Periodic orbits in the gravity field of a fixed homogeneous cube

In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different types of symmetry planes of the fixed cube, periodic orbits are obtained using the method of the Poincar\'e surface of section. While in general positions, periodic orbits are found by the homotopy method. The results show that periodic orbits exist extensively in symmetry planes of the fixed cube, and also exist near asymmetry planes that contain the regular Hex cross section. The stability of these periodic orbits is determined on the basis of the eigenvalues of the monodromy matrix. This paper proves that the homotopy method is effective to find periodic orbits in the gravity field of the cube, which provides a new thought of searching for periodic orbits around non-spherical celestial bodies. The investigation of orbits around the cube could be considered as the first step of the complicated cases, and helps to understand the dynamics of orbits around bodies with complicated shapes. The work is an extension of the previous research work about the dynamics of orbits around some simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates.Comment: 23 pages, 10 figures, accepted for publication in Astrophysics & Space Scienc

The Canonical Partition Function for Quons

We calculate the canonical partition function $Z_N$ for a system of $N$ free particles obeying so-called `quon' statistics where $q$ is real and satisfies $|q|<1$ by using simple counting arguments. We observe that this system is afflicted by the Gibbs paradox and that $Z_N$ is independent of $q$. We demonstrate that such a system of particles obeys the ideal gas law and that the internal energy $U$ ( and hence the specific heat capacity $C_V$ ) is identical to that of a system of $N$ free particles obeying Maxwell-Boltzmann statistics.Comment: 12 pages RevTex, NCL94-TP5 ( To be published in Physics Letters A

The use of high-throughput sequencing to investigate an outbreak of glycopeptide-resistant Enterococcus faecium with a novel quinupristin-dalfopristin resistance mechanism.

High-throughput sequencing (HTS) has successfully identified novel resistance genes in enterococci and determined clonal relatedness in outbreak analysis. We report the use of HTS to investigate two concurrent outbreaks of glycopeptide-resistant Enterococcus faecium (GRE) with an uncharacterised resistance mechanism to quinupristin-dalfopristin (QD).Seven QD-resistant and five QD-susceptible GRE isolates from a two-centre outbreak were studied. HTS was performed to identify genes or predicted proteins that were associated with the QD-resistant phenotype. MLST and SNP typing on HTS data was used to determine clonal relatedness.Comparative genomic analysis confirmed this GRE outbreak involved two distinct clones (ST80 and ST192). HTS confirmed the absence of known QD resistance genes, suggesting a novel mechanism was conferring resistance. Genomic analysis identified two significant genetic determinants with explanatory power for the high level of QD resistance in the ST80 QD-resistant clone: an additional 56aa leader sequence at the N-terminus of the lsaE gene and a transposon containing seven genes encoding proteins with possible drug or drug-target modification activities. However, HTS was unable to conclusively determine the QD resistance mechanism and did not reveal any genetic basis for QD resistance in the ST192 clone. This study highlights the usefulness of HTS in deciphering the degree of relatedness in two concurrent GRE outbreaks. Although HTS was able to reveal some genetic candidates for uncharacterised QD resistance, this study demonstrates the limitations of HTS as a tool for identifying putative determinants of resistance to QD

Optical properties of (AlxGa1-x)(0.52)In0.48P at the crossover from a direct-gap to an indirect-gap semiconductor

The optical properties and the dynamics of excitons and the electron-hole plasma have been studied in disordered (AlxGa1−x)0.52In0.48P near to the direct-to-indirect band gap crossover. In particular we have investigated three epitaxial layers grown by solid-source molecular beam epitaxy with varying Al content x. Two of them have compositions in the immediate vicinity of the crossover point, the other is assigned to the indirect-gap regime. Both direct and indirect recombination processes contribute to the photon emission from the material. Since the relative importance of the different recombination processes depends strongly on temperature, excitation intensity, and excitation pulse duration, the processes can be identified by changing these parameters. As a result, we can determine the relative alignment of the conduction band minima and the distribution of the electrons among them. At high excitation levels the two crossover samples show stimulated emission at a photon energy of ∼2.29 eV, i.e., in the green spectral range. Using the variable stripe length method, we find an optical gain of up to ∼600 cm−1 at excitation levels of ∼350 kW/cm2.Stimulated emission involves direct recombination. This conclusion is reached from the experiments and from line-shape modeling, including a self-consistent treatment of populations and renormalization of the conduction band minima

Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube

This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be considered as an extension of previous research work on the dynamics of orbits around simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates with backgrounds in celestial mechanics. In the synodic reference frame, the model of a rotating cube is established, the equilibria are calculated, and their linear stabilities are determined. Periodic orbits around the equilibria are computed using the traditional differential correction method, and their stabilities are determined by the eigenvalues of the monodromy matrix. The existence of homoclinic and heteroclinic orbits connecting periodic orbits around the equilibria is examined and proved numerically in order to understand the global orbit structure of the system. This study contributes to the investigation of irregular shaped celestial bodies that can be divided into a set of cubes.Comment: 29 pages, 16 figures, accepted for publication in Astrophysics & Space Scienc

Quantum correlated twin atomic beams via photo-dissociation of a molecular Bose-Einstein condensate

We study the process of photo-dissociation of a molecular Bose-Einstein condensate as a potential source of strongly correlated twin atomic beams. We show that the two beams can possess nearly perfect quantum squeezing in their relative numbers.Comment: Corrected LaTeX file layou

Effects of Long-Range Nonlinear Interactions in Double-Well Potentials

We consider the interplay of linear double-well-potential (DWP) structures and nonlinear longrange interactions of different types, motivated by applications to nonlinear optics and matter waves. We find that, while the basic spontaneous-symmetry-breaking (SSB) bifurcation structure in the DWP persists in the presence of the long-range interactions, the critical points at which the SSB emerges are sensitive to the range of the nonlocal interaction. We quantify the dynamics by developing a few-mode approximation corresponding to the DWP structure, and analyze the resulting system of ordinary differential equations and its bifurcations in detail. We compare results of this analysis with those produced by the full partial differential equation, finding good agreement between the two approaches. Effects of the competition between the local self-attraction and nonlocal repulsion on the SSB are studied too. A far more complex bifurcation structure involving the possibility for not only supercritical but also subcritical bifurcations and even bifurcation loops is identified in that case.Comment: 12 pages, 9 figure

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9

The potential science and engineering value of samples delivered to Earth by Mars sample return

Executive summary provided in lieu of abstract