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Journal articles on the topic 'DIFFUSIVE THEORY'

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Published: 10 March 2023

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1

Carpenter, J. R., T. Sommer, and A. Wüest. "Stability of a Double-Diffusive Interface in the Diffusive Convection Regime." Journal of Physical Oceanography 42, no. 5 (May 1, 2012): 840–54. http://dx.doi.org/10.1175/jpo-d-11-0118.1.

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Abstract In this paper, the authors explore the conditions under which a double-diffusive interface may become unstable. Focus is placed on the case of a cold, freshwater layer above a warm, salty layer [i.e., the diffusive convection (DC) regime]. The “diffusive interface” between these layers will develop gravitationally unstable boundary layers due to the more rapid diffusion of heat (the destabilizing component) relative to salt. Previous studies have assumed that a purely convective-type instability of these boundary layers is what drives convection in this system and that this may be parameterized by a boundary layer Rayleigh number. The authors test this theory by conducting both a linear stability analysis and direct numerical simulations of a diffusive interface. Their linear stability analysis reveals that the transition to instability always occurs as an oscillating diffusive convection mode and at boundary layer Rayleigh numbers much smaller than previously thought. However, these findings are based on making a quasi-steady assumption for the growth of the interfaces by molecular diffusion. When diffusing interfaces are modeled (using direct numerical simulations), the authors observe that the time dependence is significant in determining the instability of the boundary layers and that the breakdown is due to a purely convective-type instability. Their findings therefore demonstrate that the relevant instability in a DC staircase is purely convective.

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2

Kawamura, K., J. P. Severinghaus, M. R. Albert, Z. R. Courville, M. A. Fahnestock, T. Scambos, E. Shields, and C. A. Shuman. "Kinetic fractionation of gases by deep air convection in polar firn." Atmospheric Chemistry and Physics Discussions 13, no. 3 (March 15, 2013): 7021–59. http://dx.doi.org/10.5194/acpd-13-7021-2013.

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Abstract. A previously unrecognized type of gas fractionation occurs in firn air columns subjected to intense convection. It is a form of kinetic fractionation that depends on the fact that different gases have different molecular diffusivities. Convective mixing continually disturbs diffusive equilibrium, and gases diffuse back toward diffusive equilibrium under the influence of gravity and thermal gradients. In near-surface firn where convection and diffusion compete as gas transport mechanisms, slow-diffusing gases such as krypton and xenon are more heavily impacted by convection than fast diffusing gases such as nitrogen and argon, and the signals are preserved in deep firn and ice. We show a simple theory that predicts this kinetic effect, and the theory is confirmed by observations of stable gas isotopes from the Megadunes field site on the East Antarctic plateau. Numerical simulations confirm the effect's magnitude at this site. A main purpose of this work is to support the development of a proxy indicator of past convection in firn, for use in ice-core gas records. To this aim, we also show with the simulations that the magnitude of kinetic effect is fairly insensitive to the exact profile of convective strength, if the overall thickness of convective zone is kept constant.

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3

Sokolov, I. V., I. I. Roussev, L. A. Fisk, M. A. Lee, T. I. Gombosi, and J. I. Sakai. "Diffusive Shock Acceleration Theory Revisited." Astrophysical Journal 642, no. 1 (April 10, 2006): L81—L84. http://dx.doi.org/10.1086/504406.

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4

Maia, Daniel Souza, and Ronald Dickman. "Diffusive epidemic process: theory and simulation." Journal of Physics: Condensed Matter 19, no. 6 (January 22, 2007): 065143. http://dx.doi.org/10.1088/0953-8984/19/6/065143.

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5

Virieux, Jean, Carlos Flores-Luna, and Dominique Gibert. "Asymptotic Theory For Diffusive Electromagnetic Imaging." Geophysical Journal International 119, no. 3 (December 1994): 857–68. http://dx.doi.org/10.1111/j.1365-246x.1994.tb04022.x.

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6

Egan, Jocelyn E., David R. Bowling, and David A. Risk. "Technical Note: Isotopic corrections for the radiocarbon composition of CO<sub>2</sub> in the soil gas environment must account for diffusion and diffusive mixing." Biogeosciences 16, no. 16 (August 28, 2019): 3197–205. http://dx.doi.org/10.5194/bg-16-3197-2019.

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Abstract. Earth system scientists working with radiocarbon in organic samples use a stable carbon isotope (δ13C) correction to account for mass-dependent fractionation, but it has not been evaluated for the soil gas environment, wherein both diffusive gas transport and diffusive mixing are important. Using theory and an analytical soil gas transport model, we demonstrate that the conventional correction is inappropriate for interpreting the radioisotopic composition of CO2 from biological production because it does not account for important gas transport mechanisms. Based on theory used to interpret δ13C of soil production from soil CO2, we propose a new solution for radiocarbon applications in the soil gas environment that fully accounts for both mass-dependent diffusion and mass-independent diffusive mixing.

