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.

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

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

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

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

Transport Properties of the One Dimensional Ferromagnetic Kondo Lattice Model : A Qualitative Approach to Oxide Manganites

The transport properties of the ferromagnetic Kondo lattice model in one dimension are studied via bosonization methods. The antiferromagnetic fluctuations, which normally appear because of the RKKY interactions, are explicitly taken into account as a direct exchange between the ``core'' spins. It is shown that in the paramagnetic regime with the local antiferromagnetic fluctuations, the resistivity decays exponentially as the temperature increases while in the ferromagnetic regime the system is an almost perfect conductor. %A non-perturbative description of localized spin polarons %in the paramagnetic region is obtained. The effect of a weak applied field is discussed to be reduced to the case of the ferromagnetic state leading to band splitting. The qualitative relevance of the results for the problem of the Oxide Manganites is emphasized.Comment: 4 pages, REVTe

Numerical Evaluation of Feynman Integrals by a Direct Computation Method

A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision arithmetic and parallelization technique can be used in this method if required. We present the recent progress in development of this method and show results such as one-loop 5-point and two-loop 3-point integrals.Comment: 5 pages,9 figures, LaTeX, PoS style; ACAT2008, XII International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Erice, Sicily, Italy November 3-7, 200