2,568,540 research outputs found
Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia
We calculate the dynamical relativistic corrections, originating from
radiative one-gluon-exchange, to the leptonic decay width of heavy quarkonia in
the framework of a covariant formulation of Light-Front Dynamics. Comparison
with the non-relativistic calculations of the leptonic decay width of J=1
charmonium and bottomonium S-ground states shows that relativistic corrections
are large. Most importantly, the calculation of these dynamical relativistic
corrections legitimate a perturbative expansion in , even in the
charmonium sector. This is in contrast with the ongoing belief based on
calculations in the non-relativistic limit. Consequences for the ability of
several phenomenological potential to describe these decays are drawn.Comment: 17 pages, 7 figure
The classical point-electron in Colombeau's theory of nonlinear generalized functions
The electric and magnetic fields of a pole-dipole singularity attributed to a
point-electron-singularity in the Maxwell field are expressed in a Colombeau
algebra of generalized functions. This enables one to calculate dynamical
quantities quadratic in the fields which are otherwise mathematically
ill-defined: The self-energy (i.e., `mass'), the self-angular momentum (i.e.,
`spin'), the self-momentum (i.e., `hidden momentum'), and the self-force. While
the total self-force and self-momentum are zero, therefore insuring that the
electron-singularity is stable, the mass and the spin are diverging integrals
of delta-squared-functions. Yet, after renormalization according to standard
prescriptions, the expressions for mass and spin are consistent with quantum
theory, including the requirement of a gyromagnetic ratio greater than one. The
most striking result, however, is that the electric and magnetic fields differ
from the classical monopolar and dipolar fields by delta-function terms which
are usually considered as insignificant, while in a Colombeau algebra these
terms are precisely the sources of the mechanical mass and spin of the
electron-singularity.Comment: 30 pages. Final published version with a few minor correction
The pressure moments for two rigid spheres in low-Reynolds-number flow
The pressure moment of a rigid particle is defined to be the trace of the first moment of the surface stress acting on the particle. A Faxén law for the pressure moment of one spherical particle in a general low-Reynolds-number flow is found in terms of the ambient pressure, and the pressure moments of two rigid spheres immersed in a linear ambient flow are calculated using multipole expansions and lubrication theory. The results are expressed in terms of resistance functions, following the practice established in other interaction studies. The osmotic pressure in a dilute colloidal suspension at small Péclet number is then calculated, to second order in particle volume fraction, using these resistance functions. In a second application of the pressure moment, the suspension or particle-phase pressure, used in two-phase flow modeling, is calculated using Stokesian dynamics and results for the suspension pressure for a sheared cubic lattice are reported
Equilibrium spin-glass transition of magnetic dipoles with random anisotropy axes on a site diluted lattice
We study partially occupied lattice systems of classical magnetic dipoles
which point along randomly oriented axes. Only dipolar interactions are taken
into account. The aim of the model is to mimic collective effects in disordered
assemblies of magnetic nanoparticles. From tempered Monte Carlo simulations, we
obtain the following equilibrium results. The zero temperature entropy
approximately vanishes. Below a temperature T_c, given by k_B T_c= (0.95 +-
0.1)x e_d, where e_d is a nearest neighbor dipole-dipole interaction energy and
x is the site occupancy rate, we find a spin glass phase. In it, (1) the mean
value , where q is the spin overlap, decreases algebraically with system
size N as N increases, and (2) D|q| = 0.5 (T/x)^1/2, independently of N,
where D|q| is the root mean square deviation of |q|.Comment: 7 LaTeX pages, 7 eps figures. Submitted to PRB on 30 December 200
Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions
We formalise and generalise the definition of the family of univariate double
two--piece distributions, obtained by using a density--based transformation of
unimodal symmetric continuous distributions with a shape parameter. The
resulting distributions contain five interpretable parameters that control the
mode, as well as the scale and shape in each direction. Four-parameter
subfamilies of this class of distributions that capture different types of
asymmetry are discussed. We propose interpretable scale and location-invariant
benchmark priors and derive conditions for the propriety of the corresponding
posterior distribution. The prior structures used allow for meaningful
comparisons through Bayes factors within flexible families of distributions.
These distributions are applied to data from finance, internet traffic and
medicine, comparing them with appropriate competitors
Can intrinsic noise induce various resonant peaks?
We theoretically describe how weak signals may be efficiently transmitted
throughout more than one frequency range in noisy excitable media by kind of
stochastic multiresonance. This serves us here to reinterpret recent
experiments in neuroscience, and to suggest that many other systems in nature
might be able to exhibit several resonances. In fact, the observed behavior
happens in our (network) model as a result of competition between (1) changes
in the transmitted signals as if the units were varying their activation
threshold, and (2) adaptive noise realized in the model as rapid
activity-dependent fluctuations of the connection intensities. These two
conditions are indeed known to characterize heterogeneously networked systems
of excitable units, e.g., sets of neurons and synapses in the brain. Our
results may find application also in the design of detector devices.Comment: 10 pages, 2 figure
Lie systems: theory, generalisations, and applications
Lie systems form a class of systems of first-order ordinary differential
equations whose general solutions can be described in terms of certain finite
families of particular solutions and a set of constants, by means of a
particular type of mapping: the so-called superposition rule. Apart from this
fundamental property, Lie systems enjoy many other geometrical features and
they appear in multiple branches of Mathematics and Physics, which strongly
motivates their study. These facts, together with the authors' recent findings
in the theory of Lie systems, led to the redaction of this essay, which aims to
describe such new achievements within a self-contained guide to the whole
theory of Lie systems, their generalisations, and applications.Comment: 161 pages, 2 figure
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