Finite linear diffusion model for design of overcharge protection for rechargeable lithium batteries

NASA Technical Reports Server (NTRS)

Narayanan, S. R.; Surampudi, S.; Attia, A. I.

1991-01-01

The overcharge condition in secondary lithium batteries employing redox additives for overcharge protection has been theoretically analyzed in terms of a finite linear diffusion model. The analysis leads to expressions relating the steady-state overcharge current density and cell voltage to the concentration, diffusion coefficient, standard reduction potential of the redox couple, and interelectrode distance. The model permits the estimation of the maximum permissible overcharge rate for any chosen set of system conditions. The model has been experimentally verified using 1,1-prime-dimethylferrocene as a redox additive. The theoretical results may be exploited in the design and optimization of overcharge protection by the redox additive approach.

Molecular surface area based predictive models for the adsorption and diffusion of disperse dyes in polylactic acid matrix.

PubMed

Xu, Suxin; Chen, Jiangang; Wang, Bijia; Yang, Yiqi

2015-11-15

Two predictive models were presented for the adsorption affinities and diffusion coefficients of disperse dyes in polylactic acid matrix. Quantitative structure-sorption behavior relationship would not only provide insights into sorption process, but also enable rational engineering for desired properties. The thermodynamic and kinetic parameters for three disperse dyes were measured. The predictive model for adsorption affinity was based on two linear relationships derived by interpreting the experimental measurements with molecular structural parameters and compensation effect: ΔH° vs. dye size and ΔS° vs. ΔH°. Similarly, the predictive model for diffusion coefficient was based on two derived linear relationships: activation energy of diffusion vs. dye size and logarithm of pre-exponential factor vs. activation energy of diffusion. The only required parameters for both models are temperature and solvent accessible surface area of the dye molecule. These two predictive models were validated by testing the adsorption and diffusion properties of new disperse dyes. The models offer fairly good predictive ability. The linkage between structural parameter of disperse dyes and sorption behaviors might be generalized and extended to other similar polymer-penetrant systems. Copyright © 2015 Elsevier Inc. All rights reserved.

Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hnat, B.

2011-09-22

Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.

Diffusion, Viscosity and Crystal Growth in Microgravity

NASA Technical Reports Server (NTRS)

Myerson, Allan S.

1996-01-01

The diffusivity of TriGlycine Sulfate (TGS), Potassium Dihydrogen Phosphate (KDP), Ammonium Dihydrogen Phosphate (ADF) and other compounds of interest to microgravity crystal growth, in supersaturated solutions as a function of solution concentration, 'age' and 'history was studied experimentally. The factors that affect the growth of crystals from water solutions in microgravity have been examined. Three non-linear optical materials have been studied, potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP) and triglycine sulfate (TGC). The diffusion coefficient and viscosity of supersaturated water solutions were measured. Also theoretical model of diffusivity and viscosity in a metastable state, model of crystal growth from solution including non-linear time dependent diffusivity and viscosity effect and computer simulation of the crystal growth process which allows simulation of the microgravity crystal growth were developed.

Long-time behavior and Turing instability induced by cross-diffusion in a three species food chain model with a Holling type-II functional response.

PubMed

Haile, Dawit; Xie, Zhifu

2015-09-01

In this paper, we study a strongly coupled reaction-diffusion system describing three interacting species in a food chain model, where the third species preys on the second one and simultaneously the second species preys on the first one. An intra-species competition b2 among the second predator is introduced to the food chain model. This parameter produces some very interesting result in linear stability and Turing instability. We first show that the unique positive equilibrium solution is locally asymptotically stable for the corresponding ODE system when the intra-species competition exists among the second predator. The positive equilibrium solution remains linearly stable for the reaction diffusion system without cross diffusion, hence it does not belong to the classical Turing instability scheme. But it becomes linearly unstable only when cross-diffusion also plays a role in the reaction-diffusion system, hence the instability is driven solely from the effect of cross diffusion. Our results also exhibit some interesting combining effects of cross-diffusion, intra-species competitions and inter-species interactions. Numerically, we conduct a one parameter analysis which illustrate how the interactions change the existence of stable equilibrium, limit cycle, and chaos. Some interesting dynamical phenomena occur when we perform analysis of interactions in terms of self-production of prey and intra-species competition of the middle predator. By numerical simulations, it illustrates the existence of nonuniform steady solutions and new patterns such as spot patterns, strip patterns and fluctuations due to the diffusion and cross diffusion in two-dimension. Published by Elsevier Inc.

New Monte Carlo model of cylindrical diffusing fibers illustrates axially heterogeneous fluorescence detection: simulation and experimental validation

PubMed Central

Baran, Timothy M.; Foster, Thomas H.

2011-01-01

We present a new Monte Carlo model of cylindrical diffusing fibers that is implemented with a graphics processing unit. Unlike previously published models that approximate the diffuser as a linear array of point sources, this model is based on the construction of these fibers. This allows for accurate determination of fluence distributions and modeling of fluorescence generation and collection. We demonstrate that our model generates fluence profiles similar to a linear array of point sources, but reveals axially heterogeneous fluorescence detection. With axially homogeneous excitation fluence, approximately 90% of detected fluorescence is collected by the proximal third of the diffuser for μs'/μa = 8 in the tissue and 70 to 88% is collected in this region for μs'/μa = 80. Increased fluorescence detection by the distal end of the diffuser relative to the center section is also demonstrated. Validation of these results was performed by creating phantoms consisting of layered fluorescent regions. Diffusers were inserted into these layered phantoms and fluorescence spectra were collected. Fits to these spectra show quantitative agreement between simulated fluorescence collection sensitivities and experimental results. These results will be applicable to the use of diffusers as detectors for dosimetry in interstitial photodynamic therapy. PMID:21895311

A new frequency domain analytical solution of a cascade of diffusive channels for flood routing

NASA Astrophysics Data System (ADS)

Cimorelli, Luigi; Cozzolino, Luca; Della Morte, Renata; Pianese, Domenico; Singh, Vijay P.

2015-04-01

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

Reactive diffusion in the presence of a diffusion barrier: Experiment and model

NASA Astrophysics Data System (ADS)

Mangelinck, D.; Luo, T.; Girardeaux, C.

2018-05-01

Reactions in thin films and diffusion barriers are important for applications such as protective coatings, electrical contact, and interconnections. In this work, the effect of a barrier on the kinetics of the formation for a single phase by reactive diffusion is investigated from both experimental and modeling point of views. Two types of diffusion barriers are studied: (i) a thin layer of W deposited between a Ni film and Si substrate and (ii) Ni alloy films, Ni(1%W) and Ni(5%Pt), that form a diffusion barrier during the reaction with the Si substrate. The effect of the barriers on the kinetics of δ-Ni2Si formation is determined by in situ X ray diffraction and compared to models that explain the kinetic slowdown induced by both types of barrier. A linear parabolic growth is found for the deposited barrier with an increasing linear contribution for increasing barrier thickness. On the contrary, the growth is mainly parabolic for the barrier formed by the reaction between an alloy film and the substrate. The permeability of the two types of barrier is determined and discussed. The developed models fit well with the dedicated model experiments, leading to a better understanding of the barrier effect on the reactive diffusion and allowing us to predict the barrier behaviour in various applications.

Gyrokinetic modelling of the quasilinear particle flux for plasmas with neutral-beam fuelling

NASA Astrophysics Data System (ADS)

Narita, E.; Honda, M.; Nakata, M.; Yoshida, M.; Takenaga, H.; Hayashi, N.

2018-02-01

A quasilinear particle flux is modelled based on gyrokinetic calculations. The particle flux is estimated by determining factors, namely, coefficients of off-diagonal terms and a particle diffusivity. In this paper, the methodology to estimate the factors is presented using a subset of JT-60U plasmas. First, the coefficients of off-diagonal terms are estimated by linear gyrokinetic calculations. Next, to obtain the particle diffusivity, a semi-empirical approach is taken. Most experimental analyses for particle transport have assumed that turbulent particle fluxes are zero in the core region. On the other hand, even in the stationary state, the plasmas in question have a finite turbulent particle flux due to neutral-beam fuelling. By combining estimates of the experimental turbulent particle flux and the coefficients of off-diagonal terms calculated earlier, the particle diffusivity is obtained. The particle diffusivity should reflect a saturation amplitude of instabilities. The particle diffusivity is investigated in terms of the effects of the linear instability and linear zonal flow response, and it is found that a formula including these effects roughly reproduces the particle diffusivity. The developed framework for prediction of the particle flux is flexible to add terms neglected in the current model. The methodology to estimate the quasilinear particle flux requires so low computational cost that a database consisting of the resultant coefficients of off-diagonal terms and particle diffusivity can be constructed to train a neural network. The development of the methodology is the first step towards a neural-network-based particle transport model for fast prediction of the particle flux.

