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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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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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Gadomski, Adam. "(Nano)Granules-Involving Aggregation at a Passage to the Nanoscale as Viewed in Terms of a Diffusive Heisenberg Relation." Entropy 26, no. 1 (January 17, 2024): 76. http://dx.doi.org/10.3390/e26010076.
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We are looking at an aggregation of matter into granules. Diffusion plays a pivotal role here. When going down to the nanometer scale (the so-called nanoscale quantum-size effect limit), quantum mechanics, and the Heisenberg uncertainty relation, may take over the role of classical diffusion, as viewed typically in the mesoscopic/stochastic limit. A d-dimensional entropy-production aggregation of the granules-involving matter in the granule-size space is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg-type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive, very slow granules-including environment that, within the granule-size analogy invoked, matches the quantum limit of h/2πμ (μ—average mass of a granule; h—the Planck’s constant) for the diffusion coefficient of the aggregation, first proposed by Fürth in 1933 and qualitatively foreseen by Schrödinger some years before, with both in the context of a diffusing particle. The classical quantum passage uncovered here, also termed insightfully as the quantum-size effect (as borrowed from the quantum dots’ parlance), works properly for the three-dimensional (d = 3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also-granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the entropy-productive (nano)aggregation of interest.
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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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Da Silva, Marly Terezinha Quadri Simões, and Wellington Mazer. "Diffusion coefficient and tortuosity: Brownian Motion." CONTRIBUCIONES A LAS CIENCIAS SOCIALES 16, no. 9 (September 28, 2023): 18281–302. http://dx.doi.org/10.55905/revconv.16n.9-264.
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The objective of this research is to determine the chloride ion diffusion through Brownian motion using images. The research also aims at the search for diffusional physical tortuosity due to Brownian motion to understand the transport flow of the chloride ion. Through micro-CT scanned images of concrete samples, a 3D reconstruction is performed for the representative element and define its microscopic properties. The implementation of the Brownian motion of the chloride ion particles in the porous network of the representative element considered the initial diffusion coefficient defined by the Stokes-Einstein equation. The diffusion coefficient is an important parameter for predicting the depth of attack of the chloride ion and its displacement due to Brownian motion helps to define the tortuosity of this diffusive transport. The research used computational modeling with MATLAB® software. The results show diffusion due to Brownian motion and tortuousness.
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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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Lens, Piet N. L., Rakel Gastesi, Frank Vergeldt, Adriaan C. van Aelst, Antonio G. Pisabarro, and Henk Van As. "Diffusional Properties of Methanogenic Granular Sludge: 1H NMR Characterization." Applied and Environmental Microbiology 69, no. 11 (November 2003): 6644–49. http://dx.doi.org/10.1128/aem.69.11.6644-6649.2003.
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ABSTRACT The diffusive properties of anaerobic methanogenic and sulfidogenic aggregates present in wastewater treatment bioreactors were studied using diffusion analysis by relaxation time-separated pulsed-field gradient nuclear magnetic resonance (NMR) spectroscopy and NMR imaging. NMR spectroscopy measurements were performed at 22°C with 10 ml of granular sludge at a magnetic field strength of 0.5 T (20 MHz resonance frequency for protons). Self-diffusion coefficients of H2O in the investigated series of mesophilic aggregates were found to be 51 to 78% lower than the self-diffusion coefficient of free water. Interestingly, self-diffusion coefficients of H2O were independent of the aggregate size for the size fractions investigated. Diffusional transport occurred faster in aggregates growing under nutrient-rich conditions (e.g., the bottom of a reactor) or at high (55°C) temperatures than in aggregates cultivated in nutrient-poor conditions or at low (10°C) temperatures. Exposure of aggregates to 2.5% glutaraldehyde or heat (70 or 90°C for 30 min) modified the diffusional transport up to 20%. In contrast, deactivation of aggregates by HgCl2 did not affect the H2O self-diffusion coefficient in aggregates. Analysis of NMR images of a single aggregate shows that methanogenic aggregates possess a spin-spin relaxation time and self-diffusion coefficient distribution, which are due to both physical (porosity) and chemical (metal sulfide precipitates) factors.
