On the manifolds of total collapse orbits and of completely parabolic orbits for the n-body problem

In this paper we show for most choices of masses in the coplanar n-body problem and for certain masses in the three-dimensional n-body problem that the set of initial conditions leading to complete collapse forms a smooth submanifold in phase space where the dimension depends upon properties of the limiting configuration. A similar statement holds for completely parabolic motion. By a proper scaling, these two motions become dual to each other in the sense that one forms the unstable set while the other forms the stable set of a particular set of points in the new phase space. Most of the paper is devoted to solving the Painleve-Wintner problem which asserts that these types of orbits cannot enter in an infinite spin.     

The ArNe-N2O van der Waals trimer: a high resolution spectroscopic study of its rotational spectrum,structure and dynamics

A new ternary van der Waals complex of the type rare gas-rare gas'-linear molecule, ArNe-N₂O, was investigated using a pulsed molecular beam cavity Fourier transform microwave spectrometer. The rotational spectra of six isotopomers of the trimer were studied in detail. These include Ar²⁰Ne-¹⁴N¹⁴NO, Ar²²Ne-¹⁴N¹⁴NO, Ar²⁰Ne-15N¹⁴NO, Ar²²Ne-¹⁵N¹⁴N0, Ar²⁰Ne-¹⁴N¹⁵NO and Ar²²Ne-¹⁴N¹⁵NO. Nuclear quadrupole hyperfine structures of the rotational transitions that are due to the one or two ¹⁴N nuclei were resolved and analysed. The resulting spectroscopic constants were used to provide structural and dynamical information about the trimer. Based on the quartic centrifugal distortion constants, a harmonic force field analysis was performed to estimate the frequencies of the van der Waals vibrational modes. A perturbation of the electronic charge distribution at the site of the central ¹⁴N nucleus of N²0 upon complex formation was detected and discussed. Differences of structural parameters of the trimer as compared to those of the respective dimer units are indicative of the presence of significant three-body non-additive contributions to the interaction energy.     

Robust chaos synchronization based on adaptive fuzzy delayed feedback ${\bf{\mathcal{H}}}_{\bf{\infty}}$ control

In this paper, we propose a new adaptive H_￥\mathcal H_\infty synchronization strategy, called an adaptive fuzzy delayed feedback H_￥\mathcal H_\infty synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback H_￥\mathcal H_\infty control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed H_￥\mathcal{H}_{\infty } performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.     

Rapid identification of bacteria with a disposable colorimetric sensing array

Rapid identification of both species and even specific strains of human pathogenic bacteria grown on standard agar has been achieved from the volatiles they produce using a disposable colorimetric sensor array in a Petri dish imaged with an inexpensive scanner. All 10 strains of bacteria tested, including Enterococcus faecalis and Staphylococcus aureus and their antibiotic-resistant forms, were identified with 98.8% accuracy within 10 h, a clinically important time frame. Furthermore, the colorimetric sensor arrays also proved useful as a simple research tool for the study of bacterial metabolism and as an easy method for the optimization of bacterial production of fine chemicals or other fermentation processes.