Nonlinear input-normal realizations based on the differential eigenstructure of hankel operators

This paper investigates the differential eigenstructure of Hankel operators for nonlinear systems. First, it is proven that the variational system and the Hamiltonian extension with extended input and output spaces can be interpreted as the Gâteaux differential and its adjoint of a dynamical input-output system, respectively. Second, the Gâteaux differential is utilized to clarify the main result the differential eigenstructure of the nonlinear Hankel operator which is closely related to the Hankel norm of the original system. Third, a new characterization of the nonlinear extension of Hankel singular values are given based on the differential eigenstructure. Finally, a balancing procedure to obtain a new input-normal/output-diagonal realization is derived. The results in this paper thus provide new insights to the realization and balancing theory for nonlinear systems.

Environmental dependence of star formation induced by cloud collisions in a barred galaxy

Cloud collision have been proposed as a way to link the small-scale star formation process with the observed global relation between the surface star formation rate and gas surface density. We suggest that this model can be improved further by allowing the productivity of such collisions to depend on the relative velocity of the two clouds. Our adjustment implements a simple step function that results in the most successful collisions being at the observed velocities for triggered star formation. By applying this to a high resolution simulation of a barred galaxy, we successfully reproduce the observational result that the star formation efficiency (SFE) in the bar is lower than that in the spiral arms. This is not possible when we use an efficiency dependent on the internal turbulence properties of the clouds. Our results suggest that high velocity collisions driven by the gravitational pull of the clouds are responsible for the low bar SFE.Comment: 6 pages, 4 figures. Accepted for publication in MNRAS Letter

Test of QEDPS: A Monte Carlo for the hard photon distributions in e+ e- annihilation proecss

The validity of a photon shower generator QEDPS has been examined in detail. This is formulated based on the leading-logarithmic renormalization equation for the electron structure function and it provides a photon shower along the initial e+-. The main interest in the present work is to test the reliability of the generator to describe a process accompanying hard photons which are detected. For this purpose, by taking the HZ production as the basic reaction, the total cross section and some distributions of the hard photons are compared between two cases that these photons come from either those generated by QEDPS or the hard process e+e- -> H Z gamma gamma. The comparison performed for the single and the double hard photon has shown a satisfactory agreement which demonstrated that the model is self-consistent.Comment: 22 pages, 4 Postscript figures, LaTeX, uses epsf.te

The X-ray Line Emission from the Supernova Remnant W49B

The Galactic supernova remnant W49B has one of the most impressive X-ray emission line spectra obtained with the Advanced Satellite for Cosmology and Astronomy (ASCA). We use both plasma line diagnostics and broadband model fits to show that the Si and S emission lines require multiple spectral components. The spectral data do not necessarily require individual elements to be spatially stratified, as suggested by earlier work, although when ASCA line images are considered, it is possible that Fe is stratified with respect to Si and S. Most of the X-ray emitting gas is from ejecta, based on the element abundances required, but is surprisingly close to being in collisional ionization equilibrium. A high ionization age implies a high internal density in a young remnant. The fitted emission measure for W49B indicates a minimum density of 2 cm^-3, with the true density likely to be significantly higher. W49B probably had a Type Ia progenitor, based on the relative element abundances, although a low-mass Type II progenitor is still possible. We find persuasive evidence for Cr and possibly Mn emission in the ASCA spectrum--the first detection of these elements in X-rays from a cosmic source.Comment: 22 pages incl 8 postscript figures, to appear in Ap

A QED Shower Including the Next-to-leading Logarithm Correction in e+e- Annihilation

We develop an event generator, NLL-QEDPS, based on the QED shower including the next-to-leading logarithm correction in the e^+e^- annihilation. The shower model is the Monte Carlo technique to solve the renormalization group equation so that they can calculate contributions of alpha^m log^n(S/m_e^2) for any m and n systematically. Here alpha is the QED coupling, m_e is the mass of electron and S is the square of the total energy in the e^+e^- system. While the previous QEDPS is limited to the leading logarithm approximation which includes only contributions of (alpha log(S/m_e^2))^n, the model developed here contains terms of alpha(alpha log(S/m_e^2))^n, the the next-to-leading logarithm correction. The shower model is formulated for the initial radiation in the e^+e^- annihilation. The generator based on it gives us events with q^2, which is a virtual mass squared of the virtual photon and/or Z-boson, in accuracy of 0.04%, except for small q^2/S.Comment: 35 pages, 1 figure(eps-file

Comment on `Equilibrium crystal shape of the Potts model at the first-order transition point'

We comment on the article by Fujimoto (1997 J. Phys. A: Math. Gen., Vol. 30, 3779), where the exact equilibrium crystal shape (ECS) in the critical Q-state Potts model on the square lattice was calculated, and its equivalence with ECS in the Ising model was established. We confirm these results, giving their alternative derivation applying the transformation properties of the one-particle dispersion relation in the six-vertex model. It is shown, that this dispersion relation is identical with that in the Ising model on the square lattice.Comment: 4 pages, 1 figure, LaTeX2

Do Giant Molecular Clouds Care About the Galactic Structure?

We investigate the impact of galactic environment on the properties of simulated giant molecular clouds formed in a M83-type barred spiral galaxy. Our simulation uses a rotating stellar potential to create the grand design features and resolves down to 1.5 pc. From the comparison of clouds found in the bar, spiral and disc regions, we find that the typical GMC is environment independent, with a mass of 5e+5 Msun and radius 11 pc. However, the fraction of clouds in the property distribution tails varies between regions, with larger, more massive clouds with a higher velocity dispersion being found in greatest proportions in the bar, spiral and then disc. The bar clouds also show a bimodality that is not reflected in the spiral and disc clouds except in the surface density, where all three regions show two distinct peaks. We identify these features as being due to the relative proportion of three cloud types, classified via the mass-radius scaling relation, which we label A, B and C. Type A clouds have the typical values listed above and form the largest fraction in each region. Type B clouds are massive giant molecular associations while Type C clouds are unbound, transient clouds that form in dense filaments and tidal tails. The fraction of each clouds type depends on the cloud-cloud interactions, which cause mergers to build up the GMA Type Bs and tidal features in which the Type C clouds are formed. The number of cloud interactions is greatest in the bar, followed by the spiral, causing a higher fraction of both cloud types compared to the disc. While the cloud types also exist in lower resolution simulations, their identification becomes more challenging as they are not well separated populations on the mass-radius relation or distribution plots. Finally, we compare the results for three star formation models to estimate the star formation rate and efficiency in each region.Comment: 21 pages, 14 figures. Accepted for publication in MNRA

Chain breaks and the susceptibility of Sr_2Cu_{1-x}Pd_xO_{3+\delta} and other doped quasi one-dimensional antiferromagnets

We study the magnetic susceptibility of one-dimensional S=1/2 antiferromagnets containing non-magnetic impurities which cut the chain into finite segments. For the susceptibility of long anisotropic Heisenberg chain-segments with open boundaries we derive a parameter-free result at low temperatures using field theory methods and the Bethe Ansatz. The analytical result is verified by comparing with Quantum-Monte-Carlo calculations. We then show that the partitioning of the chain into finite segments can explain the Curie-like contribution observed in recent experiments on Sr_2Cu_{1-x}Pd_xO_{3+\delta}. Possible additional paramagnetic impurities seem to play only a minor role.Comment: 4 pages, 3 figures, final versio