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7

Kawamura, K., J. P. Severinghaus, M. R. Albert, Z. R. Courville, M. A. Fahnestock, T. Scambos, E. Shields, and C. A. Shuman. "Kinetic fractionation of gases by deep air convection in polar firn." Atmospheric Chemistry and Physics 13, no. 21 (November 15, 2013): 11141–55. http://dx.doi.org/10.5194/acp-13-11141-2013.

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Abstract. A previously unrecognized type of gas fractionation occurs in firn air columns subjected to intense convection. It is a form of kinetic fractionation that depends on the fact that different gases have different molecular diffusivities. Convective mixing continually disturbs diffusive equilibrium, and gases diffuse back toward diffusive equilibrium under the influence of gravity and thermal gradients. In near-surface firn where convection and diffusion compete as gas transport mechanisms, slow-diffusing gases such as krypton (Kr) and xenon (Xe) are more heavily impacted by convection than fast diffusing gases such as nitrogen (N2) and argon (Ar), and the signals are preserved in deep firn and ice. We show a simple theory that predicts this kinetic effect, and the theory is confirmed by observations using a newly-developed Kr and Xe stable isotope system in air samples from the Megadunes field site on the East Antarctic plateau. Numerical simulations confirm the effect's magnitude at this site. A main purpose of this work is to support the development of a proxy indicator of past convection in firn, for use in ice-core gas records. To this aim, we also show with the simulations that the magnitude of the kinetic effect is fairly insensitive to the exact profile of convective strength, if the overall thickness of the convective zone is kept constant. These results suggest that it may be feasible to test for the existence of an extremely deep (~30–40 m) convective zone, which has been hypothesized for glacial maxima, by future ice-core measurements.

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8

Parker, Ben. "Incalculably Diffusive." Novel 54, no. 2 (August 1, 2021): 287–91. http://dx.doi.org/10.1215/00295132-9004549.

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9

Carpenter, J. R., T. Sommer, and A. Wüest. "Simulations of a double-diffusive interface in the diffusive convection regime." Journal of Fluid Mechanics 711 (September 14, 2012): 411–36. http://dx.doi.org/10.1017/jfm.2012.399.

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AbstractThree-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A ‘double-boundary-layer’ structure is found in all of the simulations, in which the temperature ($T$) interface has a greater thickness than the salinity ($S$) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The $TS$-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the $TS$-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the $S$-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

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10

Fumarola, Francesco. "A Diffusive-Particle Theory of Free Recall." Advances in Cognitive Psychology 13, no. 3 (September 30, 2017): 201–13. http://dx.doi.org/10.5709/acp-0220-4.

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11

Fabrizio, M. "Integration of Migration Flows. A Diffusive Theory." International Journal of Energy and Environment 16 (March 10, 2022): 35–37. http://dx.doi.org/10.46300/91012.2022.16.7.

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The subject of this research is the presentation of a model for studying the integration of migration flows with the resident population. The basic element for social cohesion is the cultural level of the people involved. In this study, we hypothesize a similarity between diffusion laws of the heat and culture, represented respectively by equations on the knowledge and temperature. The integration of migration flows is described by the use of the Cahn-Hilliard equation.

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12

Nuan, Wang Shu. "Channel theory of fission with diffusive dynamics." Il Nuovo Cimento A 107, no. 2 (February 1994): 299–303. http://dx.doi.org/10.1007/bf02781561.

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13

van Beijeren, Henk. "Mode coupling theory for purely diffusive system." Journal of Statistical Physics 39, no. 3-4 (May 1985): 449–50. http://dx.doi.org/10.1007/bf01018674.

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14

Kamenshchikov, Sergey A. "Transport Catastrophe Analysis as an Alternative to a Monofractal Description: Theory and Application to Financial Crisis Time Series." Journal of Chaos 2014 (September 14, 2014): 1–8. http://dx.doi.org/10.1155/2014/346743.

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The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for monofractal Brownian processes: nondifferentiability, Brownian nature of process, and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that precatastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. An efficiency of a diffusive analysis has been experimentally compared to the Reynolds stability model application. An extended Reynolds parameter has been introduced as an indicator of phase transition. A combination of diffusive and Reynolds analyses has been applied for a description of a time series of Dow Jones Industrial weekly prices for the world financial crisis of 2007–2009. Diffusive and Reynolds parameters showed extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of market evolution short-memory and long-memory shifts. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.

