Share This Article:

Advection Dispersion Equation and BMO Space

Full-Text HTML Download Download as PDF (Size:148KB) PP. 121-127
DOI: 10.4236/jamp.2013.15018    3,308 Downloads   5,036 Views  

ABSTRACT

In this paper, we provide a new way of characterizing the upper and lower bound for the concentration and the gradient of concentration in advection dispersion equation under the condition that source term, concentration and stirring term belong to BMO space.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Zhang, K. , Wang, T. and Feng, X. (2013) Advection Dispersion Equation and BMO Space. Journal of Applied Mathematics and Physics, 1, 121-127. doi: 10.4236/jamp.2013.15018.

References

[1] H. Aref, “Stirring by Chaotic Advection,” Journal of Fluid Mechanics, Vol. 143, No. 1, 1984, pp. 1-21.
http://dx.doi.org/10.1017/S0022112084001233
[2] J. M. Ottino, “The Kinematics of Mixing: Stretching, Chaos, and Transprot,” Cambridge University Press, Cambridge, 1989.
[3] J. Schumacher, K. R. Sreenivasan and P. K. Yeung, “Schmidt Number Dependence of Derivative Moments for Quasi-Static Straining Motion,” Journal of Fluid Mechanics, Vol. 479, No. 1, 2003, pp. 221-230.
http://dx.doi.org/10.1017/S0022112003003756
[4] J. L. Thiffeault, C. R. Doering and J. D. Gibbon, “A Bound on Mixing Efficiency for the Advection-Diffusion Equation,” Journal of Fluid Mechanics, Vol. 521, No. 1, 2004, pp. 105-114.
http://dx.doi.org/10.1017/S0022112004001739
[5] P. V. Danckwerts, “The Definition and Measurement of Some Characteristics of Mixtures,” Applied Scientific Research, Section A, Vol. 3, No. 4, 1952, pp. 279-296.
[6] H. Rehab, R. A. Antonia, L. Djenidi and J. Mi, “Characteristics of Fluorescein Dye and Temperature Fluctuations in a Turbulent Near-Wake,” Experiments in Fluids, Vol. 28, No. 5, 2000, pp. 462-470.
http://dx.doi.org/10.1007/s003480050406
[7] W. Rudin, “Function Theory in the Unit Ball of Cn,” Springer-Verlage, New York, 1980.
http://dx.doi.org/10.1007/978-1-4613-8098-6
[8] J. Garnett, “Bounded Analytic Functions,” Academic Press, New York, 1981.
[9] F. John and L. Nirenberg, “On Functions of Bounded Mean Oscillation,” Communications on Pure and Applied Mathematics, Vol. 14, No. 3, 1961, pp. 415-426.
http://dx.doi.org/10.1002/cpa.3160140317
[10] D. Békollé, C. A. Berger, L. A. Coburn and K. H. Zhu, “BMO in the Bergman Metric on Bounded Symmetric Domains,” Journal of Functional Analysis, Vol. 93, No. 2, 1990, pp. 310-350.
http://dx.doi.org/10.1016/0022-1236(90)90131-4
[11] C. A. Berger, L. A. Coburn and K. H. Zhu, “BMO on the Bergman Spaces of the Classical Domains,” Bulletin of the American Mathematical Society, Vol. 17, No. 1, 1987, pp. 133-136.
http://dx.doi.org/10.1090/S0273-0979-1987-15539-X
[12] K. H. Zhu, “BMO and Hankel Operators on Bergman Spaces,” Pacific Journal of Mathematics, Vol. 155, No. 2, 1992, pp. 377-395.
http://dx.doi.org/10.2140/pjm.1992.155.377
[13] K. H. Zhu, “Spaces of Holomorphic Functions in the Unit Ball,” Springer-Verlage, New York, 2004.
[14] K. Zhang, C. M. Liu and Y. F. Lu, “Toeplitz Operators with BMO Symbols on the Weighted Bergman Space of the Unit Ball,” Acta Mathematica Sinica, English Series, Vol. 27, No. 6, 2011, pp. 2129-2142.
http://dx.doi.org/10.1007/s10114-011-0038-3
[15] K. E. Petersen, “Brownian Motion, Hardy Spaces and Bounded Mean Oscillation,” Cambridge University Press, Cambridge, 1977.
