom Clay.
Aertsens, Marc; De Cannière, Pierre; Moors, Hugo
2003-03-01
A mathematical model describing the dissolution of nuclear glass directly disposed in clay combines a first-order dissolution rate law with the diffusion of dissolved silica in clay. According to this model, the main parameters describing the long-term dissolution of the glass are etaR, the product of the diffusion accessible porosity eta and the retardation factor R, and the apparent diffusion coefficient D(app) of dissolved silica in clay. For determining the migration parameters needed for long-term predictions, four Through-Diffusion (T-D) experiments and one percolation test have been performed on undisturbed clay cores. In the Through-Diffusion experiments, the concentration decrease after injection of 32Si (radioactive labelled silica) was measured in the inlet compartment. At the end of the T-D experiments, the clay cores were cut in thin slices and the activity of labelled silica in each slice was determined. The measured activity profiles for these four clay cores are well reproducible. Since no labelled silica could be detected in the outlet compartments, the Through-Diffusion experiments are fitted by two In-Diffusion models: one model assuming linear and reversible sorption equilibrium and a second model taking into account sorption kinetics. Although the kinetic model provides better fits, due to the sufficiently long duration of the experiments, both models give approximately similar values for the fit parameters. The single percolation test leads to an apparent diffusion coefficient value about two to three times lower than those of the Through-Diffusion tests. Therefore, dissolved silica appears to be strongly retarded in Boom Clay. A retardation factor R between 100 and 300 was determined. The corresponding in situ distribution coefficient K(d) is in the range 25-75 cm(3) g(-1). The apparent diffusion coefficient of dissolved silica in Boom Clay is estimated between 2 x 10(-13) and 7 x 10(-13) m(2) s(-1). The pore diffusion coefficient is in the
Wang, Jing
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.
Modeling diffusion of adsorbed polymer with explicit solvent.
Desai, Tapan G; Keblinski, Pawel; Kumar, Sanat K; Granick, Steve
2007-05-25
Computer simulations of a polymer chain of length N strongly adsorbed at the solid-liquid interface in the presence of explicit solvent are used to delineate the factors affecting the N dependence of the polymer lateral diffusion coefficient, D(||). We find that surface roughness has a large influence, and D(||) scales as D(||) approximately N(-x), with x approximately 3/4 and x approximately 1 for ideal smooth and corrugated surfaces, respectively. The first result is consistent with the hydrodynamics of a "particle" of radius of gyration R(G) approximately N(nu) (nu=0.75) translating parallel to a planar interface, while the second implies that the friction of the adsorbed chains dominates. These results are discussed in the context of recent measurements.
Reconstruction of two constant coefficients in linear anisotropic diffusion model
NASA Astrophysics Data System (ADS)
Mola, Gianluca; Okazawa, Noboru; Yokota, Tomomi
2016-11-01
Let (H,< \\cdot ,\\cdot > ) be a complex Hilbert space and A:D(A)\\to H and B:D(B)\\to H be nonnegative and selfadjoint operators. We study the inverse problem consisting in the identification of the function u:[0,T]\\to H and two constants α, β \\in {{{R}}}+=(0,∞ ) (diffusion coefficients) that fulfill the initial-value problem u ‧ ( t ) + α Au ( t ) + β Bu ( t ) = 0 , t ∈ ( 0 , T ) , u ( 0 ) = x , and the additional conditions < Au ( T ) , u ( T ) > = φ and < Bu ( T ) , u ( T ) > = ψ . Under suitable assumptions on the operators A and B, and on the data x\\in H and \\varphi ,\\psi \\gt 0, we shall construct a solution and prove its uniqueness and continuous dependence on the data. Applications are considered.
A novel rumor diffusion model considering the effect of truth in online social media
NASA Astrophysics Data System (ADS)
Sun, Ling; Liu, Yun; Zeng, Qing-An; Xiong, Fei
2015-12-01
In this paper, we propose a model to investigate how truth affects rumor diffusion in online social media. Our model reveals a relation between rumor and truth — namely, when a rumor is diffusing, the truth about the rumor also diffuses with it. Two patterns of the agents used to identify rumor, self-identification and passive learning are taken into account. Combining theoretical proof and simulation analysis, we find that the threshold value of rumor diffusion is negatively correlated to the connectivity between nodes in the network and the probability β of agents knowing truth. Increasing β can reduce the maximum density of the rumor spreaders and slow down the generation speed of new rumor spreaders. On the other hand, we conclude that the best rumor diffusion strategy must balance the probability of forwarding rumor and the probability of agents losing interest in the rumor. High spread rate λ of rumor would lead to a surge in truth dissemination which will greatly limit the diffusion of rumor. Furthermore, in the case of unknown λ, increasing β can effectively reduce the maximum proportion of agents who do not know the truth, but cannot narrow the rumor diffusion range in a certain interval of β.