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation

PubMed Central

Duarte-Carvajalino, Julio M.; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis. PMID:23596381

A Framework for Linear and Non-Linear Registration of Diffusion-Weighted MRIs Using Angular Interpolation.

PubMed

Duarte-Carvajalino, Julio M; Sapiro, Guillermo; Harel, Noam; Lenglet, Christophe

2013-01-01

Registration of diffusion-weighted magnetic resonance images (DW-MRIs) is a key step for population studies, or construction of brain atlases, among other important tasks. Given the high dimensionality of the data, registration is usually performed by relying on scalar representative images, such as the fractional anisotropy (FA) and non-diffusion-weighted (b0) images, thereby ignoring much of the directional information conveyed by DW-MR datasets itself. Alternatively, model-based registration algorithms have been proposed to exploit information on the preferred fiber orientation(s) at each voxel. Models such as the diffusion tensor or orientation distribution function (ODF) have been used for this purpose. Tensor-based registration methods rely on a model that does not completely capture the information contained in DW-MRIs, and largely depends on the accurate estimation of tensors. ODF-based approaches are more recent and computationally challenging, but also better describe complex fiber configurations thereby potentially improving the accuracy of DW-MRI registration. A new algorithm based on angular interpolation of the diffusion-weighted volumes was proposed for affine registration, and does not rely on any specific local diffusion model. In this work, we first extensively compare the performance of registration algorithms based on (i) angular interpolation, (ii) non-diffusion-weighted scalar volume (b0), and (iii) diffusion tensor image (DTI). Moreover, we generalize the concept of angular interpolation (AI) to non-linear image registration, and implement it in the FMRIB Software Library (FSL). We demonstrate that AI registration of DW-MRIs is a powerful alternative to volume and tensor-based approaches. In particular, we show that AI improves the registration accuracy in many cases over existing state-of-the-art algorithms, while providing registered raw DW-MRI data, which can be used for any subsequent analysis.

Proposing an Educational Scaling-and-Diffusion Model for Inquiry-Based Learning Designs

ERIC Educational Resources Information Center

Hung, David; Lee, Shu-Shing

2015-01-01

Education cannot adopt the linear model of scaling used by the medical sciences. "Gold standards" cannot be replicated without considering process-in-learning, diversity, and student-variedness in classrooms. This article proposes a nuanced model of educational scaling-and-diffusion, describing the scaling (top-down supports) and…

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Linear single-step image reconstruction in the presence of nonscattering regions.

PubMed

Dehghani, H; Delpy, D T

2002-06-01

There is growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in using this technique for obtaining tomographic images of the neonatal head, with the view of determining the level of oxygenated and deoxygenated blood within the brain. Because of computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases where a nonscattering region exists. We present reconstructed images, using linear algorithms, of models that contain a nonscattering region within a diffusing material. The forward data are calculated by using the radiosity-diffusion model, and the inverse problem is solved by using either the radiosity-diffusion model or the diffusion-only model. When using data from a model containing a clear layer and reconstructing with the correct model, one can reconstruct the anomaly, but the qualitative accuracy and the position of the reconstructed anomaly depend on the size and the position of the clear regions. If the inverse model has no information about the clear regions (i.e., it is a purely diffusing model), an anomaly can be reconstructed, but the resulting image has very poor qualitative accuracy and poor localization of the anomaly. The errors in quantitative and localization accuracies depend on the size and location of the clear regions.

Linear single-step image reconstruction in the presence of nonscattering regions

NASA Astrophysics Data System (ADS)

Dehghani, H.; Delpy, D. T.

2002-06-01

There is growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in using this technique for obtaining tomographic images of the neonatal head, with the view of determining the level of oxygenated and deoxygenated blood within the brain. Because of computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases where a nonscattering region exists. We present reconstructed images, using linear algorithms, of models that contain a nonscattering region within a diffusing material. The forward data are calculated by using the radiosity-diffusion model, and the inverse problem is solved by using either the radiosity-diffusion model or the diffusion-only model. When using data from a model containing a clear layer and reconstructing with the correct model, one can reconstruct the anomaly, but the qualitative accuracy and the position of the reconstructed anomaly depend on the size and the position of the clear regions. If the inverse model has no information about the clear regions (i.e., it is a purely diffusing model), an anomaly can be reconstructed, but the resulting image has very poor qualitative accuracy and poor localization of the anomaly. The errors in quantitative and localization accuracies depend on the size and location of the clear regions.

A new model integrating short- and long-term aging of copper added to soils

PubMed Central

Zeng, Saiqi; Li, Jumei; Wei, Dongpu

2017-01-01

Aging refers to the processes by which the bioavailability/toxicity, isotopic exchangeability, and extractability of metals added to soils decline overtime. We studied the characteristics of the aging process in copper (Cu) added to soils and the factors that affect this process. Then we developed a semi-mechanistic model to predict the lability of Cu during the aging process with descriptions of the diffusion process using complementary error function. In the previous studies, two semi-mechanistic models to separately predict short-term and long-term aging of Cu added to soils were developed with individual descriptions of the diffusion process. In the short-term model, the diffusion process was linearly related to the square root of incubation time (t1/2), and in the long-term model, the diffusion process was linearly related to the natural logarithm of incubation time (lnt). Both models could predict short-term or long-term aging processes separately, but could not predict the short- and long-term aging processes by one model. By analyzing and combining the two models, we found that the short- and long-term behaviors of the diffusion process could be described adequately using the complementary error function. The effect of temperature on the diffusion process was obtained in this model as well. The model can predict the aging process continuously based on four factors—soil pH, incubation time, soil organic matter content and temperature. PMID:28820888

Exact Solutions of Linear Reaction-Diffusion Processes on a Uniformly Growing Domain: Criteria for Successful Colonization

PubMed Central

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

PubMed

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0

Pickup protons and water ions at Comet Halley - Comparisons with Giotto observations

NASA Astrophysics Data System (ADS)

Ye, G.; Cravens, T. E.; Gombosi, T. I.

1993-02-01

The cometary ion pickup process along the sun-comet line at Comet Halley is investigated using a quasi-linear diffusion model including both pitch angle and energy diffusion, adiabatic compression, and convective motion with the solar wind flow. The model results are compared with energetic ion distributions observed by instruments on board the Giotto spacecraft. The observed power spectrum index of magnetic turbulence (gamma) is 2-2.5. The present simulation shows that when gamma was 2, the calculated proton distributions were much more isotropic than the observed ones. The numerical solutions of the quasi-linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock. Given the observed turbulence level, quasi-linear theory yields pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.

Diffusive Public Goods and Coexistence of Cooperators and Cheaters on a 1D Lattice

PubMed Central

Scheuring, István

2014-01-01

Many populations of cells cooperate through the production of extracellular materials. These materials (enzymes, siderophores) spread by diffusion and can be applied by both the cooperator and cheater (non-producer) cells. In this paper the problem of coexistence of cooperator and cheater cells is studied on a 1D lattice where cooperator cells produce a diffusive material which is beneficial to the individuals according to the local concentration of this public good. The reproduction success of a cell increases linearly with the benefit in the first model version and increases non-linearly (saturates) in the second version. Two types of update rules are considered; either the cooperative cell stops producing material before death (death-production-birth, DpB) or it produces the common material before it is selected to die (production-death-birth, pDB). The empty space is occupied by its neighbors according to their replication rates. By using analytical and numerical methods I have shown that coexistence of the cooperator and cheater cells is possible although atypical in the linear version of this 1D model if either DpB or pDB update rule is assumed. While coexistence is impossible in the non-linear model with pDB update rule, it is one of the typical behaviors in case of the non-linear model with DpB update rule. PMID:25025985

The Influence of Preferential Flow on Pressure Propagation and Landslide Triggering of the Rocca Pitigliana Landslide

NASA Astrophysics Data System (ADS)

Shao, W.; Bogaard, T.; Bakker, M.; Berti, M.; Savenije, H. H. G.