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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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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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Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 4 (December 2010): 1147–71. http://dx.doi.org/10.1239/aap/1293113155.
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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.
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Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 04 (December 2010): 1147–71. http://dx.doi.org/10.1017/s0001867800004560.
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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.
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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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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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LACHTIOUI, Y., M. MAZROUI, and Y. BOUGHALEB. "COMMENSURABILITY EFFECTS ON DIFFUSION PROCESS IN STEPPED STRUCTURES." Modern Physics Letters B 25, no. 21 (August 20, 2011): 1749–60. http://dx.doi.org/10.1142/s0217984911027005.
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This study deals with the investigation of diffusion process of one-dimensional system with steps for adsorbates interacting via the nearest-neighbor harmonic forces. The results are obtained from numerical studies, utilizing the method of stochastic Langevin dynamics. To study commensurability effects and the role of steps in the behavior of the diffusing particles, we have computed the diffusion coefficient for large concentrations and several interaction strengths. Our numerical results show that the diffusive behavior is reduced for commensurate structure case when the ground state has only one particle per one period of the substrate potential and enhanced for incommensurate density. Furthermore, the dynamic is qualitatively similar to that obtained in the case of no steps but with a clear reduction of the diffusion rate. Implications of these findings are discussed.
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Tupper, P. F., and Xin Yang. "A paradox of state-dependent diffusion and how to resolve it." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2148 (September 5, 2012): 3864–81. http://dx.doi.org/10.1098/rspa.2012.0259.
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Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region, the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal proportions of time in the two regions in the long term? Statistical mechanics would suggest yes, since the number of accessible states in each region is presumably the same. However, another line of reasoning suggests that the particle should spend less time in the region with faster diffusion, since it will exit that region more quickly. We demonstrate with a simple microscopic model system that both predictions are consistent with the information given. Thus, specifying the diffusion rate as a function of position is not enough to characterize the behaviour of a system, even assuming the absence of external forces. We propose an alternative framework for modelling diffusive dynamics in which both the diffusion rate and equilibrium probability density for the position of the particle are specified by the modeller. We introduce a numerical method for simulating dynamics in our framework that samples from the equilibrium probability density exactly and is suitable for discontinuous diffusion coefficients.
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De Leo, Cinzia, Domenica Paoletti, and Dario Ambrosini. "Effect of noise on measurements of diffusivity in transparent liquid mixtures by digital speckle photography." European Physical Journal Applied Physics 82, no. 3 (June 2018): 30501. http://dx.doi.org/10.1051/epjap/2018180115.
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Interfacing two liquid mixtures in a diffusion cell induces noise in the initial state of the diffusing system, which produces a gap between the diffusion boundary and the ideally boundary assumed in the theory. Measured diffusivity values systematically drift with time and they are often corrected by using a linear shift of the zero-time of the process after sufficiently long time when the system reaches the free one-dimensional diffusion regime. In data analysis methods which involve optical correlation between pairs of successive digital images of the cell, it is not easy to establish how long the transient lasts. We show that when the initial perturbation between solution and solvent relaxes slowly toward the diffusive regime no simple zero-time correction can be applied.
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Kaler, Logan, Katherine Joyner, and Gregg A. Duncan. "Machine learning-informed predictions of nanoparticle mobility and fate in the mucus barrier." APL Bioengineering 6, no. 2 (June 1, 2022): 026103. http://dx.doi.org/10.1063/5.0091025.
