Journal articles: 'Diffusion'

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Khair, Abul, Nilay Kumar Dey, Mohammad Harun-Ur-Rashid, Mohammad Abdul Alim, Newas Mohammad Bahadur, Sultan Mahamud, and Syekat Ahmed. "Diffusimetry Renounces Graham’s Law, Achieves Diffusive Convection, Concentration Gradient Induced Diffusion, Heat and Mass Transfer." Defect and Diffusion Forum 407 (March 2021): 173–84. http://dx.doi.org/10.4028/www.scientific.net/ddf.407.173.

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Absolute diffusion rates of KMnO4 in vertical and flattened diffusimeters show the concentration gradient force as being stronger than the gravitational force. Hot water molecules move downward on self-diffusion against buoyancy. Diffusive convection (DC) in warm water and double-diffusive convection (DDC) in warm, saline water take place inside the diffusimeter with DDC transferring more heat than DC. In the diffusing medium the original reagents change or retain their compositions to give the diffusate molecules to diffuse. In water, the change is mostly hydration. The syngener BaCl2.2H2O separately with congeners 3CdSO4.8H2O, ZnSO4.7H2O, and ZnSO4.H2O presents two distinct pairs of overlapping concentration versus rate curves, first for having very close MWs of BaCl2 and CdSO4 and second for having ZnSO4.H2O as the common congener for both the zinc sulfates. Chlorides of Li, Na, and K diffusing at hindered rates in glucose solution show the least rate for LiCl inevitably on grounds of low mass and high Li+ hydration radius. Diffusion blocking occurs at higher glucose concentration. Diffusion of 0.6M AgNO3-0.6M NH4Cl standardizes this diffusimeter. Mass transfer of HCl, H2SO4, and H2C2O4 show oxalic acid diffusing as hydrate and 88 percentage transfer of sulfuric acid in 5 minutes. The Superdiffusive Anti Graham’s Law, Vd , is further consolidated by Ca (NO3)2-M2CO3(M = Na, K, NH4+) and Ca (NO3)2-Na2HPO4 diffusions. Odd and even diffusions are illustrated by AgNO3-NH4Cl and AgNO3-BaCl2 diffusions.

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SCHUMANN, Andrew, Zozan TARHAN, and Vladimir SAZONOV. "Ideologies and Encounters of Ideas at the Crossroads of the Ancient World." STUDIA ANTIQUA ET ARCHAEOLOGICA 30, no. 2 (2024): 235–42. https://doi.org/10.47743/saa-2024-30-2-1.

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In the article introducing this special issue, we consider the prospects of cultural diffusionism. We show that diffusion is not a uniform phenomenon since it includes direct, partial, multi-layered, and reverse forms. The complex approach to diverse forms of diffusions is called by us the crossroads concept. It aligns with cultural relativism which examines cultural traits through diffusion and modification. In world-systems analysis, cultural diffusion is analyzed within the world-economy framework, rooted in the classical Marxism view of economic systems as foundational with culture as a superstructure. Neo-Marxism and dependency theory highlight a division between developed and developing countries, positing that cultural influences often flow from the center to the periphery. However, this view oversimplifies cultural diffusion’s complexities, as we demonstrate. Moreover, cultural diffusion often precedes trade route establishment, with religious diffusion frequently facilitating subsequent trade communications. This special issue, edited by us, explores cultural diffusion and its varied forms, challenging the notion that it fits neatly into a center-to-periphery movement.

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Benga, Gheorghe, Octavian Popescu, and Victor I. Pop. "Water exchange through erythrocyte membranes: p-choloromercuribenzene sulfonate inhibition of water diffusion in ghosts studied by a nuclear magnetic resonance technique." Bioscience Reports 5, no. 3 (March 1, 1985): 223–28. http://dx.doi.org/10.1007/bf01119591.

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A comparison of water diffusion in human erythrocytes and ghosts revealed a longer relaxation time in ghosts, A comparison of water diffusion in human erythrocytes and ghosts revealed a longer relaxation time in ghosts, corresponding to a decreased exchange rate. However, the diffusional permeability of ghosts was not significantly different from that of erythrocytes. The changes in water diffusion following exposure to p-chloromercuribenzene sulfonate (PCMBS) have been studied on ghosts suspended in isotonic solutions. It was found that a significant inhibitory effect of PCMBS on water diffusion occurred only after several minutes of incubation at 37°C. No inhibition was noticed after short incubation at 0°C as previously used in some labelling experiments. This indicates the location in the membrane interior of the SH groups involved in water diffusion across human erythrocyte membranes. The nuclear magnetic resonance (n. m. r.) method appears as a useful tool for studying changes in water diffusiofl in erythrocyte ghosts with the aim of locating the water channel.

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Khoulif, S., E. B. Hannech, and N. Lamoudi. "Study of Reactive Diffusion in Cu/Zn Diffusion Couple." Indian Journal Of Science And Technology 15, no. 48 (December 27, 2022): 2740–47. http://dx.doi.org/10.17485/ijst/v15i48.13.

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Pinholt, Henrik D., Søren S. R. Bohr, Josephine F. Iversen, Wouter Boomsma, and Nikos S. Hatzakis. "Single-particle diffusional fingerprinting: A machine-learning framework for quantitative analysis of heterogeneous diffusion." Proceedings of the National Academy of Sciences 118, no. 31 (July 28, 2021): e2104624118. http://dx.doi.org/10.1073/pnas.2104624118.

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Single-particle tracking (SPT) is a key tool for quantitative analysis of dynamic biological processes and has provided unprecedented insights into a wide range of systems such as receptor localization, enzyme propulsion, bacteria motility, and drug nanocarrier delivery. The inherently complex diffusion in such biological systems can vary drastically both in time and across systems, consequently imposing considerable analytical challenges, and currently requires an a priori knowledge of the system. Here we introduce a method for SPT data analysis, processing, and classification, which we term “diffusional fingerprinting.” This method allows for dissecting the features that underlie diffusional behavior and establishing molecular identity, regardless of the underlying diffusion type. The method operates by isolating 17 descriptive features for each observed motion trajectory and generating a diffusional map of all features for each type of particle. Precise classification of the diffusing particle identity is then obtained by training a simple logistic regression model. A linear discriminant analysis generates a feature ranking that outputs the main differences among diffusional features, providing key mechanistic insights. Fingerprinting operates by both training on and predicting experimental data, without the need for pretraining on simulated data. We found this approach to work across a wide range of simulated and experimentally diverse systems, such as tracked lipases on fat substrates, transcription factors diffusing in cells, and nanoparticles diffusing in mucus. This flexibility ultimately supports diffusional fingerprinting’s utility as a universal paradigm for SPT diffusional analysis and prediction.