A kinetic model for molecular diffusion through pores.
D'Agostino, Tommaso; Salis, Samuele; Ceccarelli, Matteo
2016-07-01
The number of pathogens developing multiple drug resistance is ever increasing. The impact on healthcare systems is huge and the need for novel antibiotics as well a new way to develop them is urgent, especially against Gram-negative bacteria. The first defense of these bacteria is the outer membrane, where unspecific protein channels (porins) modulate nutrients passive diffusion. Also polar antibiotics enter through this path and down-regulation and/or mutation of porins are very common in drug resistant strains. Our inability to come up with novel effective antibiotics mostly relies upon the insufficient comprehension of the key molecular features enabling better penetration through porins. Molecular dynamics simulations offer an extraordinary tool in the study of the dynamics of biological systems; however, one of the major drawbacks of this method is that its use is currently restricted to study time scales of the order of microsecond. Enhanced sampling methods like Metadynamics have been recently used to investigate the diffusion of antibiotics through bacterial porins. The main limitation is that dynamical properties cannot be estimated because of the different potential that the systems under study are experiencing. Recently, the scope of Metadynamics has been extended. By applying an a posteriori analysis one can obtain rates of transitions and rate-limiting steps of the process under study, directly comparable with kinetic data extracted from electrophysiology experiments. In this work, we apply this method to the study of the permeability of Escherichia coli's OmpF with respect to Meropenem, finding good agreement with the residence time obtained analyzing experimental current noise. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.
Plimpton, Steven J.; Sershen, Cheryl L.; May, Elebeoba E.
2015-01-01
This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Moreover, presented in figure 1 is the evolution of the diffusion profiles of a containment granuloma over time.
Plimpton, Steven J.; Sershen, Cheryl L.; May, Elebeoba E.
2015-01-01
This paper describes a method for incorporating a diffusion field modeling oxygen usage and dispersion in a multi-scale model of Mycobacterium tuberculosis (Mtb) infection mediated granuloma formation. We implemented this method over a floating-point field to model oxygen dynamics in host tissue during chronic phase response and Mtb persistence. The method avoids the requirement of satisfying the Courant-Friedrichs-Lewy (CFL) condition, which is necessary in implementing the explicit version of the finite-difference method, but imposes an impractical bound on the time step. Instead, diffusion is modeled by a matrix-based, steady state approximate solution to the diffusion equation. Moreover, presented in figuremore » 1 is the evolution of the diffusion profiles of a containment granuloma over time.« less
Waxman, D
2011-01-21
We investigate the detailed connection between the Wright-Fisher model of random genetic drift and the diffusion approximation, under the assumption that selection and drift are weak and so cause small changes over a single generation. A representation of the mathematics underlying the Wright-Fisher model is introduced which allows the connection to be made with the corresponding mathematics underlying the diffusion approximation. Two 'hybrid' models are also introduced which lie 'between' the Wright-Fisher model and the diffusion approximation. In model 1 the relative allele frequency takes discrete values while time is continuous; in model 2 time is discrete and relative allele frequency is continuous. While both hybrid models appear to have a similar status and the same level of plausibility, the different nature of time and frequency in the two models leads to significant mathematical differences. Model 2 is mathematically inconsistent and has to be ruled out as being meaningful. Model 1 is used to clarify the content of Kimura's solution of the diffusion equation, which is shown to have the natural interpretation as describing only those populations where alleles are segregating. By contrast the Wright-Fisher model and the solution of the diffusion equation of McKane and Waxman cover populations of all categories, namely populations where alleles segregate, are lost, or fix.
Uncertainty quantification in modeling of microfluidic T-sensor based diffusion immunoassay.
