scholarly journals Convergence for global curve diffusion flows

2021 ◽  
Vol 4 (1) ◽  
pp. 1-13
Author(s):  
Glen Wheeler ◽  
Keyword(s):  
Diffusion Flows

scholarly journals A Dissipation of Relative Entropy by Diffusion Flows

Entropy ◽  
2016 ◽  
Vol 19 (1) ◽  
pp. 9 ◽  
Author(s):  
Hiroaki Yoshida
Keyword(s):  
Relative Entropy ◽  
Diffusion Flows

scholarly journals Microscopic kinetics of isothermal sintering of Fe-20 % (mаs.) Mo alloy

2021 ◽  
pp. 30-36
Author(s):  
V. Mazur ◽  
Р. Loboda ◽  
Т. Soloviova ◽  
M. Vterkovskyi ◽  
D. Remizov ◽  
...  
Keyword(s):  
Microscopic Analysis ◽  
Phenomenological Theory ◽  
Transformation Rate ◽  
Isothermal Exposure ◽  
X Ray ◽  
Intermediate Phases ◽  
Peritectoid Transformation ◽  
Local Diffusion ◽  
Kinetics Of ◽  
Diffusion Flows

Purpose of work. To investigate the features of microscopic kinetics of peritectoid transformation in Fe-Mo system alloys in an isothermal mode. Experimental part. Microscopic analysis of samples on light (Jenaphot 2000, K. Zeiss) and scanning electron (REM 106I, Selmi) microscopes, X-ray spectral microanalysis of the component’s concentrations distribution between the phases, X-ray phase analysis (Rigaku Ultima IV diffractometer). Results. Microstructure changes, phase composition and crystal lattices parameters of the phase constituents of the powder alloy during sintering at 920 °C were investigated. Variation in the phase constituents mass fraction during 7 hours of the isothermal exposure is analyzed. The formation of anomalous diffusion porosity at the beginning of the process, the nonmonotonic change in the phase constituents fraction and formation of intermediate phases with an unstable component’s concentration are the main features of the microscopic kinetics. The sintering mechanism is proposed. Scientific novelty. A local peritectoid transformation existence at the Fe/Mo interface was established by analyzing the local diffusion flows of components atoms. This transformation occurs upon isothermal supply of Mo atoms with the formation of a cooperative peritectoid structural constituents according to the α- Fe + Mo → α + μ scheme with residual Mo crystals. Formulation of the problem. This work aims to clarify the phenomenological theory of peritectoid transformation during isothermal α-Fe grains enrichment with molybdenum by studying the features of microscopic kinetics in the Fe-Mo system alloys. Practical value. Peritectoid (α + μ) with branched phase соnstituents of cooperative genesis forms a developed system of local diffusion flows of Mo atoms in α -Fe. This increases the molybdenum peritectoid transformation rate at a relatively low sintering temperature for these alloys and reduces the energy consumption in the technological process.

The Thermoinduced Self-Action of the Gaussian Beam of Radiation in the Dispersion Liquid Medium

2010 ◽  
Vol 5 (1) ◽  
pp. 5-8
Author(s):  
Valeriy I. Ivanov ◽  
Albert I. Livashvili
Keyword(s):  
Liquid Medium ◽  
Gaussian Beam ◽  
Light Beam ◽  
Thermal Diffusion ◽  
Analytical Solutions ◽  
Thermal Conduction ◽  
Light Field ◽  
Focal Distance ◽  
Fluid Medium ◽  
Diffusion Flows

The change of the concentration of nanoparticles in the fluid medium which is under the influence of a Gaussian light beam is theoretically explored. Analytical solutions of the nonsteady equations of a thermal conduction and transport of particles taking into account thermal diffusion flows are gained. The expression for a focal distance of the thermoinduced lens resulting self-action of a light field is found.

Metal halide lamps: Gravitational influence on color separation

2006 ◽  
Vol 78 (6) ◽  
pp. 1239-1252 ◽  
Author(s):  
W. W. Stoffels ◽  
A. J. Flikweert ◽  
T. Nimalasuriya ◽  
J. J. A. M. van der Mullen ◽  
G. M. W. Kroesen ◽  
...  
Keyword(s):  
Large Scale ◽  
High Efficiency ◽  
Numerical Models ◽  
Metal Halide ◽  
Light Sources ◽  
Color Separation ◽  
Gravitational Influence ◽  
Metal Halide Lamps ◽  
And Diffusion ◽  
Diffusion Flows

Metal halide lamps are very efficient light sources based on a Hg plasma arc with metal halide salt additions. In spite of their high efficiency, the lamps suffer from several problems, such as color separation and instabilities, which currently hinder large-scale use. These phenomena are caused by a complex interaction of convection and diffusion flows in the plasma. In order to unravel the various contributions, experiments under microgravity have been performed where convection is absent. The experiments confirm the previously held qualitative views, but also provide absolute data on densities and temperatures that will be used to validate numerical models of these lamps.