2016-12-01

The fast pore water pressure response to rain events is an important triggering factor for slope instability. The fast pressure response may be caused by preferential flow that bypasses the soil matrix. Currently, most of the hydro-mechanical models simulate pore water pressure using a single-permeability model, which cannot quantify the effects of preferential flow on pressure propagation and landslide triggering. Previous studies showed that a model based on the linear-diffusion equation can simulate the fast pressure propagation in near-saturated landslides such as the Rocca Pitigliana landslide. In such a model, the diffusion coefficient depends on the degree of saturation, which makes it difficult to use the model for predictions. In this study, the influence of preferential flow on pressure propagation and slope stability is investigated with a 1D dual-permeability model coupled with an infinite-slope stability approach. The dual-permeability model uses two modified Darcy-Richards equations to simultaneously simulate the matrix flow and preferential flow in hillslopes. The simulated pressure head is used in an infinite-slope stability analysis to identify the influence of preferential flow on the fast pressure response and landslide triggering. The dual-permeability model simulates the height and arrival of the pressure peak reasonably well. Performance of the dual-permeability model is as good as or better than the linear-diffusion model even though the dual-permeability model is calibrated for two single pulse rain events only, while the linear-diffusion model is calibrated for each rain event separately.

Influence of magnetic flutter on tearing growth in linear and nonlinear theory

NASA Astrophysics Data System (ADS)

Kreifels, L.; Hornsby, W. A.; Weikl, A.; Peeters, A. G.

2018-06-01

Recent simulations of tearing modes in turbulent regimes show an unexpected enhancement in the growth rate. In this paper the effect is investigated analytically. The enhancement is linked to the influence of turbulent magnetic flutter, which is modelled by diffusion terms in magnetohydrodynamics (MHD) momentum balance and Ohm’s law. Expressions for the linear growth rate as well as the island width in nonlinear theory for small amplitudes are derived. The results indicate an enhanced linear growth rate and a larger linear layer width compared with resistive MHD. Also the island width in the nonlinear regime grows faster in the diffusive model. These observations correspond well to simulations in which the effect of turbulence on the magnetic island width and tearing mode growth is analyzed.

Transport of polar and non-polar volatile compounds in polystyrene foam and oriented strand board

NASA Astrophysics Data System (ADS)

Yuan, Huali; Little, John C.; Hodgson, Alfred T.

Transport of hexanal and styrene in polystyrene foam (PSF) and oriented strand board (OSB) was characterized. A microbalance was used to measure sorption/desorption kinetics and equilibrium data. While styrene transport in PSF can be described by Fickian diffusion with a symmetrical and reversible sorption/desorption process, hexanal transport in both PSF and OSB exhibited significant hysteresis, with desorption being much slower than sorption. A porous media diffusion model that assumes instantaneous local equilibrium governed by a nonlinear Freundlich isotherm was found to explain the hysteresis in hexanal transport. A new nonlinear sorption and porous diffusion emissions model was, therefore, developed and partially validated using independent chamber data. The results were also compared to the more conventional linear Fickian-diffusion emissions model. While the linear emissions model predicts styrene emissions from PSF with reasonable accuracy, it substantially underestimates the rate of hexanal emissions from OSB. Although further research and more rigorous validation is needed, the new nonlinear emissions model holds promise for predicting emissions of polar VOCs such as hexanal from porous building materials.

Optimal Network Modularity for Information Diffusion

NASA Astrophysics Data System (ADS)

Nematzadeh, Azadeh; Ferrara, Emilio; Flammini, Alessandro; Ahn, Yong-Yeol

2014-08-01

We investigate the impact of community structure on information diffusion with the linear threshold model. Our results demonstrate that modular structure may have counterintuitive effects on information diffusion when social reinforcement is present. We show that strong communities can facilitate global diffusion by enhancing local, intracommunity spreading. Using both analytic approaches and numerical simulations, we demonstrate the existence of an optimal network modularity, where global diffusion requires the minimal number of early adopters.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant.

PubMed

Eidi, Zahra; Mohammad-Rafiee, Farshid; Khorrami, Mohammad; Gholami, Azam

2017-11-15

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

NMR Water Self–Diffusion and Relaxation Studies on Sodium Polyacrylate Solutions and Gels in Physiologic Ionic Solutions

PubMed Central

Bai, Ruiliang; Basser, Peter J.; Briber, Robert M.; Horkay, Ferenc

2013-01-01

Water self-diffusion coefficients and longitudinal relaxation rates in sodium polyacrylate solutions and gels were measured by NMR, as a function of polymer content and structure in a physiological concentration range of monovalent and divalent cations, Ca2+ and Na+. Several physical models describing the self-diffusion of the solvent were applied and compared. A free-volume model was found to be in good agreement with the experimental results over a wide range of polymer concentrations. The longitudinal relaxation rate exhibited linear dependence on polymer concentration below a critical concentration and showed non-linear behavior at higher concentrations. Both the water self-diffusion and relaxation were less influenced by the polymer in the gel state than in the uncrosslinked polymer solutions. The effect of Na+ on the mobility of water molecules was practically undetectable. By contrast, addition of Ca2+ strongly increased the longitudinal relaxation rate while its effect on the self-diffusion coefficient was much less pronounced. PMID:24409001

NMR Water Self-Diffusion and Relaxation Studies on Sodium Polyacrylate Solutions and Gels in Physiologic Ionic Solutions.

PubMed

Bai, Ruiliang; Basser, Peter J; Briber, Robert M; Horkay, Ferenc

2014-03-15

Water self-diffusion coefficients and longitudinal relaxation rates in sodium polyacrylate solutions and gels were measured by NMR, as a function of polymer content and structure in a physiological concentration range of monovalent and divalent cations, Ca 2+ and Na + . Several physical models describing the self-diffusion of the solvent were applied and compared. A free-volume model was found to be in good agreement with the experimental results over a wide range of polymer concentrations. The longitudinal relaxation rate exhibited linear dependence on polymer concentration below a critical concentration and showed non-linear behavior at higher concentrations. Both the water self-diffusion and relaxation were less influenced by the polymer in the gel state than in the uncrosslinked polymer solutions. The effect of Na + on the mobility of water molecules was practically undetectable. By contrast, addition of Ca 2+ strongly increased the longitudinal relaxation rate while its effect on the self-diffusion coefficient was much less pronounced.

The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

NASA Astrophysics Data System (ADS)

Leyva, J. Francisco; Málaga, Carlos; Plaza, Ramón G.

2013-11-01

This paper studies a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.

A Nth-order linear algorithm for extracting diffuse correlation spectroscopy blood flow indices in heterogeneous tissues.

PubMed

Shang, Yu; Yu, Guoqiang

2014-09-29

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a N th-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD B ). The purpose of this study is to extend the capability of the N th-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD B in the brain layer with a step decrement of 10% while maintaining αD B values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order ( N  ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The N th-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.

The influence of preferential flow on pressure propagation and landslide triggering of the Rocca Pitigliana landslide

NASA Astrophysics Data System (ADS)

Shao, Wei; Bogaard, Thom; Bakker, Mark; Berti, Matteo

2016-12-01

The fast pore water pressure response to rain events is an important triggering factor for slope instability. The fast pressure response may be caused by preferential flow that bypasses the soil matrix. Currently, most of the hydro-mechanical models simulate pore water pressure using a single-permeability model, which cannot quantify the effects of preferential flow on pressure propagation and landslide triggering. Previous studies showed that a model based on the linear-diffusion equation can simulate the fast pressure propagation in near-saturated landslides such as the Rocca Pitigliana landslide. In such a model, the diffusion coefficient depends on the degree of saturation, which makes it difficult to use the model for predictions. In this study, the influence of preferential flow on pressure propagation and slope stability is investigated with a 1D dual-permeability model coupled with an infinite-slope stability approach. The dual-permeability model uses two modified Darcy-Richards equations to simultaneously simulate the matrix flow and preferential flow in hillslopes. The simulated pressure head is used in an infinite-slope stability analysis to identify the influence of preferential flow on the fast pressure response and landslide triggering. The dual-permeability model simulates the height and arrival of the pressure peak reasonably well. Performance of the dual-permeability model is as good as or better than the linear-diffusion model even though the dual-permeability model is calibrated for two single pulse rain events only, while the linear-diffusion model is calibrated for each rain event separately. In conclusion, the 1D dual-permeability model is a promising tool for landslides under similar conditions.

Product diffusion through on-demand information-seeking behaviour.

PubMed

Riedl, Christoph; Bjelland, Johannes; Canright, Geoffrey; Iqbal, Asif; Engø-Monsen, Kenth; Qureshi, Taimur; Sundsøy, Pål Roe; Lazer, David

2018-02-01

Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product-a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers. © 2018 The Authors.