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Cherniak, D. J., and E. B. Watson. "Ti diffusion in feldspar." American Mineralogist 105, no. 7 (July 1, 2020): 1040–51. http://dx.doi.org/10.2138/am-2020-7272.

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Abstract Chemical diffusion of Ti has been measured in natural K-feldspar and plagioclase. The sources of diffusant used were TiO2 powders or pre-annealed mixtures of TiO2 and Al2O3. Experiments were run in crimped Pt capsules in air or in sealed silica glass capsules with solid buffers (to buffer at NNO). Rutherford backscattering spectrometry (RBS) was used to measure Ti diffusion profiles. From these measurements, the following Arrhenius relations are obtained for diffusion normal to (001):For oligoclase, over the temperature range 750–1050 °C:DOlig=6.67×10-12exp(-207±31kJ/mol/RT)m2s-1For labradorite, over the temperature range 900–1150 °C:DLab=of4.37×10-14exp(-181±57kJ/mol/RT)m2s-1For K-feldspar, over the temperature range 800–1000 °C:DKsp=3.01×10-6exp(-342±47kJ/mol/RT)m2s-1. Diffusivities for experiments buffered at NNO are similar to those run in air, and the presence of hydrous species appears to have little effect on Ti diffusion. Ti diffusion also shows little evidence of anisotropy. In plagioclase, there appears to be a dependence of Ti diffusion on An content of the feldspar, with Ti diffusing more slowly in more calcic plagioclase. This trend is similar to that observed for other cations in plagioclase, including Sr, Pb, Ba, REE, Si, and Mg. In the case of Ti, an increase of 30% in An content would result in an approximate decrease in diffusivity of an order of magnitude. These data indicate that feldspar should be moderately retentive of Ti chemical signatures, depending on feldspar composition. Ti will be more resistant to diffusional alteration than Sr. For example, Ti zoning on a 50 μm scale in oligoclase would be preserved at 600 °C for durations of ~1 million years, with Sr zoning preserved only for ~70 000 yr at this temperature. These new data for a trace impurity that is relatively slow-diffusing and ubiquitous in feldspars (Hoff and Watson 2018) have the potential to extend the scope and applicability of t-T models for crustal rocks based on measurements of trace elements in feldspars.

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Al-Mashrafi, Khaled. "The influence of longitudinal diffusion on the transport of dust particles emitted from a fixed source." International Journal of Applied Mathematical Research 5, no. 1 (January 9, 2016): 11. http://dx.doi.org/10.14419/ijamr.v5i1.5367.

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<p>The mathematical model for the diffusion of dust particles emitted from a fixed source in the presence of the longitudinal diffusion and absence of latitudinal and vertical diffusions, is investigated. The diffusion of dust particles in the atmosphere is governed by the atmospheric diffusion equation. In the previous paper [1], the general case of the time-dependent diffusion equation in the presence of a point source whose strength is dependent on time, was solved. The calculations showed that the diffusion parameters play an important role in the spread of the dust particles in the atmosphere. In the previous paper, we examined the model in the presence of vertical diffusion and absence of other diffusions to show that for small times, the dust spreads with a front that travels with the speed of the wind. In the current paper, the vertical and latitudinal diffusions are absent while the longitudinal diffusion is present. It is found that the solution depends on the source of time dependence. To study the nature of the solution, two special cases of the source are specified. In the both cases, it is found that there is no discontinuity front, and the dust particles spread slowly into the direction of the wind.</p>

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Zhang, Siwei, Size Chen, Dan Xiao, Chao Wang, Haixia Wang, Yong Zhang, and Taosheng Li. "Investigating the Impact of Displacement Cascades on Tritium Diffusion in MgT2: A Molecular Dynamics Study." Materials 16, no. 9 (April 25, 2023): 3359. http://dx.doi.org/10.3390/ma16093359.

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Molecular dynamics methods were utilized to investigate displacement cascades and tritium diffusion in α-MgT2. It was observed from collision cascades results that the stable number of defects weakly depended on temperature, while the peak and stable number of defects linearly increased with increasing the primary knock-on atom energy. The results of the mean square displacement study revealed that defects had a significant impact on tritium diffusion. The clustering of magnesium self-interstitial atoms and diffusing tritium atoms results in an increased diffusion barrier, whereas the formation of clusters between tritium interstitial atoms is relatively difficult and has no significant impact on the diffusion barrier. The presence of magnesium and tritium vacancies has a minimal effect on the diffusion barrier due to the large number of diffusing tritium atoms that offset the adsorption of vacancies on diffusing atoms. Both magnesium and tritium interstitial atoms increase the collision probability of diffusing atoms, leading to an increased diffusion prefactor. Magnesium vacancies cause significant lattice distortion, increasing the diffusion barrier, while the impact of tritium vacancies on the diffusion barrier is small due to their minimal lattice distortion effect. The research uncovered significant disparities in the diffusion properties of hydrogen and tritium, indicating that the results of the study of hydrogen storage could not be applied to tritium.

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Lin, C. C., C. L. Tsai, P. K. Wu, and H. J. Lee. "Advancing Diffusion Model for Diffusion in a Cube of Medium." Journal of Mechanics 28, no. 2 (May 8, 2012): 345–54. http://dx.doi.org/10.1017/jmech.2012.38.

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AbstractA solution based on an advancing model for the content of diffusion material in a cube of medium is derived. The cube is assumed to be surrounded by diffusion material, and the diffusion material penetrates through all six surfaces and diffuses toward the center of the cube. The model accounts for the interaction between the diffusions in the three principle coordinates of the Cartesian coordinate system. For the first time, an exact solution of the content of the diffusion material based on the advancing model is derived in a clean form for a three-dimensional case.

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10

Dalík, Josef. "A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems." Applications of Mathematics 36, no. 5 (1991): 329–54. http://dx.doi.org/10.21136/am.1991.104471.

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11

Mittal, Jagjiwan, and Kwang-Lung Lin. "Diffusion of elements during reflow ageing of Sn-Zn solder in liquid state on Ni/Cu substrate – theoretical and experimental study." Soldering & Surface Mount Technology 30, no. 3 (June 4, 2018): 137–44. http://dx.doi.org/10.1108/ssmt-10-2017-0035.