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Nanomaterial diffusion through mucus is important to basic and applied areas of research such as drug delivery. However, it is often challenging to interpret nanoparticle dynamics within the mucus gel due to its heterogeneous microstructure and biochemistry. In this study, we measured the diffusion of polyethylene glycolylated nanoparticles (NPs) in human airway mucus ex vivo using multiple particle tracking and utilized machine learning to classify diffusive vs sub-diffusive NP movement. Using mathematic models that account for the mode of NP diffusion, we calculate the percentage of NPs that would cross the mucus barrier over time in airway mucus with varied total solids concentration. From this analysis, we predict rapidly diffusing NPs will cross the mucus barrier in a physiological timespan. Although less efficient, sub-diffusive “hopping” motion, a characteristic of a continuous time random walk, may also enable NPs to cross the mucus barrier. However, NPs exhibiting fractional Brownian sub-diffusion would be rapidly removed from the airways via mucociliary clearance. In samples with increased solids concentration (>5% w/v), we predict up to threefold reductions in the number of nanoparticles capable of crossing the mucus barrier. We also apply this approach to explore diffusion and to predict the fate of influenza A virus within human mucus. We predict only a small fraction of influenza virions will cross the mucus barrier presumably due to physical obstruction and adhesive interactions with mucin-associated glycans. These results provide new tools to evaluate the extent of synthetic and viral nanoparticle penetration through mucus in the lung and other tissues.
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Xu, W., B. Zhang, X. Y. Li, and K. Lu. "Suppressing atomic diffusion with the Schwarz crystal structure in supersaturated Al–Mg alloys." Science 373, no. 6555 (August 5, 2021): 683–87. http://dx.doi.org/10.1126/science.abh0700.
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High atomic diffusivity in metals enables substantial tuneability of their structure and properties by tailoring the diffusional processes, but this causes their customized properties to be unstable at elevated temperatures. Eliminating diffusive interfaces by fabricating single crystals or heavily alloying helps to address this issue but does not inhibit atomic diffusion at high homologous temperatures. We discovered that the Schwarz crystal structure was effective at suppressing atomic diffusion in a supersaturated aluminum–magnesium alloy with extremely fine grains. By forming these stable structures, diffusion-controlled intermetallic precipitation from the nanosized grains and their coarsening were inhibited up to the equilibrium melting temperature, around which the apparent across-boundary diffusivity was reduced by about seven orders of magnitude. Developing advanced engineering alloys using the Schwarz crystal structure may lead to useful properties for high-temperature applications.
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Gomez, Francisco, Victor Morales, and Marco Taneco. "Analytical solution of the time fractional diffusion equation and fractional convection-diffusion equation." Revista Mexicana de Física 65, no. 1 (December 31, 2018): 82. http://dx.doi.org/10.31349/revmexfis.65.82.
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In this paper, we obtain analytical solutions for the time-fractional diffusion and time-fractional convection-diffusion equations. These equations are obtained from the standard equations by replacing the time derivative with a fractional derivative of order $\alpha$. Fractional operators of type Liouville-Caputo, Atangana-Baleanu-Caputo, fractional conformable derivative in Liouville-Caputo sense and Atangana-Koca-Caputo were used to model diffusion and convection-diffusion equation. The Laplace and Fourier transforms were applied to obtain the analytical solutions for the fractional order diffusion and convection-diffusion equations. The solutions obtained can be useful to understand the modeling of anomalous diffusive, subdiffusive systems and super-diffusive systems, transport processes, random walk and wave propagation phenomenon.
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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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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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An-Nufuus, Digwanggi Arum Tazkiyatu, Barlah Rumhayati, Qonitah Fardiyah, Diah Mardiana, Ulfa Andayani, and Layta Dinira. "Diffusion Coefficient of Phosphate Ion in Citric Acid-Agarose Gel Used in Diffusive Gradient in Thin Films (DGT) Passive Sampler." Jurnal Penelitian Pendidikan IPA 9, no. 8 (August 25, 2023): 6035–44. http://dx.doi.org/10.29303/jppipa.v9i8.3593.
