Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for $m$ between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when $0.54\leq m\leq 1$, and are linearly unstable when $0<m\leq0.53$.Comment: 6 figure

Discrete Laplace Cycles of Period Four

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction

Surgical Treatment of Kawasaki Disease with Intestinal Pseudo-obstruction

A 5-year-old boy suffering from abdominal pain accompanied by a fever of up to 39.5 degrees C for 2 days was admitted to the hospital. Although Flomoxef was administered following admission, the boy's fever persisted and abdominal distension gradually worsened. On the 4th day, dry lips, red eyes and a strawberry tongue were noted. An echocardiogram revealed pericoronary enhancement with mild mitral valve regurgitation and a small degree of pericardial effusion, characteristics compatible with Kawasaki disease. Although intravenous immunoglobulin was administered, the fever and abdominal distension persisted. On the 8th day, a pediatric surgeon was consulted and an exploratory laparotomy was arranged. During the operation, intestinal pseudo-obstruction and fibrin coatings around the intestine near the splenic flexure were found. A colostomy was performed for decompression of the dilated bowel and a biopsy of the lymph node surrounding the splenic flexure was taken. The fever subsided dramatically after decompression of the bowel and the recovery course was uneventful. The pathologic report revealed necrotic lymphadenitis. We report this rare case and review the literature

Collective Modes of Soliton-Lattice States in Double-Quantum-Well Systems

In strong perpendicular magnetic fields double-quantum-well systems can sometimes occur in unusual broken symmetry states which have interwell phase coherence in the absence of interwell hopping. When hopping is present in such systems and the magnetic field is tilted away from the normal to the quantum well planes, a related soliton-lattice state can occur which has kinks in the dependence of the relative phase between electrons in opposite layers on the coordinate perpendicular to the in-plane component of the magnetic field. In this article we evaluate the collective modes of this soliton-lattice state in the generalized random-phase aproximation. We find that, in addition to the Goldstone modes associated with the broken translational symmetry of the soliton-lattice state, higher energy collective modes occur which are closely related to the Goldstone modes present in the spontaneously phase-coherent state. We study the evolution of these collective modes as a function of the strength of the in-plane magnetic field and comment on the possibility of using the in-plane field to generate a finite wave probe of the spontaneously phase-coherent state.Comment: REVTEX, 37 pages (text) and 15 uuencoded postscript figure

Dark Synergy: Gravitational Lensing and the CMB

Power spectra and cross-correlation measurements from the weak gravitational lensing of the cosmic microwave background (CMB) and the cosmic shearing of faint galaxies images will help shed light on quantities hidden from the CMB temperature anisotropies: the dark energy, the end of the dark ages, and the inflationary gravitational wave amplitude. Even with modest surveys, both types of lensing power spectra break CMB degeneracies and they can ultimately improve constraints on the dark energy equation of state w by over an order of magnitude. In its cross correlation with the integrated Sachs-Wolfe effect, CMB lensing offers a unique opportunity for a more direct detection of the dark energy and enables study of its clustering properties. By obtaining source redshifts and cross-correlations with CMB lensing, cosmic shear surveys provide tomographic handles on the evolution of clustering correspondingly better precision on the dark energy equation of state and density. Both can indirectly provide detections of the reionization optical depth and modest improvements in gravitational wave constraints which we compare to more direct constraints. Conversely, polarization B-mode contamination from CMB lensing, like any other residual foreground, darkens the prospects for ultra-high precision on gravitational waves through CMB polarization requiring large areas of sky for statistical subtraction. To evaluate these effects we provide fitting formula for the evolution and transfer function of the Newtonian gravitational potential.Comment: 16 pages, 11 figures submitted to PR