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Purpose This paper aims to study the diffusion of Zn, Ni and Sn in the liquid state during the reflow ageing of the Sn-Zn solder above its melting point on an Ni/Cu substrate in relation to the formation of intermetallic compounds (IMCs). Design/methodology/approach The Sn-Zn solder is reflowed on Ni/Cu substrates and is aged at 503 K. The formation of IMCs and their composition is characterized using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). Diffusion coefficients and diffusion distances of Zn, Ni and Sn in the liquid state during reflow and ageing are theoretically calculated. Both experimental and theoretical behaviours for Ni and Zn diffusions are compared. Findings Calculations show a linear increment in the liquid-state diffusion coefficients of Ni, Zn and Sn in the solder matrix with a rise in temperature, but they remained constant during ageing. However, diffusion distances increased slowly with temperature but manifold with ageing time. The experimental results revealed segregation of Zn and Ni at the interface in the as-reflow aged specimens. The Zn was concentrated at the solder–substrate interface and it reacted with Ni diffusing from the substrate to form Ni-Sn-Zn IMCs. The rapid diffusion of Zn and Ni with the increase in ageing time increased their atomic concentrations in the IMCs against the reduction in Sn concentration owing to a comparatively slower diffusion. Originality/value The novelty of the paper is the detailed study of theoretical diffusion of Zn, Sn and Ni in the liquid state during reflow ageing of Sn-Zn above its melting points on a Ni/Cu substrate. This is compared with values obtained experimentally and related to the mechanisms of IMC formation.

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Lou, Yuan, and Wei-Ming Ni. "Diffusion, Self-Diffusion and Cross-Diffusion." Journal of Differential Equations 131, no. 1 (October 1996): 79–131. http://dx.doi.org/10.1006/jdeq.1996.0157.

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Zhai, Bao-gai, Meng Meng Chen, and Yuan Ming Huang. "Diffusing Mn4+ into Dy3+ Doped SrAl2O4 for Full-Color Tunable Emissions." Materials 15, no. 22 (November 17, 2022): 8170. http://dx.doi.org/10.3390/ma15228170.

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Dy3+ and Mn4+ codoped SrAl2O4 (SrAl2O4:Dy3+, Mn4+) phosphors were obtained by diffusing Mn4+ ions into Dy3+-doped SrAl2O4 via the constant-source diffusion technique. The influences of diffusion temperature and diffusion time on the emissions of SrAl2O4:Dy3+,Mn4+ were investigated. It was found that: (i) efficient red emission peaking at 651 nm can be readily achieved for SrAl2O4:Dy3+ by simply diffusing Mn4+ into SrAl2O4:Dy3+ at 800 °C and above; (ii) the red emission of Mn4+ becomes dominant over the characteristic emissions of Dy3+ when the diffusion temperature is 900 °C or higher; and (iii) the intensity of the red emission of SrAl2O4:Dy3+,Mn4+ is far more sensitive to diffusion temperature than to diffusion time. Our results have demonstrated that full-color tunable emissions can be realized for SrAl2O4:Dy3+, Mn4+ by tuning the parameters of diffusion temperature and diffusion time, which opens up a space for realizing easy color control of Dy3+-doped inorganic materials.

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Wirbeleit, Frank. "Non-Gaussian Local Density Diffusion (LDD-) Model for Boron Diffusion in Si- and Si_xGe_1-x Ultra-Shallow Junction Post-Implant and Advanced Rapid-Thermal-Anneals." Defect and Diffusion Forum 305-306 (October 2010): 71–84. http://dx.doi.org/10.4028/www.scientific.net/ddf.305-306.71.

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Boron diffusion after implant and anneal has been studied extensively in the past, without de-convoluting the Boron diffusion behavior by the initial post implant Boron concentration profile, which is done in this work first time. To support the de-convolution approach, the local density diffusion (LDD) model is selected, because this model is based on just one single arbitrary diffusion parameter per atomic species and host lattice combination. The LDD model is used for Phosphorus and Arsenic diffusion so far and an extension to simulate Boron diffusion in presence of Boron clusters is presented here. As the result, maximum Boron penetration depth post different rapid thermal anneals and the quantification of diffusing and clustering (non-diffusing) Boron in silicon and silicon-germanium host lattice systems are given.

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Kim, J. S., F. A. Williams, and P. D. Ronney. "Diffusional-thermal instability of diffusion flames." Journal of Fluid Mechanics 327 (November 25, 1996): 273–301. http://dx.doi.org/10.1017/s0022112096008543.

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The diffusional–thermal instability, which gives rise to striped quenching patterns that have been observed for diffusion flames, is analysed by studying the model of a one-dimensional convective diffusion flame in the diffusion-flame regime of activation-energy asymptotics. Attention is focused principally on near-extinction conditions with Lewis numbers less than unity, in which the reactants with high diffusivity diffuse into the strong segments of the reaction sheet, so that the regions between the strong segments become deficient in reactant and subject to the local quenching that leads to the striped patterns. This analysis differs from other flame stability analyses in that the complete description of the dispersion relation is obtained from a composite expansion of the results of an analysis with the conventional convective-diffusive scaling and one with reaction-zone scaling. The results predict that striped patterns will occur, for flames sufficiently close to quasi-steady extinction, with a finite wavenumber that in convective–diffusive scaling is proportional to the cube root of the Zel'dovich number. The convective–diffusive response contributes to the stabilization of long-wavelength disturbances by through positive excess enthalpies by which the flame becomes more resistant to instability, while the reaction-zone response provides stabilization of short-wavelength disturbances by transverse diffusion, within the reactive inner layer, which relaxes the perturbed scalar fields towards their unperturbed states. As quasi-steady extinction is approached, marginal stability arises first at an intermediate range between these two scalings. Parametric results for this bifurcation point are obtained through numerical solutions of the associated generalized eigenvalue problems. Comparisons with measured pattern dimensions for different sets of reactants and diluents reveal excellent qualitative agreement.

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Doremus, R. H. "Diffusion of water in crystalline and glassy oxides: Diffusion–reaction model." Journal of Materials Research 14, no. 9 (September 1999): 3754–58. http://dx.doi.org/10.1557/jmr.1999.0508.

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Diffusion of water in oxides is modeled as resulting from the solution and diffusion of molecular water in the oxide. This dissolved water can react and exchange with the oxide network to form immobile OH groups and different hydrogen and oxygen isotopes in the oxide. The model agrees with many experiments on water diffusion in oxides. The activation energy for diffusion of water in oxides correlates with the structural openness of the oxide, suggesting that molecular water is the diffusing species.

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Lenaz, Giorgio. "Lipid fluidity and membrane protein dynamics." Bioscience Reports 7, no. 11 (November 1, 1987): 823–37. http://dx.doi.org/10.1007/bf01119473.