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In this research, the diffusion coefficient of phosphate ions in agarose-citric acid diffusive gel has been studied. The agarose-citric acid diffusion layer was prepared by mixing 1.5% agarose solution with the addition of citric acid solutions at various concentration. The diffusive gel was casted between two glass plates which were separated using a spacer of 0.1 cm thickness and clamped together in the three sides. Gel was formed for 15 minutes in an oven at 40oC. The diffusion coefficient then was calculated using Fick's First law formula. Gel that produced with addition of 0.45% citric acid absorbed more water during immersion in water for 3 hours for facilitating phosphate diffusion. Swelling degree of the agarose citric acid diffusive gels was not affected by the storing solution condition either in water or in NaNO3 0.1 M. Coefficient diffusion of phosphate in the agarose-citric acid diffusive gel was 1.009×10-7 cm2s-1, less than the diffusion in the pure agarose gel 1.367×10-7 cm2s-1. The diffusion is affected by the ionic strength of solution. Phosphate diffusion coefficient is higher in the phosphate solution with addition of 2 mgL-1 nitrate. Increasing the ionic strength causes lower phosphate diffusion coefficient because the electrostatic attractive and repulsive force
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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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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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Kusova, Aleksandra M., Ilnaz T. Rakipov, and Yuriy F. Zuev. "Effects of Homogeneous and Heterogeneous Crowding on Translational Diffusion of Rigid Bovine Serum Albumin and Disordered Alfa-Casein." International Journal of Molecular Sciences 24, no. 13 (July 6, 2023): 11148. http://dx.doi.org/10.3390/ijms241311148.
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Intracellular environment includes proteins, sugars, and nucleic acids interacting in restricted media. In the cytoplasm, the excluded volume effect takes up to 40% of the volume available for occupation by macromolecules. In this work, we tested several approaches modeling crowded solutions for protein diffusion. We experimentally showed how the protein diffusion deviates from conventional Brownian motion in artificial conditions modeling the alteration of medium viscosity and rigid spatial obstacles. The studied tracer proteins were globular bovine serum albumin and intrinsically disordered α-casein. Using the pulsed field gradient NMR, we investigated the translational diffusion of protein probes of different structures in homogeneous (glycerol) and heterogeneous (PEG 300/PEG 6000/PEG 40,000) solutions as a function of crowder concentration. Our results showed fundamentally different effects of homogeneous and heterogeneous crowded environments on protein self-diffusion. In addition, the applied “tracer on lattice” model showed that smaller crowding obstacles (PEG 300 and PEG 6000) create a dense net of restrictions noticeably hindering diffusing protein probes, whereas the large-sized PEG 40,000 creates a “less restricted” environment for the diffusive motion of protein molecules.
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Szmyt, Wojciech, Carlos Guerra, and Ivo Utke. "Diffusion of dilute gas in arrays of randomly distributed, vertically aligned, high-aspect-ratio cylinders." Beilstein Journal of Nanotechnology 8 (January 9, 2017): 64–73. http://dx.doi.org/10.3762/bjnano.8.7.
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In this work we modelled the diffusive transport of a dilute gas along arrays of randomly distributed, vertically aligned nanocylinders (nanotubes or nanowires) as opposed to gas diffusion in long pores, which is described by the well-known Knudsen theory. Analytical expressions for (i) the gas diffusion coefficient inside such arrays, (ii) the time between collisions of molecules with the nanocylinder walls (mean time of flight), (iii) the surface impingement rate, and (iv) the Knudsen number of such a system were rigidly derived based on a random-walk model of a molecule that undergoes memoryless, diffusive reflections from nanocylinder walls assuming the molecular regime of gas transport. It can be specifically shown that the gas diffusion coefficient inside such arrays is inversely proportional to the areal density of cylinders and their mean diameter. An example calculation of a diffusion coefficient is delivered for a system of titanium isopropoxide molecules diffusing between vertically aligned carbon nanotubes. Our findings are important for the correct modelling and optimisation of gas-based deposition techniques, such as atomic layer deposition or chemical vapour deposition, frequently used for surface functionalisation of high-aspect-ratio nanocylinder arrays in solar cells and energy storage applications. Furthermore, gas sensing devices with high-aspect-ratio nanocylinder arrays and the growth of vertically aligned carbon nanotubes need the fundamental understanding and precise modelling of gas transport to optimise such processes.