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15

KOMIN, NIKO, UDO ERDMANN, and LUTZ SCHIMANSKY-GEIER. "RANDOM WALK THEORY APPLIED TO DAPHNIA MOTION." Fluctuation and Noise Letters 04, no. 01 (March 2004): L151—L159. http://dx.doi.org/10.1142/s0219477504001756.

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The zooplankton Daphnia or "water flea" — one of the most common crustacean to be found in freshwater — is subject to recent studies. It is known to perform vortex motions under certain light conditions as well as more complex navigational tasks. Experimental data show that Daphnia move with a preferred turning angle, what is of main interest in this paper. The above-mentioned experimental fact is taken in order to derive a diffusion law for these types of motion. Deviations from the free diffusive behavior are investigated, based on random walk theory.

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16

Amano, Takanobu, and Masahiro Hoshino. "Theory of Electron Injection at Oblique Shock of Finite Thickness." Astrophysical Journal 927, no. 1 (March 1, 2022): 132. http://dx.doi.org/10.3847/1538-4357/ac4f49.

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Abstract A theory of electron injection into diffusive shock acceleration (DSA) for the generation of cosmic-ray electrons at collisionless shocks is presented. We consider a recently proposed particle acceleration mechanism called stochastic shock drift acceleration (SSDA). We find that SSDA may be understood as a diffusive particle acceleration mechanism at an oblique shock of finite thickness. More specifically, it is described by a solution to the diffusion–convection equation for particles with the characteristic diffusion length comparable to the shock thickness. On the other hand, the same equation yields the standard DSA if the diffusion length is much longer than the thickness. Although SSDA predicts, in general, a spectral index steeper than DSA, it is much more efficient for low-energy electron acceleration and is favorable for injection. The injection threshold energy corresponds to the transition energy between the two different regimes. It is of the order of 0.1–1 MeV in typical interstellar and interplanetary conditions if the dissipation scale of turbulence around the shock is determined by the ion inertial length. The electron injection is more efficient at high M A / cos θ Bn , where M A and θ Bn are the Alfvén Mach number and the shock obliquity, respectively. The theory suggests that efficient acceleration of electrons to ultrarelativistic energies will be more easily realized at high Mach number, young supernova remnant shocks, but not at weak or moderate shocks in the heliosphere unless the upstream magnetic field is nearly perpendicular to the shock normal.

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17

Radko, Timour, and Melvin E. Stern. "Finescale Instabilities of the Double-Diffusive Shear Flow*." Journal of Physical Oceanography 41, no. 3 (March 1, 2011): 571–85. http://dx.doi.org/10.1175/2010jpo4459.1.

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Abstract This study examines dynamics of finescale instabilities in thermohaline–shear flows. It is shown that the presence of the background diapycnal temperature and salinity fluxes due to double diffusion has a destabilizing effect on the basic current. Using linear stability analysis based on the Floquet theory for the sinusoidal basic velocity profile, the authors demonstrate that the well-known Richardson number criterion (Ri < ¼) cannot be directly applied to doubly diffusive fluids. Rigorous instabilities are predicted to occur for Richardson numbers as high as—or even exceeding—unity. The inferences from the linear theory are supported by the fully nonlinear numerical simulations. Since the Richardson number in the main thermocline rarely drops below ¼, whereas the observations of turbulent patches are common, the authors hypothesize that some turbulent mixing events can be attributed to the finescale instabilities associated with double-diffusive processes.

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18

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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19

Rudraiah, N., and M. S. Malashetty. "The Influence of Coupled Molecular Diffusion on Double-Diffusive Convection in a Porous Medium." Journal of Heat Transfer 108, no. 4 (November 1, 1986): 872–76. http://dx.doi.org/10.1115/1.3247026.

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The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.

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20

Wu, Xiao, and Mingkang Ni. "Dynamics in diffusive Leslie–Gower prey–predator model with weak diffusion." Nonlinear Analysis: Modelling and Control 27, no. 6 (October 19, 2022): 1168–88. http://dx.doi.org/10.15388/namc.2022.27.29535.

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This paper is concerned with the diffusive Leslie–Gower prey–predator model with weak diffusion. Assuming that the diffusion rates of prey and predator are sufficiently small and the natural growth rate of prey is much greater than that of predators, the diffusive Leslie–Gower prey–predator model is a singularly perturbed problem. Using travelling wave transformation, we firstly transform our problem into a multiscale slow-fast system with two small parameters. We prove the existence of heteroclinic orbit, canard explosion phenomenon and relaxation oscillation cycle for the slow-fast system by applying the geometric singular perturbation theory. Thus, we get the existence of travelling waves and periodic solutions of the original reaction–diffusion model. Furthermore, we also give some numerical examples to illustrate our theoretical results.

