3,956 research outputs found
Superconducting Quantum Interference in Fractal Percolation Films. Problem of 1/f Noise
An oscillatory magnetic field dependence of the DC voltage is observed when a
low-frequency current flows through superconducting Sn-Ge thin-film composites
near the percolation threshold. The paper also studies the experimental
realisations of temporal voltage fluctuations in these films. Both the
structure of the voltage oscillations against the magnetic field and the time
series of the electric "noise" possess a fractal pattern. With the help of the
fractal analysis procedure, the fluctuations observed have been shown to be
neither a noise with a large number of degrees of freedom, nor the realisations
of a well defined dynamic system. On the contrary the model of voltage
oscillations induced by the weak fluctuations of a magnetic field of arbitrary
nature gives the most appropriate description of the phenomenon observed. The
imaging function of such a transformation possesses a fractal nature, thus
leading to power-law spectra of voltage fluctuations even for the simplest
types of magnetic fluctuations including the monochromatic ones. Thus, the
paper suggests a new universal mechanism of a "1/f noise" origin. It consists
in a passive transformation of any natural fluctuations with a fractal-type
transformation function.Comment: 17 pages, 13 eps-figures, Latex; title page and figures include
The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs
We study with Monte Carlo methods an ensemble of c=-5 gravity graphs,
generated by coupling a conformal field theory with central charge c=-5 to
two-dimensional quantum gravity. We measure the fractal properties of the
ensemble, such as the string susceptibility exponent gamma_s and the intrinsic
fractal dimensions d_H. We find gamma_s = -1.5(1) and d_H = 3.36(4), in
reasonable agreement with theoretical predictions. In addition, we study the
critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs
and show that it agrees, within numerical accuracy, with theoretical
predictions for the critical behavior of an Ising model coupled dynamically to
two-dimensional quantum gravity, provided the total central charge of the
matter sector is c=-5. From this we conjecture that the critical behavior of
the Ising model is determined solely by the average fractal properties of the
graphs, the coupling to the geometry not playing an important role.Comment: 23 pages, Latex, 7 figure
Systems, Resilience, and Organization: Analogies and Points of Contact with Hierarchy Theory
Aim of this paper is to provide preliminary elements for discussion about the
implications of the Hierarchy Theory of Evolution on the design and evolution
of artificial systems and socio-technical organizations. In order to achieve
this goal, a number of analogies are drawn between the System of Leibniz; the
socio-technical architecture known as Fractal Social Organization; resilience
and related disciplines; and Hierarchy Theory. In so doing we hope to provide
elements for reflection and, hopefully, enrich the discussion on the above
topics with considerations pertaining to related fields and disciplines,
including computer science, management science, cybernetics, social systems,
and general systems theory.Comment: To appear in the Proceedings of ANTIFRAGILE'17, 4th International
Workshop on Computational Antifragility and Antifragile Engineerin
The notion of dimension in geometry and algebra
This talk reviews some mathematical and physical ideas related to the notion
of dimension. After a brief historical introduction, various modern
constructions from fractal geometry, noncommutative geometry, and theoretical
physics are invoked and compared.Comment: 29 pages, a revie
Google matrix analysis of directed networks
In past ten years, modern societies developed enormous communication and
social networks. Their classification and information retrieval processing
become a formidable task for the society. Due to the rapid growth of World Wide
Web, social and communication networks, new mathematical methods have been
invented to characterize the properties of these networks on a more detailed
and precise level. Various search engines are essentially using such methods.
It is highly important to develop new tools to classify and rank enormous
amount of network information in a way adapted to internal network structures
and characteristics. This review describes the Google matrix analysis of
directed complex networks demonstrating its efficiency on various examples
including World Wide Web, Wikipedia, software architecture, world trade, social
and citation networks, brain neural networks, DNA sequences and Ulam networks.
The analytical and numerical matrix methods used in this analysis originate
from the fields of Markov chains, quantum chaos and Random Matrix theory.Comment: 56 pages, 58 figures. Missed link added in network example of Fig3
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