Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions

In this paper we prove an optimal error estimate for the H(curl)-conforming projection based p-interpolation operator introduced in [L. Demkowicz and I. Babuska, p interpolation error estimates for edge finite elements of variable order in two dimensions, SIAM J. Numer. Anal., 41 (2003), pp. 1195-1208]. This result is proved on the reference element (either triangle or square) K for regular vector fields in H^r(curl,K) with arbitrary r>0. The formulation of the result in the H(div)-conforming setting, which is relevant for the analysis of high-order boundary element approximations for Maxwell's equations, is provided as well

Universal Spin Transport in a Strongly Interacting Fermi Gas

Transport of fermions is central in many elds of physics. Electron transport runs modern technology, de ning states of matter such as superconductors and insulators, and electron spin, rather than charge, is being explored as a new carrier of information [1]. Neutrino transport energizes supernova explosions following the collapse of a dying star [2], and hydrodynamic transport of the quark-gluon plasma governed the expansion of the early Universe [3]. However, our understanding of non-equilibrium dynamics in such strongly interacting fermionic matter is still limited. Ultracold gases of fermionic atoms realize a pristine model for such systems and can be studied in real time with the precision of atomic physics [4, 5]. It has been established that even above the super uid transition such gases ow as an almost perfect uid with very low viscosity [3, 6] when interactions are tuned to a scattering resonance. However, here we show that spin currents, as opposed to mass currents, are maximally damped, and that interactions can be strong enough to reverse spin currents, with opposite spin components reflecting off each other. We determine the spin drag coefficient, the spin di usivity, and the spin susceptibility, as a function of temperature on resonance and show that they obey universal laws at high temperatures. At low temperatures, the spin di usivity approaches a minimum value set by ħ/m, the quantum limit of di usion, where ħ is the reduced Planck's constant and m the atomic mass. For repulsive interactions, our measurements appear to exclude a metastable ferromagnetic state [7{9].National Science Foundation (U.S.)United States. Office of Naval ResearchUnited States. Army Research Office (DARPA OLE programme)Alfred P. Sloan FoundationUnited States. Air Force Office of Scientific Research. Multidisciplinary University Research InitiativeUnited States. Army Research Office. Multidisciplinary University Research InitiativeUnited States. Defense Advanced Research Projects Agency. Young Faculty AwardDavid & Lucile Packard Foundatio