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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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Zimmerman, R. A., G. Severino, and D. M. Tartakovsky. "Hydrodynamic dispersion in a tube with diffusive losses through its walls." Journal of Fluid Mechanics 837 (January 5, 2018): 546–61. http://dx.doi.org/10.1017/jfm.2017.870.
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Advective–diffusive transport of passive or reactive scalars in confined environments (e.g. tubes and channels) is often accompanied by diffusive losses/gains through the confining walls. We present analytical solutions for transport of a reactive solute in a tube, whose walls are impermeable to flow but allow for solute diffusion into the surrounding medium. The solute undergoes advection, diffusion and first-order chemical reaction inside the tube, while diffusing and being consumed in the surrounding medium. These solutions represent a leading-order (in the radius-to-length ratio) approximation, which neglects the longitudinal variability of solute concentration in the surrounding medium. A numerical solution of the full problem is used to demonstrate the accuracy of this approximation for a physically relevant range of model parameters. Our analysis indicates that the solute delivery rate can be quantified by a dimensionless parameter, the ratio of a solute’s residence time in a tube to the rate of diffusive losses through the tube’s wall.
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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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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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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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Wade, R. C. "Simulation of enzyme-substrate interactions: the diffusional encounter step." Acta Biochimica Polonica 42, no. 4 (December 31, 1995): 419–25. http://dx.doi.org/10.18388/abp.1995_4895.
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Enzymes are targets for structure-based redesign and drug design. One potentially important design strategy is to create molecules--enzymes and ligands--with desired diffusional encounter properties. Rates of diffusive bimolecular encounter can be calculated by Brownian dynamics simulation. This methodology and its application to study the factors influencing the rates of diffusion-influenced enzymes are described here.
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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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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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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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Lo, Wing-Cheong, Likun Zheng, and Qing Nie. "A hybrid continuous-discrete method for stochastic reaction–diffusion processes." Royal Society Open Science 3, no. 9 (September 2016): 160485. http://dx.doi.org/10.1098/rsos.160485.
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Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.
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Kapoor, Rajat, and S. T. Oyama. "Measurement of solid state diffusion coefficients by a temperature-programmed method." Journal of Materials Research 12, no. 2 (February 1997): 467–73. http://dx.doi.org/10.1557/jmr.1997.0068.
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This paper presents a method for determining diffusivities in solids where the diffusing species desorbs or reacts at the external surfaces, and where the diffusivity does not vary appreciably with concentration. The method involves measuring the flux of the diffusive species out of the solid under the influence of a temperature program. A general model is developed, based on nonisothermal Fickian diffusion, which is applicable to solid particles with slab or spherical geometry. The solution is presented both as an analytical expression and as correlation charts of experimentally observable quantities. These charts are contour diagrams of the temperatures of peak diffusion rate with ln(E/R) and ln(D0/h2) as the axes, where E and D0 are the activation energy and pre-exponential terms of the diffusivity expression D = D0 exp(−E/RT), where R is the gas constant, and h the size of the particles. This paper deals exclusively with the case of oxygen diffusion in the vanadium oxide system. In this case, vanadium oxide was reduced in a reactive ammonia stream at conditions in which the surface reaction was fast compared to the diffusive transport process. Using this method the diffusion parameters were found to be D0 = 1.9 × 10−5 cm2 s−1 and E = 101 kJ/mol. The method was checked by varying the crystallite size of the vanadium oxide sample in the range 2h = 0.14−0.29 μm.
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Balch, J., and C. Guéguen. "Determination of diffusion coefficients of dissolved organic matter in the Churchill River estuary system, Hudson Bay (Canada)." Environmental Chemistry 12, no. 2 (2015): 253. http://dx.doi.org/10.1071/en14182.