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21

Underhill, Dwight W. "Basic Theory for the Diffusive Sampling of Radon." Health Physics 65, no. 1 (July 1993): 17–24. http://dx.doi.org/10.1097/00004032-199307000-00003.

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22

de Hoop, Adrianus T., Michael L. Oristaglio, Tarek M. Habashy, and Carlos Torres-Verdin. "Asymptotic ray theory for transient diffusive electromagnetic fields." Radio Science 31, no. 1 (January 1996): 41–49. http://dx.doi.org/10.1029/95rs02593.

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23

Wu, Zhigang, Nam-Trung Nguyen, and Xiaoyang Huang. "Nonlinear diffusive mixing in microchannels: theory and experiments." Journal of Micromechanics and Microengineering 14, no. 4 (February 6, 2004): 604–11. http://dx.doi.org/10.1088/0960-1317/14/4/022.

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24

TIAN, CHU-SHUN, SAI-KIT CHEUNG, and ZHAO-QING ZHANG. "CAN DIFFUSION MODEL LOCALIZATION IN OPEN MEDIA?" International Journal of Modern Physics: Conference Series 11 (January 2012): 96–101. http://dx.doi.org/10.1142/s201019451200596x.

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We employed a first-principles theory – the supersymmetric field theory – formulated for wave transport in very general open media to study static transport of waves in quasi-one-dimensional localized samples. We predicted analytically and confirmed numerically that in these systems, localized waves display an unconventional diffusive phenomenon. Different from the prevailing self-consistent local diffusion model, our theory is capable of capturing all disorder-induced resonant transmissions, which give rise to significant enhancement of local diffusion inside a localized sample. Our theory should be able to be generalized to two- and three-dimensional open media, and open a new direction in the study of Anderson localization in open media.

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25

McDermott, R. M., C. Angioni, M. Cavedon, A. Kappatou, R. Dux, R. Fischer, P. Manas, and the ASDEX Upgrade Team. "Validation of low-Z impurity transport theory using boron perturbation experiments at ASDEX upgrade." Nuclear Fusion 62, no. 2 (December 17, 2021): 026006. http://dx.doi.org/10.1088/1741-4326/ac3cd9.

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Abstract An experimental technique has been developed at ASDEX upgrade (AUG) to separately identify the diffusive and convective components of the boron particle flux. Using this technique a database of B transport coefficients has been assembled that shows that the normalized ion temperature gradient ( R / L T i ) is the strongest organizing parameter for both the B diffusion and convection and large R / L T i is a necessary ingredient to obtain hollow B density profiles in AUG. This database also shows that large changes in the applied neutral beam injection (NBI) have a relatively small impact on impurity transport compared to similar changes in electron cyclotron resonance heating (ECRH). Even low levels of ECRH power dramatically increase both the diffusive and convective fluxes and lead to peaking of the impurity density profile. Comparisons to a combination of neoclassical and quasi-linear gyrokinetic simulations show good agreement in the measured and predicted diffusion coefficients. The outward convection measured in NBI dominated plasmas, however, is not well captured by the simulations, despite the inclusion of fast ions. In contrast, the convection is reasonably well reproduced for plasmas with flat or peaked boron density profiles. This dataset provides an excellent experimental validation of the non-monotonic, predicted, convective-particle-flux created by the combination of pure-pinch, thermo-diffusion, and roto-diffusion. In addition, this dataset demonstrates a non-monotonic dependence of the experimental particle diffusivity to ion heat conductivity (D/χ i) in qualitative agreement with theoretical predictions.

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26

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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27

Smyth, William D., and Satoshi Kimura. "Instability and Diapycnal Momentum Transport in a Double-Diffusive, Stratified Shear Layer." Journal of Physical Oceanography 37, no. 6 (June 1, 2007): 1551–65. http://dx.doi.org/10.1175/jpo3070.1.

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Abstract The linear stability of a double-diffusively stratified, inflectional shear flow is investigated. Double-diffusive stratification has little effect on shear instability except when the density ratio Rρ is close to unity. Double-diffusive instabilities have significant growth rates and can represent the fastest-growing mode even in the presence of inflectionally unstable shear with a low Richardson number. In the linear regime, background shear has no effect on double-diffusive modes except to select the orientation of the wave vector. The converse is not true: double-diffusive modes modify the mean shear via momentum fluxes. The momentum flux driven by salt sheets is parameterized in terms of a Schmidt number (ratio of eddy viscosity to saline diffusivity) Scs. In the oceanic parameter regime, Scs is less than unity and can be approximated as Scs = 0.08 ln[Rρ/(Rρ − 1)]. Enhanced molecular dissipation by unstable motions is quantified in terms of the dissipation ratio Γ, and the results are compared with observations. Corresponding results are given for diffusive convection in an inflectional shear flow, though linear theory is expected to give a less accurate description of this mechanism.

