L^{2}-restriction bounds for eigenfunctions along curves in the quantum completely integrable case

We show that for a quantum completely integrable system in two dimensions,the $L^{2}$-normalized joint eigenfunctions of the commuting semiclassical pseudodifferential operators satisfy restriction bounds ofthe form $\int_{\gamma} |\phi_{j}^{\hbar}|^2 ds = {\mathcal O}(|\log \hbar|)$ for generic curves $\gamma$ on the surface. We also prove that the maximal restriction bounds of Burq-Gerard-Tzvetkov are always attained for certain exceptional subsequences of eigenfunctions.Comment: Correct some typos and added some more detail in section

A Marine Biology Laboratory Facility and Course of Instruction at an Inland University

Author Institution: Department of Biology, Bowling Green State University, Bowling Green, OhioThe development of an easily maintained marine biological facility, with artificial sea water and adequate filtration systems, has made possible a course of instruction in marine biology at an inland university. The laboratory facility and the instructional program are described in detail so that individuals at other institutions can adapt desirable elements to instructional and research use

Stellar winds, dead zones, and coronal mass ejections

Axisymmetric stellar wind solutions are presented, obtained by numerically solving the ideal magnetohydrodynamic (MHD) equations. Stationary solutions are critically analysed using the knowledge of the flux functions. These flux functions enter in the general variational principle governing all axisymmetric stationary ideal MHD equilibria. The magnetized wind solutions for (differentially) rotating stars contain both a `wind' and a `dead' zone. We illustrate the influence of the magnetic field topology on the wind acceleration pattern, by varying the coronal field strength and the extent of the dead zone. This is evident from the resulting variations in the location and appearance of the critical curves where the wind speed equals the slow, Alfven, and fast speed. Larger dead zones cause effective, fairly isotropic acceleration to super-Alfvenic velocities as the polar, open field lines are forced to fan out rapidly with radial distance. A higher field strength moves the Alfven transition outwards. In the ecliptic, the wind outflow is clearly modulated by the extent of the dead zone. The combined effect of a fast stellar rotation and an equatorial `dead' zone in a bipolar field configuration can lead to efficient thermo-centrifugal equatorial winds. Such winds show both a strong poleward collimation and some equatorward streamline bending due to significant toroidal field pressure at mid-latitudes. We discuss how coronal mass ejections are then simulated on top of the transonic outflows.Comment: scheduled for Astrophys. J. 530 #2, Febr.20 2000 issue. 9 figures (as 6 jpeg and 8 eps files

Trends in Elasticity and Electronic Structure of Transition-Metal Nitrides and Carbides from First Principles

The elastic properties of the $B_1$-structured transition-metal nitrides and their carbide counterparts are studied using the {\it ab initio\} density functional perturbation theory. The linear response results of elastic constants are in excellent agreement with those obtained from numerical derivative methods, and are also consistent with measured data. We find the following trends: (1) Bulk moduli $B$ and tetragonal shear moduli $G^{\prime}=(C_{11}-C_{12})/2$, increase and lattice constants $a_{0}$ decrease rightward or downward on the Periodic Table for the metal component or if C is replaced by N; (2) The inequality $B > G^{\prime} > G > 0$ holds for $G=C_{44}$; (3) $G$ depends strongly on the number of valence electrons per unit cell ($Z_{V}$). From the fitted curve of $G$ as a function of $Z_{V}$, we can predict that MoN is unstable in $B_{1}$ structure, and transition-metal carbonitrides ($e.g.$ ZrC$_{x}$N$_{1-x}$) and di-transition-metal carbides ($e.g.$ Hf$_{x}$Ta$_{1-x}$C) have maximum $G$ at $Z_{V} \approx 8.3$.Comment: 4 pages, 2 figures, submitted to PRL. 2 typos in ref. 15 were correcte

Algebraic volume density property of affine algebraic manifolds

We introduce the notion of algebraic volume density property for affine algebraic manifolds and prove some important basic facts about it, in particular that it implies the volume density property. The main results of the paper are producing two big classes of examples of Stein manifolds with volume density property. One class consists of certain affine modifications of \C^n equipped with a canonical volume form, the other is the class of all Linear Algebraic Groups equipped with the left invariant volume form.Comment: 35 page

Quantum dynamics, dissipation, and asymmetry effects in quantum dot arrays

We study the role of dissipation and structural defects on the time evolution of quantum dot arrays with mobile charges under external driving fields. These structures, proposed as quantum dot cellular automata, exhibit interesting quantum dynamics which we describe in terms of equations of motion for the density matrix. Using an open system approach, we study the role of asymmetries and the microscopic electron-phonon interaction on the general dynamical behavior of the charge distribution (polarization) of such systems. We find that the system response to the driving field is improved at low temperatures (and/or weak phonon coupling), before deteriorating as temperature and asymmetry increase. In addition to the study of the time evolution of polarization, we explore the linear entropy of the system in order to gain further insights into the competition between coherent evolution and dissipative processes.Comment: 11pages,9 figures(eps), submitted to PR

Rheology of distorted nematic liquid crystals

We use lattice Boltzmann simulations of the Beris--Edwards formulation of nematodynamics to probe the response of a nematic liquid crystal with conflicting anchoring at the boundaries under shear and Poiseuille flow. The geometry we focus on is that of the hybrid aligned nematic (HAN) cell, common in devices. In the nematic phase, backflow effects resulting from the elastic distortion in the director field render the velocity profile strongly non-Newtonian and asymmetric. As the transition to the isotropic phase is approached, these effects become progressively weaker. If the fluid is heated just above the transition point, however, another asymmetry appears, in the dynamics of shear band formation.Comment: 7 pages, 4 figures. Accepted for publication in Europhys. Let

Athena: A New Code for Astrophysical MHD

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher-order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume-averages for mass, momentum, and energy, and face-centered area-averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally-split time advance, and (3) the extension to MHD of two different dimensionally-unsplit integration methods. Implementation of the algorithm in both C and Fortran95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web.Comment: 61 pages, 36 figures. accepted by ApJ

Spin-Orbit-Induced Orbital Excitations in Sr2RuO4 and Ca2RuO4: A Resonant Inelastic X-ray Scattering Study

High-resolution resonant inelastic X-ray scattering (RIXS) at the oxygen K-edge has been used to study the orbital excitations of Ca2RuO4 and Sr2RuO4. In combination with linear dichroism X-ray absorption spectroscopy, the ruthenium 4d-orbital occupation and excitations were probed through their hybridization with the oxygen p-orbitals. These results are described within a minimal model, taking into account crystal field splitting and a spin-orbit coupling \lambda_{so}=200~meV. The effects of spin-orbit interaction on the electronic structure and implications for the Mott and superconducting ground states of (Ca,Sr)2RuO4 are discussed.Comment: accepted in PRB 201