Product diffusion through on-demand information-seeking behaviour

PubMed Central

Bjelland, Johannes; Canright, Geoffrey; Iqbal, Asif; Qureshi, Taimur; Sundsøy, Pål Roe

2018-01-01

Most models of product adoption predict S-shaped adoption curves. Here we report results from two country-scale experiments in which we find linear adoption curves. We show evidence that the observed linear pattern is the result of active information-seeking behaviour: individuals actively pulling information from several central sources facilitated by modern Internet searches. Thus, a constant baseline rate of interest sustains product diffusion, resulting in a linear diffusion process instead of the S-shaped curve of adoption predicted by many diffusion models. The main experiment seeded 70 000 (48 000 in Experiment 2) unique voucher codes for the same product with randomly sampled nodes in a social network of approximately 43 million individuals with about 567 million ties. We find that the experiment reached over 800 000 individuals with 80% of adopters adopting the same product—a winner-take-all dynamic consistent with search engine driven rankings that would not have emerged had the products spread only through a network of social contacts. We provide evidence for (and characterization of) this diffusion process driven by active information-seeking behaviour through analyses investigating (a) patterns of geographical spreading; (b) the branching process; and (c) diffusion heterogeneity. Using data on adopters' geolocation we show that social spreading is highly localized, while on-demand diffusion is geographically independent. We also show that cascades started by individuals who actively pull information from central sources are more effective at spreading the product among their peers. PMID:29467257

CRITICAL EVALUATION OF THE DIFFUSION HYPOTHESIS IN THE THEORY OF POROUS MEDIA VOLATILE ORGANIC COMPOUND (VOC) SOURCES AND SINKS

EPA Science Inventory

The paper proposes three alternative, diffusion-limited mathematical models to account for volatile organic compound (VOC) interactions with indoor sinks, using the linear isotherm model as a reference point. (NOTE: Recent reports by both the U.S. EPA and a study committee of the...

Mass Transport of Macromolecules within an In Vitro Model of Supragingival Plaque

PubMed Central

Thurnheer, Thomas; Gmür, Rudolf; Shapiro, Stuart; Guggenheim, Bernhard

2003-01-01

The aim of this study was to examine the diffusion of macromolecules through an in vitro biofilm model of supragingival plaque. Polyspecies biofilms containing Actinomyces naeslundii, Fusobacterium nucleatum, Streptococcus oralis, Streptococcus sobrinus, Veillonella dispar, and Candida albicans were formed on sintered hydroxyapatite disks and then incubated at room temperature for defined periods with fluorescent markers with molecular weights ranging from 3,000 to 900,000. Subsequent examination by confocal laser scanning microscopy revealed that the mean square penetration depths for all tested macromolecules except immunoglobulin M increased linearly with time, diffusion coefficients being linearly proportional to the cube roots of the molecular weights of the probes (range, 10,000 to 240,000). Compared to diffusion in bulk water, diffusion in the biofilms was markedly slower. The rate of diffusion for each probe appeared to be constant and not a function of biofilm depth. Analysis of diffusion phenomena through the biofilms suggested tortuosity as the most probable explanation for retarded diffusion. Selective binding of probes to receptors present in the biofilms could not explain the observed extent of retardation of diffusion. These results are relevant to oral health, as selective attenuated diffusion of fermentable carbohydrates and acids produced within dental plaque is thought to be essential for the development of carious lesions. PMID:12620862

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

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. Diffusion within the pores is subject to a strict single-file (no passing) constraint. 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 in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

NASA Astrophysics Data System (ADS)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.

Effect of non-linear fluid pressure diffusion on modeling induced seismicity during reservoir stimulation

NASA Astrophysics Data System (ADS)

Gischig, V.; Goertz-Allmann, B. P.; Bachmann, C. E.; Wiemer, S.

2012-04-01

Success of future enhanced geothermal systems relies on an appropriate pre-estimate of seismic risk associated with fluid injection at high pressure. A forward-model based on a semi-stochastic approach was created, which is able to compute synthetic earthquake catalogues. It proved to be able to reproduce characteristics of the seismic cloud detected during the geothermal project in Basel (Switzerland), such as radial dependence of stress drop and b-values as well as higher probability of large magnitude earthquakes (M>3) after shut-in. The modeling strategy relies on a simplistic fluid pressure model used to trigger failure points (so-called seeds) that are randomly distributed around an injection well. The seed points are assigned principal stress magnitudes drawn from Gaussian distributions representative of the ambient stress field. Once the effective stress state at a seed point meets a pre-defined Mohr-Coulomb failure criterion due to a fluid pressure increase a seismic event is induced. We assume a negative linear relationship between b-values and differential stress. Thus, for each event a magnitude can be drawn from a Gutenberg-Richter distribution with a b-value corresponding to differential stress at failure. The result is a seismic cloud evolving in time and space. Triggering of seismic events depends on appropriately calculating the transient fluid pressure field. Hence an effective continuum reservoir model able to reasonably reproduce the hydraulic behavior of the reservoir during stimulation is required. While analytical solutions for pressure diffusion are computationally efficient, they rely on linear pressure diffusion with constant hydraulic parameters, and only consider well head pressure while neglecting fluid injection rate. They cannot be considered appropriate in a stimulation experiment where permeability irreversibly increases by orders of magnitude during injection. We here suggest a numerical continuum model of non-linear pressure diffusion. Permeability increases both reversibly and, if a certain pressure threshold is reached, irreversibly in the form of a smoothed step-function. The models are able to reproduce realistic well head pressure magnitudes for injection rates common during reservoir stimulation. We connect this numerical model with the semi-stochastic seismicity model, and demonstrate the role of non-linear pressure diffusion on earthquakes probability estimates. We further use the model to explore various injection histories to assess the dependence of seismicity on injection strategy. It allows to qualitatively explore the probability of larger magnitude earthquakes (M>3) for different injection volumes, injection times, as well as injection build-up and shut-in strategies.

A HIGHWAY MODEL FOR THE ADVECTION, DIFFUSION AND CHEMICAL REACTION OF POLLUTANTS RELEASED BY AUTOMOBILES: PART I. ADVECTION AND DIFFUSION OF SF6 TRACER GAS

EPA Science Inventory

A two-dimensional, finite-difference model simulating a highway has been developed which is able to handle linear and nonlinear chemical reactions. Transport of the pollutants is accomplished by use of an upstream-flux-corrected algorithm developed at the Naval Research Laborator...

Knowledge diffusion in complex networks by considering time-varying information channels

NASA Astrophysics Data System (ADS)

Zhu, He; Ma, Jing

2018-03-01

In this article, based on a model of epidemic spreading, we explore the knowledge diffusion process with an innovative mechanism for complex networks by considering time-varying information channels. To cover the knowledge diffusion process in homogeneous and heterogeneous networks, two types of networks (the BA network and the ER network) are investigated. The mean-field theory is used to theoretically draw the knowledge diffusion threshold. Numerical simulation demonstrates that the knowledge diffusion threshold is almost linearly correlated with the mean of the activity rate. In addition, under the influence of the activity rate and distinct from the classic Susceptible-Infected-Susceptible (SIS) model, the density of knowers almost linearly grows with the spreading rate. Finally, in consideration of the ubiquitous mechanism of innovation, we further study the evolution of knowledge in our proposed model. The results suggest that compared with the effect of the spreading rate, the average knowledge version of the population is affected more by the innovation parameter and the mean of the activity rate. Furthermore, in the BA network, the average knowledge version of individuals with higher degree is always newer than those with lower degree.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Diffusion in Ordered Alloys, Symposium Held in Chicago, Illinois on November 3 - 4, 1992

DTIC Science & Technology

1992-11-04

calculation of transport proneres The essence of an atomistic theory of diffusion within the linear approximation of the Onsager formalism is to derive...the pair model may be extended to the low temperature range and that this linear behavior exists nearly over the whole temperature range where SRO...being the concentration of the component X. The successive jumps of vacancies are considered to be the elementary process of orde- ring. The jump

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

Incorporating Non-Linear Sorption into High Fidelity Subsurface Reactive Transport Models

NASA Astrophysics Data System (ADS)

Matott, L. S.; Rabideau, A. J.; Allen-King, R. M.

