11,046 research outputs found
Fractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media
Equations built on fractional derivatives prove to be a powerful tool in the
description of complex systems when the effects of singularity, fractal
supports, and long-range dependence play a role. In this paper, we advocate an
application of the fractional derivative formalism to a fairly general class of
critical phenomena when the organization of the system near the phase
transition point is influenced by a competing nonlocal ordering. Fractional
modifications of the free energy functional at criticality and of the widely
known Ginzburg-Landau equation central to the classical Landau theory of
second-type phase transitions are discussed in some detail. An implication of
the fractional Ginzburg-Landau equation is a renormalization of the transition
temperature owing to the nonlocality present.Comment: 10 pages, improved content, submitted for publication to Phys. Lett.
L\'evy flights on a comb and the plasma staircase
We formulate the problem of confined L\'evy flight on a comb. The comb
represents a sawtooth-like potential field , with the asymmetric teeth
favoring net transport in a preferred direction. The shape effect is modeled as
a power-law dependence within the sawtooth period,
followed by an abrupt drop-off to zero, after which the initial power-law
dependence is reset. It is found that the L\'evy flights will be confined in
the sense of generalized central limit theorem if (i) the spacing between the
teeth is sufficiently broad, and (ii) , where is the fractal
dimension of the flights. In particular, for the Cauchy flights (),
. The study is motivated by recent observations of
localization-delocalization of transport avalanches in banded flows in the Tore
Supra tokamak and is intended to devise a theory basis to explain the observed
phenomenology.Comment: 13 pages; 3 figures; accepted for publication in Physical Review
Stretched exponential relaxation and ac universality in disordered dielectrics
This paper is concerned with the connection between the properties of
dielectric relaxation and ac (alternating-current) conduction in disordered
dielectrics. The discussion is divided between the classical linear-response
theory and a self-consistent dynamical modeling. The key issues are, stretched
exponential character of dielectric relaxation, power-law power spectral
density, and anomalous dependence of ac conduction coefficient on frequency. We
propose a self-consistent model of dielectric relaxation, in which the
relaxations are described by a stretched exponential decay function.
Mathematically, our study refers to the expanding area of fractional calculus
and we propose a systematic derivation of the fractional relaxation and
fractional diffusion equations from the property of ac universality.Comment: 8 pages, 2 figure
On conformal Jordan cells of finite and infinite rank
This work concerns in part the construction of conformal Jordan cells of
infinite rank and their reductions to conformal Jordan cells of finite rank. It
is also discussed how a procedure similar to Lie algebra contractions may
reduce a conformal Jordan cell of finite rank to one of lower rank. A conformal
Jordan cell of rank one corresponds to a primary field. This offers a picture
in which any finite conformal Jordan cell of a given conformal weight may be
obtained from a universal covering cell of the same weight but infinite rank.Comment: 9 pages, LaTeX, v2: typo corrected, comments added, version to be
publishe
E-pile model of self-organized criticality
The concept of percolation is combined with a self-consistent treatment of
the interaction between the dynamics on a lattice and the external drive. Such
a treatment can provide a mechanism by which the system evolves to criticality
without fine tuning, thus offering a route to self-organized criticality (SOC)
which in many cases is more natural than the weak random drive combined with
boundary loss/dissipation as used in standard sand-pile formulations. We
introduce a new metaphor, the e-pile model, and a formalism for electric
conduction in random media to compute critical exponents for such a system.
Variations of the model apply to a number of other physical problems, such as
electric plasma discharges, dielectric relaxation, and the dynamics of the
Earth's magnetotail.Comment: 4 pages, 2 figure
Bursts in discontinuous Aeolian saltation
Close to the onset of Aeolian particle transport through saltation we find in
wind tunnel experiments a regime of discontinuous flux characterized by bursts
of activity. Scaling laws are observed in the time delay between each burst and
in the measurements of the wind fluctuations at the fluid threshold Shields
number . The time delay between each burst decreases on average with
the increase of the Shields number until sand flux becomes continuous. A
numerical model for saltation including the wind-entrainment from the turbulent
fluctuations can reproduce these observations and gives insight about their
origin. We present here also for the first time measurements showing that with
feeding it becomes possible to sustain discontinuous flux even below the fluid
threshold
The Discipleship Home Pergola and Firepit Area
This report illustrates the complete process of the implementation of an outdoor space consisting of a hardscaped firepit area covered by a pergola in the backyard of the Discipleship Home in Oceano, CA. This project was carried out by two construction management students, Andreas Rasmussen and Logan Smith. Logan Smith’s primary focus was the pergola while I was in charge of the hardscaping and natural gas firepit directly underneath the structure. The project was completed in December of 2020 with the use of quality materials purchased from local businesses and the help of local equipment rental store, Grover Tool & Rentals. This area now provides beautiful aesthetics and great function for an organization designed to get men in the community, that have taken a wrong turn in life, back on track. Together, Logan and I were able to improve our construction skills, teamwork, and our community in just a few months
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