Subdiffusion with External Time Modulation

• Authors: R. Wojnar
• Languages of publication: EN

Abstracts

EN

A subdiffusion process, similar to a Zeldovich-Kompaneets heat conduction process, is defined by a nonlinear diffusion equation in which the diffusion coefficient takes the form D=a(t)f^n, where a=a(t) is an external time modulation, n is a positive constant, and f=f(x, t) is a solution to the nonlinear diffusive equation. It is shown that a Zeldovich-Kompaneets solution satisfies the subdiffusion equation if a=a(t) is replaced by the mean value of a. Also, a solution to the subdiffusion equation is constructed that may be useful in description of biological, social, and financial processes.

Keywords

EN

05.40.Jc; 05.70.Ln; 82.39.Rt; 87.18.Hf; 89.65.Gh; 89.65.Lm

Discipline

• 82.39.Rt: Reactions in complex biological systems(see also 87.18.-h Biological complexity)
• 89.65.Lm: Urban planning and construction(for energy efficient buildings utilizing solar power, see 88.40.M-)
• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)
• 05.40.Jc: Brownian motion
• 87.18.Hf: Spatiotemporal pattern formation in cellular populations
• 05.70.Ln: Nonequilibrium and irreversible thermodynamics(see also 82.40.Bj Oscillations, chaos, and bifurcations in physical chemistry and chemical physics)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2008
• Volume: 114
• Issue: 3
• Pages: 607-611

Dates

published

2008-09

received

2007-11-22

Contributors

author

R. Wojnar

• IPPT PAN, Świętokrzyska 21, 00-049 Warszawa, Poland

References

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• 2. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon, Oxford 1959
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• 5. J.A. Shapiro, Annu. Rev. Microbiol. 52, 81 (1998)
• 6. E. Ben-Jacob, I. Cohen, I. Golding, D.L. Gutnick, M. Tcherpakov, D. Helbing, I.G. Ron, Physica A 282, 247 (2000)
• 7. H. Bloom, Who`s smarter: chimps, baboons or bacteria? The power of group IQ, Submitted by Howard Bloom on 7 Nov. 2007 -- www.scientificblogging.com
• 8. M. Weiss, M. Elsner, F. Kartberg, T. Nilssony, Biophys. J. 87, 3518 (2004)
• 9. F. Michael, M.D. Johnson, Physica A 320, 525 (2003)

Identifiers

DOI

10.12693/APhysPolA.114.607