Jha, Aman Kumar; Bahga, Supreet Singh
2016-01-01
Comparison of experimental data with modeling predictions is essential for making quantitative measurements of species properties, such as diffusion coefficients and species concentrations using a T-sensor. To make valid comparisons between experimental data and model predictions, it is necessary to account for uncertainty in model predictions due to uncertain values of model parameters. We present an analysis of uncertainty induced in model predictions of a T-sensor based competitive diffusion immunoassay due to uncertainty in diffusion constants, binding reaction rate constants, and inlet flow speed. We use a non-intrusive stochastic uncertainty quantification method employing polynomial chaos expansions to represent the dependence of uncertain species concentrations on the uncertainty in model parameters. Our simulations show that the uncertainties in model parameters lead to significant spatially varying uncertainty in predicted concentration. In particular, the diffusivity of fluorescently labeled probe antigen dominates the overall uncertainty. The predicted uncertainty in fluorescence intensity is minimum near the centerline of T-sensor and relatively high in the regions with gradients in fluorescence intensity. We show that using centerline fluorescence intensity instead of first derivative of fluorescence intensity as the system response for measuring sample antigen concentration in T-sensor based competitive diffusion immunoassay leads to lower uncertainty and higher detection sensitivity. PMID:26858817
Assessing cognitive processes with diffusion model analyses: a tutorial based on fast-dm-30
Voss, Andreas; Voss, Jochen; Lerche, Veronika
2015-01-01
Diffusion models can be used to infer cognitive processes involved in fast binary decision tasks. The model assumes that information is accumulated continuously until one of two thresholds is hit. In the analysis, response time distributions from numerous trials of the decision task are used to estimate a set of parameters mapping distinct cognitive processes. In recent years, diffusion model analyses have become more and more popular in different fields of psychology. This increased popularity is based on the recent development of several software solutions for the parameter estimation. Although these programs make the application of the model relatively easy, there is a shortage of knowledge about different steps of a state-of-the-art diffusion model study. In this paper, we give a concise tutorial on diffusion modeling, and we present fast-dm-30, a thoroughly revised and extended version of the fast-dm software (Voss and Voss, 2007) for diffusion model data analysis. The most important improvement of the fast-dm version is the possibility to choose between different optimization criteria (i.e., Maximum Likelihood, Chi-Square, and Kolmogorov-Smirnov), which differ in applicability for different data sets. PMID:25870575
The Effect of Depth Jumps and Weight Training on Leg Strength and Vertical Jump.
ERIC Educational Resources Information Center
Clutch, David; And Others
1983-01-01
Two experiments examined the results of depth jumping programs to determine: (1) whether certain depth jumping routines, when combined with weight training, are better than others; and (2) the effect of depth jumping on athletes already in training. Results indicated that depth jumping is effective, but no more so than regular jumping routines.…
Wang, Xiaoqiang; Du, Qiang
2008-03-01
Diffuse interface (phase field) models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and the line tension energy with prescribed volume and surface area constraints. By comparing our numerical simulations with recent biological experiments, it is demonstrated that the diffuse interface models can effectively capture the rich phenomena associated with the multi-component vesicle transformation and thus offering great functionality in their simulation and modelling.
Using a Quasipotential Transformation for Modeling Diffusion Media inPolymer-Electrolyte Fuel Cells
Weber, Adam Z.; Newman, John
2008-08-29
In this paper, a quasipotential approach along with conformal mapping is used to model the diffusion media of a polymer-electrolyte fuel cell. This method provides a series solution that is grid independent and only requires integration along a single boundary to solve the problem. The approach accounts for nonisothermal phenomena, two-phase flow, correct placement of the electronic potential boundary condition, and multilayer media. The method is applied to a cathode diffusion medium to explore the interplay between water and thermal management and performance, the impact of the rib-to-channel ratio, and the existence of diffusion under the rib and flooding phenomena.
Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion
NASA Astrophysics Data System (ADS)
Lin, Zhigui; Ruiz-Baier, Ricardo; Tian, Canrong
2014-01-01
This paper is concerned with the study of pattern formation for an inhomogeneous Brusselator model with cross-diffusion, modeling an autocatalytic chemical reaction taking place in a three-dimensional domain. For the spatial discretization of the problem we develop a novel finite volume element (FVE) method associated to a piecewise linear finite element approximation of the cross-diffusion system. We study the main properties of the unique equilibrium of the related dynamical system. A rigorous linear stability analysis around the spatially homogeneous steady state is provided and we address in detail the formation of Turing patterns driven by the cross-diffusion effect. In addition we focus on the spatial accuracy of the FVE method, and a series of numerical simulations confirm the expected behavior of the solutions. In particular we show that, depending on the spatial dimension, the magnitude of the cross-diffusion influences the selection of spatial patterns.
