2,568,453 research outputs found
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
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
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
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
Interaction of moving breathers with an impurity
We analyze the influence of an impurity in the evolution of moving discrete
breathers in a Klein--Gordon chain with non-weak nonlinearity. Three different
behaviours can be observed when moving breathers interact with the impurity:
they pass through the impurity continuing their direction of movement; they are
reflected by the impurity; they are trapped by the impurity, giving rise to
chaotic breathers. Resonance with a breather centred at the impurity site is
conjectured to be a necessary condition for the appearance of the trapping
phenomenon.Comment: 4 pages, 2 figures, Proceedings of the Third Conference, San Lorenzo
De El Escorial, Spain 17-21 June 200
On the computation of -flat outputs for differential-delay systems
We introduce a new definition of -flatness for linear differential delay
systems with time-varying coefficients. We characterize - and -0-flat
outputs and provide an algorithm to efficiently compute such outputs. We
present an academic example of motion planning to discuss the pertinence of the
approach.Comment: Minor corrections to fit with the journal versio
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