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28

Fernando, Harindra J. S. "Buoyancy transfer across a diffusive interface." Journal of Fluid Mechanics 209 (December 1989): 1–34. http://dx.doi.org/10.1017/s0022112089003010.

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An experimental investigation of various aspects of buoyancy transfer across a diffusive density interface that separates stably stratified, turbulently convecting layers of relatively fresh cold water overlying hot salty water is described. It is argued that the interfacial layer should possess a double boundary-layer structure, in which the thicknesses of the salt and heat interfacial layers are determined by a balance between the opposing effects of diffusion and entrainment. Based on this argument, a simple theory, that predicts the interfacial-layer thickness, the diffusive heat and salt fluxes across the density interface, and the time variation of the temperature and salt concentrations in the convecting layers, is proposed for the case in which the convection is driven by a constant heat flux supplied to the lower layer. During a certain time interval, the theory and experiment agree well, but thereafter distinct differences can be seen. Measurements suggest that these differences may be due to the distortion of the density interface at low interfacial stabilities by turbulent eddies, which leads to a change in the buoyancy transfer mechanism. When the Richardson number falls below a critical value Riv, the interface was found to migrate slowly upwards and the mechanism of entrainment was the detachment of thin sheets of fluid by eddies scouring the interface.

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29

Moreno Soto, Álvaro, Oscar R. Enríquez, Andrea Prosperetti, Detlef Lohse, and Devaraj van der Meer. "Transition to convection in single bubble diffusive growth." Journal of Fluid Mechanics 871 (May 20, 2019): 332–49. http://dx.doi.org/10.1017/jfm.2019.276.

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We investigate the growth of gas bubbles in a water solution at rest with a supersaturation level that is generally associated with diffusive mass transfer. For $\text{CO}_{2}$ bubbles, it has been previously observed that, after some time of growing in a diffusive regime, a density-driven convective flow enhances the mass transfer rate into the bubble. This is due to the lower density of the gas-depleted liquid which surrounds the bubble. In this work, we report on experiments with different supersaturation values, measuring the time $t_{conv}$ it takes for convection to dominate over the diffusion-driven growth. We demonstrate that by considering buoyancy and drag forces on the depleted liquid around the bubble, we can satisfactorily predict the transition time. In fact, our analysis shows that this onset does not only depend on the supersaturation, but also on the absolute pressure, which we corroborate in experiments. Subsequently, we study how the depletion caused by the growth of successive single bubbles influences the onset of convection. Finally, we study the convection onset around diffusively growing nitrogen $\text{N}_{2}$ bubbles. As $\text{N}_{2}$ is much less soluble in water, the growth takes much longer. However, after waiting long enough and consistent with our theory, convection still occurs as for any gas–liquid combination, provided that the density of the solution sufficiently changes with the gas concentration.

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30

GRAY, J. M. N. T., and C. ANCEY. "Multi-component particle-size segregation in shallow granular avalanches." Journal of Fluid Mechanics 678 (June 1, 2011): 535–88. http://dx.doi.org/10.1017/jfm.2011.138.