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Environmental context Reliable interpretation of metal levels measured by diffusive gradients in thin film (DGT) requires a sound understanding of the diffusion properties of dissolved organic matter (DOM), the main ligand of metals in natural waters. The present study determined that the molecular weight of DOM and conductivity are the main factors controlling the diffusion of freshly collected estuarine DOM across the DGT diffusive gel. Abstract Diffusion coefficients (D) and the molecular weight distribution (MW) of 18 dissolved organic matter (DOM) samples collected in the Churchill River estuary system (Manitoba, Canada) were determined using a diffusive cell apparatus. NaN3 addition has been shown to preserve the DOM MW distribution within 5 weeks of collection whereas the diffusive properties (i.e. D) were strongly influenced by storage conditions, suggesting D must be determined on freshly collected material. Aquatic DOM from the river and estuarine sites was capable of diffusing across a polyacrylamide diffusive gel membrane with mean D values ranging from 2.74×10–6 to 6.98×10–6cm2s–1 and from 2.42×10–6 to 10.7×10–6cm2s–1 respectively, congruent with previous studies using humic substances and natural DOM. The molecular weight of the river and estuary DOM samples (~400–830Da) measured using asymmetrical flow-field flow fractionation (AF4) strongly influenced D, with larger MW DOM having lower D values. Conductivity had a significant negative correlation with D in estuarine samples collected at high and low tides (R2=0.82 and 0.46 respectively). These results suggest that MW and conductivity can significantly influence D of DOM in river and marine-dominated sites respectively.
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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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Rout, Smruti Sourav, Burkhard C. Schmidt, and Gerhard Wörner. "Constraints on non-isothermal diffusion modeling: An experimental analysis and error assessment using halogen diffusion in melts." American Mineralogist 105, no. 2 (February 1, 2020): 227–38. http://dx.doi.org/10.2138/am-2020-7193.
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Abstract Diffusion chronometry on zoned crystals allows constraining duration of magmatic evolution and storage of crystals once temperatures are precisely known. However, non-isothermal diffusion is common in natural samples, and thus timescales may not be determined with confidence while assuming isothermal conditions. The “non-isothermal diffusion incremental step (NIDIS) model” (Petrone et al. 2016) is proposed for such cases for a non-isothermal diffusive analysis. We conducted diffusion experiments with stepwise temperature changes to analyze and test the model, evaluated the associated errors and improved the accuracy by suggesting an alternative algorithm to model diffusion times. We used Cl and F (≤0.4 wt%) as the diffusing elements in nominally anhydrous (H2O ≤ 0.3 wt%) phonolitic melt with composition of Montana Blanca (Tenerife, Spain) in an experimental setup that successively generates multiple diffusive interfaces for different temperatures by adding glass blocks of different Cl and F concentrations. This compound set of two diffusion interfaces represents distinct compositional zones that diffusively interact at different temperatures, which can be taken as an equivalent to non-isothermal diffusion in zoned magmatic crystals. The starting temperature ranged from 975 to 1150 °C, and each set of experiments included a temperature change of 85–150 °C and a total duration of 8–12 h. The experiments were carried out in an internally heated pressure vessel equipped with a rapid quench device at 1 kbar pressure. Cl and F concentration profiles were obtained from the quenched samples by electron microprobe analysis. Although the estimated diffusion times from the NIDIS-model matched well with true experimental values, the errors on estimated timescales, due to errors in curve-fitting and uncertainty in temperature, were ±10–62% (1σ). The errors are much larger at 61–288% (1σ) when the uncertainty in diffusivity parameters is included. We discuss the efficiency and limitations of the model, assess the contribution from different sources of error, and their extent of propagation. A simpler alternative algorithm is proposed that reduces errors on the estimates of diffusion time to 10–32% (1σ) and 60–75% (1σ), with and without including uncertainty in diffusivity parameters, respectively. Using this new algorithm, we recalculated the individual diffusion times for the clinopyroxene crystals analyzed by Petrone et al. (2016) and obtained a significantly reduced error of 26–40% compared to the original error of 61–100%. We also analyzed a sanidine megacryst from Taapaca volcano (N. Chile) as a test case for non-isothermal modeling and obtained diffusion times of 1.5–9.4 ky, which is significantly different from isothermal analyses including a previous study on similar sample. In this analysis, the error estimated by our new method is reduced by 63–70%.