Franck-Condon Effect in Central Spin System

We study the quantum transitions of a central spin surrounded by a collective-spin environment. It is found that the influence of the environmental spins on the absorption spectrum of the central spin can be explained with the analog of the Franck-Condon (FC) effect in conventional electron-phonon interaction system. Here, the collective spins of the environment behave as the vibrational mode, which makes the electron to be transitioned mainly with the so-called "vertical transitions" in the conventional FC effect. The "vertical transition" for the central spin in the spin environment manifests as, the certain collective spin states of the environment is favored, which corresponds to the minimal change in the average of the total spin angular momentum.Comment: 8 pages, 8 figure

Large Scale Pressure Fluctuations and Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect associated with pressure fluctuations of the large scale structure gas distribution will be probed with current and upcoming wide-field small angular scale cosmic microwave background experiments. We study the generation of pressure fluctuations by baryons which are present in virialized dark matter halos and by baryons present in small overdensities. For collapsed halos, assuming the gas distribution is in hydrostatic equilibrium with matter density distribution, we predict the pressure power spectrum and bispectrum associated with the large scale structure gas distribution by extending the dark matter halo approach which describes the density field in terms of correlations between and within halos. The projected pressure power spectrum allows a determination of the resulting SZ power spectrum due to virialized structures. The unshocked photoionized baryons present in smaller overdensities trace the Jeans-scale smoothed dark matter distribution. They provide a lower limit to the SZ effect due to large scale structure in the absence of massive collapsed halos. We extend our calculations to discuss higher order statistics, such as bispectrum and skewness in SZ data. The SZ-weak lensing cross-correlation is suggested as a probe of correlations between dark matter and baryon density fields, while the probability distribution functions of peak statistics of SZ halos in wide field CMB data can be used as a probe of cosmology and non-Gaussian evolution of large scale structure pressure fluctuations.Comment: 16 pages, 9 figures; Revised with expanded discussions. Phys. Rev. D. (in press

Constraining the dark energy dynamics with the cosmic microwave background bispectrum

We consider the influence of the dark energy dynamics at the onset of cosmic acceleration on the Cosmic Microwave Background (CMB) bispectrum, through the weak lensing effect induced by structure formation. We study the line of sight behavior of the contribution to the bispectrum signal at a given angular multipole $l$: we show that it is non-zero in a narrow interval centered at a redshift $z$ satisfying the relation $l/r(z)\simeq k_{NL}(z)$, where the wavenumber corresponds to the scale entering the non-linear phase, and $r$ is the cosmological comoving distance. The relevant redshift interval is in the range 0.1\lsim z\lsim 2 for multipoles 1000\gsim\ell\gsim 100; the signal amplitude, reflecting the perturbation dynamics, is a function of the cosmological expansion rate at those epochs, probing the dark energy equation of state redshift dependence independently on its present value. We provide a worked example by considering tracking inverse power law and SUGRA Quintessence scenarios, having sensibly different redshift dynamics and respecting all the present observational constraints. For scenarios having the same present equation of state, we find that the effect described above induces a projection feature which makes the bispectra shifted by several tens of multipoles, about 10 times more than the corresponding effect on the ordinary CMB angular power spectrum.Comment: 15 pages, 7 figures, matching version accepted by Physical Review D, one figure improve

WMAP constraints on inflationary models with global defects

We use the cosmic microwave background angular power spectra to place upper limits on the degree to which global defects may have aided cosmic structure formation. We explore this under the inflationary paradigm, but with the addition of textures resulting from the breaking of a global O(4) symmetry during the early stages of the Universe. As a measure of their contribution, we use the fraction of the temperature power spectrum that is attributed to the defects at a multipole of 10. However, we find a parameter degeneracy enabling a fit to the first-year WMAP data to be made even with a significant defect fraction. This degeneracy involves the baryon fraction and the Hubble constant, plus the normalization and tilt of the primordial power spectrum. Hence, constraints on these cosmological parameters are weakened. Combining the WMAP data with a constraint on the physical baryon fraction from big bang nucleosynthesis calculations and high-redshift deuterium abundance, limits the extent of the degeneracy and gives an upper bound on the defect fraction of 0.13 (95% confidence).Comment: 10pp LaTeX/RevTeX, 6 eps figs; matches accepted versio