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A general continuum theory for particle-size segregation and diffusive remixing in polydisperse granular avalanches is formulated using mixture theory. Comparisons are drawn to existing segregation theories for bi-disperse mixtures and the case of a ternary mixture of large, medium and small particles is investigated. In this case, the general theory reduces to a system of two coupled parabolic segregation–remixing equations, which have a single diffusion coefficient and three parameters which control the segregation rates between each pair of constituents. Considerable insight into many problems where the effect of diffusive remixing is small is provided by the non-diffusive case. Here the equations reduce to a system of two first-order conservation laws, whose wave speeds are real for a very wide class of segregation parameters. In this regime, the system is guaranteed to be non-strictly hyperbolic for all admissible concentrations. If the segregation rates do not increase monotonically with the grain-size ratio, it is possible to enter another region of parameter space, where the equations may either be hyperbolic or elliptic, depending on the segregation rates and the local particle concentrations. Even if the solution is initially hyperbolic everywhere, regions of ellipticity may develop during the evolution of the problem. Such regions in a time-dependent problem necessarily lead to short wavelength Hadamard instability and ill-posedness. A linear stability analysis is used to show that the diffusive remixing terms are sufficient to regularize the theory and prevent unbounded growth rates at high wave numbers. Numerical solutions for the time-dependent segregation of an initially almost homogeneously mixed state are performed using a standard Galerkin finite element method. The diffuse solutions may be linearly stable or unstable, depending on the initial concentrations. In the linearly unstable region, ‘sawtooth’ concentration stripes form that trap and focus the medium-sized grains. The large and small particles still percolate through the avalanche and separate out at the surface and base of the flow due to the no-flux boundary conditions. As these regions grow, the unstable striped region is annihilated. The theory is used to investigate inverse distribution grading and reverse coarse-tail grading in multi-component mixtures. These terms are commonly used by geologists to describe particle-size distributions in which either the whole grain-size population coarsens upwards, or just the coarsest clasts are inversely graded and a fine-grained matrix is found everywhere. An exact solution is constructed for the steady segregation of a ternary mixture as it flows down an inclined slope from an initially homogeneously mixed inflow. It shows that for distribution grading, the particles segregate out into three inversely graded sharply segregated layers sufficiently far downstream, with the largest particles on top, the fines at the bottom and the medium-sized grains sandwiched in between. The heights of the layers are strongly influenced by the downstream velocity profile, with layers becoming thinner in the faster moving near-surface regions of the avalanche, and thicker in the slowly moving basal layers, for the same mass flux. Conditions for the existence of the solution are discussed and a simple and useful upper bound is derived for the distance at which all the particles completely segregate. When the effects of diffusive remixing are included, the sharp concentration discontinuities are smoothed out, but the simple shock solutions capture many features of the evolving size distribution for typical diffusive remixing rates. The theory is also used to construct a simple model for reverse coarse-tail grading, in which the fine-grained material does not segregate. The numerical method is used to calculate diffuse solutions for a ternary mixture and a sharply segregated shock solution is derived that looks similar to the segregation of a bi-disperse mixture of large and medium grains. The presence of the fine-grained material, however, prevents high concentrations of large or medium particles being achieved and there is a significant lengthening of the segregation distance.

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31

Pagnini, Gianni. "Subordination Formulae for Space-time Fractional Diffusion Processes via Mellin Convolution." International Journal of Mathematical Models and Methods in Applied Sciences 16 (March 12, 2022): 71–76. http://dx.doi.org/10.46300/9101.2022.16.13.

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Fundamental solutions of space-time fractional diffusion equations can be interpret as probability density functions. This fact creates a strong link with stochastic processes. Recasting probability density functions in terms of subordination laws has emerged to be important to built up stochastic processes. In particular, for diffusion processes, subordination can be understood as a diffusive process in space, which is called parent process, that depends on a parameter which is also random and depends on time, which is called directing process. Stochastic processes related to fractional diffusion are self-similar processes. The integral representation of the resulting probability density function for self-similar stochastic processes can be related to the convolution integral within the Mellin transform theory. Here, subordination formulae for space-time fractional diffusion are provided. In particular, a noteworthy new formula is derived in the diffusive symmetric case that is spatially driven by the Gaussian density. Future developments of the research on the basis of this new subordination law are discussed.

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32

Frankel, M. L., and G. I. Sivashinsky. "On the nonlinear thermal diffusive theory of curved flames." Journal de Physique 48, no. 1 (1987): 25–28. http://dx.doi.org/10.1051/jphys:0198700480102500.

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33

Dickman, Ronald. "Mean-field theory of the driven diffusive lattice gas." Physical Review A 38, no. 5 (September 1, 1988): 2588–93. http://dx.doi.org/10.1103/physreva.38.2588.

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34

Schomerus, H., E. G. Mishchenko, and C. W. J. Beenakker. "Kinetic theory of shot noise in nondegenerate diffusive conductors." Physical Review B 60, no. 8 (August 15, 1999): 5839–50. http://dx.doi.org/10.1103/physrevb.60.5839.

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35

Afonin, V. V., and Yu M. Galperin. "Magnetization of a diffusive ring: Beyond the perturbation theory." Journal of Experimental and Theoretical Physics 84, no. 3 (March 1997): 584–91. http://dx.doi.org/10.1134/1.558178.

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36

Malvagi, F., M. Sammartino, and G. C. Pomraning. "Asymptotically exact diffusive boundary conditions in linear kinetic theory." Journal of Mathematical Physics 33, no. 7 (July 1992): 2639–47. http://dx.doi.org/10.1063/1.529583.

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37

Celaschi, M., and B. Montagnini. "The quasi-diffusive approximation in transport theory: Local solutions." Transport Theory and Statistical Physics 24, no. 1-3 (January 1995): 57–88. http://dx.doi.org/10.1080/00411459508205120.

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38

Si, Yuanzheng, Heng Mao, Bin Zhang, and Ming Jiang. "Diffusive reflectance for the free-space light propagation theory." Applied Physics Letters 96, no. 1 (January 4, 2010): 013702. http://dx.doi.org/10.1063/1.3284520.

