Concentration distribution of fractional anomalous diffusion caused by an instantaneous point source

2003 ◽  
Vol 24 (11) ◽  
pp. 1302-1308 ◽  
Author(s):  
Duan Jun-sheng ◽  
Xu Ming-yu
Keyword(s):  
Point Source ◽  
Anomalous Diffusion ◽  
Concentration Distribution ◽  
Instantaneous Point

Uniform Horizontal Groundwater Flow against Dispersion in a Shallow Aquifer: Two Analytical Models

1992 ◽  
Vol 23 (1) ◽  
pp. 1-12
Author(s):  
Ram Raj Vinda ◽  
Raja Ram Yadava ◽  
Naveen Kumar
Keyword(s):  
Point Source ◽  
Groundwater Flow ◽  
Cross Section ◽  
Analytical Solutions ◽  
Concentration Distribution ◽  
Analytical Models ◽  
Shallow Aquifer ◽  
Horizontal Cross Section ◽  
Flow Components ◽  
Reactive Pollutant

Analytical solutions converging rapidly at large and small values of times have been obtained for two mathematical models which describe the concentration distribution of a non reactive pollutant from a point source against the flow in a horizontal cross-section of a finite saturated shallow aquifer possessing uniform horizontal groundwater flow. Zero concentration or the conditions in which the flux across the extreme boundaries are proportional to the respective flow components are applied. The effects of flow and dispersion on concentration distribution are also discussed.

Diffusion in branching regions

1960 ◽  
Vol 56 (1) ◽  
pp. 55-63 ◽  
Author(s):  
J. C. Jaeger
Keyword(s):  
Point Source ◽  
Numerical Results ◽  
Instantaneous Point ◽  
Plane Sheet ◽  
Transmitter Substance

ABSTRACTThe problem of diffusion from an instantaneous point source in a thin plane sheet which is intersected by one or more other thin plane sheets of the same material is considered. This problem arises in the study of the diffusion of packets of transmitter substance in synaptic clefts, and some numerical results for the amphibian neuro-muscular junction are presented. A similar discussion applies to branching rods and to cases where there is loss of diffusing substance at the surfaces of the sheets.

scholarly journals Instantaneous point source solutions in nonlinear diffusion with nonlinear loss or gain

2000 ◽  
Vol 41 (3) ◽  
pp. 281-300 ◽  
Author(s):  
J. R. Philip
Keyword(s):  
Point Source ◽  
Power Law ◽  
Finite Time ◽  
Nonlinear Diffusion ◽  
Blow Up ◽  
Central Place ◽  
Point Sources ◽  
Nonlinear Loss ◽  
Instantaneous Point ◽  
Central Concentration

AbstractExact solutions are developed for instantaneous point sources subject to nonlinear diffusion and loss or gain proportional to nth power of concentration, with n > 1. The solutions for the loss give, at large times, power-law decrease to zero of slug central concentration and logarithmic increase of slug semi-width. Those for gain give concentration decreasing initially, going through a minimum, and then increasing, with blow-up to infinite concentration in finite time. Slug semi-width increases with time to a finite maximum in finite time at a blow-up. Taken in conjunction with previous studies, these new results provide an overall schema for instantaneous nonlinear diffusion point sources with nonlinear loss or gain for the total range n ≥ 0. Six distinct regimes of behaviour of slug semi-width and concentration are identified, depending on the range of n, 0 ≤ n < 1, n = 1, or n > 1. Three of them are for loss, and three for gain. The classical Barenblatt-Pattle nonlinear instantaneous point-source solutions with material concentration occupy a central place in the total schema.

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