Subcompact cardinals, squares, and stationary reflection

We generalise Jensen's result on the incompatibility of subcompactness with square. We show that alpha^+-subcompactness of some cardinal less than or equal to alpha precludes square_alpha, but also that square may be forced to hold everywhere where this obstruction is not present. The forcing also preserves other strong large cardinals. Similar results are also given for stationary reflection, with a corresponding strengthening of the large cardinal assumption involved. Finally, we refine the analysis by considering Schimmerling's hierarchy of weak squares, showing which cases are precluded by alpha^+-subcompactness, and again we demonstrate the optimality of our results by forcing the strongest possible squares under these restrictions to hold.Comment: 18 pages. Corrections and improvements from referee's report mad

The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis

The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping Reflection Principle, a consequence of PFA. While the results fall short of showing that MRP implies SCH, it will be shown that MRP implies that if SCH fails first at kappa then every stationary subset of S_{kappa^+}^omega = {a < kappa^+ : cf(a) = omega} reflects. It will also be demonstrated that MRP always fails in a generic extension by Prikry forcing.Comment: 7 page

Real-time extraction of growth rates from rotating substrates during molecular-beam epitaxy

We present a method for measuring molecular‐beam epitaxy growth rates in near real‐time on rotating substrates. This is done by digitizing a video image of the reflection high‐energy electron diffraction screen, automatically tracking and measuring the specular spot width, and using numerical techniques to filter the resulting signal. The digitization and image and signal processing take approximately 0.4 s to accomplish, so this technique offers the molecular‐beam epitaxy grower the ability to actively adjust growth times in order to deposit a desired layer thickness. The measurement has a demonstrated precision of approximately 2%, which is sufficient to allow active control of epilayer thickness by counting monolayers as they are deposited. When postgrowth techniques, such as frequency domain analysis, are also used, the reflection high‐energy electron diffraction measurement of layer thickness on rotating substrates improves to a precision of better than 1%. Since all of the components in the system described are commercially available, duplication is straightforward

Amplitude measurements of Faraday waves

A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the bifurcation diagrams exhibit a frequency independent scaling proportional to the wavelength. We also provide numerical simulations of the full Navier-Stokes equations, which are in quantitative agreement up to supercritical drive amplitudes of 20%. The validity of an existing perturbation analysis is found to be limited to 2.5% overcriticaly.Comment: 7 figure

Numerical simulation of prominence oscillations

We present numerical simulations, obtained with the Versatile Advection Code, of the oscillations of an inverse polarity prominence. The internal prominence equilibrium, the surrounding corona and the inert photosphere are well represented. Gravity and thermodynamics are not taken into account, but it is argued that these are not crucial. The oscillations can be understood in terms of a solid body moving through a plasma. The mass of this solid body is determined by the magnetic field topology, not by the prominence mass proper. The model also allows us to study the effect of the ambient coronal plasma on the motion of the prominence body. Horizontal oscillations are damped through the emission of slow waves while vertical oscillations are damped through the emission of fast waves.Comment: 12 pages, 14 figures, accepted by Astronomy and Astrophysic

Quantum Mesoscopic Scattering: Disordered Systems and Dyson Circular Ensembles

We consider elastic reflection and transmission of electrons by a disordered system characterized by a $2N\!\times\!2N$ scattering matrix $S$. Expressing $S$ in terms of the $N$ radial parameters and of the four $N\!\times\!N$ unitary matrices used for the standard transfer matrix parametrization, we calculate their probability distributions for the circular orthogonal (COE) and unitary (CUE) Dyson ensembles. In this parametrization, we explicitely compare the COE--CUE distributions with those suitable for quasi--$1d$ conductors and insulators. Then, returning to the usual eigenvalue--eigenvector parametrization of $S$, we study the distributions of the scattering phase shifts. For a quasi--$1d$ metallic system, microscopic simulations show that the phase sift density and correlation functions are close to those of the circular ensembles. When quasi--$1d$ longitudinal localization breaks $S$ into two uncorrelated reflection matrices, the phase shift form factor $b(k)$ exhibits a crossover from a behavior characteristic of two uncoupled COE--CUE (small $k$) to a single COE--CUE behavior (large $k$). Outside quasi--one dimension, we find that the phase shift density is no longer uniform and $S$ remains nonzero after disorder averaging. We use perturbation theory to calculate the deviations to the isotropic Dyson distributions. When the electron dynamics is noComment: 39 pages, 14 figures available under request, RevTex, IPNO/TH 94-6