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.

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

The infrared-dark dust content of high redshift galaxies

We present a theoretical model aimed at explaining the IRX-$\beta$ relation for high redshift (z >5) galaxies. Recent observations (Capak+2015; Bouwens+2016) have shown that early Lyman Break Galaxies, although characterized by a large UV attenuation (e.g. flat UV beta slopes), show a striking FIR deficit, i.e. they are "infrared-dark". This marked deviation from the local IRX-beta relation can be explained by the larger molecular gas content of these systems. While dust in the diffuse ISM attains relatively high temperatures (Td = 45 K for typical size a=0.1 um; smaller grains can reach Td = 60 K), a sizable fraction of the dust mass is embedded in dense gas, and therefore remains cold. If confirmed, the FIR deficit might represent a novel, powerful indicator of the molecular content of high-z galaxies which can be used to pre-select candidates for follow-up deep CO observations. Thus, high-z CO line searches with ALMA might be much more promising than currently thought.Comment: 8 pages, 4 Figures, MNRAS Submitte

Balancing and model reduction for discrete-time nonlinear systems based on Hankel singular value analysis

This paper is concerned with balanced realization and model reduction for discrete-time nonlinear systems. Singular perturbation type balanced truncation method is proposed. In this procedure, the Hankel singular values and the related controllability and observability properties are preserved, which is a natural generalization of both the linear discrete-time case and the nonlinear continuous-time case.

Topological Hall Effect in Inhomogeneous Superconductors

We propose a possible mechanism of topological Hall effect in inhomogeneous superconducting states. In our scenario, the Berry phase effect associated with spatially modulated superconducting order parameter gives rise to a fictitious Lorentz force acting on quasiparticles. In the case of the Fulde-Ferrell-Larkin-Ovchinnikov state, the topological Hall effect is detected by applying an electromagnetic wave with a tuned wave number on a surface of the system.Comment: 4 page

A New Method for Measuring Tail Exponents of Firm Size Distributions

We propose a new method for estimating the power-law exponents of firm size variables. Our focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. As is well known, a firm size variable follows a power-law distribution only beyond some threshold. On the other hand, in almost all empirical exercises, the right end part of a distribution deviates from a power-law due to finite size effect. We modify the method proposed by Malevergne et al. (2011) so that we can identify both of the lower and the upper thresholds and then estimate the power-law exponent using observations only in the range defined by the two thresholds. We apply this new method to various firm size variables, including annual sales, the number of workers, and tangible fixed assets for firms in more than thirty countries.Econophysics, power-law distributions, power-law exponents, firm size variables, finite size effect