Complexity and non-separability of classical Liouvillian dynamics

We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an arbitrary fixed product basis. We show that linear growth of separability entropy provides stricter criterion of complexity than Kolmogorov-Sinai entropy, namely it requires that dynamics is exponentially unstable, non-linear and non-markovian.Comment: Revised version, 5 pages (RevTeX), with 6 pdf-figure

Follow up on the crystal growth experiments of the LDEF

The results of the 4 solution growth experiments on the LDEF have been published elsewhere. Both the crystals of CaCO3, which were large and well shaped, and the much smaller TTF-TCNQ crystals showed unusual morphological behavior. The follow up on these experiments was begun in 1981, when ESA initiated a 'Concept Definition Study' on a large, 150 kg, Solution Growth Facility (SGF) to be included in the payload of EURECA-1, the European Retrievable Carrier. This carrier was a continuation of the European Spacelab and at that time planned for launch in 1987. The long delay of the LDEF retrieval and of subsequent missions brought about reflections both on the concept of crystal growth in space and on the choice of crystallization materials that had been made for the LDEF. Already before the LDEF retrieval, research on TTF-TCNQ had been stopped, and a planned growth experiment with TTF-TCNQ on the SGF/EURECA had been cancelled. The target of the SGF investigation is now more fundamental in nature. None of the crystals to be grown here are, like TTF-TCNQ, in particular demand by science or industry, and the crystals only serve the purpose of model crystals. The real purpose of the investigation is to study the growth behavior. One of the experiments, the Soret Coefficient Measurement experiment is not growing crystals at all, but has it as its sole purpose to obtain accurate information on thermal diffusion, a process of importance in crystal growth from solution

Experiment MA-028 crystal growth

A crystal growth experiment is reported on orbital space flights. The experiment was performed during the Apollo-Soyuz Test Project. The Crystal Growth Experiment assessed a novel process for growing single crystals of insoluble substances by allowing two or more reactant solutions to diffuse toward each other through a region of pure solvent in zero gravity. The experiment was entirely successful and yielded crystals of about the expected size, quality, and number

Searching for optimal variables in real multivariate stochastic data

By implementing a recent technique for the determination of stochastic eigendirections of two coupled stochastic variables, we investigate the evolution of fluctuations of NO2 concentrations at two monitoring stations in the city of Lisbon, Portugal. We analyze the stochastic part of the measurements recorded at the monitoring stations by means of a method where the two concentrations are considered as stochastic variables evolving according to a system of coupled stochastic differential equations. Analysis of their structure allows for transforming the set of measured variables to a set of derived variables, one of them with reduced stochasticity. For the specific case of NO2 concentration measures, the set of derived variables are well approximated by a global rotation of the original set of measured variables. We conclude that the stochastic sources at each station are independent from each other and typically have amplitudes of the order of the deterministic contributions. Such findings show significant limitations when predicting such quantities. Still, we briefly discuss how predictive power can be increased in general in the light of our methods

The interstellar gas experiment

The Interstellar Gas Experiment (IGE) exposed thin metallic foils to collect neutral interstellar gas particles. These particles penetrate the solar system due to their motion relative to the sun. Thus, it is possible to entrap them in the collecting foils along with precipitating magnetospheric and perhaps some ambient atmospheric particles. For the entire duration of the Long Duration Exposure Facility (LDEF) mission, seven of these foils collected particles arriving from seven different directions as seen from the spacecraft. In the mass spectroscopic analysis of the noble gas component of these particles, we have detected the isotopes of He-3, He-4, Ne-20, and Ne-22. In the foil analyses carried out so far, we find a distribution of particle arrival directions which shows that a significant part of the trapped particles are indeed interstellar atoms. The analysis needed to subtract the competing fluxes of magnetospheric and atmospheric particles is still in progress

The Interstellar Gas Experiment: Analysis in progress

The Interstellar Gas Experiment (IGE) exposed thin metallic foils aboard the LDEF spacecraft in low Earth orbit in order to collect neutral interstellar particles which penetrate the solar system due to their motion relative to the sun. By mechanical penetration these atoms were imbedded in the collecting foils along with precipitating magnetospheric ions and, possibly, with ambient atmospheric atoms. During the entire LDEF mission, seven of these foils collected particles arriving from seven different directions as seen from the spacecraft. After the foils were returned to Earth, a mass spectrometric analysis of the noble gas component of the trapped particles was begun. The isotopes of He-3, He-4, Ne-20, and Ne-22 were detected. We have given a first account of the experiment. In order to infer the isotopic ratios in the interstellar medium from the concentrations found in the foils, several lines of investigation had to be initiated. The flux of ambient atmospheric noble gas atoms moving toward the foils due to the orbital motion of LDEF was estimated by detailed calculations. Any of these particles which evaded the baffles in the IGE collector could be entrapped in the foils as a background flux. However, the calculations have shown that this flux is negligible, which was the intent of the experiment hardware design. This conclusion is supported by the measurements. However, both the concentration of trapped helium and its impact energy indicate that the flux of magnetospheric ions which was captured was larger than had been expected. In fact, it appears that the magnetospheric particles constitute the largest fraction of the particles in the foils. Since little is known about this particle flux, their presence in the IGE foils appears fortunate. The analysis of these particles provides information about their isotropic composition and average flux

Multiaxial analyzer detects low-energy electrons

Three curved plate energy analyzers coupled with three electron multiplier tubes detect and measure low energy electron flux in several directions simultaneously

Deposition of general ellipsoidal particles

We present a systematic overview of granular deposits composed of ellipsoidal particles with different particle shapes and size polydispersities. We study the density and anisotropy of such deposits as functions of size polydispersity and two shape parameters that fully describe the shape of a general ellipsoid. Our results show that, while shape influences significantly the macroscopic properties of the deposits, polydispersity plays apparently a secondary role. The density attains a maximum for a particular family of non-symmetrical ellipsoids, larger than the density observed for prolate or oblate ellipsoids. As for anisotropy measures, the contact forces show are increasingly preferred along the vertical direction as the shape of the particles deviates for a sphere. The deposits are constructed by means of an efficient molecular dynamics method, where the contact forces are efficiently and accurately computed. The main results are discussed in the light of applications for porous media models and sedimentation processes.Comment: 7 pages, 8 figure

Spacings and pair correlations for finite Bernoulli convolutions

We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure $\nu_r$, as $N$ tends to infinity. Numerical evidence suggests that for a generic $r$, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some partial results in this direction; for instance, we show that, on average, the pair correlations do not exhibit attraction or repulsion in the limit. On the other hand, for certain algebraic $r$ the behavior is totally different.Comment: 17 pages, 6 figure

Trapping of Bose-Einstein condensates in a three-dimensional dark focus generated by conical refraction

We present a novel type of three-dimensional dark focus optical trapping potential for ultra-cold atoms and Bose-Einstein condensates. This 'optical bottle' is created with blue-detuned laser light exploiting the phenomenon of conical refraction occurring in biaxial crystals. We present experiments on confining a Rb87 Bose-Einstein condensate in this potential and derive the trapping frequencies and potential barriers under the harmonic approximation and the conical refraction theory