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

Detecting phonons and persistent currents in toroidal Bose-Einstein condensates by means of pattern formation

We theoretically investigate the dynamic properties of a Bose-Einstein condensate in a toroidal trap. A periodic modulation of the transverse confinement is shown to produce a density pattern due to parametric amplification of phonon pairs. By imaging the density distribution after free expansion one obtains i) a precise determination of the Bogoliubov spectrum and ii) a sensitive detection of quantized circulation in the torus. The parametric amplification is also sensitive to thermal and quantum fluctuations.Comment: 4 pages, 4 figures; new figures, revised version to appear as a Rapid Communication in Physical Review

Fluctuations from dissipation in a hot non-Abelian plasma

We consider a transport equation of the Boltzmann-Langevin type for non-Abelian plasmas close to equilibrium to derive the spectral functions of the underlying microscopic fluctuations from the entropy. The correlator of the stochastic source is obtained from the dissipative processes in the plasma. This approach, based on classical transport theory, exploits the well-known link between a linearized collision integral, the entropy and the spectral functions. Applied to the ultra-soft modes of a hot non-Abelian (classical or quantum) plasma, the resulting spectral functions agree with earlier findings obtained from the microscopic theory. As a by-product, it follows that B\"odeker's effective theory is consistent with the fluctuation-dissipation theorem.Comment: 9 pages, revtex, no figures, identical to published versio

Spatial and Temporal Habitat Use of an Asian Elephant in Sumatra

Increasingly, habitat fragmentation caused by agricultural and human development has forced Sumatran elephants into relatively small areas, but there is little information on how elephants use these areas and thus, how habitats can be managed to sustain elephants in the future. Using a Global Positioning System (GPS) collar and a land cover map developed from TM imagery, we identified the habitats used by a wild adult female elephant (Elephas maximus sumatranus) in the Seblat Elephant Conservation Center, Bengkulu Province, Sumatra during 2007–2008. The marked elephant (and presumably her 40–60 herd mates) used a home range that contained more than expected medium canopy and open canopy land cover. Further, within the home range, closed canopy forests were used more during the day than at night. When elephants were in closed canopy forests they were most often near the forest edge vs. in the forest interior. Effective elephant conservation strategies in Sumatra need to focus on forest restoration of cleared areas and providing a forest matrix that includes various canopy types

Effective Kinetic Theory for High Temperature Gauge Theories

Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature $T$) can be described by an effective kinetic theory, valid on sufficiently large time and distance scales. The appropriate Boltzmann equations depend on effective scattering rates for various types of collisions that can occur in the plasma. The resulting effective kinetic theory may be used to evaluate observables which are dominantly sensitive to the dynamics of typical ultrarelativistic excitations. This includes transport coefficients (viscosities and diffusion constants) and energy loss rates. We show how to formulate effective Boltzmann equations which will be adequate to compute such observables to leading order in the running coupling $g(T)$ of high-temperature gauge theories [and all orders in $1/\log g(T)^{-1}$]. As previously proposed in the literature, a leading-order treatment requires including both $22$ particle scattering processes as well as effective ``$12$'' collinear splitting processes in the Boltzmann equations. The latter account for nearly collinear bremsstrahlung and pair production/annihilation processes which take place in the presence of fluctuations in the background gauge field. Our effective kinetic theory is applicable not only to near-equilibrium systems (relevant for the calculation of transport coefficients), but also to highly non-equilibrium situations, provided some simple conditions on distribution functions are satisfied.Comment: 40 pages, new subsection on soft gauge field instabilities adde

Pesin's Formula for Random Dynamical Systems on RdR^d

Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure which is absolutely continuous with respect to the Lebesgue measure. We will show that this formula remains true for random dynamical systems on $R^d$ which have an invariant probability measure absolutely continuous to the Lebesgue measure on $R^d$. Finally we will show that a broad class of stochastic flows on $R^d$ of a Kunita type satisfies Pesin's formula.Comment: 35 page

Analytic linearization of nonlinear perturbations of Fuchsian systems

Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the case when the linear part has commuting monodromy, and the eigenvalues have positive real parts, there exists a unique correction function of the nonlinear part so that the corrected system becomes analytically linearizable

Looking for CP Violation in W Production and Decay

We describe CP violating observables in resonant $W^\pm$ and $W^\pm$ plus one jet production at the Tevatron. We present simple examples of CP violating effective operators, consistent with the symmetries of the Standard Model, which would give rise to these observables. We find that CP violating effects coming from new physics at the $TeV$ scale could in principle be observable at the Tevatron with $10^6$ $W^\pm$ decays.Comment: 15 pgs with standard LATEX, 7 ps figures embedded with eps

Demonstration of an inductively coupled ring trap for cold atoms

We report the first demonstration of an inductively coupled magnetic ring trap for cold atoms. A uniform, ac magnetic field is used to induce current in a copper ring, which creates an opposing magnetic field that is time-averaged to produce a smooth cylindrically symmetric ring trap of radius 5 mm. We use a laser-cooled atomic sample to characterize the loading efficiency and adiabaticity of the magnetic potential, achieving a vacuum-limited lifetime in the trap. This technique is suitable for creating scalable toroidal waveguides for applications in matter-wave interferometry, offering long interaction times and large enclosed areas

Generalized Boltzmann equations for on-shell particle production in a hot plasma

A novel refinement of the conventional treatment of Kadanoff--Baym equations is suggested. Besides the Boltzmann equation another differential equation is used for calculating the evolution of the non-equilibrium two-point function. Although it was usually interpreted as a constraint on the solution of the Boltzmann equation, we argue that its dynamics is relevant to the determination and resummation of the particle production cut contributions. The differential equation for this new contribution is illustrated in the example of the cubic scalar model. The analogue of the relaxation time approximation is suggested. It results in the shift of the threshold location and in smearing out of the non-analytic threshold behaviour of the spectral function. Possible consequences for the dilepton production are discussed.Comment: 22 pages, latex, 2 ps figure