2014-12-01

A variety of studies, including multiple NRC (National Research Council) reports, have stressed the need for simulation models that can provide realistic predictions of contaminant behavior during the groundwater remediation process, most recently highlighting the specific technical challenges of "back diffusion and desorption in plume models". For a typically-sized remediation site, a minimum of about 70 million grid cells are required to achieve desired cm-level thickness among low-permeability lenses responsible for driving the back-diffusion phenomena. Such discretization is nearly three orders of magnitude more than is typically seen in modeling practice using public domain codes like RT3D (Reactive Transport in Three Dimensions). Consequently, various extensions have been made to the RT3D code to support efficient modeling of recently proposed dual-mode non-linear sorption processes (e.g. Polanyi with linear partitioning) at high-fidelity scales of grid resolution. These extensions have facilitated development of exploratory models in which contaminants are introduced into an aquifer via an extended multi-decade "release period" and allowed to migrate under natural conditions for centuries. These realistic simulations of contaminant loading and migration provide high fidelity representation of the underlying diffusion and sorption processes that control remediation. Coupling such models with decision support processes is expected to facilitate improved long-term management of complex remediation sites that have proven intractable to conventional remediation strategies.

Mechanisms underlying anomalous diffusion in the plasma membrane.

PubMed

Krapf, Diego

2015-01-01

The plasma membrane is a complex fluid where lipids and proteins undergo diffusive motion critical to biochemical reactions. Through quantitative imaging analyses such as single-particle tracking, it is observed that diffusion in the cell membrane is usually anomalous in the sense that the mean squared displacement is not linear with time. This chapter describes the different models that are employed to describe anomalous diffusion, paying special attention to the experimental evidence that supports these models in the plasma membrane. We review models based on anticorrelated displacements, such as fractional Brownian motion and obstructed diffusion, and nonstationary models such as continuous time random walks. We also emphasize evidence for the formation of distinct compartments that transiently form on the cell surface. Finally, we overview heterogeneous diffusion processes in the plasma membrane, which have recently attracted considerable interest. Copyright © 2015. Published by Elsevier Inc.

Linear bubble plume model for hypolimnetic oxygenation: Full-scale validation and sensitivity analysis

NASA Astrophysics Data System (ADS)

Singleton, V. L.; Gantzer, P.; Little, J. C.

2007-02-01

An existing linear bubble plume model was improved, and data collected from a full-scale diffuser installed in Spring Hollow Reservoir, Virginia, were used to validate the model. The depth of maximum plume rise was simulated well for two of the three diffuser tests. Temperature predictions deviated from measured profiles near the maximum plume rise height, but predicted dissolved oxygen profiles compared very well with observations. A sensitivity analysis was performed. The gas flow rate had the greatest effect on predicted plume rise height and induced water flow rate, both of which were directly proportional to gas flow rate. Oxygen transfer within the hypolimnion was independent of all parameters except initial bubble radius and was inversely proportional for radii greater than approximately 1 mm. The results of this work suggest that plume dynamics and oxygen transfer can successfully be predicted for linear bubble plumes using the discrete-bubble approach.

Linear model describing three components of flow in karst aquifers using 18O data

USGS Publications Warehouse

Long, Andrew J.; Putnam, L.D.

2004-01-01

The stable isotope of oxygen, 18O, is used as a naturally occurring ground-water tracer. Time-series data for ??18O are analyzed to model the distinct responses and relative proportions of the conduit, intermediate, and diffuse flow components in karst aquifers. This analysis also describes mathematically the dynamics of the transient fluid interchange between conduits and diffusive networks. Conduit and intermediate flow are described by linear-systems methods, whereas diffuse flow is described by mass-balance methods. An automated optimization process estimates parameters of lognormal, Pearson type III, and gamma distributions, which are used as transfer functions in linear-systems analysis. Diffuse flow and mixing parameters also are estimated by these optimization methods. Results indicate the relative proximity of a well to a main conduit flowpath and can help to predict the movement and residence times of potential contaminants. The three-component linear model is applied to five wells, which respond to changes in the isotopic composition of point recharge water from a sinking stream in the Madison aquifer in the Black Hills of South Dakota. Flow velocities as much as 540 m/d and system memories of as much as 71 years are estimated by this method. Also, the mean, median, and standard deviation of traveltimes; time to peak response; and the relative fraction of flow for each of the three components are determined for these wells. This analysis infers that flow may branch apart and rejoin as a result of an anastomotic (or channeled) karst network.

The Dynamics of Entangled DNA Networks using Single-Molecule Methods

NASA Astrophysics Data System (ADS)

Chapman, Cole David

Single molecule experiments were performed on DNA, a model polymer, and entangled DNA networks to explore diffusion within complex polymeric fluids and their linear and non-linear viscoelasticity. DNA molecules of varying length and topology were prepared using biological methods. An ensemble of individual molecules were then fluorescently labeled and tracked in blends of entangled linear and circular DNA to examine the dependence of diffusion on polymer length, topology, and blend ratio. Diffusion was revealed to possess a non-monotonic dependence on the blend ratio, which we believe to be due to a second-order effect where the threading of circular polymers by their linear counterparts greatly slows the mobility of the system. Similar methods were used to examine the diffusive and conformational behavior of DNA within highly crowded environments, comparable to that experienced within the cell. A previously unseen gamma distributed elongation of the DNA in the presence of crowders, proposed to be due to entropic effects and crowder mobility, was observed. Additionally, linear viscoelastic properties of entangled DNA networks were explored using active microrheology. Plateau moduli values verified for the first time the predicted independence from polymer length. However, a clear bead-size dependence was observed for bead radii less than ~3x the tube radius, a newly discovered limit, above which microrheology results are within the continuum limit and may access the bulk properties of the fluid. Furthermore, the viscoelastic properties of entangled DNA in the non-linear regime, where the driven beads actively deform the network, were also examined. By rapidly driving a bead through the network utilizing optical tweezers, then removing the trap and tracking the bead's subsequent motion we are able to model the system as an over-damped harmonic oscillator and find the elasticity to be dominated by stress-dependent entanglements.

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.

1991-01-01

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

Monte Carlo simulations of coupled diffusion and surface reactions during the aqueous corrosion of borosilicate glasses

DOE PAGES

Kerisit, Sebastien; Pierce, Eric M.; Ryan, Joseph V.

2014-09-19

Borosilicate nuclear waste glasses develop complex altered layers as a result of coupled processes such as hydrolysis of network species, condensation of Si species, and diffusion. However, diffusion has often been overlooked in Monte Carlo models of the aqueous corrosion of borosilicate glasses. Therefore, in this paper three different models for dissolved Si diffusion in the altered layer were implemented in a Monte Carlo model and evaluated for glasses in the compositional range (75 - x) mol% SiO 2 (12.5 + x/2) mol% B 2O 3 and (12.5 + x/2) mol% Na 2O, where 0 ≤ x ≤ 20%, andmore » corroded in static conditions at a surface-area-to-volume ratio of 1000 m -1. The three models considered instantaneous homogenization (M1), linear concentration gradients (M2), and concentration profiles determined by solving Fick's 2nd law using a finite difference method (M3). Model M3 revealed that concentration profiles in the altered layer are not linear and show changes in shape and magnitude as corrosion progresses, unlike those assumed in model M2. Furthermore, model M3 showed that, for borosilicate glasses with a high forward dissolution rate compared to the diffusion rate, the gradual polymerization and densification of the altered layer is significantly delayed compared to models M1 and M2. Finally, models M1 and M2 were found to be appropriate models only for glasses with high release rates such as simple borosilicate glasses with low ZrO 2 content.« less

Bayesian inference of radiation belt loss timescales.

NASA Astrophysics Data System (ADS)

Camporeale, E.; Chandorkar, M.

2017-12-01

Electron fluxes in the Earth's radiation belts are routinely studied using the classical quasi-linear radial diffusion model. Although this simplified linear equation has proven to be an indispensable tool in understanding the dynamics of the radiation belt, it requires specification of quantities such as the diffusion coefficient and electron loss timescales that are never directly measured. Researchers have so far assumed a-priori parameterisations for radiation belt quantities and derived the best fit using satellite data. The state of the art in this domain lacks a coherent formulation of this problem in a probabilistic framework. We present some recent progress that we have made in performing Bayesian inference of radial diffusion parameters. We achieve this by making extensive use of the theory connecting Gaussian Processes and linear partial differential equations, and performing Markov Chain Monte Carlo sampling of radial diffusion parameters. These results are important for understanding the role and the propagation of uncertainties in radiation belt simulations and, eventually, for providing a probabilistic forecast of energetic electron fluxes in a Space Weather context.