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Membrane fluidity plays an important role in cellular functions. Membrane proteins are mobile in the lipid fluid environment; lateral diffusion of membrane proteins is slower than expected by theory, due to both the effect of protein crowding in the membrane and to constraints from the aqueous matrix. A major aspect of diffusion is in macromolecular associations: reduction of dimensionality for membrane diffusion facilitates collisional encounters, as those concerned with receptor-mediated signal transduction and with electron transfer chains. In mitochondrial electron transfer, diffusional control is prevented by the excess of collisional encounters between fast-diffusing ubiquinone and the respiratory complexes. Another aspect of dynamics of membrane proteins is their conformational flexibility. Lipids may induce the optimal conformation for catalytic activity. Breaks in Arrhenius plots of membrane-bound enzymes may be related to lipid fluidity: the break could occur when a limiting viscosity is reached for catalytic activity. Viscosity can affect protein conformational changes by inhibiting thermal fluctuations to the inner core of the protein molecule.

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Han, Deren, Liqun Qi, and Ed X. Wu. "Extreme diffusion values for non-Gaussian diffusions." Optimization Methods and Software 23, no. 5 (October 2008): 703–16. http://dx.doi.org/10.1080/10556780802367171.

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Zhitao Xiao, Zhitao Xiao, Zhenbei Xu Zhenbei Xu, Fang Zhang Fang Zhang, Lei Geng Lei Geng, Jun Wu Jun Wu, Quan Yuan Quan Yuan, and Jiangtao Xi Jiangtao Xi. "ESPI filtering method based on anisotropic coherence diffusion and Perona-Malik diffusion." Chinese Optics Letters 11, no. 10 (2013): 101101–4. http://dx.doi.org/10.3788/col201311.101101.

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Boltz, Horst-Holger, Alexei Sirbu, Nina Stelzer, Primal de Lanerolle, Stefanie Winkelmann, and Paolo Annibale. "The Impact of Membrane Protein Diffusion on GPCR Signaling." Cells 11, no. 10 (May 17, 2022): 1660. http://dx.doi.org/10.3390/cells11101660.

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Spatiotemporal signal shaping in G protein-coupled receptor (GPCR) signaling is now a well-established and accepted notion to explain how signaling specificity can be achieved by a superfamily sharing only a handful of downstream second messengers. Dozens of Gs-coupled GPCR signals ultimately converge on the production of cAMP, a ubiquitous second messenger. This idea is almost always framed in terms of local concentrations, the differences in which are maintained by means of spatial separation. However, given the dynamic nature of the reaction-diffusion processes at hand, the dynamics, in particular the local diffusional properties of the receptors and their cognate G proteins, are also important. By combining some first principle considerations, simulated data, and experimental data of the receptors diffusing on the membranes of living cells, we offer a short perspective on the modulatory role of local membrane diffusion in regulating GPCR-mediated cell signaling. Our analysis points to a diffusion-limited regime where the effective production rate of activated G protein scales linearly with the receptor–G protein complex’s relative diffusion rate and to an interesting role played by the membrane geometry in modulating the efficiency of coupling.

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Uematsu, Masashi. "Unified Simulation of Diffusion in Silicon and Silicon Dioxide." Defect and Diffusion Forum 237-240 (April 2005): 38–49. http://dx.doi.org/10.4028/www.scientific.net/ddf.237-240.38.

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We present a unified simulation of diffusion in silicon (Si) and silicon dioxide (SiO2) that is based on the diffusing dopant species and point defects that primarily contribute to the diffusion. We first present the simulation of phosphorus (P) diffusion in Si based on the integrated diffusion model that we have developed and elucidate the mechanism of the appearance of the anomalous P in-diffusion profile. The vacancy mechanism governs P diffusion in the plateau region, while the kick-out mechanism governs it in the deeper region, where Si self-interstitials dominate in the kink region and P interstitials dominate in the tail region. Next, we present the simulation of boron (B) diffusion and Si self-diffusion in SiO2. We examined the co-diffusion of implanted B and 30Si in thermally grown 28SiO2, which shows increasing diffusivities with decreasing distance between the diffusers and Si/SiO2 interface and with higher B concentration in SiO2. We propose a model in which SiO molecules generated at the interface and diffusing into SiO2 enhance both B diffusion and Si self-diffusion. The simulation showed that the SiO diffusion is so slow that the SiO concentration at the B and 30Si region critically depends on the distance from the interface. In addition, the simulation predicts the possibility of time-dependent diffusivities for B and Si because more SiO molecules should be arriving from the interface with time, and this time dependence was experimentally observed. Moreover, based on the B concentration dependence, the simulation result indicates that B and Si atoms in SiO2 diffuse correlatively via SiO; namely, the enhanced SiO diffusion by the existence of B enhances B diffusion and Si self-diffusion.

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Zhang, Hongtao, and Jingfu Zhao. "Stationary Patterns of a Cross-Diffusion Prey-Predator Model with Holling Type II Functional Response." Journal of Mathematics 2023 (October 3, 2023): 1–9. http://dx.doi.org/10.1155/2023/2588998.

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In this paper, we consider positive steady-state solutions of a cross-diffusions prey-predator model with Holling type II functional response. We investigate sufficient conditions for the existence and the nonexistence of nonconstant positive steady state solutions. It is observed that nonconstant positive steady states do not exist with small cross-diffusion coefficients, and the constant positive steady state is global asymptotically stable without cross-diffusion. Furthermore, we show that if natural diffusion coefficient or cross-diffusion coefficient of the predator is large enough and other diffusion coefficients are fixed, then under some conditions, at least one nonconstant positive steady state exists.

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Cheung, S. C. H. "Methods to measure apparent diffusion coefficients in compacted bentonite clays and data interpretation." Canadian Journal of Civil Engineering 16, no. 4 (August 1, 1989): 434–43. http://dx.doi.org/10.1139/l89-073.

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The methods used to determine apparent diffusion coefficients and the appropriate parameters for modelling diffusion through compacted bentonite–water systems are assessed and discussed. The measured apparent diffusion coefficient can vary between methods. The discrepancies are shown to be due to heterogeneous diffusivities arising from the proximity of the surface of clay particles. Two different diffusivity pathways are identified and the diffusive flux is shown to be dictated by the charge of diffusing species, diffusion time, and soil fabric. Key words: apparent diffusion coefficient, methods, compacted bentonite, heterogeneous diffusion, parameters, pathways.

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PRASAD, P. V. SIVA RAMA, and D. P. TEWARI. "Effect of a stochastic electron background on low-m tearing modes." Journal of Plasma Physics 57, no. 2 (February 1997): 247–57. http://dx.doi.org/10.1017/s0022377896004655.

