42,560 research outputs found
Fractional Calculus as a Macroscopic Manifestation of Randomness
We generalize the method of Van Hove so as to deal with the case of
non-ordinary statistical mechanics, that being phenomena with no time-scale
separation. We show that in the case of ordinary statistical mechanics, even if
the adoption of the Van Hove method imposes randomness upon Hamiltonian
dynamics, the resulting statistical process is described using normal calculus
techniques. On the other hand, in the case where there is no time-scale
separation, this generalized version of Van Hove's method not only imposes
randomness upon the microscopic dynamics, but it also transmits randomness to
the macroscopic level. As a result, the correct description of macroscopic
dynamics has to be expressed in terms of the fractional calculus.Comment: 20 pages, 1 figur
Galaxy Orientations in the Coma Cluster
We have examined the orientations of early-type galaxies in the Coma cluster
to see whether the well-established tendency for brightest cluster galaxies to
share the same major axis orientation as their host cluster also extends to the
rest of the galaxy population. We find no evidence of any preferential
orientations of galaxies within Coma or its surroundings. The implications of
this result for theories of the formation of clusters and galaxies
(particularly the first-ranked members) are discussed.Comment: Accepted for publication in the Astrophysical Journal Letters. 4
pages, 4 figure
Development of optical modulators for measurements of solar magnetic fields
The measurement of polarized light allows solar astronomers to infer the magnetic field on the Sun. The accuracy of these measurements is dependent on the stable retardation characteristics of the polarization modulators used to minimize the atmospheric effects seen in ground-based observations. This report describes the work by the Space Science Laboratory at Marshall Space Flight Center to improve two types of polarization modulators. As a result, the timing characteristics for both electrooptic crystals (KD*Ps) and liquid crystal devices (LCDs) have been studied and will be used to enhance the capabilities of the MSFC Vector Magnetograph
An intensity-expansion method to treat non-stationary time series: an application to the distance between prime numbers
We study the fractal properties of the distances between consecutive primes.
The distance sequence is found to be well described by a non-stationary
exponential probability distribution. We propose an intensity-expansion method
to treat this non-stationarity and we find that the statistics underlying the
distance between consecutive primes is Gaussian and that, by transforming the
distance sequence into a stationary one, the range of Gaussian randomness of
the sequence increases.Comment: 11 pages, 7 figures, in press on 'Chaos, Solitons & Fractals
Invisible Pixels Are Dead, Long Live Invisible Pixels!
Privacy has deteriorated in the world wide web ever since the 1990s. The
tracking of browsing habits by different third-parties has been at the center
of this deterioration. Web cookies and so-called web beacons have been the
classical ways to implement third-party tracking. Due to the introduction of
more sophisticated technical tracking solutions and other fundamental
transformations, the use of classical image-based web beacons might be expected
to have lost their appeal. According to a sample of over thirty thousand images
collected from popular websites, this paper shows that such an assumption is a
fallacy: classical 1 x 1 images are still commonly used for third-party
tracking in the contemporary world wide web. While it seems that ad-blockers
are unable to fully block these classical image-based tracking beacons, the
paper further demonstrates that even limited information can be used to
accurately classify the third-party 1 x 1 images from other images. An average
classification accuracy of 0.956 is reached in the empirical experiment. With
these results the paper contributes to the ongoing attempts to better
understand the lack of privacy in the world wide web, and the means by which
the situation might be eventually improved.Comment: Forthcoming in the 17th Workshop on Privacy in the Electronic Society
(WPES 2018), Toronto, AC
Standard and Non-standard Extensions of Lie algebras
We study the problem of quadruple extensions of simple Lie algebras. We find
that, adding a new simple root , it is not possible to have an
extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links
and no loops between the dots, while it is possible if is a
Borcherds imaginary simple root. We also comment on the root lattices of these
new algebras. The folding procedure is applied to the simply-laced triple
extended Lie algebras, obtaining all the non-simply laced ones. Non- standard
extension procedures for a class of Lie algebras are proposed. It is shown that
the 2-extensions of , with a dot simply linked to the Dynkin-Kac diagram
of , are rank 10 subalgebras of . Finally the simple root
systems of a set of rank 11 subalgebras of , containing as sub-algebra
, are explicitly written.Comment: Revised version. Inaccurate statements corrected. Expanded version
with added reference
Asynchronous Variational Integrators
We describe a new class of asynchronous variational integrators (AVI) for nonlinear
elastodynamics. The AVIs are distinguished by the following attributes: (i)
The algorithms permit the selection of independent time steps in each element, and
the local time steps need not bear an integral relation to each other; (ii) the algorithms
derive from a spacetime form of a discrete version of Hamilton’s variational
principle. As a consequence of this variational structure, the algorithms conserve
local momenta and a local discrete multisymplectic structure exactly.
To guide the development of the discretizations, a spacetime multisymplectic
formulation of elastodynamics is presented. The variational principle used incorporates
both configuration and spacetime reference variations. This allows a unified
treatment of all the conservation properties of the system.A discrete version of reference
configuration is also considered, providing a natural definition of a discrete
energy. The possibilities for discrete energy conservation are evaluated.
Numerical tests reveal that, even when local energy balance is not enforced
exactly, the global and local energy behavior of the AVIs is quite remarkable, a
property which can probably be traced to the symplectic nature of the algorith
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