The Dynamic Foundation of Fractal Operators.

The Dynamic Foundation of Fractal Operators.

Date: May 2003
Creator: Bologna, Mauro
Description: The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and the second part of this dissertation aims at this important task. This dissertation proves that the adoption of a master equation approach, and so of probabilistic as well as dynamical argument yields a satisfactory solution of the problem, as shown in a work by the candidate already published. At the same time, this dissertation shows that the foundation of Levy statistics is compatible with ordinary statistical mechanics and thermodynamics. The problem of the connection with the Kolmogorov-Sinai entropy is a delicate problem that, however, can be successfully solved. The derivation from a microscopic Liouville-like approach based on densities, however, is shown to be impossible. ...
Contributing Partner: UNT Libraries
Linear response at criticality

Linear response at criticality

Date: October 24, 2012
Creator: Svenkeson, Adam; Bologna, Mauro & Grigolini, Paolo
Description: In this article, the authors study a set of cooperatively interacting units at criticality, and prove with analytical and numerical arguments that they generate the same renewal non-Poisson intermittency as that produced by blinking quantum dots.
Contributing Partner: UNT College of Arts and Sciences
Renewal and memory origin of anomalous diffusion: A discussion of their joint action

Renewal and memory origin of anomalous diffusion: A discussion of their joint action

Date: December 2, 2013
Creator: Bologna, Mauro; West, Bruce J. & Grigolini, Paolo
Description: Article on the renewal and memory origin of anomalous diffusion and a discussion of their joint action.
Contributing Partner: UNT College of Arts and Sciences
Linear Response to Perturbation of Nonexponential Renewal Processes

Linear Response to Perturbation of Nonexponential Renewal Processes

Date: November 23, 2005
Creator: Barbi, Francesco; Bologna, Mauro & Grigolini, Paolo
Description: This article discusses the linear response to perturbation of nonexponential renewal processes.
Contributing Partner: UNT College of Arts and Sciences
Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

Date: August 2000
Creator: Bologna, Mauro; Tsallis, Constantino & Grigolini, Paolo
Description: Article discussing research on anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation.
Contributing Partner: UNT College of Arts and Sciences
Lévy diffusion as an effect of sporadic randomness

Lévy diffusion as an effect of sporadic randomness

Date: December 1999
Creator: Bologna, Mauro; Grigolini, Paolo & Riccardi, Juri
Description: This article discusses Lévy diffusion as an effect of sporadic randomness.
Contributing Partner: UNT College of Arts and Sciences
Memory Effects in Fractional Brownian Motion with Hurst Exponent H<1/3

Memory Effects in Fractional Brownian Motion with Hurst Exponent H<1/3

Date: August 27, 2010
Creator: Bologna, Mauro; Vanni, Fabio; Krokhin, Arkadii A. & Grigolini, Paolo
Description: This article discusses a study on the regression to the origin of a walker driven by dynamically generated fractional Brownian motion.
Contributing Partner: UNT College of Arts and Sciences
Beyond the Death of Linear Response: 1/f Optimal Information Transport

Beyond the Death of Linear Response: 1/f Optimal Information Transport

Date: July 21, 2010
Creator: Aquino, Gerardo; Bologna, Mauro; Grigolini, Paolo & West, Bruce J.
Description: Article discussing research on linear response and 1/f optimal information transport.
Contributing Partner: UNT College of Arts and Sciences
Transmission of Information Between Complex Systems: 1/ f resonance

Transmission of Information Between Complex Systems: 1/ f resonance

Date: May 31, 2011
Creator: Aquino, Gerardo; Bologna, Mauro; West, Bruce J. & Grigolini, Paolo
Description: In this article, the authors study the transport of information between two complex systems with similar properties.
Contributing Partner: UNT College of Arts and Sciences
Publisher's Note: Beyond the Death of Linear Response: 1/f Optimal Information Transport [Phys. Rev. Lett. 105,040601 (2010)]

Publisher's Note: Beyond the Death of Linear Response: 1/f Optimal Information Transport [Phys. Rev. Lett. 105,040601 (2010)]

