Regularity of weak minimizers of the K-energy and applications to properness and K-stability

Let $(X,\omega)$ be a compact K\"ahler manifold and $\mathcal H$ the space of K\"ahler metrics cohomologous to $\omega$. If a cscK metric exists in $\mathcal H$, we show that all finite energy minimizers of the extended K-energy are smooth cscK metrics, partially confirming a conjecture of Y.A. Rubinstein and the second author. As an immediate application, we obtain that existence of a cscK metric in $\mathcal H$ implies J-properness of the K-energy, thus confirming one direction of a conjecture of Tian. Exploiting this properness result we prove that an ample line bundle $(X,L)$ admitting a cscK metric in $c_1(L)$ is $K$-polystable.Comment: v1 Comments welcome v2 New introduction and references added v3 Final version. Preliminaries section added. Some notation changed. No other change

Effects of motion on jet exhaust noise from aircraft

The various problems involved in the evaluation of the jet noise field prevailing between an observer on the ground and an aircraft in flight in a typical takeoff or landing approach pattern were studied. Areas examined include: (1) literature survey and preliminary investigation, (2) propagation effects, (3) source alteration effects, and (4) investigation of verification techniques. Sixteen problem areas were identified and studied. Six follow-up programs were recommended for further work. The results and the proposed follow-on programs provide a practical general technique for predicting flyover jet noise for conventional jet nozzles

Direct comparison of Viking 2.3-GHz signal phase fluctuation and columnar electron density between 2 and 160 solar radii

The relationship between solar wind induced signal phase fluctuation and solar wind columnar electron density has been the subject of intensive analysis during the last two decades. In this article, a sizeable volume of 2.3-GHz signal phase fluctuation and columnar electron density measurements separately and concurrently inferred from Viking spacecraft signals are compared as a function of solar geometry. These data demonstrate that signal phase fluctuation and columnar electron density are proportional over a very wide span of solar elongation angle. A radially dependent electron density model which provides a good fit to the columnar electron density measurements and, when appropriately scaled, to the signal phase fluctuation measurements, is given. This model is also in good agreement with K-coronameter observations at 2 solar radii (2r0), with pulsar time delay measurements at 10r0, and with spacecraft in situ electron density measurements at 1 AU

Dynamical Stability and Quantum Chaos of Ions in a Linear Trap

The realization of a paradigm chaotic system, namely the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev

Doppler cooling with coherent trains of laser pulses and tunable "velocity comb"

We explore the possibility of decelerating and Doppler cooling of an ensemble of two-level atoms by a coherent train of short, non-overlapping laser pulses. We develop a simple analytical model for dynamics of a two-level system driven by the resulting frequency comb field. We find that the effective scattering force mimics the underlying frequency comb structure. The force pattern depends strongly on the ratio of the atomic lifetime to the repetition time and pulse area. For example, in the limit of short lifetimes, the frequency peaks of the optical force wash out. We show that laser cooling with pulse trains results in a "velocity comb", a series of narrow peaks in the velocity space

A Bell pair in a generic random matrix environment

Two non-interacting qubits are coupled to an environment. Both coupling and environment are represented by random matrix ensembles. The initial state of the pair is a Bell state, though we also consider arbitrary pure states. Decoherence of the pair is evaluated analytically in terms of purity; Monte Carlo calculations confirm these results and also yield the concurrence of the pair. Entanglement within the pair accelerates decoherence. Numerics display the relation between concurrence and purity known for Werner states, allowing us to give a formula for concurrence decay.Comment: 4 pages, 3 figure

Maximally Entangled Mixed States and Conditional Entropies

The maximally entangled mixed states of Munro, James, White, and Kwiat [Phys. Rev. A {\bf 64} (2001) 030302] are shown to exhibit interesting features vis a vis conditional entropic measures. The same happens with the Ishizaka and Hiroshima states [Phys. Rev. A {\bf 62} 022310 (2000)], whose entanglement-degree can not be increased by acting on them with logic gates. Special types of entangled states that do not violate classical entropic inequalities are seen to exist in the space of two qubits. Special meaning can be assigned to the Munro {\it et al.} special participation ratio of 1.8

Study of stability and control moment gyro wobble damping of flexible, spinning space stations

An executive summary and an analysis of the results are discussed. A user's guide for the digital computer program that simulates the flexible, spinning space station is presented. Control analysis activities and derivation of dynamic equations of motion and the modal analysis are also cited

Derivation of Internally-Consistent Thermodynamic Data by the Technique of Mathematical Programming: a Review with Application the System MgO-SiO2-H2O

The problem of deriving an optimal set of thermodynamic properties of minerals from a diverse experimental data base is reviewed and a preferred methodology proposed. Mathematical pro-gramming(MAP) methods extend the linear programming (LIP) approach first presented by Gordon (1973), and make it possible to account for the type of information conveyed, and the uncertainties attending both phase equilibrium data and direct measurements of phase properties. For phase equilibrium data which are (in most cases) characterized by non-normal error distributions across experimental brackets, the midpoint of a bracket is no more probable than other points, and the data are best treated by considering the inequality in the change in Gibbs free energy of reaction at each half-bracket. Direct measurements of phase properties can be assumed to have approximately normal error distributions, and the MAP technique optimizes agreement with these values by using the principles of least squares in the definition of an objective function. The structure of this problem, treatment of uncertainties in various types of experimental data, and method of optimizing final solutions are discussed in some detail. The method is applied to experimental data in the MgO-SiO2-H2O system, where inconsistencies among the data are resolved and an optimal set of thermodynamic properties is presented. The derived standard state entropies and volumes agree with all direct measurements (within their uncertainties), as do enthalpies of formation from the elements except for those of talc (+16 kJ mol−1), anthophyllite (+ 14 kJ mol−1), and brucite (−1 kJ mol−1). Stable phase relations in the system have the topology predicted by Greenwood (1963, 1971), with quartz- and forsterite-absent invariant points at 683 °C-6-4 kb and 797 °C-12 kb respectively, repeating at 552 °C-120 b and 550 °C-55 b. The thermodynamic analysis indicates little remaining flexibility in the phase relations, which, when combined with suitable activity models for solid solution, should allow for accurate determination of the conditions of metamorphism of ultramafic rock