Protein gradients in single cells induced by their coupling to "morphogen"-like diffusion

NASA Astrophysics Data System (ADS)

Nandi, Saroj Kumar; Safran, Sam A.

2018-05-01

One of the many ways cells transmit information within their volume is through steady spatial gradients of different proteins. However, the mechanism through which proteins without any sources or sinks form such single-cell gradients is not yet fully understood. One of the models for such gradient formation, based on differential diffusion, is limited to proteins with large ratios of their diffusion constants or to specific protein-large molecule interactions. We introduce a novel mechanism for gradient formation via the coupling of the proteins within a single cell with a molecule, that we call a "pronogen," whose action is similar to that of morphogens in multi-cell assemblies; the pronogen is produced with a fixed flux at one side of the cell. This coupling results in an effectively non-linear diffusion degradation model for the pronogen dynamics within the cell, which leads to a steady-state gradient of the protein concentration. We use stability analysis to show that these gradients are linearly stable with respect to perturbations.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields.

PubMed

Hong, Tao; Tang, Zhengming; Zhu, Huacheng

2016-12-28

The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps, there will be a standard linear reaction kinetics term but a fractional order temporal derivative operating on an anomalous diffusion term. The dielectric polarization is analyzed based on the Legendre polynomials and the dielectric properties of both reactions can be expressed by the effective rotational diffusion function and component concentration function, which is similar to the standard reaction-diffusion process. The results show that the effective permittivity can be used to describe the dielectric properties in these reactions if the chemical reaction time is much longer than the relaxation time.

Monotonic non-linear transformations as a tool to investigate age-related effects on brain white matter integrity: A Box-Cox investigation.

PubMed

Morozova, Maria; Koschutnig, Karl; Klein, Elise; Wood, Guilherme

2016-01-15

Non-linear effects of age on white matter integrity are ubiquitous in the brain and indicate that these effects are more pronounced in certain brain regions at specific ages. Box-Cox analysis is a technique to increase the log-likelihood of linear relationships between variables by means of monotonic non-linear transformations. Here we employ Box-Cox transformations to flexibly and parsimoniously determine the degree of non-linearity of age-related effects on white matter integrity by means of model comparisons using a voxel-wise approach. Analysis of white matter integrity in a sample of adults between 20 and 89years of age (n=88) revealed that considerable portions of the white matter in the corpus callosum, cerebellum, pallidum, brainstem, superior occipito-frontal fascicle and optic radiation show non-linear effects of age. Global analyses revealed an increase in the average non-linearity from fractional anisotropy to radial diffusivity, axial diffusivity, and mean diffusivity. These results suggest that Box-Cox transformations are a useful and flexible tool to investigate more complex non-linear effects of age on white matter integrity and extend the functionality of the Box-Cox analysis in neuroimaging. Copyright © 2015 Elsevier Inc. All rights reserved.

A non-Linear transport model for determining shale rock characteristics

NASA Astrophysics Data System (ADS)

Ali, Iftikhar; Malik, Nadeem

2016-04-01

Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas through them is not well understood at the present time, and realistic transport models are needed in order to determine rock properties and for estimating future gas pressure distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport equation [3], ∂p-+ U ∂p- = D ∂2p-, t > 0, (1) ∂t ∂x ∂x2 complimented with suitable initial and boundary conditions, in order to determine shale rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity D = D(p), are both highly non-linear functions of the pressure. The model incorporate various flow regimes (slip, surface diffusion, transition, continuum) based upon the Knudsen number Kn, and also includes Forchchiemers turbulence correction terms. In application, the model parameters and associated compressibility factors are fully pressure dependent, giving the model more realism than previous models. See [4]. Rock properties are determined by solving an inverse problem, with model parameters adjustment to minimise the error between the model simulation and available data. It is has been found that the proposed model performs better than previous models. Results and details of the model will be presented at the conference. Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net References [1] Cui, X., Bustin, A.M. and Bustin, R., "Measurements of gas permeability and diffusivity of tight reservoir rocks: different approaches and their applications", Geofluids 9, 208-223 (2009). [2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., "Numerical Simulation of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer", AIP Conference Proceedings 898, 75 (2007); doi: 10.1063/1.2721253 [3] Ali, I. "A numerical study of shale gas flow in tight porous media through non-linear transport model", PhD Dissertation, King Fahd University of Petroleum and Minerals. Submitted (2016). [4]. Civan, F., Rai, C.S., Sondergeld, C.H.: Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms. Transport in Porous Media, 86(3), 925-944 (2011). Acknowledgement: The authors would like to acknowledge the support provided by King Abdulaziz City for Science and Technology (KACST) through the Science Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through project No. 14-OIL280-04.

Bayesian uncertainty quantification in linear models for diffusion MRI.

PubMed

Sjölund, Jens; Eklund, Anders; Özarslan, Evren; Herberthson, Magnus; Bånkestad, Maria; Knutsson, Hans

2018-03-29

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification. Copyright © 2018 Elsevier Inc. All rights reserved.

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Elia, M.; Edwards, H. C.; Hu, J.

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems

DOE PAGES

D'Elia, M.; Edwards, H. C.; Hu, J.; ...

2018-01-18

Previous work has demonstrated that propagating groups of samples, called ensembles, together through forward simulations can dramatically reduce the aggregate cost of sampling-based uncertainty propagation methods [E. Phipps, M. D'Elia, H. C. Edwards, M. Hoemmen, J. Hu, and S. Rajamanickam, SIAM J. Sci. Comput., 39 (2017), pp. C162--C193]. However, critical to the success of this approach when applied to challenging problems of scientific interest is the grouping of samples into ensembles to minimize the total computational work. For example, the total number of linear solver iterations for ensemble systems may be strongly influenced by which samples form the ensemble whenmore » applying iterative linear solvers to parameterized and stochastic linear systems. In this paper we explore sample grouping strategies for local adaptive stochastic collocation methods applied to PDEs with uncertain input data, in particular canonical anisotropic diffusion problems where the diffusion coefficient is modeled by truncated Karhunen--Loève expansions. Finally, we demonstrate that a measure of the total anisotropy of the diffusion coefficient is a good surrogate for the number of linear solver iterations for each sample and therefore provides a simple and effective metric for grouping samples.« less

Overall adsorption rate of metronidazole, dimetridazole and diatrizoate on activated carbons prepared from coffee residues and almond shells.

PubMed

Flores-Cano, J V; Sánchez-Polo, M; Messoud, J; Velo-Gala, I; Ocampo-Pérez, R; Rivera-Utrilla, J

2016-03-15

This study analyzed the overall adsorption rate of metronidazole, dimetridazole, and diatrizoate on activated carbons prepared from coffee residues and almond shells. It was also elucidated whether the overall adsorption rate was controlled by reaction on the adsorbent surface or by intraparticle diffusion. Experimental data of the pollutant concentration decay curves as a function of contact time were interpreted by kinetics (first- and second-order) and diffusion models, considering external mass transfer, surface and/or pore volume diffusion, and adsorption on an active site. The experimental data were better interpreted by a first-order than second-order kinetic model, and the first-order adsorption rate constant varied linearly with respect to the surface area and total pore volume of the adsorbents. According to the diffusion model, the overall adsorption rate is governed by intraparticle diffusion, and surface diffusion is the main mechanism controlling the intraparticle diffusion, representing >90% of total intraparticle diffusion. Copyright © 2015 Elsevier Ltd. All rights reserved.

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration.

PubMed

Chen, Yunjin; Pock, Thomas

2017-06-01

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (i.e., linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD-Trainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.

A diffusion model of protected population on bilocal habitat with generalized resource

NASA Astrophysics Data System (ADS)

Vasilyev, Maxim D.; Trofimtsev, Yuri I.; Vasilyeva, Natalya V.

2017-11-01

A model of population distribution in a two-dimensional area divided by an ecological barrier, i.e. the boundaries of natural reserve, is considered. Distribution of the population is defined by diffusion, directed migrations and areal resource. The exchange of specimens occurs between two parts of the habitat. The mathematical model is presented in the form of a boundary value problem for a system of non-linear parabolic equations with variable parameters of diffusion and growth function. The splitting space variables, sweep method and simple iteration methods were used for the numerical solution of a system. A set of programs was coded in Python. Numerical simulation results for the two-dimensional unsteady non-linear problem are analyzed in detail. The influence of migration flow coefficients and functions of natural birth/death ratio on the distributions of population densities is investigated. The results of the research would allow to describe the conditions of the stable and sustainable existence of populations in bilocal habitat containing the protected and non-protected zones.

