Geometric Finite Element Discretization of Maxwell Equations in Primal and Dual Spaces

Based on a geometric discretization scheme for Maxwell equations, we unveil a mathematical\textit{\}transformation between the electric field intensity $E$ and the magnetic field intensity $H$, denoted as Galerkin duality. Using Galerkin duality and discrete Hodge operators, we construct two system matrices, $[ X_{E}]$ (primal formulation) and $[ X_{H}$ (dual formulation) respectively, that discretize the second-order vector wave equations. We show that the primal formulation recovers the conventional (edge-element) finite element method (FEM) and suggests a geometric foundation for it. On the other hand, the dual formulation suggests a new (dual) type of FEM. Although both formulations give identical dynamical physical solutions, the dimensions of the null spaces are different.Comment: 22 pages and 4 figure

On the degrees of freedom of lattice electrodynamics

Using Euler's formula for a network of polygons for 2D case (or polyhedra for 3D case), we show that the number of dynamic\textit{\}degrees of freedom of the electric field equals the number of dynamic degrees of freedom of the magnetic field for electrodynamics formulated on a lattice. Instrumental to this identity is the use (at least implicitly) of a dual lattice and of a (spatial) geometric discretization scheme based on discrete differential forms. As a by-product, this analysis also unveils a physical interpretation for Euler's formula and a geometric interpretation for the Hodge decomposition.Comment: 14 pages, 6 figure

A Biased Review of Sociophysics

Various aspects of recent sociophysics research are shortly reviewed: Schelling model as an example for lack of interdisciplinary cooperation, opinion dynamics, combat, and citation statistics as an example for strong interdisciplinarity.Comment: 16 pages for J. Stat. Phys. including 2 figures and numerous reference

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Search for Anomalous Couplings in the Higgs Sector at LEP

Anomalous couplings of the Higgs boson are searched for through the processes e^+ e^- -> H gamma, e^+ e^- -> e^+ e^- H and e^+ e^- -> HZ. The mass range 70 GeV < m_H < 190 GeV is explored using 602 pb^-1 of integrated luminosity collected with the L3 detector at LEP at centre-of-mass energies sqrt(s)=189-209 GeV. The Higgs decay channels H -> ffbar, H -> gamma gamma, H -> Z\gamma and H -> WW^(*) are considered and no evidence is found for anomalous Higgs production or decay. Limits on the anomalous couplings d, db, Delta(g1z), Delta(kappa_gamma) and xi^2 are derived as well as limits on the H -> gamma gamma and H -> Z gamma decay rates

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Bose-Einstein Correlations of Neutral and Charged Pions in Hadronic Z Decays

Bose-Einstein correlations of both neutral and like-sign charged pion pairs are measured in a sample of 2 million hadronic Z decays collected with the L3 detector at LEP. The analysis is performed in the four-momentum difference range 300 MeV < Q < 2 GeV. The radius of the neutral pion source is found to be smaller than that of charged pions. This result is in qualitative agreement with the string fragmentation model

Z Boson Pair-Production at LEP

Events stemming from the pair-production of Z bosons in e^+e^- collisions are studied using 217.4 pb^-1 of data collected with the L3 detector at centre-of-mass energies from 200 GeV up to 209 GeV. The special case of events with b quarks is also investigated. Combining these events with those collected at lower centre-of-mass energies, the Standard Model predictions for the production mechanism are verified. In addition, limits are set on anomalous couplings of neutral gauge bosons and on effects of extra space dimensions

Neutral-Current Four-Fermion Production in e+e- Interactions at LEP

Neutral-current four-fermion production, e+e- -> ffff is studied in 0.7/fb of data collected with the L3 detector at LEP at centre-of-mass energies root(s)=183-209GeV. Four final states are considered: qqvv, qqll, llll and llvv, where l denotes either an electron or a muon. Their cross sections are measured and found to agree with the Standard Model predictions. In addition, the e+e- -> Zgamma* -> ffff process is studied and its total cross section at the average centre-of-mass energy 196.6GeV is found to be 0.29 +/- 0.05 +/- 0.03 pb, where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass spectra of the qqll final states are analysed to search for the possible production of a new neutral heavy particle, for which no evidence is found

Measurement of Exclusive rho+rho- Production in Mid-Virtuality Two-Photon Interactions and Study of the gamma gamma* -> rho rho Process at LEP

Exclusive rho+rho- production in two-photon collisions between a quasi-real photon, gamma, and a mid-virtuality photon, gamma*, is studied with data collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* -> rho+ rho- process is determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, W_gg, in the kinematic region: 0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2 < 30 GeV^2