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39

Janssen, H. K., and B. Schmittmann. "Field theory of critical behaviour in driven diffusive systems." Zeitschrift f�r Physik B Condensed Matter 64, no. 4 (December 1986): 503–14. http://dx.doi.org/10.1007/bf01312845.

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40

Aouadi, Moncef. "A generalized thermoelastic diffusion problem for an infinitely long solid cylinder." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–15. http://dx.doi.org/10.1155/ijmms/2006/25976.

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The theory of generalized thermoelastic diffusion, based on the theory of Lord and Shulman, is used to study the thermoelastic-diffusion interactions in an infinitely long solid cylinder subjected to a thermal shock on its surface which is in contact with a permeating substance. By means of the Laplace transform and numerical Laplace inversion the problem is solved. Numerical results predict finite speeds of propagation for thermoelastic and diffusive waves and the presence of a tensile stress region close to the cylinder surface. The problem of generalized thermoelasticity has been reduced as a special case of our problem.

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41

Hickman, A. P., D. T. Mugglin, and A. D. Streater. "Light-induced diffusive pulling and diffusion cross sections for K-He: experiment and theory." Optics Communications 102, no. 3-4 (October 1993): 281–87. http://dx.doi.org/10.1016/0030-4018(93)90396-m.

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42

Larsen, Edward W. "Asymptotic Diffusion and Simplified PNApproximations for Diffusive and Deep Penetration Problems. Part 1: Theory." Transport Theory and Statistical Physics 39, no. 2-4 (March 2010): 110–63. http://dx.doi.org/10.1080/00411450.2010.531878.

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43

Berryman, James G., and P. L. Sachdev. "Nonlinear Diffusive Waves." Mathematics of Computation 51, no. 184 (October 1988): 843. http://dx.doi.org/10.2307/2008785.

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44

RAGOT, BRIGITTE R. "Nonlinear particle dynamics in a broadband turbulence wave spectrum." Journal of Plasma Physics 60, no. 2 (September 1998): 299–329. http://dx.doi.org/10.1017/s0022377898006795.

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In the statistical quasilinear theory of weak plasma turbulence, charged particles moving in electrostatic fluctuations diffuse in velocity, i.e. the velocity variance 〈Δv2(t)〉 increases linearly with time t, for times long compared with the auto-correlation time τac of the field, which may be estimated as the reciprocal of the spectral width of the fluctuations. Recent test-particle simulations have revealed a new regime at very long timescales t[Gt ]τac where quasilinear theory breaks down, for intermediate field amplitudes. As this behaviour is not consistent with a diffusion on quasilinear timescales, the problem of the motion of particles in a broadband wave field, for the case of a slowly growing field, is considered here from a purely dynamical point of view, introducing no statistics on the field and no restriction on the amplitude of this field. By determining, on a given timescale, and in the frame of wave–particle interaction, the spectral width over which waves interact efficiently with a particle, a new timescale is found: the nonlinear time of wave–particle interaction τNL∝ (spectral density of energy)−1/3[Gt ]τac. This is the correlation time of the dynamics. For times shorter than τNL, the particles trajectories remain globally regular, and do not separate: they follow a quasifractal set of dimension 2. For times long compared with τNL, there appears a ‘true’ diffusive regime with mixing and decorrelation, due to nonlinear mixing in phase space and the localization of the wave–particle interaction. These theoretical results are confirmed by a numerical study of the velocity variance as a function of time. In particular, the particle dynamics really do become diffusive on timescales several orders of magnitude longer than that predicted by quasilinear theory (namely [Gt ]τNL[Gt ]τac). Finally, deviations from the quasilinear value of the diffusion coefficient and wave growth rate, discussed in the literature, are explained.

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45

Denissenkov, P. "Rotationally induced turbulent diffusion in early B-type stars: theory and observations." Symposium - International Astronomical Union 162 (1994): 145–46. http://dx.doi.org/10.1017/s0074180900214721.

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Available observational data indicate that some kind of additional mixing is present in radiative envelopes of O and early B-type stars. Because of these stars are known to be the fastest rotators amongst all normal stars, the most probable candidate for the role of additional mixing in their interiors is rotationally induced turbulent diffusion discovered by Zahn (1983, 1992). Recently Denissenkov (1993a,b) calculated evolution of massive main sequence (MS) stars with turbulent diffusive mixing in order to explain atmospheric abundance peculiarities in OB-stars. This note summarizes the main results which have been obtained.

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46

Sahu, Kirti Chandra. "Double-diffusive instability in core–annular pipe flow." Journal of Fluid Mechanics 789 (January 27, 2016): 830–55. http://dx.doi.org/10.1017/jfm.2015.760.

