PMID: 11308617Apr 20, 2001Paper

Nonlinear equation for anomalous diffusion: Unified power-law and stretched exponential exact solution

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
L C MalacarneE K Lenzi

Abstract

The nonlinear diffusion equation partial delta rho/delta t=D Delta rho(nu) is analyzed here, where Delta[triple bond](1/r(d-1))(delta/delta r)r(d-1-theta) delta/delta r, and d, theta, and nu are real parameters. This equation unifies the anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact point-source solution is obtained, enabling us to describe a large class of subdiffusion [ theta>(1-nu)d], "normal" diffusion [theta=(1-nu)d] and superdiffusion [theta<(1-nu)d]. Furthermore, a thermostatistical basis for this solution is given from the maximum entropic principle applied to the Tsallis entropy.

References

Nov 1, 1985·Physical Review A: General Physics·B O'Shaughnessy, I Procaccia
Sep 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C Tsallis, D J Bukman
Feb 4, 1985·Physical Review Letters·B O'Shaughnessy, I Procaccia
Oct 22, 1990·Physical Review Letters·A OttW Urbach
Dec 13, 1993·Physical Review Letters·T H SolomonH L Swinney
Jan 10, 1994·Physical Review Letters·F BardouC Cohen-Tannoudji
Mar 6, 1995·Physical Review Letters·O V Bychuk, B O'Shaughnessy

❮ Previous
Next ❯

Citations

Mar 1, 2002·Journal of Biological Physics·Till D FrankPeter J Beek
Jan 20, 2018·Physical Review. E·R S PiresJ S Andrade
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Silva, J A S Lima
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lars Meinhold, Jeremy C Smith
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G A CasasE M F Curado
Dec 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mauricio S RibeiroFernando D Nobre
Feb 27, 2015·Physics in Medicine and Biology·A C da S Senra FilhoL O Murta Junior
Jun 13, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G A MendesF D Nobre
May 22, 2019·Physical Review. E·Denner S VieiraRenio S Mendes
Mar 9, 2018·Entropy·Evaldo M F Curado, Fernando D Nobre
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S BalankinDaniel Morales Matamoros
Apr 12, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E K LenziC Tsallis
Mar 5, 2009·Physical Review Letters·Pascal BraultRod W Boswell
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Olga A Dvoretskaya, Peter S Kondratenko
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Veit SchwämmleEvaldo M F Curado
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L C MalacarneE K Lenzi
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I T PedronE K Lenzi
Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F D A Aarão Reis, Dung di Caprio
Jun 13, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L C MalacarneE K Lenzi
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E K LenziL S Lucena
Dec 13, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L C MalacarneM K Lenzi
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Evaldo M F Curado, Fernando D Nobre
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I T PedronE K Lenzi

❮ Previous
Next ❯

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
I T PedronE K Lenzi
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
E K LenziL Borland
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
L C MalacarneE K Lenzi
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
G DrazerC Tsallis
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Masatoshi Shiino, K Yoshida
© 2021 Meta ULC. All rights reserved