scholarly journals On time-dependent diffusion coefficients arising from stochastic processes with memory

2017 ◽  
Author(s):  
M. Victoria Carpio-Bernido ◽  
Wilson I. Barredo ◽  
Christopher C. Bernido
Keyword(s):  
Stochastic Processes ◽  
Diffusion Coefficients ◽  
Time Dependent ◽  
With Memory

scholarly journals Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 99 ◽  
Author(s):  
Kazuma Yamanaka ◽  
Takayuki Narumi ◽  
Megumi Hashiguchi ◽  
Hirotaka Okabe ◽  
Kazuhiro Hara ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Diffusion Coefficients ◽  
Coarse Graining ◽  
Chaotic Advection ◽  
Time Dependent ◽  
Local Order ◽  
Weak Turbulence ◽  
Normal Diffusion ◽  
Convective Rolls

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

A Time-Dependent Bifurcation Model with Control and Pulsing Oscillations

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4260-4266
Author(s):  
Qishao Lu ◽  
Cuncai Hua
Keyword(s):  
Control Problem ◽  
Memory Effects ◽  
Time Dependent ◽  
Bifurcation Parameter ◽  
Bifurcation Transition ◽  
Delayed Bifurcation ◽  
With Memory

A time-dependent bifurcation model and its control problem are studied. Firstly, the delayed bifurcating transition with memory effects due to time-dependent parameters are analysed. Secondly, a control problem with time-dependent parametric feedback in this bifurcation model is investigated. Finally, an important mechanism for pulsing oscillation is found as the result of the delayed bifurcation transition occurring when the bifurcation parameter varies periodically across the steady bifurcation value.

Refinement in the Mathematical and Numerical Treatment of the Internal Oxidation of Alloys

2005 ◽  
Vol 237-240 ◽  
pp. 1157-1162 ◽  
Author(s):  
Wiktor Miszuris ◽  
Andreas Öchsner
Keyword(s):  
Boundary Conditions ◽  
Internal Oxidation ◽  
Diffusion Coefficients ◽  
Finite Dimension ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Numerical Treatment ◽  
Constant Diffusion ◽  
Finite Difference Solution ◽  
Oxide Particles

When oxygen dissolves from atmosphere and diffuses into an alloy during oxidation, the less noble alloy components may react to form oxide particles within the metal. This process is termed internal oxidation. Classical approaches to describe this phenomenon were derived under many strong simplifications such as constant diffusion coefficients, certain boundary conditions and semi-infinite sample. The presented general approach is based on the finite difference solution of the general diffusion equations coupled through the stoichiometry of reaction between oxygen and the considered element. The main enhancement is the consideration of concentration dependent diffusion coefficients, concentration dependent source terms and arbitrary time-dependent boundary conditions formulated as a concentration, a flux or mixed conditions. Furthermore, finite dimension of the specimen is incorporated. This general treatment also allows for the incorporation of the energy balance.

scholarly journals Mathematical modeling of groundwater contamination with varying velocity field

2017 ◽  
Vol 65 (2) ◽  
pp. 192-204 ◽  
Author(s):  
Pintu Das ◽  
Sultana Begam ◽  
Mritunjay Kumar Singh
Keyword(s):  
Groundwater Contamination ◽  
Analytical Solutions ◽  
Diffusion Coefficients ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Time Dependent ◽  
Analytical Models ◽  
Retardation Factor ◽  
Hydrodynamic Dispersion ◽  
The Impact

Abstract In this study, analytical models for predicting groundwater contamination in isotropic and homogeneous porous formations are derived. The impact of dispersion and diffusion coefficients is included in the solution of the advection-dispersion equation (ADE), subjected to transient (time-dependent) boundary conditions at the origin. A retardation factor and zero-order production terms are included in the ADE. Analytical solutions are obtained using the Laplace Integral Transform Technique (LITT) and the concept of linear isotherm. For illustration, analytical solutions for linearly space- and time-dependent hydrodynamic dispersion coefficients along with molecular diffusion coefficients are presented. Analytical solutions are explored for the Peclet number. Numerical solutions are obtained by explicit finite difference methods and are compared with analytical solutions. Numerical results are analysed for different types of geological porous formations i.e., aquifer and aquitard. The accuracy of results is evaluated by the root mean square error (RMSE).

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