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The instability in a pressure-driven core–annular flow of two miscible fluids having the same densities, but different viscosities, in the presence of two scalars diffusing at different rates (double-diffusive effect) is investigated via linear stability analysis and axisymmetric direct numerical simulation. It is found that the double-diffusive flow in a cylindrical pipe exhibits strikingly different stability characteristics compared to the double-diffusive flow in a planar channel and the equivalent single-component flow (wherein viscosity stratification is achieved due to the variation of one scalar) in a cylindrical pipe. The flow which is stable in the context of single-component systems now becomes unstable in the presence of two scalars diffusing at different rates. It is shown that increasing the diffusivity ratio enhances the instability. In contrast to the single fluid flow through a pipe (the Hagen–Poiseuille flow), the faster growing axisymmetric eigenmode is found to be more unstable than the corresponding corkscrew mode for the parameter values considered, for which the equivalent single-component flow is stable to both the axisymmetric and corkscrew modes. Unlike single-component flows of two miscible fluids in a cylindrical pipe, it is shown that the diffusivity and the radial location of the mixed layer have non-monotonic influences on the instability characteristics. An attempt is made to understand the underlying mechanism of this instability by conducting the energy budget and inviscid stability analyses. The investigation of linear instability due to the double-diffusive phenomenon is extended to the nonlinear regime via axisymmetric direct numerical simulations. It is found that in the nonlinear regime the flow becomes unstable in the presence of double-diffusive effect, which is consistent with the predictions of linear stability theory. A new type of instability pattern of an elliptical shape is observed in the nonlinear simulations in the presence of double-diffusive effect.

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47

Radko, Timour, and D. Paul Smith. "Equilibrium transport in double-diffusive convection." Journal of Fluid Mechanics 692 (September 28, 2011): 5–27. http://dx.doi.org/10.1017/jfm.2011.343.

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AbstractA theoretical model for the equilibrium double-diffusive transport is presented which emphasizes the role of secondary instabilities of salt fingers in saturation of their linear growth. Theory assumes that the fully developed equilibrium state is characterized by the comparable growth rates of primary and secondary instabilities. This assumption makes it possible to formulate an efficient algorithm for computing diffusivities of heat and salt as a function of the background property gradients and molecular parameters. The model predicts that the double-diffusive transport of heat and salt rapidly intensifies with decreasing density ratio. Fluxes are less sensitive to molecular characteristics, mildly increasing with Prandtl number $(\mathit{Pr})$ and decreasing with diffusivity ratio $(\tau )$. Theory is successfully tested by a series of direct numerical simulations which span a wide range of $\mathit{Pr}$ and $\tau $.

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48

Halnes, Geir, Tuomo Mäki-Marttunen, Klas H. Pettersen, Ole A. Andreassen, and Gaute T. Einevoll. "Ion diffusion may introduce spurious current sources in current-source density (CSD) analysis." Journal of Neurophysiology 118, no. 1 (July 1, 2017): 114–20. http://dx.doi.org/10.1152/jn.00976.2016.

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Current-source density (CSD) analysis is a well-established method for analyzing recorded local field potentials (LFPs), that is, the low-frequency part of extracellular potentials. Standard CSD theory is based on the assumption that all extracellular currents are purely ohmic, and thus neglects the possible impact from ionic diffusion on recorded potentials. However, it has previously been shown that in physiological conditions with large ion-concentration gradients, diffusive currents can evoke slow shifts in extracellular potentials. Using computer simulations, we here show that diffusion-evoked potential shifts can introduce errors in standard CSD analysis, and can lead to prediction of spurious current sources. Further, we here show that the diffusion-evoked prediction errors can be removed by using an improved CSD estimator which accounts for concentration-dependent effects. NEW & NOTEWORTHY Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular.

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49

Li, Li Ben, Li Qiu Su, Zhi Qiang Zhen, Xin Zhong Li, Qing Dong Chen, and Tong Wei Li. "Extrinsic Scaling Effects on the Dielectric Response of Grained BaTiO₃ Films." Key Engineering Materials 434-435 (March 2010): 293–95. http://dx.doi.org/10.4028/www.scientific.net/kem.434-435.293.

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A set of gradient stresses is used in Landau thermodynamic theory to explain the dielectric diffusion of BaTiO3 films grown on thick copper foils. Every grain in the films is treated as a single domain core that is surrounded by boundaries with low dielectric constant. The dielectric diffusion is mainly induced by the diffusive phase transition caused by the gradient stresses. The low dielectric constant boundaries suppress the peak value of the dielectric constant. The results agree with the experiments.

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50

Nissimagoudar, Arun S., Aaditya Manjanath, and Abhishek K. Singh. "Diffusive nature of thermal transport in stanene." Physical Chemistry Chemical Physics 18, no. 21 (2016): 14257–63. http://dx.doi.org/10.1039/c5cp07957h.

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