Method for solving the nonlinear diffusion equation

Janavičius, A.J.

doi:10.1016/s0375-9601(96)00794-3

Cited by 17 publications

(33 citation statements)

References 3 publications

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“…We obtained * corresponding author; e-mail: AYanavy@gmail.com very good coincidence with experiment [4,5]. Diffusion equation was introduced [5] using first Fick's law and requiring that diffusion of impurities must emanate with finite velocity and maximum penetration depth into the crystal. This nonlinear diffusion equation in the spherical-symmetric case [6]:…”

Section: Introductionsupporting

confidence: 53%

“…Using nonlinear diffusion theory for impurities diffusion in gases [6] we can transform linear diffusion equation into nonlinear [5,6] applying Eq. (3) for self-diffusion of first kind molecules.…”

Section: Nonlinear Equation For Binary Diffusion In Gasesmentioning

confidence: 99%

“…Those complicated mass transport problems for multicomponent systems can be realized [2] using the Darken equations [3] and numerical methods. We consider the binary diffusion of gases applying the mathematical methods and analytical solutions, derived for the nonlinear diffusion equation [4][5][6]:…”

Section: Introductionmentioning

confidence: 99%

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Analytical Solution of Nonlinear Diffusion Equation Describing Interdiffusion of Gases

Janavičius

Jurgaitis

2009

Acta Phys. Pol. A

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The diffusion is the result of Brownian movement and occurs with a finite velocity. We consider the nonlinear diffusion equation, with diffusion coefficient directly proportional to the impurities concentration. In this case of diffusion from the constant source, the maximum displacements of diffusing particles are proportional to the square root of diffusion time. This result coincides with Brownian movement theory. The obtained analytically solutions were successfully applied for describing the diffusion and superdiffusion experiments' in solids. After theoretical consideration of application of this equation for diffusion in gases, we are investigating here the binary nonlinear diffusion in gases. We obtained the nonlinear interdiffusion equation, for the spherical symmetric case, and presented the approximate analytical solutions.

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Section: Introductionsupporting

confidence: 53%

Section: Nonlinear Equation For Binary Diffusion In Gasesmentioning

confidence: 99%

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Analytical Solution of Nonlinear Diffusion Equation Describing Interdiffusion of Gases

Janavičius

Jurgaitis

2009

Acta Phys. Pol. A

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“…From (18) we can obtain the diffusion coefficients like in (16) and (17) only for temperature about 800 K. We may conclude that the irradiated sample and irradiated vacancies are in some excited states and superdiffusivity through excited and very fast negative vacancies can be realized.…”

Section: Model Calculations and Discussionmentioning

confidence: 93%

“…N s1 is the concentration of impurity atoms at the surface in a one--dimensional model of impurities diffusion from the constant source [16], x 01 = 0.309 cm is its maximum penetration depth or the length of the sample edge in the case of vacancy diffusion. From this, we can obtain the concentration of vacancies at the surface of the irradiated side N V s = 2.51 × 10 12 cm −1 taking into account that only half of them will move changing charges into the bulk of the sample.…”

Section: Resultsmentioning

confidence: 99%

Superdiffusion in Si Crystal Lattice Irradiated by Soft X-Rays

et al. 2008

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We considered the reasons of superdiffusivity and measured profiles of boron and phosphorus in crystalline silicon at room temperature. The superdiffusivity or ultrafast diffusion of metastable vacancies at room temperature in Si crystal irradiated by soft X-rays was obtained experimentally. In this work, we presented experimentally obtained diffusion coefficients of singly and doubly negatively charged long-lived excited vacancies. These high concentration charged metastable vacancies (about 10 13 cm −3 ) at room temperature can very fast diffuse changing electrical conductivity and the Hall mobility of carriers. We measured the superdiffusivity of negatively charged vacancies, generated by the Auger effect in the regions of the sample, which were not affected by X-rays. In this paper, we presented the obtained superdiffusion profiles of boron and phosphorus in crystalline silicon measured with secondary-ion mass spectrometer.

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Analytical solution for one-dimensional contaminant diffusion through unsaturated soils beneath geomembrane

Chen

et al. 2019

Journal of Hydrology

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Method for solving the nonlinear diffusion equation

Cited by 17 publications

References 3 publications

Analytical Solution of Nonlinear Diffusion Equation Describing Interdiffusion of Gases

Analytical Solution of Nonlinear Diffusion Equation Describing Interdiffusion of Gases

Superdiffusion in Si Crystal Lattice Irradiated by Soft X-Rays

Analytical solution for one-dimensional contaminant diffusion through unsaturated soils beneath geomembrane

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