Spectral analysis and computation for homogenization of advection diffusion processes in steady flows

2020 ◽  
Vol 61 (1) ◽  
pp. 013102 ◽  
Author(s):  
N. B. Murphy ◽  
E. Cherkaev ◽  
J. Zhu ◽  
J. Xin ◽  
K. M. Golden
Keyword(s):  
Spectral Analysis ◽  
Diffusion Processes ◽  
Steady Flows ◽  
Advection Diffusion

scholarly journals ROLL-WAVES IN BI-LAYER FLOWS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250006 ◽  
Author(s):  
MARC BOUTOUNET ◽  
PASCAL NOBLE ◽  
JEAN-PAUL VILA
Keyword(s):  
Spectral Analysis ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Low Frequency ◽  
Newtonian Fluids ◽  
Hydrodynamic Instabilities ◽  
Steady Flows ◽  
Long Wavelength ◽  
Roll Waves ◽  
Saint Venant Equations

We derive consistent shallow water equations (so-called Saint Venant equations) for the superposition of two Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency/long wavelength regime and show the occurrence of hydrodynamic instabilities, so-called roll-waves, when steady flows are unstable.

Application of nuclear magnetic resonance imaging (MRI) to migration studies of oil-related residues in estuarine sediments (Tay Estuary)

1998 ◽  
Vol 38 (11) ◽  
pp. 187-192 ◽  
Author(s):  
A. D. Reeves ◽  
J. A. Chudek
Keyword(s):  
Magnetic Resonance Imaging ◽  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Diffusion Processes ◽  
Estuarine Sediments ◽  
Resonance Imaging ◽  
Advection Diffusion ◽  
Oil Distribution ◽  
Nearshore Environments ◽  
Magnetic Resonance Imaging Mri

The tendency for selected organic compounds to sorb to sediments has been investigated extensively. These studies, however, have not permitted the ‘observation’ or measurement of advection/diffusion processes and the breakdown of organics within sediments. MRI is a multidimensional technique allowing the position of nuclei (most commonly protons) to be charted within a volume. We introduce MRI as a means of monitoring movement of oil within a series of estuarine sediments, thus offering a method of assessing the harming potential of oils in nearshore environments. Results presented in terms of the % change of oil distribution within a sediment sample, show the great potential of MRI in studying protonated contaminants in sediments.

scholarly journals Two-Dimensional Advection–Diffusion Process with Memory and Concentrated Source

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 879 ◽  
Author(s):  
Najma Ahmed ◽  
Nehad Ali Shah ◽  
Dumitru Vieru
Keyword(s):  
Differential Equation ◽  
Fourier Transforms ◽  
Diffusion Processes ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Dimensional ◽  
Symmetry Center ◽  
Advection Diffusion ◽  
Initial Boundary Value ◽  
With Memory

Two-dimensional advection–diffusion processes with memory and a source concentrated in the symmetry center of the domain have been investigated. The differential equation of the studied model is a fractional differential equation with short-tail memory (a differential equation with Caputo–Fabrizio time-fractional derivatives). An analytical solution of the initial-boundary value problem has been determined by employing the Laplace transform and double sine-Fourier transforms. A numerical solution of the studied problem has been determined using finite difference approximations. Numerical simulations for both solutions have been carried out using the software Mathcad.

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