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.

Thermal Renormalons in Scalar Field Theory

In the frame of the scalar theory $g \phi ^{4}$, we explore the occurrence of thermal renormalons, i. e. temperature dependent singularities in the Borel plane. The discussion of a particular renormalon type diagram at finite temperature, using Thermofield Dynamics, allows us to establish that these singularities actually get a temperature dependence. This dependence appears in the residues of the poles, remaining their positions unchanged with temperature.Comment: 12 pages, 3 figures, uses feynMF. Minor correction

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

Unambiguous probe of parity-mixing of Cooper pairs in noncentrosymmetric superconductors

We propose an experimental scheme to detect unambiguously parity-mxing of Cooper pairs in noncentrosymmetric superconductors, which utilizes crossed Andreev reflection processes between two oppositely spin-polarized normal metal leads and a noncentrosymmetric superconductor. It is demonstrated that a non-local conductance exhibits a clear signature of parity breaking of Cooper pairs, and thus, can be a direct probe for the parity-mixing.Comment: 4 pages, 2figure

String tension and glueball masses of SU(2) QCD from perfect action for monopoles and strings

We study the perfect monopole action as an infrared effective theory of SU(2) QCD. It is transformed exactly into a lattice string model. Since the monopole interactions are weak in the infrared SU(2) QCD, the string interactions become strong. The strong coupling expansion of string model shows the quantum fluctuation is small. The classical string tension is estimated analytically, and we see it is very close to the quantum one in the SU(2) QCD. We also discuss how to calculate the glueball mass in our model.Comment: LATTICE99(Confinement), 3 pages and 1 EPS figure

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

Correlating Methane Production to Microbiota in Anaerobic Digesters Fed Synthetic Wastewater

A quantitative structure activity relationship (QSAR) between relative abundance values and digester methane production rate was developed. For this, 50 triplicate anaerobic digester sets (150 total digesters) were each seeded with different methanogenic biomass samples obtained from full-scale, engineered methanogenic systems. Although all digesters were operated identically for at least 5 solids retention times (SRTs), their quasi steady-state function varied significantly, with average daily methane production rates ranging from 0.09 ± 0.004 to 1 ± 0.05 L-CH4/LR-day (LR = Liter of reactor volume) (average ± standard deviation). Digester microbial community structure was analyzed using more than 4.1 million partial 16S rRNA gene sequences of Archaea and Bacteria. At the genus level, 1300 operational taxonomic units (OTUs) were observed across all digesters, whereas each digester contained 158 ± 27 OTUs. Digester function did not correlate with typical biomass descriptors such as volatile suspended solids (VSS) concentration, microbial richness, diversity or evenness indices. However, methane production rate did correlate notably with relative abundances of one Archaeal and nine Bacterial OTUs. These relative abundances were used as descriptors to develop a multiple linear regression (MLR) QSAR equation to predict methane production rates solely based on microbial community data. The model explained over 66% of the variance in the experimental data set based on 149 anaerobic digesters with a standard error of 0.12 L-CH4/LR-day. This study provides a framework to relate engineered process function and microbial community composition which can be further expanded to include different feed stocks and digester operating conditions in order to develop a more robust QSAR model