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The effect of a stochastic electron background on the stability of low-m tearing modes is studied. The coherent direct interaction approximation is applied to the drift-kinetic equation in order to include the effects of current density diffusion, electron density diffusion and magnetic field diffusion in the tearing mode equations. It is found that for the m=1 mode in the collisionless regime the magnetic field diffusion destabilizes the mode further, while in the collisional regime these diffusions may not significantly affect the mode; for the m[ges ]2 modes in the collisional and semicollisional regimes the electron density diffusion stabilizes the modes, while in the collisionless regime the effects of current density diffusion and electron density diffusion may balance each other without significantly affecting the modes.

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YANG, XIYAN, ZHANJIANG YUAN, and TIANSHOU ZHOU. "TURING PATTERN FORMATION IN A TWO-SPECIES NEGATIVE FEEDBACK SYSTEM WITH CROSS-DIFFUSION." International Journal of Bifurcation and Chaos 23, no. 09 (September 2013): 1350162. http://dx.doi.org/10.1142/s0218127413501629.

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Pattern formation is a ubiquitous phenomenon in the natural world. Previous studies showed that for an activator–inhibitor system without cross-diffusion, spatial patterns can be formed only when the diffusion of the inhibitor is significantly faster than that of the activator. However, cross-diffusion exists extensively in real systems, especially in biological systems. Here, we study a prototypic two-species negative feedback system with cross-diffusion. By performing stability analysis of equilibrium state, we find sufficient conditions for Turing instability. Both analytical and numerical results demonstrate that mutual diffusions of the two species can lead to the Turing pattern formation regardless of differences in self-diffusion coefficients. However, in the absence of the mutual diffusion or even if there is the cross-diffusion of only one species, the system cannot exhibit Turing patterns. Our results reveal the mechanism of Turing pattern formation in a class of reaction–diffusion systems, where mutual diffusion between species plays a key role.

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WANG, CHANGQING, YU JIA, XUEQING WANG, XINJIAN LI, XING HU, and SONGYOU WANG. "MOLECULAR DYNAMICS SIMULATIONS OF SINGLE Si ADATOM DIFFUSION ON THE Si(001) SURFACE AND ACROSS SINGLE-LAYER Si(001) STEPS." Modern Physics Letters B 22, no. 02 (January 20, 2008): 117–25. http://dx.doi.org/10.1142/s0217984908014602.

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By using the Stillinger–Weber atomic interactional potential, we have carried out molecular dynamics simulations of single Si adatom diffusing on the Si(001) surface and single-layer Si(001) steps at temperatures ranging from 1000 K to 1300 K. We have presented one new diffusion pathway of a single Si adatom diffusing on the Si(001) along the direction perpendicular to dimer rows, that can weaken the diffusion anisotropy. We have investigated the process of the single Si adatom diffusing across single-layer Si(001) steps as well and given adatom diffusion pathways of step-flow and transformation of single-layer into double-layer steps. Our results show that the exchange between an adatom and a surface atom plays an important role in the adatom diffusion process above 1000 K.

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Jacops, Elke, Marc Aertsens, Norbert Maes, Christophe Bruggeman, Rudy Swennen, Bernd Krooss, Alexandra Amann-Hildenbrand, and Ralf Littke. "The Dependency of Diffusion Coefficients and Geometric Factor on the Size of the Diffusing Molecule: Observations for Different Clay-Based Materials." Geofluids 2017 (2017): 1–16. http://dx.doi.org/10.1155/2017/8652560.

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In order to investigate in more detail the relation between the size of diffusing molecules and their diffusion coefficients (and geometric factors), diffusion experiments with gases of different size and tritiated water (HTO) have been performed on different clayey samples (Boom Clay, Eigenbilzen Sands, Opalinus Clay, Callovo-Oxfordian Clay, and bentonite with different dry densities). We observed that, for unreactive gases in clayey materials, the effective diffusion coefficient varies with the size of the diffusing molecule and this variation can be described by an exponential or a power law function. The variation of the geometric factor can also be described by an exponential function. The observed experimental relations can be used to estimate diffusion coefficients; by measuring experimentally in clay the effective diffusion coefficient of two unreactive dissolved gases with a different size, the diffusion coefficients of other dissolved gases (with a size in between the two measured gases) can be estimated by using the fitted exponential relationship.

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LOH, S. W., D. H. ZHANG, C. Y. LI, R. LIU, and A. T. S. WEE. "STUDY OF COPPER DIFFUSION INTO TANTALUM AND TANTALUM DIFFUSION INTO COPPER." International Journal of Modern Physics B 16, no. 01n02 (January 20, 2002): 100–107. http://dx.doi.org/10.1142/s0217979202009512.

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We have carried out direct diffusion measurements of Cu into Ta and Ta into Cu. Thin films of 50nm thickness of Cu were grown onto a thick Ta layer of 1 μm by Ionized Metal Plasma. Samples were annealed in a rapid thermal system from temperatures ranging from 400°C to 800°C for periods of 60s and 180s. The diffusion profile was performed using Secondary ion mass spectroscopy. The Cu diffusion coefficients in Ta can be described by 3.0246 × 10-15 exp(-0.1747eV/kT) at 60s and 2.7532 × 10-15 exp(-0.1737eV/kT) at 180s. The Ta diffusion coefficients in Cu can be described by 2.7532 × 10-15 exp(-0.1773eV/kT) at 60s and 2.1271 × 10-15 exp(-0.1753eV/kT) at 180s. To assure reliability, the extent of both diffusions should be considered in device design and processing.

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Grebenkov, Denis S. "Diffusion-Controlled Reactions: An Overview." Molecules 28, no. 22 (November 13, 2023): 7570. http://dx.doi.org/10.3390/molecules28227570.

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We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski, who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the underlying mathematical framework. Single-molecule reaction schemes, anomalous bulk diffusions, reversible binding/unbinding kinetics, and many other extensions are presented. An alternative encounter-based approach to diffusion-controlled reactions is introduced, with emphasis on its advantages and potential applications. Some open problems and future perspectives are outlined.

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30

Dayananda, Mysore A. "An Overview of Selected Phenomena in Multicomponent Diffusion." Diffusion Foundations 4 (July 2015): 3–21. http://dx.doi.org/10.4028/www.scientific.net/df.4.3.

