On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Exclusive measurement of coherent eta photoproduction from the deuteron

Coherent photoproduction of eta mesons from the deuteron has been measured from threshold up to incident photon energies of 750 MeV using the photon spectrometer TAPS at the tagged photon facility at the Mainz microtron MAMI. For the first time, differential coherent cross sections have been deduced from the coincident detection of the eta meson and the recoil deuteron. A missing energy analysis was used for the suppression of background events so that a very clean identification of coherent eta-photoproduction was achieved. The resulting cross sections agree with previous experimental results except for angles around 90 deg in the photon-deuteron cm-system where they are smaller. They are compared to various model calculations.Comment: 4 pages, 4 figure

A Novel Approach for Transmission of 56 Gbit/s NRZ Signal in Access Network Using Spectrum Slicing Technique

We present the spectrum slicing and stitching concept for high-capacity low optics complexity optical access networks. Spectrum slicing and stitching of a 56 Gbit/s NRZ electrical signal is experimentally demonstrated for the first time. We present the spectrum slicing and stitching concept for high-capacity low optics complexity optical access networks. Spectrum slicing and stitching of a 56 Gbit/s NRZ electrical signal is experimentally demonstrated for the first time

Dispersion Effects in Nucleon Polarisabilities

We present a formalism to extract the dynamical nucleon polarisabilities defined via a multipole expansion of the structure amplitudes in nucleon Compton scattering. In contradistinction to the static polarisabilities, dynamical polarisabilities gauge the response of the internal degrees of freedom of a composed object to an external, real photon field of arbitrary energy. Being energy dependent, they therefore contain additional information about dispersive effects induced by internal relaxation mechanisms, baryonic resonances and meson production thresholds of the nucleon. We give explicit formulae to extract the dynamical electric and magnetic dipole as well as quadrupole polarisabilities from low energy nucleon Compton scattering up to the one pion production threshold and discuss the connection to the definition of static nucleon polarisabilities. As a concrete example, we examine the results of leading order Heavy Baryon Chiral Perturbation Theory for the four leading spin independent iso-scalar polarisabilities of the nucleon. Finally, we consider the possible r{\^o}le of energy dependent effects in low energy extractions of the iso-scalar dipole polarisabilities from Compton scattering on the deuteron.Comment: 17 pages LaTeX2e with 2 figures, using includegraphicx (5 .eps files). Minor corrections, references updated. Contents identical to version to appear in Phys. Rev. C 65, spelling differen

Low-energy Compton scattering on the nucleon and sum rules

The Gerasimov-Drell-Hearn and Baldin-Lapidus sum rules are evaluated in the dressed K-matrix model for photon-induced reactions on the nucleon. For the first time the sum $\alpha+\beta$ of the electric and magnetic polarisabilities and the forward spin polarisability $\gamma_0$ are explicitly calculated in two alternative ways -- from the sum rules and from the low-energy expansion of the real Compton scattering amplitude -- within the {\em same} framework. The two methods yield compatible values for $\alpha+\beta$ but differ somewhat for $\gamma_0$. Consistency between the two ways of determining the polarisabilities is a measure of the extent to which basic symmetries of the model are obeyed.Comment: 9 pages, 4 figures, using REVTeX. More concise version, results unchanged. To appear in Phys. Rev.

A Gibbs approach to Chargaff's second parity rule

Chargaff's second parity rule (CSPR) asserts that the frequencies of short polynucleotide chains are the same as those of the complementary reversed chains. Up to now, this hypothesis has only been observed empirically and there is currently no explanation for its presence in DNA strands. Here we argue that CSPR is a probabilistic consequence of the reverse complementarity between paired strands, because the Gibbs distribution associated with the chemical energy between the bonds satisfies CSPR. We develop a statistical test to study the validity of CSPR under the Gibbsian assumption and we apply it to a large set of bacterial genomes taken from the GenBank repository.Comment: 16 page

Attitude control analysis of tethered de-orbiting

The increase of satellites and rocket upper stages in low earth orbit (LEO) has also increased substantially the danger of collisions in space. Studies have shown that the problem will continue to grow unless a number of debris are removed every year. A typical active debris removal (ADR) mission scenario includes launching an active spacecraft (chaser) which will rendezvous with the inactive target (debris), capture the debris and eventually deorbit both satellites. Many concepts for the capture of the debris while keeping a connection via a tether, between the target and chaser have been investigated, including harpoons, nets, grapples and robotic arms. The paper provides an analysis on the attitude control behaviour for a tethered de-orbiting mission based on the ESA e.Deorbit reference mission, where Envisat is the debris target to be captured by a chaser using a net which is connected to the chaser with a tether. The paper provides novel insight on the feasibility of tethered de-orbiting for the various mission phases such as stabilization after capture, de-orbit burn (plus stabilization), stabilization during atmospheric pass, highlighting the importance of various critical mission parameters such as the tether material. It is shown that the selection of the appropriate tether material while using simple controllers can reduce the effort needed for tethered deorbiting and can safely control the attitude of the debris/chaser connected with a tether, without the danger of a collision