scholarly journals The Reversing of Interfaces in Slow Diffusion Processes with Strong Absorption

2012 ◽  
Vol 72 (1) ◽  
pp. 144-162 ◽  
Author(s):  
J. M. Foster ◽  
C. P. Please ◽  
A. D. Fitt ◽  
G. Richardson
Keyword(s):  
Diffusion Processes ◽  
Strong Absorption ◽  
Slow Diffusion

GPU-based solution of Biot’s elastodynamic equations to account for fluid pressure diffusion

2020 ◽  
Author(s):  
Yury Alkhimenkov ◽  
Lyudmila Khakimova ◽  
Ludovic Raess ◽  
Beatriz Quintal ◽  
Yury Podladchikov
Keyword(s):  
Numerical Simulation ◽  
Diffusion Process ◽  
Diffusion Processes ◽  
Absorbing Boundary Conditions ◽  
Fast Wave ◽  
Time Step ◽  
Near Surface ◽  
Mechanical Coupling ◽  
Slow Diffusion ◽  
Fluid Diffusion

<p> <span>Elastodynamic hydro-mechanical coupling based on Biot’s theory describes an upscaling of the fluid-solid deformation at a porous scale. Examples of applications of this theory are near surface geophysics, CO2 monitoring, induced seismicity, etc. The dynamic response of a coupled hydro-mechanical system can produce fast and slow compressional waves and shear waves. In many earth materials, a propagating slow wave degenerates into a slow diffusion mode on orders of magnitude larger time scales compared to wave propagation. In the present work, we propose a new approach to accelerate the numerical simulation of slow diffusion processes. We solve the coupled Biot elastodynamic hydro-mechanical equations for particle velocity and stress in the time domain using the finite volume method on a rectangular grid in three dimensions. The MPI-based multi-GPU code is implemented using CUDA-C programming language. We prescribe a fluid injection at the center of the model that generates a fast propagating wave and a significantly slower fluid-diffusion event. The fast wave is attenuated due to absorbing boundary conditions after what the slow fluid-diffusion process remains active. A Courant stability condition for the fast wave controls the time-step in the entire simulation, resulting in a suboptimal short time step for the diffusion process. Once fast waves are no longer present in the model domain, the hydro-mechanical coupling vanishes in the inertial terms allowing for an order of magnitude larger time steps. We accelerate the numerical simulation of slow diffusion processes using a pseudo-transient method that permits to capture the transition in time step restrictions. This latest development enables us to simulate quasi-static and dynamic responses of two-phase media. We present benchmarks confirming the numerical efficiency and accuracy of the novel approach. The further development of the code will capture inelastic physics starting from the dynamic events (earthquake modeling) to quasi-static faulting. </span></p>

Regularity of Interfaces in Diffusion Processes under the Influence of Strong Absorption

1999 ◽  
Vol 149 (3) ◽  
pp. 183-212 ◽  
Author(s):  
Victor A. Galaktionov ◽  
Sergei I. Shmarev ◽  
Juan L. Vazquez
Keyword(s):  
Diffusion Processes ◽  
Strong Absorption

scholarly journals A localized pattern photobleaching method for the concurrent analysis of rapid and slow diffusion processes

1983 ◽  
Vol 43 (2) ◽  
pp. 175-181 ◽  
Author(s):  
D.E. Koppel ◽  
M.P. Sheetz
Keyword(s):  
Diffusion Processes ◽  
Slow Diffusion ◽  
Concurrent Analysis

On the Regional Controllability for Hadamard-Caputo Fractional Ultra-Slow Diffusion Processes

2018 ◽  
Author(s):  
Ruiyang Cai ◽  
Fudong Ge ◽  
Yang Quan Chen ◽  
Chunhai Kou
Keyword(s):  
Diffusion Processes ◽  
Slow Diffusion ◽  
Regional Controllability

scholarly journals Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption

Nonlinearity ◽  
2018 ◽  
Vol 31 (10) ◽  
pp. 4621-4648
Author(s):  
J M Foster ◽  
P Gysbers ◽  
J R King ◽  
D E Pelinovsky
Keyword(s):  
Diffusion Equation ◽  
Strong Absorption ◽  
Slow Diffusion ◽  
Self Similar ◽  
Similar Solutions ◽  
Slow Diffusion Equation

scholarly journals Rebuilding soil organic C stocks in degraded grassland by grazing exclusion: a linked decline in soil inorganic C

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8986
Author(s):  
Yi Zhang ◽  
Yingzhong Xie ◽  
Hongbin Ma ◽  
Le Jing ◽  
Cory Matthew ◽  
...  
Keyword(s):  
Soil Ph ◽  
Diffusion Processes ◽  
Soil Bulk Density ◽  
Total Carbon ◽  
Loessial Soil ◽  
Organic C ◽  
Slow Diffusion ◽  
C Stocks ◽  
Property Changes ◽  
Soil Inorganic

Background Our study evaluated how soil organic carbon (SOC) and soil inorganic carbon (SIC) recovered over time in deep loessial soil as overgrazed grassland was fenced and restored. Methods The study was conducted in the Yunwu Mountain Nature Reserve in the Ningxia Autonomous Region of China. In it we compared soil data from three grazed grassland (G) sites, three sites that were fenced for 15 years (F15), and three sites that were fenced for 30 years (F30) as a so-called ‘space for time series’. Results and Discussion We compared SOC accumulation in soil up to 200 cm below the surface in G, F15, and F30 plots. An increase in SOC correlated with a decrease in soil pH, and decreased soil bulk density. However, SOC sequestration in fenced plots was largely offset by a decrease in SIC, which was closely correlated (r = 0.713, p = 0.001) with SOC-driven soil pH decline. We observed no significant increase in soil total carbon in the F15 or F30 sites after comparing them to G. Conclusions Our data indicate that fencing causes the slow diffusion processes to intensify the soil property changes from increased litter return, and this slow diffusion process is still active 30 years after fencing at 100–200 cm soil depths in the studied deep loessial soil. These findings are likely applicable to similar sites.

scholarly journals Self-Similar Solutions for Reversing Interfaces in the Slow Diffusion Equation with Strong Absorption

2016 ◽  
Vol 15 (4) ◽  
pp. 2017-2050 ◽  
Author(s):  
Jamie M. Foster ◽  
Dmitry E. Pelinovsky
Keyword(s):  
Diffusion Equation ◽  
Strong Absorption ◽  
Slow Diffusion ◽  
Self Similar ◽  
Similar Solutions ◽  
Slow Diffusion Equation

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

Ergodic Control of Diffusion Processes

2009 ◽  
Author(s):  
Ari Arapostathis ◽  
Vivek S. Borkar ◽  
Mrinal K. Ghosh
Keyword(s):  
Diffusion Processes ◽  
Ergodic Control
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