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There exist several interesting phenomena and observations reported in literature for isothermal diffusion in multicomponent systems. Such phenomena include uphill diffusion, development of zero-flux planes and flux reversals for individual components, flux reversals at interfaces, and instability at interfaces and multiphase layer development. In addition, uncommon diffusion structures exhibiting unusual diffusion paths can develop in both single phase and multiphase diffusion assemblies. An overview of such phenomena is presented to highlight the role of interactions among diffusing components with the aid of selected diffusion studies carried out in multicomponent alloy systems, aluminides, silicides, and nuclear fuels.

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Green, Peter F., and Edward J. Kramer. "Diffusion in Polymer Alloy Melts." MRS Bulletin 12, no. 8 (December 1987): 42–47. http://dx.doi.org/10.1557/s0883769400066744.

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AbstractDiffusion in polymer alloys or blends can be used to extract information on the fundamentals of the dynamics of individual polymer chains in the melt and the thermodynamics of the interaction between unlike polymer species. The dynamics of individual chains are available from measurements of the tracer diffusion coefficients, D*, of the various species while the thermodynamics of interaction, represented by the Flory parameter, x, can be obtained from measurements of the mutual diffusion or interdiffusion coefficient, D. We will show that these quantities can be measured conveniently by forward recoil spectrometry (FRES), an ion beam analysis technique that can determine the concentration versus depth profile of polymers labeled with deuterium diffusing into unlabeled polymer matrices.For high enough molecular weight of the matrix, the tracer diffusion coefficient of both species in the blend scale as D0N−2, where N is the number of monomer segments per diffusing chain; the constant D0, however, can differ by more than 104 for chemically different molecules diffusing in the same blend, suggesting that conventional concepts of chain dynamics in melts, such as monomer friction coefficients, need to be reexamined. The mutual diffusion coefficient is controlled by the faster species in the blend (the one with the larger D*N product) in agreement with what was found in metallic alloys (but in sharp disagreement with the “slow” theory of mutual diffusion which predicts that the slower species controls). Since the combinatorial (ideal) entropy of mixing of polymers is low, the thermodynamic driving force for diffusion is dominated by enthalpy and excess entropy of mixing (x) to a degree unprecedented for atomic or small molecule systems. This means that one can observe not only a thermodynamic “slowing down” of diffusion when x becomes positive as one nears the spinodal but also a large thermodynamic “speeding up” of diffusion when x is negative. Measurements of mutual diffusion turn out to be one of the most sensitive methods available for measuring x.

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Lou, Xin, Rui Liu, Ke Chen, Xin Zhou, Rudolf Podgornik, and Mingcheng Yang. "Diffusion of a chemically active colloidal particle in composite channels." Chinese Physics B 31, no. 4 (April 1, 2022): 044704. http://dx.doi.org/10.1088/1674-1056/ac381b.

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Diffusion of colloidal particles in microchannels has been extensively investigated, where the channel wall is either a no-slip or a slip-passive boundary. However, in the context of active fluids, driving boundary walls are ubiquitous and are expected to have a substantial effect on the particle dynamics. By mesoscale simulations, we study the diffusion of a chemically active colloidal particle in composite channels, which are constructed by alternately arranging the no-slip and diffusio-osmotic boundary walls. In this case, the chemical reaction catalyzed by the active colloidal particle creates a local chemical gradient along the channel wall, which drives a diffusio-osmotic flow parallel to the wall. We show that the diffusio-osmotic flow can significantly change the spatial distribution and diffusion dynamics of the colloidal particle in the composite channels. By modulating the surface properties of the channel wall, we can achieve different patterns of colloidal position distribution. The findings thus propose a novel possibility to manipulate colloidal diffusion in microfluidics, and highlight the importance of driving boundary walls in dynamics of colloidal particles in microchannels.

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Corradi, Valentina. "Comovements Between Diffusion Processes." Econometric Theory 13, no. 5 (October 1997): 646–66. http://dx.doi.org/10.1017/s0266466600006113.

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The aim of this paper is to characterize and analyze long-run comovements among diffusion processes. Broadly speaking, if X = (X1,,X2,;t ≥ 0) is a nonergodic diffusion in R2, but there exists a linear combination, say, γ′X, that is instead ergodic in R, then we say there exists a linear stochastic comovement between the components of X. Linear diffusions exhibiting stochastic comovements admit an error correction representation. Estimation of γ and hypothesis testing, under different sampling schemes, are considered.

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Krishna, Rajamani. "Uphill diffusion in multicomponent mixtures." Chemical Society Reviews 44, no. 10 (2015): 2812–36. http://dx.doi.org/10.1039/c4cs00440j.

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Diffusional coupling effects may cause uphill transport of a species against its concentration gradient. Transient overshoots and serpentine equilibration trajectories in composition space are fingerprints of uphill diffusion. Serpentine diffusion trajectories may enter meta-stable zones, leading to spontaneous emulsification and the Ouzo effect.

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Shin, Hye-Won, and Steven C. George. "Impact of axial diffusion on nitric oxide exchange in the lungs." Journal of Applied Physiology 93, no. 6 (December 1, 2002): 2070–80. http://dx.doi.org/10.1152/japplphysiol.00129.2002.

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Nitric oxide (NO) appears in the exhaled breath and is a potentially important clinical marker. The accepted model of NO gas exchange includes two compartments, representing the airway and alveolar region of the lungs, but neglects axial diffusion. We incorporated axial diffusion into a one-dimensional trumpet model of the lungs to assess the impact on NO exchange dynamics, particularly the impact on the estimation of flow-independent NO exchange parameters such as the airway diffusing capacity and the maximum flux of NO in the airways. Axial diffusion reduces exhaled NO concentrations because of diffusion of NO from the airways to the alveolar region of the lungs. The magnitude is inversely related to exhalation flow rate. To simulate experimental data from two different breathing maneuvers, NO airway diffusing capacity and maximum flux of NO in the airways needed to be increased approximately fourfold. These results depend strongly on the assumption of a significant production of NO in the small airways. We conclude that axial diffusion may decrease exhaled NO levels; however, more advanced knowledge of the longitudinal distribution of NO production and diffusion is needed to develop a complete understanding of the impact of axial diffusion.

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Raghavan, N. S., and A. H. King. "A Mathematical Formulation for Interfacial Diffusion, Incorporating Deviation from the Classical Random Walk Theory." Defect and Diffusion Forum 266 (September 2007): 63–71. http://dx.doi.org/10.4028/www.scientific.net/ddf.266.63.

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Fisher’s model for grain boundary diffusion considers the lattice and the grain boundary on the same basis by presuming the validity of Fick’s second law for both cases, despite the significant structural differences between them. Recent studies [1-3] have, however, shown that grain boundary diffusion is profoundly different from lattice diffusion. We propose an alternative mathematical formulation that incorporates these structural differences and consequently models grain boundary diffusion phenomena more accurately than Fisher’s model. This is achieved by considering possible deviations from the classical random walk for solute atoms diffusing through grain boundaries. This formalism can also be applied to surface diffusion and triple junction diffusion.