Date: August 3, 2010
Creator: Aquino, Gerardo; Bologna, Mauro; Grigolini, Paolo & West, Bruce J.
Description: This is a Publisher's Note for the article 'Beyond the Death of Linear Response: 1/f Optimal Information Transport' [Phys. Rev. Lett. 105, 040601 (2010)].
Contributing Partner: UNT College of Arts and Sciences
From power law intermittence to macroscopic coherent regime

From power law intermittence to macroscopic coherent regime

Date: June 25, 2009
Creator: Bologna, Mauro; Budini, Adrián A.; Giraldi, Filippo & Grigolini, Paolo
Description: Article addressing the problem of establishing which is the proper form of quantum master equation generating a survival probability identical to that corresponding to the nonergodic sequence of "light on" and "light off" fluorescence fluctuations in blinking quantum dots.
Contributing Partner: UNT College of Arts and Sciences
Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect

Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect

Date: December 2006
Creator: Allegrini, Paolo; Bologna, Mauro; Grigolini, Paolo & West, Bruce J.
Description: Paper discussing the complexity matching effect.
Contributing Partner: UNT College of Arts and Sciences
Aging and Rejuvenation with Fractional Derivatives

Aging and Rejuvenation with Fractional Derivatives

Date: September 10, 2004
Creator: Aquino, Gerardo; Bologna, Mauro; Grigolini, Paolo & West, Bruce J.
Description: This article discusses aging rejuvenation with fractional derivatives.
Contributing Partner: UNT College of Arts and Sciences
Trajectory versus probability density entropy

Trajectory versus probability density entropy

Date: 2001
Creator: Bologna, Mauro; Grigolini, Paolo; Karagiorgis, Markos & Rosa, Angelo
Description: In this article, the authors show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable.
Contributing Partner: UNT College of Arts and Sciences
Aging and Rejuvenation with Fractional Derivatives

Aging and Rejuvenation with Fractional Derivatives

Date: February 2, 2008
Creator: Aquino, Gerardo; Bologna, Mauro; Grigolini, Paolo & West, Bruce J.
Description: Article on aging and rejuvenation with fractional derivatives.
Contributing Partner: UNT College of Arts and Sciences
Renewal aging and linear response

Renewal aging and linear response

Date: February 6, 2008
Creator: Allegrini, Paolo; Ascolani, Gianluca; Bologna, Mauro & Grigolini, Paolo
Description: Paper discussing the linear response to an external perturbation of a renewal process, in an aging condition that, with no perturbation, would yield super-diffusion.
Contributing Partner: UNT College of Arts and Sciences
Experimental Quenching of Harmonic Stimuli: Universality of Linear Response Theory

Experimental Quenching of Harmonic Stimuli: Universality of Linear Response Theory

Date: July 15, 2009
Creator: Allegrini, Paolo; Bologna, Mauro; Fronzoni, Leone; Grigolini, Paolo & Silvestri, Ludovico
Description: This article discusses experimental quenching of harmonic stimuli.
Contributing Partner: UNT College of Arts and Sciences
Decoherence, wave function collapses and non-ordinary statistical mechanics

Decoherence, wave function collapses and non-ordinary statistical mechanics

Date: August 2003
Creator: Bologna, Mauro; Grigolini, Paolo; Pala, Marco G. & Palatella, Luigi
Description: Article discussing decoherence, wave function collapses, and non-ordinary statistical mechanics.
Contributing Partner: UNT College of Arts and Sciences
Fluctuation-Dissipation Theorem for Event-Dominated Processes

Fluctuation-Dissipation Theorem for Event-Dominated Processes

Date: July 6, 2007
Creator: Allegrini, Paolo; Bologna, Mauro; Grigolini, Paolo & West, Bruce J.
Description: Article discussing the fluctuation-dissipation theorem for event-dominated processes.
Contributing Partner: UNT College of Arts and Sciences
Complexity and the Fractional Calculus

Complexity and the Fractional Calculus

Date: March 28, 2013
Creator: Pramukkul, Pensri; Svenkeson, Adam; Grigolini, Paolo; Bologna, Mauro & West, Bruce J.
Description: Article discussing a study on complexity and the fractional calculus.
Contributing Partner: UNT College of Arts and Sciences