15,428 research outputs found
Epilegomena to the study of semiclassical orthogonal polynomials
In his monograph [Classical and quantum orthogonal polynomials in one
variable, Cambridge University Press, 2005 (paperback edition 2009)], Ismail
conjectured that certain structure relations involving the Askey-Wilson
operator characterize proper subsets of the set of all
-classical orthogonal polynomials, here to be understood as the
Askey-Wilson polynomials and their limit cases. In this paper we give two
characterization theorems for -semiclassical (and classical)
orthogonal polynomials in consonance with the pioneering works by Maroni [Ann.
Mat. Pura. Appl. (1987)] and Bonan, Lubinsky, and Nevai [SIAM J. Math. Anal. 18
(1987)] for the standard derivative, re-establishing in this context the
perfect "symmetry" between the standard derivative and the Askey-Wilson
operator. As an application, we present a sequence of
-semiclassical orthogonal polynomials of class two that
disproves Ismail's conjectures. Further results are presented for Hahn's
operator
Coral symbiodinium community composition across the Belize Mesoamerican barrier reef system is influenced by host species and thermal variability
Accepted manuscrip
Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow
Finite Larmor radius (FLR) effects on non-diffusive transport in a
prototypical zonal flow with drift waves are studied in the context of a
simplified chaotic transport model. The model consists of a superposition of
drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow
perpendicular to the density gradient. High frequency FLR effects are
incorporated by gyroaveraging the ExB velocity. Transport in the direction of
the density gradient is negligible and we therefore focus on transport parallel
to the zonal flows. A prescribed asymmetry produces strongly asymmetric non-
Gaussian PDFs of particle displacements, with L\'evy flights in one direction
but not the other. For zero Larmor radius, a transition is observed in the
scaling of the second moment of particle displacements. However, FLR effects
seem to eliminate this transition. The PDFs of trapping and flight events show
clear evidence of algebraic scaling with decay exponents depending on the value
of the Larmor radii. The shape and spatio-temporal self-similar anomalous
scaling of the PDFs of particle displacements are reproduced accurately with a
neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma
Universal Probability Distribution Function for Bursty Transport in Plasma Turbulence
Bursty transport phenomena associated with convective motion present
universal statistical characteristics among different physical systems. In this
letter, a stochastic univariate model and the associated probability
distribution function for the description of bursty transport in plasma
turbulence is presented. The proposed stochastic process recovers the universal
distribution of density fluctuations observed in plasma edge of several
magnetic confinement devices and the remarkable scaling between their skewness
and kurtosis . Similar statistical characteristics of variabilities have
been also observed in other physical systems that are characterized by
convection such as the X-ray fluctuations emitted by the Cygnus X-1 accretion
disc plasmas and the sea surface temperature fluctuations.Comment: 10 pages, 5 figure
On classical orthogonal polynomials on bi-lattices
In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that
admit perfect state transfer, Vinet and Zhedanov found an apparently new
sequence of orthogonal polynomials, that they called para-Krawtchouk
polynomials, defined on a bilinear lattice. In this note we present necessary
and sufficient conditions for the regularity of solutions of the corresponding
functional equation. Moreover, the functional Rodrigues formula and a closed
formula for the recurrence coefficients are presented. As a consequence, we
characterize all solutions of the functional equation, including as very
particular cases the Meixner, Charlier, Krawtchouk, Hahn, and para-Krawtchouk
polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:2102.0003
Goldstone-type fluctuations and their implications for the amorphous solid state
In sufficiently high spatial dimensions, the formation of the amorphous (i.e.
random) solid state of matter, e.g., upon sufficent crosslinking of a
macromolecular fluid, involves particle localization and, concommitantly, the
spontaneous breakdown of the (global, continuous) symmetry of translations.
Correspondingly, the state supports Goldstone-type low energy, long wave-length
fluctuations, the structure and implications of which are identified and
explored from the perspective of an appropriate replica field theory. In terms
of this replica perspective, the lost symmetry is that of relative translations
of the replicas; common translations remain as intact symmetries, reflecting
the statistical homogeneity of the amorphous solid state. What emerges is a
picture of the Goldstone-type fluctuations of the amorphous solid state as
shear deformations of an elastic medium, along with a derivation of the shear
modulus and the elastic free energy of the state. The consequences of these
fluctuations -- which dominate deep inside the amorphous solid state -- for the
order parameter of the amorphous solid state are ascertained and interpreted in
terms of their impact on the statistical distribution of localization lengths,
a central diagnostic of the the state. The correlations of these order
parameter fluctuations are also determined, and are shown to contain
information concerning further diagnostics of the amorphous solid state, such
as spatial correlations in the statistics of the localization characteristics.
Special attention is paid to the properties of the amorphous solid state in two
spatial dimensions, for which it is shown that Goldstone-type fluctuations
destroy particle localization, the order parameter is driven to zero, and
power-law order-parameter correlations hold.Comment: 20 pages, 3 figure
Mass of perfect fluid black shells
The spherically symmetric singular perfect fluid shells are considered for
the case of their radii being equal to the event horizon (the black shells). We
study their observable masses, depending at least on the three parameters,
viz., the square speed of sound in the shell, instantaneous radial velocity of
the shell at a moment when it reaches the horizon, and integration constant
related to surface mass density. We discuss the features of black shells
depending on an equation of state.Comment: 1 figure, LaTeX; final version + FA
Time reparametrization invariance in arbitrary range p-spin models: symmetric versus non-symmetric dynamics
We explore the existence of time reparametrization symmetry in p-spin models.
Using the Martin-Siggia-Rose generating functional, we analytically probe the
long-time dynamics. We perform a renormalization group analysis where we
systematically integrate over short timescale fluctuations. We find three
families of stable fixed points and study the symmetry of those fixed points
with respect to time reparametrizations. One of those families is composed
entirely of symmetric fixed points, which are associated with the low
temperature dynamics. The other two families are composed entirely of
non-symmetric fixed points. One of these two non-symmetric families corresponds
to the high temperature dynamics.
Time reparametrization symmetry is a continuous symmetry that is
spontaneously broken in the glass state and we argue that this gives rise to
the presence of Goldstone modes. We expect the Goldstone modes to determine the
properties of fluctuations in the glass state, in particular predicting the
presence of dynamical heterogeneity.Comment: v2: Extensively modified to discuss both high temperature
(non-symmetric) and low temperature (symmetric) renormalization group fixed
points. Now 16 pages with 1 figure. v1: 13 page
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