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Divya, V. D., U. Ramamurty, and Aloke Paul. "Diffusion in Co-Ni System Studied by Multifoil Technique." Defect and Diffusion Forum 312-315 (April 2011): 466–71. http://dx.doi.org/10.4028/www.scientific.net/ddf.312-315.466.

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Diffusion couple experiments were performed in the Co-Ni binary system for determining inter-, impurity- and intrinsic-diffusion coefficients in the temperature range of 1050 - 1250°C. The activation energy and pre-exponential factor estimated for interdiffusion do not vary significantly with composition. The activation energy calculated for impurity diffusion experiments shows is higher than . Intrinsic diffusion coefficients estimated from the multifoil experiment show that Ni is the fastest diffusing species in this system.

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Khina, Boris B. "Extended 'Five-Stream' Model for Diffusion of Implanted Dopants in Silicon during Ultra-Shallow Junction Formation in VLSI Circuits." Defect and Diffusion Forum 277 (April 2008): 107–12. http://dx.doi.org/10.4028/www.scientific.net/ddf.277.107.

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Ion implantation of different dopants (donors and acceptors) into crystalline silicon with subsequent thermal annealing is used for the formation of ultra-shallow p-n junctions in VLSI technology. The experimentally observed phenomenon of transient enhanced diffusion (TED) during annealing hinders further downscaling of advanced VLSI circuits. However, modern mathematical models of dopant diffusion, which are based on the so-called “five-stream” approach, and software packages such as SUPREM4 encounter difficulties in describing TED. In this work, an extended five-stream model for diffusion in silicon is developed, which takes into account all the possible charge states of point defects (vacancies and silicon self-interstitials) and diffusing pairs “dopant atom–vacancy” and “dopant atom–silicon self-interstitial”. The model includes diffusion and drift of differently charged point defects and pairs in the internal electric field and the kinetics of interaction between unlike species. The expressions for diffusion fluxes and sink/source terms that appear in the non-linear, non-steady-state reaction-diffusion equations are derived for both donor and acceptor dopants accounting for multiple charge states of the diffusing species.

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KIM, MOON-SOO, and HO KIM. "INNOVATION DIFFUSION OF TELECOMMUNICATIONS: GENERAL PATTERNS, DIFFUSION CLUSTERS AND DIFFERENCES BY TECHNOLOGICAL ATTRIBUTE." International Journal of Innovation Management 08, no. 02 (June 2004): 223–41. http://dx.doi.org/10.1142/s136391960400099x.

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We investigated the patterns of the technological diffusions of 17 Korean information and telecommunications (IT) innovations by applying various diffusion models, where the Bass model was chosen the most robust one. Although the internal influence dominates diffusion process for most innovations, the external influence was found to be meaningful to Korean IT diffusion compared with US's. Based on estimated parameters — penetration rate, innovation and imitation coefficients, we conducted cluster analysis, which resulted in four clusters and two isolated innovations. Differences of diffusion patterns between circuit-based and packet-based technology were examined by the external and internal influence as well as the critical mass point. Based on these findings we proposed the several practical implications for ISPs providing packet-based services, Telecommunications carriers with circuit and packet-based services, as well as policy makers.

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Zhang, Ling Xian, Nai Xia Mou, Zhong Bo Yuan, Zi Jiang Yu, and Wen Bao Liu. "GIS-Based Visual Simulation on Two-Dimensional Diffusion of River Pollution." Advanced Materials Research 403-408 (November 2011): 2392–95. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.2392.

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The visual simulation on diffusion of water pollution is a key technology to reveal the diffusing transport of pollutants in the water. Based on Two-Dimensional diffusing model of water quality, this paper mainly does research on the methods and procedures to visualization of the diffusion of pollution combining means of visual simulation on point pollution with the GIS technology. And the diffusion of point source pollution in a certain river is taken as an example in the paper so as to verify the effectiveness of the given method.

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41

Bengtsson, Lisa, Sander Tijm, Filip Váňa, and Gunilla Svensson. "Impact of Flow-Dependent Horizontal Diffusion on Resolved Convection in AROME." Journal of Applied Meteorology and Climatology 51, no. 1 (January 2012): 54–67. http://dx.doi.org/10.1175/jamc-d-11-032.1.

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AbstractHorizontal diffusion in numerical weather prediction models is, in general, applied to reduce numerical noise at the smallest atmospheric scales. In convection-permitting models, with horizontal grid spacing on the order of 1–3 km, horizontal diffusion can improve the model skill of physical parameters such as convective precipitation. For instance, studies using the convection-permitting Applications of Research to Operations at Mesoscale model (AROME) have shown an improvement in forecasts of large precipitation amounts when horizontal diffusion is applied to falling hydrometeors. The nonphysical nature of such a procedure is undesirable, however. Within the current AROME, horizontal diffusion is imposed using linear spectral horizontal diffusion on dynamical model fields. This spectral diffusion is complemented by nonlinear, flow-dependent, horizontal diffusion applied on turbulent kinetic energy, cloud water, cloud ice, rain, snow, and graupel. In this study, nonlinear flow-dependent diffusion is applied to the dynamical model fields rather than diffusing the already predicted falling hydrometeors. In particular, the characteristics of deep convection are investigated. Results indicate that, for the same amount of diffusive damping, the maximum convective updrafts remain strong for both the current and proposed methods of horizontal diffusion. Diffusing the falling hydrometeors is necessary to see a reduction in rain intensity, but a more physically justified solution can be obtained by increasing the amount of damping on the smallest atmospheric scales using the nonlinear, flow-dependent, diffusion scheme. In doing so, a reduction in vertical velocity was found, resulting in a reduction in maximum rain intensity.

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42

Cherniak, Daniele J., and E. Bruce Watson. "Al and Si diffusion in rutile." American Mineralogist 104, no. 11 (November 1, 2019): 1638–49. http://dx.doi.org/10.2138/am-2019-7030.

