A New Test for Chaos

We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic. (This is an alternative to the usual approach of computing the largest Lyapunov exponent.) Our method is a 0-1 test for chaos (the output is a 0 signifying nonchaotic or a 1 signifying chaotic) and is independent of the dimension of the dynamical system. Moreover, the underlying equations need not be known. The test works equally well for continuous and discrete time. We give examples for an ordinary differential equation, a partial differential equation and for a map.Comment: 10 pages, 5 figure

X-ray Spectroscopy of Candidate Ultracompact X-ray Binaries

We present high-resolution spectroscopy of the neutron star/low-mass X-ray binaries (LMXBs) 4U 1850-087 and 4U 0513-40 as part of our continuing study of known and candidate ultracompact binaries. The LMXB 4U 1850-087 is one of four systems in which we had previously inferred an unusual Ne/O ratio in the absorption along the line of sight, most likely from material local to the binaries. However, our recent Chandra X-ray Observatory LETGS spectrum of 4U 1850-087 finds a Ne/O ratio by number of 0.22+/-0.05, smaller than previously measured and consistent with the expected interstellar value. We propose that variations in the Ne/O ratio due to source variability, as previously observed in these sources, can explain the difference between the low- and high-resolution spectral results for 4U 1850-087. Our XMM-Newton RGS observation of 4U 0513-40 also shows no unusual abundance ratios in the absorption along the line of sight. We also present spectral results from a third candidate ultracompact binary, 4U 1822-000, whose spectrum is well fit by an absorbed power-law + blackbody model with absorption consistent with the expected interstellar value. Finally, we present the non-detection of a fourth candidate ultracompact binary, 4U 1905+000, with an upper limit on the source luminosity of < 1 x 10^{32} erg s^{-1}. Using archival data, we show that the source has entered an extended quiescent state.Comment: 8 pages, 3 figures, accepted for publication to the Astrophysical Journa

Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

The Low Quiescent X-Ray Luminosity of the Transient X-Ray Burster EXO 1747-214

We report on X-ray and optical observations of the X-ray burster EXO 1747-214. This source is an X-ray transient, and its only known outburst was observed in 1984-1985 by the EXOSAT satellite. We re-analyzed the EXOSAT data to derive the source position, column density, and a distance upper limit using its peak X-ray burst flux. We observed the EXO 1747-214 field in 2003 July with the Chandra X-ray Observatory to search for the quiescent counterpart. We found one possible candidate just outside the EXOSAT error circle, but we cannot rule out the possibility that the source is unrelated to EXO 1747-214. Our conclusion is that the upper limit on the unabsorbed 0.3-8 keV luminosity is L < 7E31 erg/s, making EXO 1747-214 one of the faintest neutron star transients in quiescence. We compare this luminosity upper limit to the quiescent luminosities of 19 neutron star and 14 black hole systems and discuss the results in the context of the differences between neutron stars and black holes. Based on the theory of deep crustal heating by Brown and coworkers, the luminosity implies an outburst recurrence time of >1300 yr unless some form of enhanced cooling occurs within the neutron star. The position of the possible X-ray counterpart is consistent with three blended optical/IR sources with R-magnitudes between 19.4 and 19.8 and J-magnitudes between 17.2 and 17.6. One of these sources could be the quiescent optical/IR counterpart of EXO 1747-214.Comment: 7 pages, accepted by the Astrophysical Journa

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive-definite pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio L = 0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor changes in structure of pape

Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive ($U<0$) asymmetric ($t_\uparrow\neq t_\downarrow$) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. Numerical results for unbalanced Fermi-mixtures are presented within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.Comment: 9 pages, 5 figure