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Biomedical subjects

P Grigolini

Publications and source records attributed to P Grigolini.

At least 19 recordsLinked to original sources
PubMed2000

Fluctuation-dissipation process without a time scale

We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border is signaled by sharp peaks, and, in the weak dissipation limit, the central distribution body becomes identical to a truncated Levy distribution.

Journal Article↗
PubMed2000

Anomalous diffusion associated with nonlinear fractional derivative fokker-planck-like equation: exact time-dependent solutions

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives ( partial differential/ partial differentialt)P(x,t)=D( partial differential(gamma)/ partial differentialx(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2-gamma)/(1+gamma)(-infinity<gamma</=2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q=(gamma+3)/(gamma+1)(0<gamma</=2), with the solutions optimizing the nonextensive entropy characterized by index q. Interestingly enough, this relation coincides with the one already known for Levy-like superdiffusion (i.e., nu=1 and 0<gamma</=2). Finally, for (gamma,nu)=(2,0) we obtain q=5/3, which differs from the value q=2 corresponding to the gamma=2 solutions available in the literature (nu<1 porous medium equation), thus exhibiting nonuniform convergence.

Journal Article↗
PubMed2000

Towards the thermodynamics of localization processes

We study the entropy time evolution of a quantum mechanical model, which is frequently used as a prototype for Anderson's localization. Recently Latora and Baranger [Phys. Rev. Lett. 82, 520 (1999)] found that there exist three entropy regimes, a transient regime of passage from dynamics to thermodynamics, a linear-in-time regime of entropy increase, that is, a thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the nonextensive entropic indicator advocated by Tsallis [J. Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that the adoption of the "magic" value q=Q=1/2, compared to the traditional entropic index q=1, reduces the length of the transient regime and makes earlier the emergence of the Kolmogorov regime. We adopt a two-site model to explain these properties by means of an analytical treatment and we argue that Q=1/2 might be a typical signature of the occurrence of Anderson localization.

Journal Article↗
PubMed1994

Fractal properties of ion channels and diffusion.

We focus our attention on a fractal model recently proposed by Liebovitch to account for the lack of a time scale in ion channel kinetics. We establish a connection between the dwell-time distributions and the correlation time of the ion channel signal, thereby making it possible to derive analytical predictions on the diffusion properties of a random walk constructed from the sum of the current fluctuations of ion channels. With the help of a numerical simulation of the Liebovitch model, it is shown that the Hurst analysis can provide a reliable determination of the standard (or anomalous) diffusion properties. On the basis of results of computer simulation we argue that by applying the Hurst analysis to the experimental distribution of closed times it is possible, in principle, to establish whether the Liebovitch model is valid.

Computer Simulation↗