Fluid jet amplifier Patent

Fluid control jet amplifier

The Surface Region of Superfluid 4^4He as a Dilute Bose-Condensed Gas

In the low-density surface region of superfluid $^4$He, the atoms are far apart and collisions can be ignored. The only effect of the interactions is from the long-range attractive Hartree potential produced by the distant high-density bulk liquid. As a result, at $T=0$, all the atoms occupy the same single-particle state in the low-density tail. Striking numerical evidence for this 100\% surface BEC was given by Pandharipande and coworkers in 1988. We derive a generalized Gross-Pitaevskii equation for the inhomogeneous condensate wave function $\Phi(z)$ in the low-density region valid at all temperatures. The overall amplitude of $\Phi(z)$ is fixed by the bulk liquid, which ensures that it vanishes everywhere at the bulk transition temperature.Comment: 6 pages, paper submitted to Low Temperature Conference (LT21), Prague, Aug., 1996; to appear in proceeding

Small and Large Time Stability of the Time taken for a L\'evy Process to Cross Curved Boundaries

This paper is concerned with the small time behaviour of a L\'{e}vy process $X$. In particular, we investigate the {\it stabilities} of the times, \Tstarb(r) and \Tbarb(r), at which $X$, started with $X_0=0$, first leaves the space-time regions $\{(t,y)\in\R^2: y\le rt^b, t\ge 0\}$ (one-sided exit), or $\{(t,y)\in\R^2: |y|\le rt^b, t\ge 0\}$ (two-sided exit), $0\le b<1$, as r\dto 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in $L^p$. In many instances these are seen to be equivalent to relative stability of the process $X$ itself. The analogous large time problem is also discussed

Stability of the Exit Time for L\'evy Processes

This paper is concerned with the behaviour of a L\'{e}vy process when it crosses over a positive level, $u$, starting from 0, both as $u$ becomes large and as $u$ becomes small. Our main focus is on the time, $\tau_u$, it takes the process to transit above the level, and in particular, on the {\it stability} of this passage time; thus, essentially, whether or not $\tau_u$ behaves linearly as u\dto 0 or $u\to\infty$. We also consider conditional stability of $\tau_u$ when the process drifts to $-\infty$, a.s. This provides information relevant to quantities associated with the ruin of an insurance risk process, which we analyse under a Cram\'er condition

Astrometric orbits of SB9 stars

Hipparcos Intermediate Astrometric Data (IAD) have been used to derive astrometric orbital elements for spectroscopic binaries from the newly released Ninth Catalogue of Spectroscopic Binary Orbits (SB9). Among the 1374 binaries from SB9 which have an HIP entry, 282 have detectable orbital astrometric motion (at the 5% significance level). Among those, only 70 have astrometric orbital elements that are reliably determined (according to specific statistical tests discussed in the paper), and for the first time for 20 systems, representing a 10% increase relative to the 235 DMSA/O systems already present in the Hipparcos Double and Multiple Systems Annex. The detection of the astrometric orbital motion when the Hipparcos IAD are supplemented by the spectroscopic orbital elements is close to 100% for binaries with only one visible component, provided that the period is in the 50 - 1000 d range and the parallax is larger than 5 mas. This result is an interesting testbed to guide the choice of algorithms and statistical tests to be used in the search for astrometric binaries during the forthcoming ESA Gaia mission. Finally, orbital inclinations provided by the present analysis have been used to derive several astrophysical quantities. For instance, 29 among the 70 systems with reliable astrometric orbital elements involve main sequence stars for which the companion mass could be derived. Some interesting conclusions may be drawn from this new set of stellar masses, like the enigmatic nature of the companion to the Hyades F dwarf HIP 20935. This system has a mass ratio of 0.98 but the companion remains elusive.Comment: Astronomy & Astrophysics, in press (16 pages, 12 figures); also available at http://www.astro.ulb.ac.be/Html/ps.html#Astrometr