scholarly journals Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

2010 ◽  
Vol 107 (46) ◽  
pp. 19696-19701 ◽  
Author(s):  
E. A. Carlen ◽  
J. A. Carrillo ◽  
M. Loss
Keyword(s):  
Sobolev Inequalities ◽  
Fast Diffusion ◽  
Diffusion Flows

scholarly journals Three-dimensional exact solutions of the diffusion equation

2021 ◽  
pp. 48-62
Author(s):  
Александр Данилович Чернышов ◽  
Виталий Валерьевич Горяйнов ◽  
Сергей Федорович Кузнецов ◽  
Ольга Юрьевна Никифорова
Keyword(s):  
Exact Solution ◽  
Diffusion Equation ◽  
Exact Solutions ◽  
Three Dimensional ◽  
Arithmetic Mean ◽  
Internal Source ◽  
New Exact Solutions ◽  
Fast Expansions ◽  
Free Parameters ◽  
Diffusion Flows

При помощи метода быстрых разложений решается задача диффузии в параллелепипеде с граничными условиями 1-го рода и внутренним источником вещества, зависящим от координат точек параллелепипеда. Получено в общем виде решение, содержащее свободные параметры, с помощью которых можно получить множество новых точных решений с различными свойствами. Показан пример построения точного решения для случая внутреннего источника переменного только по оси OZ . Приведен анализ особенностей диффузионных потоков в параллелепипеде с указанным внутреннем источником. Получено, что концентрация вещества в центре параллелепипеда равна сумме среднеарифметического значения концентраций вещества в его вершинах и амплитуды внутреннего источника умноженного на величину The authors solve the problem of diffusion in a parallelepiped-shaped body with boundary conditions of the 1st kind and an internal source of substance, depending on the parallelepiped points coordinates with the fast expansions method. The proposed exact solution in general form contains free parameters, which can be used to obtain many new exact solutions with different properties. An example of constructing an exact solution with a variable internal source depending on one coordinate z is shown in the work. An analysis of the features of diffusion flows in a parallelepiped with the indicated internal source is given. It was found that the concentration of a substance in the center of a parallelepiped is equal to the sum of the arithmetic mean of the concentration of a substance at its vertices and the amplitude of the internal source multiplied by the value

scholarly journals Two-Stage Seebeck Effect in Charged Colloidal Suspensions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 150
Author(s):  
Ioulia Chikina ◽  
Sawako Nakamae ◽  
Valeriy Shikin ◽  
Andrey Varlamov
Keyword(s):  
Steady State ◽  
Colloidal Particles ◽  
Colloidal Suspensions ◽  
Linear Increase ◽  
Seebeck Effect ◽  
Thermoelectric Effect ◽  
Initial State ◽  
Two Stage ◽  
Mobile Ions ◽  
Diffusion Flows

We discuss the peculiarities of the Seebeck effect in stabilized electrolytes containing the colloidal particles. Its unusual feature is the two stage character, with the linear increase of differential thermopower as the function of colloidal particles concentration n⊙ during the first stage (“initial state”) and dramatic drop of it at small n⊙ during the second one (“steady state”). We show that the properties of the initial state are governed by the thermo-diffusion flows of the mobile ions of the stabilizing electrolyte medium itself and how the colloidal particles participate in the formation of the electric field in the bulk of the suspension. In its turn, we attribute the specifics of the steady state thermoelectric effect the massive colloidal particles undergoing slow thermal diffusion and the break down of their electro-neutrality in the vicinity of electrodes.

scholarly journals Euler-Bernoulli cantilever beam bending considering the inner diffusion flows finite propagation speed

2020 ◽  
pp. 107-114
Author(s):  
Андрей Владимирович Земсков ◽  
Георгий Михайлович Файкин
Keyword(s):  
Mass Transfer ◽  
Propagation Speed ◽  
Bernoulli Beam ◽  
Elastic Diffusion ◽  
Multicomponent Media ◽  
Equivalent Boundary ◽  
Beam Bending ◽  
Finite Propagation Speed ◽  
Euler Bernoulli Beam ◽  
Diffusion Flows

Исследуются нестационарные колебания балки Эйлера-Бернулли с учетом массопереноса. Используется модель упругой диффузии для многокомпонентных сред. Для получения решения задачи используются вариационный принцип Даламбера и метод эквивалентный граничных условий. Unsteady vibrations of the Euler-Bernoulli beam are studied taking into account mass transfer. The model of elastic diffusion for multicomponent media is used. To obtain a solution to the problem, the d’Alembert variational principle and the equivalent boundary conditions method are used.

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