Turing pattern dynamics and adaptive discretization for a super-diffusive Lotka-Volterra model.

PubMed

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.

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Anomalous Impact in Reaction-Diffusion Financial Models

NASA Astrophysics Data System (ADS)

Mastromatteo, I.; Tóth, B.; Bouchaud, J.-P.

2014-12-01

We generalize the reaction-diffusion model A +B → /0 in order to study the impact of an excess of A (or B ) at the reaction front. We provide an exact solution of the model, which shows that the linear response breaks down: the average displacement of the reaction front grows as the square root of the imbalance. We argue that this model provides a highly simplified but generic framework to understand the square-root impact of large orders in financial markets.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Regression-based model of skin diffuse reflectance for skin color analysis

NASA Astrophysics Data System (ADS)

Tsumura, Norimichi; Kawazoe, Daisuke; Nakaguchi, Toshiya; Ojima, Nobutoshi; Miyake, Yoichi

2008-11-01

A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.

Antifungal susceptibility testing of Malassezia yeast: comparison of two different methodologies.

PubMed

Rojas, Florencia D; Córdoba, Susana B; de Los Ángeles Sosa, María; Zalazar, Laura C; Fernández, Mariana S; Cattana, María E; Alegre, Liliana R; Carrillo-Muñoz, Alfonso J; Giusiano, Gustavo E

2017-02-01

All Malassezia species are lipophilic; thus, modifications are required in susceptibility testing methods to ensure their growth. Antifungal susceptibility of Malassezia species using agar and broth dilution methods has been studied. Currently, few tests using disc diffusion methods are being performed. The aim was to evaluate the in vitro susceptibility of Malassezia yeast against antifungal agents using broth microdilution and disc diffusion methods, then to compare both methodologies. Fifty Malassezia isolates were studied. Microdilution method was performed as described in reference document and agar diffusion test was performed using antifungal tablets and discs. To support growth, culture media were supplemented. To correlate methods, linear regression analysis and categorical agreement was determined. The strongest linear association was observed for fluconazole and miconazole. The highest agreement between both methods was observed for itraconazole and voriconazole and the lowest for amphotericin B and fluconazole. Although modifications made to disc diffusion method allowed to obtain susceptibility data for Malassezia yeast, variables cannot be associated through a linear correlation model, indicating that inhibition zone values cannot predict MIC value. According to the results, disc diffusion assay may not represent an alternative to determine antifungal susceptibility of Malassezia yeast. © 2016 Blackwell Verlag GmbH.

A generalized reaction diffusion model for spatial structure formed by motile cells.

PubMed

Ochoa, F L

1984-01-01

A non-linear stability analysis using a multi-scale perturbation procedure is carried out on a model of a generalized reaction diffusion mechanism which involves only a single equation but which nevertheless exhibits bifurcation to non-uniform states. The patterns generated by this model by variation in a parameter related to the scalar dimensions of domain of definition, indicate its capacity to represent certain key morphogenetic features of multicellular systems formed by motile cells.

Angular intensity and polarization dependence of diffuse transmission through random media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eliyahu, D.; Rosenbluh, M.; Feund, I.

1993-03-01

A simple theoretical model involving only a single sample parameter, the depolarization ratio [rho] for linearly polarized normally incident and normally scattered light, is developed to describe the angular intensity and all other polarization-dependent properties of diffuse transmission through multiple-scattering media. Initial experimental results that tend to support the theory are presented. Results for diffuse reflection are also described. 63 refs., 15 figs.

A prospective microstructure imaging study in mixed-martial artists using geometric measures and diffusion tensor imaging: methods and findings

PubMed Central

Mayer, Andrew R.; Ling, Josef M.; Dodd, Andrew B.; Meier, Timothy B.; Hanlon, Faith M.; Klimaj, Stefan D.

2018-01-01

Although diffusion magnetic resonance imaging (dMRI) has been widely used to characterize the effects of repetitive mild traumatic brain injury (rmTBI), to date no studies have investigated how novel geometric models of microstructure relate to more typical diffusion tensor imaging (DTI) sequences. Moreover, few studies have evaluated the sensitivity of different registration pipelines (non-linear, linear and tract-based spatial statistics) for detecting dMRI abnormalities in clinical populations. Results from single-subject analyses in healthy controls (HC) indicated a strong negative relationship between fractional anisotropy (FA) and orientation dispersion index (ODI) in both white and gray matter. Equally important, only moderate relationships existed between all other estimates of free/intracellular water volume fractions and more traditional DTI metrics (FA, mean, axial and radial diffusivity). These findings suggest that geometric measures provide differential information about the cellular microstructure relative to traditional DTI measures. Results also suggest greater sensitivity for non-linear registration pipelines that maximize the anatomical information available in T1-weighted images. Clinically, rmTBI resulted in a pattern of decreased FA and increased ODI, largely overlapping in space, in conjunction with increased intracellular and free water fractions, highlighting the potential role of edema following repeated head trauma. In summary, current results suggest that geometric models of diffusion can provide relatively unique information regarding potential mechanisms of pathology that contribute to long-term neurological damage. PMID:27071950

A prospective microstructure imaging study in mixed-martial artists using geometric measures and diffusion tensor imaging: methods and findings.

PubMed

Mayer, Andrew R; Ling, Josef M; Dodd, Andrew B; Meier, Timothy B; Hanlon, Faith M; Klimaj, Stefan D

2017-06-01

Although diffusion magnetic resonance imaging (dMRI) has been widely used to characterize the effects of repetitive mild traumatic brain injury (rmTBI), to date no studies have investigated how novel geometric models of microstructure relate to more typical diffusion tensor imaging (DTI) sequences. Moreover, few studies have evaluated the sensitivity of different registration pipelines (non-linear, linear and tract-based spatial statistics) for detecting dMRI abnormalities in clinical populations. Results from single-subject analyses in healthy controls (HC) indicated a strong negative relationship between fractional anisotropy (FA) and orientation dispersion index (ODI) in both white and gray matter. Equally important, only moderate relationships existed between all other estimates of free/intracellular water volume fractions and more traditional DTI metrics (FA, mean, axial and radial diffusivity). These findings suggest that geometric measures provide differential information about the cellular microstructure relative to traditional DTI measures. Results also suggest greater sensitivity for non-linear registration pipelines that maximize the anatomical information available in T 1 -weighted images. Clinically, rmTBI resulted in a pattern of decreased FA and increased ODI, largely overlapping in space, in conjunction with increased intracellular and free water fractions, highlighting the potential role of edema following repeated head trauma. In summary, current results suggest that geometric models of diffusion can provide relatively unique information regarding potential mechanisms of pathology that contribute to long-term neurological damage.

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

NASA Astrophysics Data System (ADS)

Sposini, Vittoria; Chechkin, Aleksei V.; Seno, Flavio; Pagnini, Gianni; Metzler, Ralf

2018-04-01

A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.

Effects of sorption competition on caesium diffusion through compacted argillaceous rock

NASA Astrophysics Data System (ADS)

Jakob, Andreas; Pfingsten, Wilfried; Van Loon, Luc

2009-05-01

We carried out a small-scale laboratory diffusion experiment on a disk-like sample of Opalinus clay from the Mont Terri underground laboratory (Switzerland) using 134Cs as tracer. A through-diffusion phase was followed by an out-diffusion phase where the tracer taken up by the sample was released again. Since the tracer concentration at both boundaries was monitored, careful mass-balance considerations were feasible. A first analysis of the experimental data was done in the frame of a single-species model accounting only for transport and non-linear sorption of caesium. The model could match the data of the through-diffusion phase, however only, when strongly reducing the sorption data based on batch sorption experiments. Yet, such a procedure was in strong contradiction with sorption measurements performed on dispersed and compacted systems. In addition, predictions concerning tracer out-diffusion and mass-balance considerations clearly revealed the shortcomings of this type of model. In a second attempt we applied a multi-species transport model where now the whole water chemistry and a sorption model for caesium were considered. First, the value for the diffusion coefficient was fixed to the best-fit value of the single-species model. But again, the sorption site densities had to be reduced strongly albeit the reduction factor was smaller. Only when fixing the sorption site densities to those values of the sorption model and letting the effective diffusion coefficient D e free for the adjustment, could through-diffusion data be reasonably well fitted and out-diffusion as well as mass-balances be predicted in a satisfying manner. The main results are: (1) The best-fit could be achieved with a value for D e of 1.8 × 10 -10 m 2 s -1 which is rather high but corroborated by results of a molecular modelling study. (2) If caesium arrives in the Opalinus clay sample potassium and sodium (calcium etc.) ions are released and caesium ions are sorbed. The released cations diffuse to lower concentration regions according to their individual concentration gradients. Since locally the cation concentration for potassium, (sodium and calcium) is increased, sorption of these cations is also locally enhanced, affecting in return the sorption behaviour of migrating caesium. Consequently, the sorption process of caesium in such diffusion experiments cannot be addressed by a non-linear isotherm formalism any longer. (3) A reasonable analysis of such single tracer diffusion experiments therefore requires the combined description of transport (diffusion) and sorption of many cations and the whole complex water chemistry of the system. Thus, single-species models can only be applied with care in the considered concentration ranges.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress

NASA Astrophysics Data System (ADS)

Tchitchekova, Deyana S.; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-01

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ˜3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

A novel method for calculating the energy barriers for carbon diffusion in ferrite under heterogeneous stress.