http://dx.doi.org/10.1017/CBO9780511662386
[16] M. Rosso, J. F. Gouyet and B. Sapoval, “Determination of Percolation Probability from the Use of a Concentration Gradient,” Physical Review B, Condensed Matter, Vol. 32, No. 9, 1985, pp. 6053-6054.
http://dx.doi.org/10.1103/PhysRevB.32.6053
[17] V. Markin, T. Tsong, R. Astumian and B. Robertson, “Energy Transduction between a Concentration Gradient and an Alternating Electric Field,” The Journal of Chemical Physics, Vol. 93, No. 7, 1990, pp. 5062-5066.
http://dx.doi.org/10.1063/1.458644
[18] F. Stümpel and K. Jungermann, “Sensing by Intrahepatic Muscarinic Nerves of a Portal-Arterial Glucose Concentration Gradient as a Signal for Insulin-Dependent Glucose Uptake in the Perfused Rat Liver,” FEBS Letters, Vol. 406, No. 1, 1997, pp. 119-122.
[19] A. Lasia, “Porous Electrodes in the Presence of a Concentration Gradient,” Journal of Electroanalytical Chemistry, Vol. 428, No. 1, 1997, pp. 155-164.
[20] M. Higa, A. Tanioka and K. Miyasaka, “Simulation of the Transport of Ions against Their Concentration Gradient across Charged Membranes,” Journal of Membrane Science, Vol. 37, No. 3, 1988, pp. 251-266.
http://dx.doi.org/10.1016/S0376-7388(00)82432-1
[21] M. B. Isichenko, “Percolation, Statistical Topography, and Transport in Random Media,” Reviews of Modern Physics, Vol. 64, No. 4, 1992, pp. 961-1043.
http://dx.doi.org/10.1103/RevModPhys.64.961
[22] S. B. Pope, “Turbulent Flow,” Cambridge University Press, Cambridge, 2000.
http://dx.doi.org/10.1017/CBO9780511840531
[23] N. J. Balmforth, W. R. Young, J. Fields, J. L. Thiffeault and C. Pasquero, “Stirring and Mixing: 1999 Program of Summer Study in Geophysical Fluid Dynamics,” Woods Hole Oceanographic Institution, 2000.
http://dx.doi.org/10.1575/1912/94
[24] B. Gaylord and S. D. Gaines, “Temperature or Transport Range Limits in Marine Species Mediated Solely by Flow,” The American Naturalist, Vol. 155, No. 6, 2000, pp. 769-789. http://dx.doi.org/10.1086/303357
[25] N. Margvelashvily, V. Maderich and M. Zheleznyak, “THREETOX—A Computer Code to Simulate Three-Dimensional Dispersion of Radionuclides in Stratified Water Bodies,” Radiation Protection Dosimetry, Vol. 73, No. 1-4, 1997, pp. 177-180.
http://dx.doi.org/10.1093/oxfordjournals.rpd.a032128
[26] D. T. Ho, P. Schlosser and T. Caplow, “Determination of Longitudinal Dispersion Coefficient and Net Advection in the Tidal Hudson River with a Large-Scale, High Resolution SF6 Tracer Release Experiment,” Environmental Science and Technology, Vol. 36, No. 15, 2002, pp. 3234-3241. http://dx.doi.org/10.1021/es015814+
[27] G. H. O. Essink, “Salt Water Intrusion in a Three-Dimensional Groundwater System in the Netherlands: A Numerical Study,” Transport in Porous Media, Vol. 43, No. 1, 2001, pp. 137-158.
http://dx.doi.org/10.1023/A:1010625913251
[28] E. Sierra, F. G. Acien, J. M. Fernandez, J. L. Garcia, C. Gonzalez and E. Molina, “Characterization of a Flat Plate Photobioreactor for the Production of Microalgae,” Chemical Engineering Journal, Vol. 138, No. 1, 2008, pp. 136-147. http://dx.doi.org/10.1016/j.cej.2007.06.004
[29] L. Y. Chang and W. C. Chen, “Data Mining of Tree-Based Models to Analyze Freeway Accident Frequency,” Journal of Safety Research, Vol. 36, No. 4, 2005, pp. 365-375. http://dx.doi.org/10.1016/j.jsr.2005.06.013

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.