On the application of kinematic models to simulate the diffusive processes of debris flows
NASA Astrophysics Data System (ADS)
Arattano, M.; Franzi, L.
2010-08-01
Debris flows generally propagate along steep mountain torrents with dynamics primarily governed by gravitational and frictional forces. Thus, debris flows modelling can be successfully performed through the application of kinematic models, which consider only the effects of slope and friction and neglect the remaining terms of the momentum equation. However, the diffusion processes that can be observed in the field, such as the spreading of the debris flow wave as it flows downstream, can not be theoretically predicted by kinematic models, since diffusion is a second-order process neglected in the kinematic approximation. In this paper, this issue is discussed and an application for both a generalized diffusion wave model and a kinematic model is proposed of a debris flow which occurred in an Italian instrumented torrent to identify, in a real case scenario, the effective value of the neglected terms in the kinematic approximation.
Modeling and Uncertainty Quantification of Vapor Sorption and Diffusion in Heterogeneous Polymers
Sun, Yunwei; Harley, Stephen J.; Glascoe, Elizabeth A.
2015-08-13
A high-fidelity model of kinetic and equilibrium sorption and diffusion is developed and exercised. The gas-diffusion model is coupled with a triple-sorption mechanism: Henry’s law absorption, Langmuir adsorption, and pooling or clustering of molecules at higher partial pressures. Sorption experiments are conducted and span a range of relative humidities (0-95 %) and temperatures (30-60 °C). Kinetic and equilibrium sorption properties and effective diffusivity are determined by minimizing the absolute difference between measured and modeled uptakes. Uncertainty quantification and sensitivity analysis methods are described and exercised herein to demonstrate the capability of this modeling approach. Water uptake in silica-filled and unfilled poly(dimethylsiloxane) networks is investigated; however, the model is versatile enough to be used with a wide range of materials and vapors.
Ocampo-Perez, Raul; Leyva-Ramos, Roberto; Mendoza-Barron, Jovita; Guerrero-Coronado, Rosa M
2011-12-01
The concentration decay curves for the adsorption of phenol on organobentonite were obtained in an agitated tank batch adsorber. The experimental adsorption rate data were interpreted with diffusional models as well as first-order, second-order and Langmuir kinetic models. The surface diffusion model adjusted the data quite well, revealing that the overall rate of adsorption was controlled by surface diffusion. Furthermore, the surface diffusion coefficient increased raising the mass of phenol adsorbed at equilibrium and was independent of the particle diameter in the range 0.042-0.0126 cm. It was demonstrated that the overall rate of adsorption was essentially not affected by the external mass transfer. The second-order and the Langmuir kinetic models fitted the experimental data quite well; however, the kinetic constants of both models varied without any physical meaning while increasing the particle size and the mass of phenol adsorbed at equilibrium.
Field measurements in unwadeable natural hydraulic jumps
NASA Astrophysics Data System (ADS)
Valle, B.; Pasternack, G.
2003-04-01
Recent research in fluvial geomorphology has emphasized the development and application of digital terrain models to better understand process-form relations. However, field measurements in mountain channels have largely been restricted to low velocity or ephemeral flow conditions. To address this problem, a new high-resolution mechanical surveying system was developed at UC Davis and used to measure the 3D bed and water surface topographies of an unwadeable plunging hydraulic jump in the Cache Creek basin, CA. Labeled as the River Truss, the system is capable of making high-resolution form and process measurements over a 30 to 115 m2 area. Bed and water surface DTMs were derived from the field data using AutoCAD. River Truss precision was assessed by DTM differencing the hydraulic jump bed surface topography with a DTM developed from tacheometric survey at low base flows. Bed surface DTMs indicate significant spatial complexity of the underlying bed step in the supercritical flow region and significant downstream bed scour. Water surface DTMs indicate 3D complexity of the plunging flow surface and divergence from 1D free-fall theory. Further study will emphasize the development and deployment of process-based instrumentation such that the complex turbulent air-water flow dynamics associated with natural hydraulic jumps may be better understood. Also, a second generation River Truss that has a larger coverage area and automated data collection has been designed and is now being built.