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Wirbeleit, Frank. "Non-Gaussian Local Density Diffusion (LDD-) Model for Boron Diffusion in Si- and SixGe1-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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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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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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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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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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Feisel, Yves, Jonathan M. Castro, and Donald B. Dingwell. "Diffusion of F and Cl in dry rhyodacitic melt." American Mineralogist 104, no. 11 (November 1, 2019): 1689–99. http://dx.doi.org/10.2138/am-2019-7095.
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Abstract Chemical diffusion of F and Cl has been experimentally determined in a rhyodacitic melt obtained from remelting a sample of Hekla pumice (Iceland). Diffusion couple experiments were conducted in a vertical tube furnace over a temperature range of 750–950 °C and in air for durations of 1 to 35 days. Concentration profiles of F and Cl were obtained for the quenched samples using an electron microprobe. Fluorine and chlorine exhibit Arrhenian behavior over the range of temperature investigated here. The pre-exponential factors of F and Cl are D0(F) = 4.3 × 10−4 and D0(Cl) = 1.6 × 10−5 m2/s. Fluorine diffusion coefficients vary in the order of 1 × 10−15 to 1 × 10−13 m2/s, whereas Cl diffusivity is up to two orders of magnitude slower. The activation energies for F and Cl diffusivities are equal within error at 223 ± 31 and 229 ± 52 kJ/mol, respectively. The difference in diffusivity between F and Cl is particularly pronounced in the melt of our study, compared to results obtained for other magmatic melt compositions. This means that the potential for diffusive fractionation exists and may occur especially under conditions of magma ascent and bubble growth, as this would favor partitioning of the relatively fast-diffusing halogens into growing bubbles, due to H2O exsolution. A dependence of diffusivity on atomic radius observed here is enhanced over that observed in more basic, less viscous melts, indicating that diffusive fractionation is more likely to be pronounced in more silicic, more viscous systems. A proper parameterization and modeling of diffusive fractionation of halogens in actively degassing volcanic systems thus holds the potential of serving as a tool for quantifying the processes responsible for volcanic unrest.
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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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Mandal, Sudipta, and Anirban Ghosh. "Diffusion dynamics of an overdamped active ellipsoidal Brownian particle in two dimensions." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 7 (July 26, 2024): 073209. http://dx.doi.org/10.1088/1742-5468/ad5715.
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Abstract Shape asymmetry is the most abundant in nature and has attracted considerable interest in recent research. The phenomenon is widely recognized: a free ellipsoidal Brownian particle displays anisotropic diffusion during short time intervals, which subsequently transitions to an isotropic diffusion pattern over longer timescales. We have further expanded this concept to incorporate active ellipsoidal particles characterized by an initial self-propelled velocity. This paper provides analytical and simulation results of diffusion dynamics of an active ellipsoidal particle. The active ellipsoidal particle manifests three distinct regimes in its diffusion dynamics over time. In the transient regime, it displays diffusive behavior followed by a super-diffusive phase, and in the longer time duration, it transitions to purely diffusive dynamics. We investigated the diffusion dynamics of a free particle as well as a particle in a harmonic trap, and a particle subject to a constant field force. Moreover, we have studied the rotational diffusion dynamics and torque production resulting from an external constant force field. Furthermore, our investigation extends to the examination of the scaled average velocity of an ellipsoidal active particle, considering both a constant force field and a one-dimensional ratchet.
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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.