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 $\alpha_s$, 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 π\pi-flat outputs for differential-delay systems

We introduce a new definition of $\pi$-flatness for linear differential delay systems with time-varying coefficients. We characterize $\pi$- and $\pi$-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