Two‐dimensional, steady‐state diffusion of a passive scalar in a flow field

1983 ◽  
Vol 24 (6) ◽  
pp. 1630-1632
Author(s):  
Leaf Turner ◽  
Carl M. Bender
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Passive Scalar ◽  
Two Dimensional ◽  
State Diffusion ◽  
Steady State Diffusion

Growth of microorganisms in two-dimensional steady-state diffusion gradients

1973 ◽  
Vol 19 (1) ◽  
pp. 53-58 ◽  
Author(s):  
D. E. Caldwell ◽  
P. Hirsch
Keyword(s):  
Steady State ◽  
Gradient System ◽  
Two Dimensional ◽  
Concentration Gradients ◽  
Differential Growth ◽  
Waste Products ◽  
State Diffusion ◽  
Test Organisms ◽  
Rhodomicrobium Vannielii ◽  
Steady State Diffusion

A two-dimensional, steady-state diffusion system has been devised for growth of microorganisms in nutrient concentration gradients. Two reservoirs continually supply substrates, while unused substrates and waste products are washed into a third reservoir. Substrates are supplied in the form of a steady-state gradient within an agar sheet which contains the test organisms. Microbial populations can thus be exposed to all values and combinations of two test variables. The system was tested with Escherichia coli grown in glucose and bicarbonate gradients. Hyphomicrobium sp., Rhodomicrobium vannielii, and Thiopedia sp. in a mixed population were segregated by use of a gradient system of methylamine and sodium sulfide. Exposure of natural aquatic populations to a gradient of pond mud and acetate resulted in differential growth of Bacillus sp. and rod-shaped bacteria with terminal endospores. Thus the potential value of gradients in predicting the response of natural microbial communities to nutrients or toxicants and in enriching for specific organisms has been demonstrated qualitatively.

Hedge's Ultimate Numerical Technique (HUNT) for Steady State Diffusion Problem

2007 ◽  
Vol 2 (3) ◽  
Author(s):  
Ganesh S Hegde ◽  
Madhu Gattumane
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Numerical Technique ◽  
Taylor Series Expansion ◽  
Diffusion Problem ◽  
Two Dimensional ◽  
One Dimensional ◽  
Partial Derivatives ◽  
State Diffusion ◽  
Steady State Diffusion

A more realistic numerical technique hereafter known as Hegde's Ultimate Numerical Technique (HUNT) is developed and demonstrated on a one dimensional and a two dimensional steady state diffusion problem of heat transfer. The available numerical methods developed are based on finite difference technique neglecting the contribution of higher order terms in Taylor series expansion of the function leading to an approximation and the error in the solution. In the present effort of the HUNT, the optimization of the partial derivatives leads to the elimination of the error and justifies the stability and the convergence of the solution. The HUNT procedure based on the interface theory developed by the author, is capable of providing the ultimate optimum solution to all the partial derivatives considered as decision vectors. Even though the HUNT is demonstrated on one dimensional and two dimensional steady state diffusion equations, it does not require rigorous efforts to apply it to three dimensional problems of fluid flow and heat transfer. As pilot exercises the HUNT is demonstrated on a one dimensional circular fin and a two dimensional plate to obtain the temperature distribution. The result is compared with the analytical method and the finite volume method for which the results are available in the literature. To the knowledge of the authors, HUNT is both different and a unique example of its kind.

scholarly journals Bioelectrocatalytic endpoint assays based on steady-state diffusion current at microelectrode array

2010 ◽  
Vol 12 (6) ◽  
pp. 839-842 ◽  
Author(s):  
Tatsuo Noda ◽  
Katsumi Hamamoto ◽  
Maiko Tsutsumi ◽  
Seiya Tsujimura ◽  
Osamu Shirai ◽  
...  
Keyword(s):  
Steady State ◽  
Microelectrode Array ◽  
Diffusion Current ◽  
State Diffusion ◽  
Steady State Diffusion

scholarly journals Numerical Solution of Continuation Problem for 3D Steady-State Diffusion in Cylindrically Layered Medium

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Magira Kulbay ◽  
Saule Maussumbekova ◽  
Balgaisha Mukanova
Keyword(s):  
Steady State ◽  
Layered Medium ◽  
Outer Boundary ◽  
Cauchy Data ◽  
Piecewise Constant Function ◽  
Piecewise Constant ◽  
State Diffusion ◽  
Solution Methods ◽  
Continuation Problem ◽  
Steady State Diffusion

This work is based on the application of Fourier and quasi-solution methods for solving the continuation inverse problem for 3D steady-state diffusion model inside a cylindrical layered medium. The diffusion coefficient is supposed to be a piecewise constant function, Cauchy data are given on the outer boundary of the cylinder, and we seek to recover the temperature at the inner boundary of the cylinder. Numerical experiments are investigated and show the capacity of proposed method only for smooth boundary condition. Under the suitable choice of regularization parameters we recover the distribution of temperature on the inner boundary with satisfactory quality for noisy data.

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