Spaces of finite element differential forms

We discuss the construction of finite element spaces of differential forms which satisfy the crucial assumptions of the finite element exterior calculus, namely that they can be assembled into subcomplexes of the de Rham complex which admit commuting projections. We present two families of spaces in the case of simplicial meshes, and two other families in the case of cubical meshes. We make use of the exterior calculus and the Koszul complex to define and understand the spaces. These tools allow us to treat a wide variety of situations, which are often treated separately, in a unified fashion.Comment: To appear in: Analysis and Numerics of Partial Differential Equations, U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, eds., Springer 2013. v2: a few minor typos corrected. v3: a few more typo correction

Gauge Dependence of the High-Temperature 2-Loop Effective Potential for the Higgs Field

The high-temperature limit of the 2-loop effective potential for the Higgs field is calculated from an effective 3d theory, in a general covariant gauge. It is shown explicitly that a gauge-independent result can be extracted for the equation of state from the gauge-dependent effective potential. The convergence of perturbation theory is estimated in the broken phase, utilizing the gauge dependence of the effective potential.Comment: 13 LaTeX-pages + 2 ps-figure (Instructions added to uudecode the ps-file.

Equivariant singularity theory with distinguished parameters: Two case studies of resonant Hamiltonian systems

We consider Hamiltonian systems near equilibrium that can be (formally) reduced to one degree of freedom. Spatio-temporal symmetries play a key role. The planar reduction is studied by equivariant singularity theory with distinguished parameters. The method is illustrated on the conservative spring-pendulum system near resonance, where it leads to integrable approximations of the iso-energetic Poincaré map. The novelty of our approach is that we obtain information on the whole dynamics, regarding the (quasi-) periodic solutions, the global configuration of their invariant manifolds, and bifurcations of these.

Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness

In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of explaining the robustness of the phenotype structure is rephrased as a real geometrical problem on a fixed domain. We further suggest a generalization of path integrals that reduces the problem of deciding whether a given molecular network can generate specific phenotypes to a numerical property of a robustness function with complex output, for which we give heuristic justification. Finally, we use our formalism to interpret a pointedly quantitative developmental biology problem on the allowed number of pairs of legs in centipedes

Systematic study of the effect of short range correlations on the form factors and densities of s-p and s-d shell nuclei

Analytical expressions of the one- and two-body terms in the cluster expansion of the charge form factors and densities of the s-p and s-d shell nuclei with N=Z are derived. They depend on the harmonic oscillator parameter b and the parameter $\beta$ which originates from the Jastrow correlation function. These expressions are used for the systematic study of the effect of short range correlations on the form factors and densities and of the mass dependence of the parameters b and $\beta$. These parameters have been determined by fit to the experimental charge form factors. The inclusion of the correlations reproduces the experimental charge form factors at the high momentum transfers ($q\geq 2 1/fm$). It is found that while the parameter $\beta$ is almost constant for the closed shell nuclei, $^4$He, $^{16}$O and $^{40}$Ca, its values are larger (less correlated systems) for the open shell nuclei, indicating a shell effect in the closed shell nuclei.Comment: Latex, 21 pages, 6 figures, 1 tabl

The clustering of ultra-high energy cosmic rays and their sources

The sky distribution of cosmic rays with energies above the 'GZK cutoff' holds important clues to their origin. The AGASA data, although consistent with isotropy, shows evidence for small-angle clustering, and it has been argued that such clusters are aligned with BL Lacertae objects, implicating these as sources. It has also been suggested that clusters can arise if the cosmic rays come from the decays of very massive relic particles in the Galactic halo, due to the expected clumping of cold dark matter. We examine these claims and show that both are in fact not justified.Comment: 13 pages, 8 figures, version in press at Phys. Rev.

Joint resummation in electroweak boson production

We present a phenomenological application of the joint resummation formalism to electroweak annihilation processes at measured boson momentum Q_T. This formalism simultaneously resums at next-to-leading logarithmic accuracy large threshold and recoil corrections to partonic scattering. We invert the impact parameter transform using a previously described analytic continuation procedure. This leads to a well-defined, resummed perturbative cross section for all nonzero Q_T, which can be compared to resummation carried out directly in Q_T space. From the structure of the resummed expressions, we also determine the form of nonperturbative corrections to the cross section and implement these into our analysis. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Tevatron collider.Comment: 27 pages, LaTeX, 8 figures as eps files. Some additions to earlier version, this version as published in Phys. Rev. D66 (2002) 01401

Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure

Nuclear dependence coefficient α(A,qT)\alpha(A,q_T) for the Drell-Yan and J/ψ\psi production

Define the nuclear dependence coefficient $\alpha(A,q_T)$ in terms of ratio of transverse momentum spectrum in hadron-nucleus and in hadron-nucleon collisions: $\frac{d\sigma^{hA}}{dq_T^2}/ \frac{d\sigma^{hN}}{dq_T^2}\equiv A^{\alpha(A,q_T)}$. We argue that in small $q_T$ region, the $\alpha(A,q_T)$ for the Drell-Yan and J/$\psi$ production is given by a universal function:\ $a+b q_T^2$, where parameters a and b are completely determined by either calculable quantities or independently measurable physical observables. We demonstrate that this universal function $\alpha(A,q_T)$ is insensitive to the A for normal nuclear targets. For a color deconfined nuclear medium, the $\alpha(A,q_T)$ becomes strongly dependent on the A. We also show that our $\alpha(A,q_T)$ for the Drell-Yan process is naturally linked to perturbatively calculated $\alpha(A,q_T)$ at large $q_T$ without any free parameters, and the $\alpha(A,q_T)$ is consistent with E772 data for all $q_T$.Comment: latex, 28 pages, 10 figures, updated two figures, and add more discussion