Some Approaches to Modeling Diffuse Flow at Mid-Ocean Ridges
NASA Astrophysics Data System (ADS)
Farough, A.; Lowell, R. P.; Craft, K.; Germanovich, L. N.
2011-12-01
To obtain a sound understanding of subsurface temperatures and the extent of the subsurface biosphere in young oceanic crust, one must understand the mechanisms of diffuse flow at oceanic spreading centers. Mathematical modeling of diffuse flow at oceanic spreading centers has received relatively little attention compared to high-temperature black smoker discharge, in part because the temperature and fluid flow data required to constrain the models are scarce. We review a number of different approaches to modelling diffuse flow: (1) The simplest method considers 1-D steady-state uniform upflow from below subject to a heat transfer boundary condition at the surface, which represents the effects of mixing of hydrothermal fluid with seawater. These models, in which the heat transfer coefficient and the velocity of the ascending fluid are constrained by observed diffuse flow vent temperature and heat flux, typically result in a steep temperature gradient near the seafloor and subsurface biological activity may be limited to the upper few cm of the crust. (2) A related method uses data on the partitioning of heat flux between focused and diffuse flow and chemical data from the focused and diffuse flow components in a two-limb single pass modeling approach to determine the fraction of high-temperature fluid that is incorporated in the diffuse flow. Using data available from EPR 950', the Main Endeavour Field, and ASHES vent field at Axial Volcano on the Juan de Fuca Ridge in conjunction with Mg as a passive tracer, we find that the mixing ratio of high temperature in diffuse flow is <10%. The high-temperature contribution to the diffuse heat flux remains large, however, and high-temperature vent fluid ultimately contributes ~ 90% of the total heat output from the vent field. In these models mixing between high-temperature fluid and seawater may occur over a considerable depth, and the subsurface biosphere may be ~ 100 m deep beneath diffuse flow sites. (3) Finally, in
ERIC Educational Resources Information Center
Ucke, C.; Schlichting, H-J.
2009-01-01
Snap discs made of bimetal have many technical applications as thermostats. Jumping discs are a toy version of such snap discs. Besides giving technical information, we describe physical investigations. We show especially how, through simple measurements and calculations, you can determine the initial speed ([approximately equal to]3.5 m…
Yuste, S B; Abad, E; Baumgaertner, A
2016-07-01
We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ,P(ℓ)∼ℓ^{-(1+α)} (α>0). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.
NASA Astrophysics Data System (ADS)
Yuste, S. B.; Abad, E.; Baumgaertner, A.
2016-07-01
We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ ,P (ℓ ) ˜ℓ-(1 +α ) (α >0 ). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems.
Yuste, S B; Abad, E; Baumgaertner, A
2016-07-01
We address the problem of diffusion on a comb whose teeth display varying lengths. Specifically, the length ℓ of each tooth is drawn from a probability distribution displaying power law behavior at large ℓ,P(ℓ)∼ℓ^{-(1+α)} (α>0). To start with, we focus on the computation of the anomalous diffusion coefficient for the subdiffusive motion along the backbone. This quantity is subsequently used as an input to compute concentration recovery curves mimicking fluorescence recovery after photobleaching experiments in comblike geometries such as spiny dendrites. Our method is based on the mean-field description provided by the well-tested continuous time random-walk approach for the random-comb model, and the obtained analytical result for the diffusion coefficient is confirmed by numerical simulations of a random walk with finite steps in time and space along the backbone and the teeth. We subsequently incorporate retardation effects arising from binding-unbinding kinetics into our model and obtain a scaling law characterizing the corresponding change in the diffusion coefficient. Finally, we show that recovery curves obtained with the help of the analytical expression for the anomalous diffusion coefficient cannot be fitted perfectly by a model based on scaled Brownian motion, i.e., a standard diffusion equation with a time-dependent diffusion coefficient. However, differences between the exact curves and such fits are small, thereby providing justification for the practical use of models relying on scaled Brownian motion as a fitting procedure for recovery curves arising from particle diffusion in comblike systems. PMID:27575088