Role of Li_2B_(12)H_(12) for the Formation and Decomposition of LiBH_4

By in situ X-ray diffraction (XRD) and nuclear magnetic resonance (NMR) spectroscopy, the role of Li_2B_(12)H_(12) for the sorption of LiBH_4 is analyzed. We demonstrate that Li_2B_(12)H_(12) and an amorphous Li_2B_(10)H_(10) phase are formed by the reaction of LiBH_4 with diborane (B_2H_6) at 200 °C. Based on our present results, we propose that the Li -2B - (12)H_(12) formation in the desorption of LiBH_4 can be explained as a result of reaction of diborane and LiBH_4. This reaction of the borohydride with diborane may also be observed for other borohydrides, where B_(12)H_(12) phases are found during decomposition

Symmetric hyperbolic systems for Bianchi equations

We obtain a family of first-order symmetric hyperbolic systems for the Bianchi equations. They have only physical characteristics: the light cone and timelike hypersurfaces. In the proof of the hyperbolicity, new positivity properties of the Bel tensor are used.Comment: latex, 7 pages, accepted for publication in Class. Quantum Gra

Polynomials for Crystal Frameworks and the Rigid Unit Mode Spectrum

To each discrete translationally periodic bar-joint framework \C in \bR^d we associate a matrix-valued function \Phi_\C(z) defined on the d-torus. The rigid unit mode spectrum \Omega(\C) of \C is defined in terms of the multi-phases of phase-periodic infinitesimal flexes and is shown to correspond to the singular points of the function z \to \rank \Phi_\C(z) and also to the set of wave vectors of harmonic excitations which have vanishing energy in the long wavelength limit. To a crystal framework in Maxwell counting equilibrium, which corresponds to \Phi_\C(z) being square, the determinant of \Phi_\C(z) gives rise to a unique multi-variable polynomial p_\C(z_1,\dots,z_d). For ideal zeolites the algebraic variety of zeros of p_\C(z) on the d-torus coincides with the RUM spectrum. The matrix function is related to other aspects of idealised framework rigidity and flexibility and in particular leads to an explicit formula for the number of supercell-periodic floppy modes. In the case of certain zeolite frameworks in dimensions 2 and 3 direct proofs are given to show the maximal floppy mode property (order $N$). In particular this is the case for the cubic symmetry sodalite framework and some other idealised zeolites.Comment: Final version with new examples and figures, and with clearer streamlined proof

Assimilating bio-optical glider data during a phytoplankton bloom in the southern Ross Sea

The Ross Sea is a region characterized by high primary productivity in comparison to other Antarctic coastal regions, and its productivity is marked by considerable variability both spatially (1-50 km) and temporally (days to weeks). This variability presents a challenge for inferring phytoplankton dynamics from observations that are limited in time or space, which is often the case due to logistical limitations of sampling. To better understand the spatio-temporal variability in Ross Sea phytoplankton dynamics and to determine how restricted sampling may skew dynamical interpretations, high-resolution bio-optical glider measurements were assimilated into a one-dimensional biogeochemical model adapted for the Ross Sea. The assimilation of data from the entire glider track using the micro-genetic and local search algorithms in the Marine Model Optimization Testbed improves the model-data fit by similar to 50 %, generating rates of integrated primary production of 104 g C m(-2) yr(-1) and export at 200 m of 27 g C m(-2) yr(-1). Assimilating glider data from three different latitudinal bands and three different longitudinal bands results in minimal changes to the simulations, improves the model-data fit with respect to unassimilated data by similar to 35 %, and confirms that analyzing these glider observations as a time series via a one-dimensional model is reasonable on these scales. Whereas assimilating the full glider data set produces well-constrained simulations, assimilating subsampled glider data at a frequency consistent with cruise-based sampling results in a wide range of primary production and export estimates. These estimates depend strongly on the timing of the assimilated observations, due to the presence of high mesoscale variability in this region. Assimilating surface glider data subsampled at a frequency consistent with available satellite-derived data results in 40% lower carbon export, primarily resulting from optimized rates generating more slowly sinking diatoms. This analysis highlights the need for the strategic consideration of the impacts of data frequency, duration, and coverage when combining observations with biogeochemical modeling in regions with strong mesoscale variability

On hybrid states of two and three level atoms

We calculate atom-photon resonances in the Wigner-Weisskopf model, admitting two photons and choosing a particular coupling function. We also present a rough description of the set of resonances in a model for a three-level atom coupled to the photon field. We give a general picture of matter-field resonances these results fit into.Comment: 33 pages, 12 figure

On the Theory of Superfluidity in Two Dimensions

The superfluid phase transition of the general vortex gas, in which the circulations may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence of a superfluid phase is shown. When the net circulation of the vortices vanishes, the presence of off-diagonal long range order is demonstrated and the existence of an order parameter is proposed. The transition temperature for the general vortex gas is shown to be the Kosterlitz---Thouless temperature. An upper bound for the average vortex number density is established for the general vortex gas and an exact expression is derived for the Kosterlitz---Thouless ensemble.Comment: 22 pages, one figure, written in plain TeX, published in J. Phys. A24 (1991) 502

Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $\epsilon$-away below the two-boson threshold) spectrum of Fr\"ohlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{(0)}$, where $G^{(0)}\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated