More ergodic billiards with an infinite cusp

In a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f: [0, +\infty) \longrightarrow (0, +\infty)$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.Comment: 13 pages, 4 figure

Sub-Doppler resonances in the back-scattered light from random porous media infused with Rb vapor

We report on the observation of sub-Doppler resonances on the back-scattered light from a random porous glass medium with rubidium vapor filling its interstices. The sub-Doppler spectral lines are the consequence of saturated absorption where the incident laser beam saturates the atomic medium and the back-scattered light probes it. Some specificities of the observed spectra reflect the transient atomic evolution under confinement inside the pores. Simplicity, robustness and potential miniaturization are appealing features of this system as a spectroscopic reference.Comment: 6 pages, 4 figure

Escape Orbits for Non-Compact Flat Billiards

It is proven that, under some conditions on $f$, the non-compact flat billiard $\Omega = \{ (x,y) \in \R_0^{+} \times \R_0^{+};\ 0\le y \le f(x) \}$ has no orbits going {\em directly} to $+\infty$. The relevance of such sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at http://www.princeton.edu/~marco/papers/ . Minor changes since previously posted version. Submitted to 'Chaos

Magnetometer suitable for Earth field measurement based on transient atomic response

We describe the development of a simple atomic magnetometer using $^{87}$Rb vapor suitable for Earth magnetic field monitoring. The magnetometer is based on time-domain determination of the transient precession frequency of the atomic alignment around the measured field. A sensitivity of 1.5 nT/$\sqrt{Hz}$ is demonstrated on the measurement of the Earth magnetic field in the laboratory. We discuss the different parameters determining the magnetometer precision and accuracy and predict a sensitivity of 30 pT/$\sqrt{Hz}$Comment: 6 pages, 5 figure

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.Comment: Final version for J. Stat. Phys., 18 pages, 4 figure

Semantic priming study of Russian aspect and resultativity

This paper reports four priming experiments, in which resultative, processual, and delimitative Russian verbs were tested. The experiments were based on the semantic decision task: the participants had to decide whether the target denoted an event / situation with a clear outcome. To assess the impact of morphological cues on the decision latencies, verbs of different morphological complexity (prefixed and unprefixed perfectives) were used. The results obtained suggest that the aspectual feature of resultativity is consistently exploited in semantic priming (processual targets were primed in two experiments), and that the morphological cues facilitate the identification of resultative targets (prefixed perfectives exhibited faster decision latencies than unprefixed perfectives). As far as the delimitative forms are concerned, a category-induction experiment was designed to investigate the subjects’ tendency to group them with resultatives or with processuals, since the delimitatives represent an in-between category. The proportion of yes/no answers confirmed that the speakers place the delimitatives between these two domains, but much closer to the processuals than to the resultatives. These findings support the distinction of boundedness vs. telicity from both the theoretical and the behavioural perspective. The fact that the resultative interpretation of the delimitatives was not ruled out completely for most verbs suggests that, when certain conditions are met (when no cognate resultative form is readily available and when the delimitative is frequent enough), the delimitative can be conceptualized as the perfective counterpart of the basic imperfective, thus taking on the prototypical perfective role (resultativity)

Effective Forchheimer Coefficient for Layered Porous Media

Inertial flow in porous media, governed by the Forchheimer equation, is affected by domain heterogeneity at the field scale. We propose a method to derive formulae of the effective Forchheimer coefficient with application to a perfectly stratified medium. Consider uniform flow under a constant pressure gradient Delta P/L in a layered permeability field with a given probability distribution. The local Forchheimer coefficient beta is related to the local permeability k via the relation beta = a/k(c), where a > 0 being a constant and c is an element of [0, 2]. Under ergodicity, an effective value of beta is derived for flow (i) perpendicular and (ii) parallel to layers. Expressions for effective Forchheimer coefficient, beta(e), generalize previous formulations for discrete permeability variations. Closed-form beta(e) expressions are derived for flow perpendicular to layers and under two limit cases, F << 1 and F >> 1, for flow parallel to layering, with F a Forchheimer number depending on the pressure gradient. For F of order unity, beta(e) is obtained numerically: when realistic values of Delta P/L and a are adopted, beta(e) approaches the results valid for the high Forchheimer approximation. Further, beta(e) increases with heterogeneity, with values always larger than those it would take if the beta - k relationship was applied to the mean permeability; it increases (decreases) with increasing (decreasing) exponent c for flow perpendicular (parallel) to layers. beta(e) is also moderately sensitive to the permeability distribution, and is larger for the gamma than for the lognormal distribution