PubMed

Tchitchekova, Deyana S; Morthomas, Julien; Ribeiro, Fabienne; Ducher, Roland; Perez, Michel

2014-07-21

A novel method for accurate and efficient evaluation of the change in energy barriers for carbon diffusion in ferrite under heterogeneous stress is introduced. This method, called Linear Combination of Stress States, is based on the knowledge of the effects of simple stresses (uniaxial or shear) on these diffusion barriers. Then, it is assumed that the change in energy barriers under a complex stress can be expressed as a linear combination of these already known simple stress effects. The modifications of energy barriers by either uniaxial traction/compression and shear stress are determined by means of atomistic simulations with the Climbing Image-Nudge Elastic Band method and are stored as a set of functions. The results of this method are compared to the predictions of anisotropic elasticity theory. It is shown that, linear anisotropic elasticity fails to predict the correct energy barrier variation with stress (especially with shear stress) whereas the proposed method provides correct energy barrier variation for stresses up to ∼3 GPa. This study provides a basis for the development of multiscale models of diffusion under non-uniform stress.

A Mass Diffusion Model for Dry Snow Utilizing a Fabric Tensor to Characterize Anisotropy

NASA Astrophysics Data System (ADS)

Shertzer, Richard H.; Adams, Edward E.

2018-03-01

A homogenization algorithm for randomly distributed microstructures is applied to develop a mass diffusion model for dry snow. Homogenization is a multiscale approach linking constituent behavior at the microscopic level—among ice and air—to the macroscopic material—snow. Principles of continuum mechanics at the microscopic scale describe water vapor diffusion across an ice grain's surface to the air-filled pore space. Volume averaging and a localization assumption scale up and down, respectively, between microscopic and macroscopic scales. The model yields a mass diffusivity expression at the macroscopic scale that is, in general, a second-order tensor parameterized by both bulk and microstructural variables. The model predicts a mass diffusivity of water vapor through snow that is less than that through air. Mass diffusivity is expected to decrease linearly with ice volume fraction. Potential anisotropy in snow's mass diffusivity is captured due to the tensor representation. The tensor is built from directional data assigned to specific, idealized microstructural features. Such anisotropy has been observed in the field and laboratories in snow morphologies of interest such as weak layers of depth hoar and near-surface facets.

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Oleschko, K.; Khrennikov, A.

2017-10-01

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.

Moist, Double-diffusive convection

NASA Astrophysics Data System (ADS)

Oishi, Jeffrey; Burns, Keaton; Brown, Ben; Lecoanet, Daniel; Vasil, Geoffrey

2017-11-01

Double-diffusive convection occurs when the competition between stabilizing and a destabilizing buoyancy source is mediated by a difference in the diffusivity of each source. Such convection is important in a wide variety of astrophysical and geophysical flows. However, in giant planets, double-diffusive convection occurs in regions where condensation of important components of the atmosphere occurs. Here, we present preliminary calculations of moist, double-diffusive convection using the Dedalus pseudospectral framework. Using a simple model for phase change, we verify growth rates for moist double diffusive convection from linear calculations and report on preliminary relationships between the ability to form liquid phase and the resulting Nusselt number in nonlinear simulations.

A minimally-resolved immersed boundary model for reaction-diffusion problems

NASA Astrophysics Data System (ADS)

Pal Singh Bhalla, Amneet; Griffith, Boyce E.; Patankar, Neelesh A.; Donev, Aleksandar

2013-12-01

We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blob model can provide an accurate representation at low to moderate packing densities of the reactive particles, at a cost not much larger than solving a Poisson equation in the same domain. Unlike multipole expansion methods, our method does not require analytically computed Green's functions, but rather, computes regularized discrete Green's functions on the fly by using a standard grid-based discretization of the Poisson equation. This allows for great flexibility in implementing different boundary conditions, coupling to fluid flow or thermal transport, and the inclusion of other effects such as temporal evolution and even nonlinearities. We develop multigrid-based preconditioners for solving the linear systems that arise when using implicit temporal discretizations or studying steady states. In the diffusion-limited case the resulting linear system is a saddle-point problem, the efficient solution of which remains a challenge for suspensions of many particles. We validate our method by comparing to published results on reaction-diffusion in ordered and disordered suspensions of reactive spheres.

Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed

NASA Astrophysics Data System (ADS)

Menzel, Andreas M.

2015-11-01

Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the surroundings and the particle motion has to be taken into account. We analyze a simplified diffusion model that includes some aspects of a complex environment in the framework of a nonlinear friction process: at low particle speeds, friction grows linearly with the particle velocity as for regular viscous friction; it grows more than linearly at higher particle speeds; finally, at a maximum of the possible particle speed, the friction diverges. In addition to bare diffusion, we study the influence of a constant drift force acting on the diffusing particle. While the corresponding stationary velocity distributions can be derived analytically, the displacement statistics generally must be determined numerically. However, as a benefit of our model, analytical progress can be made in one case of a special maximum particle speed. The effect of a drift force in this case is analytically determined by perturbation theory. It will be interesting in the future to compare our results to real experimental systems. One realization could be magnetic colloidal particles diffusing through a shear-thickening environment such as starch suspensions, possibly exposed to an external magnetic field gradient.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

NASA Astrophysics Data System (ADS)

Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar

2017-03-01

We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.

Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach

DOE PAGES

Kim, Changho; Nonaka, Andy; Bell, John B.; ...

2017-03-24

Here, we develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules,more » to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. Furthermore, by comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.« less

A Novel Diffuse Fraction-Based Two-Leaf Light Use Efficiency Model: An Application Quantifying Photosynthetic Seasonality across 20 AmeriFlux Flux Tower Sites

NASA Astrophysics Data System (ADS)

Yan, Hao; Wang, Shao-Qiang; Yu, Kai-Liang; Wang, Bin; Yu, Qin; Bohrer, Gil; Billesbach, Dave; Bracho, Rosvel; Rahman, Faiz; Shugart, Herman H.

2017-10-01

Diffuse radiation can increase canopy light use efficiency (LUE). This creates the need to differentiate the effects of direct and diffuse radiation when simulating terrestrial gross primary production (GPP). Here, we present a novel GPP model, the diffuse-fraction-based two-leaf model (DTEC), which includes the leaf response to direct and diffuse radiation, and treats maximum LUE for shaded leaves (ɛmsh defined as a power function of the diffuse fraction (Df)) and sunlit leaves (ɛmsu defined as a constant) separately. An Amazonian rainforest site (KM67) was used to calibrate the model by simulating the linear relationship between monthly canopy LUE and Df. This showed a positive response of forest GPP to atmospheric diffuse radiation, and suggested that diffuse radiation was more limiting than global radiation and water availability for Amazon rainforest GPP on a monthly scale. Further evaluation at 20 independent AmeriFlux sites showed that the DTEC model, when driven by monthly meteorological data and MODIS leaf area index (LAI) products, explained 70% of the variability observed in monthly flux tower GPP. This exceeded the 51% accounted for by the MODIS 17A2 big-leaf GPP product. The DTEC model's explicit accounting for the impacts of diffuse radiation and soil water stress along with its parameterization for C4 and C3 plants was responsible for this difference. The evaluation of DTEC at Amazon rainforest sites demonstrated its potential to capture the unique seasonality of higher GPP during the diffuse radiation-dominated wet season. Our results highlight the importance of diffuse radiation in seasonal GPP simulation.