Mass and momentum conservation of the least-squares spectral collocation method for the Navier-Stokes equations

From the literature, it is known that the Least-Squares Spectral Element Method (LSSEM) for the stationary Stokes equations performs poorly with respect to mass conservation but compensates this lack by a superior conservation of momentum. Furthermore, it is known that the Least-Squares Spectral Collocation Method (LSSCM) leads to superior conservation of mass and momentum for the stationary Stokes equations. In the present paper, we consider mass and momentum conservation of the LSSCM for time-dependent Stokes and Navier-Stokes equations. We observe that the LSSCM leads to improved conservation of mass (and momentum) for these problems. Furthermore, the LSSCM leads to the well-known time-dependent profiles for the velocity and the pressure profiles. To obtain these results, we use only a few elements, each with high polynomial degree, avoid normal equations for solving the overdetermined linear systems of equations and introduce the Clenshaw-Curtis quadrature rule for imposing the average pressure to be zero. Furthermore, we combined the transformation of Gordon and Hall (transfinite mapping) with the least-squares spectral collocation scheme to discretize the internal flow problems.     

Photosynthetic energy conversion in the diatom <Emphasis Type="Italic">Phaeodactylum tricornutum</Emphasis>

Isothermal microcalorimetry can be used to investigate the photosynthetic energy conversion of autotrophic organisms. In this study, for the first time a diatom alga was used to compare the calorimetrically measured heat flux with measurements of the photosynthetic performance by oxygen evolution and pulse-amplitude modulated fluorescence. The presented experimental setup proved suitable to compare calorimetric data with those of conventional methods of the determination of photosynthesis rates. Special attention was paid to the contribution of energy dissipation via non-photochemical quenching (NPQ) of chlorophyll fluorescence to the metabolic energy balance. This was achieved by a combination of different light conditions and the use of an inhibitor of NPQ. Although NPQ is an important photoprotective mechanism in diatoms, the inhibition of NPQ resulted in an activation of alternative, energy dissipating pathways for absorbed radiation which completely compensated for the fraction of energy dissipation by NPQ.     

Non-local order in Mott insulators,duality and Wilson loops

It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local ‘parity order parameter’ which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M.C. Bañuls, L. Pollet, I. Bloch, et al., Science 334 (2011) 200]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U(1)$U\left(1\right)$ gauge theory in 2+1$2+1$ dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.     

L-Uniqueness of regularized 2D-Euler and stochastic Navier-Stokes equations

A regularization of the 2D-Euler equation with periodic boundary conditions is introduced, having the same infinitesimal invariants as the Euler equation. A flow of measure-preserving transformations is constructed on L¹-spaces induced by the Gaussian measure with covariance given by the inverse of the enstrophy and it is shown that this flow is the only measure-preserving flow inducing a strongly continuous semigroup on the corresponding L¹-space. We also prove similar uniqueness results for a corresponding class of regularized stochastic 2D-Navier-Stokes equations.