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Abstract Diffusion of Al and Si has been measured in synthetic and natural rutile under anhydrous conditions. Experiments used Al2O3 or Al2O3-TiO2 powder mixtures for Al diffusant sources, and SiO2-TiO2 powder mixtures or quartz-rutile diffusion couples for Si. Experiments were run in air in crimped Pt capsules, or in sealed silica glass ampoules with solid buffers (to buffer at NNO or IW). Al profiles were measured with Nuclear Reaction Analysis (NRA) using the reaction 27Al(p,γ)28Si. Rutherford Backscattering spectrometry (RBS) was used to measure Si diffusion profiles, with RBS also used in measurements of Al to complement NRA profiles. We determine the following Arrhenius relations from these measurements: For Al diffusion parallel to c, for experiments buffered at NNO, over the temperature range 1100–1400 °C: D Al = 1.21 × 10 − 2 exp ⁡ ( − 531 ± 27 kJ/ mol − 1 / RT ) m 2 s − 1 . For Si diffusion parallel to c, for both unbuffered and NNO-buffered experiments, over the temperature range 1100–1450 °C: D Si = 8.53 × 10 − 13 exp ⁡ ( − 254 ± 31 kJ/ mol − 1 / RT ) m 2 s − 1 . Diffusion normal to (100) is similar to diffusion normal to (001) for both Al and Si, indicating little diffusional anisotropy for these elements. Diffusivities measured for synthetic and natural rutile are in good agreement, indicating that these diffusion parameters can be applied in evaluating diffusivities in rutile in natural systems Diffusivities of Al and Si for experiments buffered at IW are faster (by a half to three-quarters of a log unit) than those buffered at NNO. Si and Al are among the slowest-diffusing species in rutile measured thus far. Diffusivities of Al and Si are significantly slower than the diffusion of Pb and slower than the diffusion of tetravalent Zr and Hf and pentavalent Nb and Ta. These data indicate that Al compositional information will be strongly retained in rutile, providing evidence for the robustness of the recently developed Al in rutile thermobarometer. For example, at 900 °C, Al compositional information would be preserved over ~3 Gyr in the center of 250 μm radius rutile grains, but Zr compositional information would be preserved for only about 300 000 yr at this temperature. Al-in-rutile compositions will also be much better preserved during subsolidus thermal events subsequent to crystallization than those for Ti-in-quartz and Zr-in-titanite crystallization thermometers.

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43

Wang, Lei. "Research of Air Pollution Dispersion Visualization Based on GPU and Volume Rendering." Advanced Materials Research 765-767 (September 2013): 3058–60. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.3058.

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To address the air pollution diffusing problem, a visualization algorithm based on fluid diffusion physical model and volume rendering is proposed to simulate the diffusion process epically for the urgent pollution accidents. The diffusion model is based on the simplified heat diffusion equation and the basic vortex constraint. The texture mapping based volume rendering method is adapted to handle the visualization algorithm. In addition, the render process adopts the GPU to implement the real-time visualization rendering.

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Lin, C. S., R. A. Rapp, and J. P. Hirth. "Diffusional breakdown of a Ag diffusion barrier in a Cu-Ag-Ni diffusion triple." Metallurgical Transactions A 17, no. 6 (June 1986): 933–44. http://dx.doi.org/10.1007/bf02661259.

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Nwagbogwu, Akaezue N., Ngiangia A. Thompson, and Onyeaju M. Chukwudi. "Diffusing species into some host metals in spherical solids." Caliphate Journal of Science and Technology 6, no. 3 (December 9, 2024): 360–70. https://doi.org/10.4314/cajost.v6i3.13.

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This study investigates the diffusion of various species into host metals in spherical solids. The time-dependent diffusion equation in radial spherical coordinates was transformed into a time-independent form, resulting in a Bessel differential equation of the zeroth kind. The concentration profile within the system was obtained using the Frobenius method. This solution, combined with the fractional Stokes-Einstein model, was used to plot graphs showing the effect of the fractional exponent and temperature on the diffusing species. The results indicate that a rise in temperature leads to early saturation or convergence, followed by divergence, reflecting an increase in the concentration of the diffusing species. Additionally, it was observed that as the fractional exponent increases, the concentration of the diffusing species is enhanced. A model for determining the diffusion coefficient of the host metals is also proposed. The characteristics of the host metals, as shown, significantly affect their diffusion rates. The experimental model is presented alongside the calculated concentration values. The unique approach and findings of this research offer a valuable contribution to diffusion analysis, with potential implications for a wide range of applications involving solid-state materials.

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Kovacevic, S., and S. Dj Mesarovic. "Diffusion-induced stress concentrations in diffusional creep." International Journal of Solids and Structures 239-240 (March 2022): 111440. http://dx.doi.org/10.1016/j.ijsolstr.2022.111440.

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Kondratyev, Vladimir V., Alexander G. Kesarev, and Ilya L. Lomaev. "Grain Boundary Diffusion in Nanocrystalline Materials Produced by Severe Plastic Deformation." Diffusion Foundations 5 (July 2015): 129–43. http://dx.doi.org/10.4028/www.scientific.net/df.5.129.

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The model of diffusional mass transfer in the medium with a strong spatial dependence of diffusivity and its application to the grain boundary (GB) diffusion problem is presented. A significant decrease of diffusion activation energy is shown to take place takes place in the vicinity of non-equilibrium grain boundary, which leads to the formation of a region of enhanced diffusion. The generalization of grain boundary diffusion theory is given which accounts for the diffusion enhancement near GB. An original mathematical approach is developed and general asymptotic solutions of the one-and two-dimensional diffusion problems are derived for two types of diffusant source — constant and instant. The applicability domain of presented model is discussed.

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Krumscheid, S., G. A. Pavliotis, and S. Kalliadasis. "Semiparametric Drift and Diffusion Estimation for Multiscale Diffusions." Multiscale Modeling & Simulation 11, no. 2 (January 2013): 442–73. http://dx.doi.org/10.1137/110854485.

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ZHANG, T. S. "FINITE DIMENSIONAL APPROXIMATIONS OF DIFFUSION PROCESSES ON BANACH SPACES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 04, no. 04 (December 2001): 521–31. http://dx.doi.org/10.1142/s0219025701000577.

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In this paper, we prove that the laws of diffusion processes on a Banach space X associated with quadratic forms (not necessarily symmetric) are the weak limits of laws of finite dimensional diffusions. A new existence proof for the infinite dimensional diffusion processes is obtained as a by-product.

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Tsap, Yuriy. "On the magnetic flux conservation in the partially ionized plasma." Proceedings of the International Astronomical Union 8, S294 (August 2012): 371–72. http://dx.doi.org/10.1017/s1743921313002809.

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AbstractOhm, Hall, and ambipolar diffusions in the partially ionized plasma are considered. The statement of Pandey & Wardle (2011,2012) that only Ohmic diffusion is capable of destroying the magnetic flux is not sufficiently correct due to the formal dependence of the magnetic diffusion on a frame of reference.

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Journal articles on the topic 'Diffusion'

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