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.

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

Finite Temperature Renormalization of the (ϕ3)6(\phi^3)_6- and (ϕ4)4(\phi^4)_4-Models at Zero Momentum

A self-consistent renormalization scheme at finite temperature and zero momentum is used together with the finite temperature renormalization group to study the temperature dependence of the mass and the coupling to one-loop order in the $(\phi^3)_6$- and $(\phi^4)_4$-models. It is found that the critical temperature is shifted relative to the naive one-loop result and the coupling constants at the critical temperature get large corrections. In the high temperature limit of the \phiff-model the coupling decreases.Comment: 16 pages, plain Latex, NORDITA-92/38

Quasiperpendicular high Mach number Shocks

Shock waves exist throughout the universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasi-perpendicular shocks across two orders of magnitude in Alfven Mach number (MA) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted timescale of ~0.3 {\tau}c, where {\tau}c is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and MA and focus on the magnetic structure of such shocks to further show that for the same MA, a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming.Comment: Accepted and Published in Physical Review Letters (2015

A study to assess COPD Symptom-based Management and to Optimise treatment Strategy in Japan (COSMOS-J) based on GOLD 2011

Background and objective: The Global initiative for chronic Obstructive Lung Disease(GOLD) Committee has proposed a chronic obstructive pulmonary disease (COPD) assessment framework focused on symptoms and on exacerbation risk. This study will evaluate a symptom and exacerbation risk-based treatment strategy based on GOLD in a real-world setting in Japan. Optimal management of COPD will be determined by assessing symptoms using the COPD Assessment Test (CAT) and by assessing the frequency of exacerbations. Methods: This study (ClinicalTrials.gov identifier: NCT01762800) is a 24-week, multicenter, randomized, double-blind, double-dummy, parallel-group study. It aims to recruit 400 patients with moderate-to-severe COPD. Patients will be randomized to receive treatment with either salmeterol/fluticasone propionate (SFC) 50/250μg twice daily or with tiotropium bromide 18μg once daily. Optimal management of patients will be assessed at four-weekly intervals and, if patients remain symptomatic, as measured using the CAT, or experience an exacerbation, they have the option to step up to treatment with both drugs, ie, SFC twice daily and tiotropium once daily (TRIPLE therapy). The primary endpoint of the study will be the proportion of patients who are able to remain on the randomized therapy. Results: No data are available. This paper summarizes the methodology of the study in advance of the study starting. Conclusion: The results of this study will help physicians to understand whether TRIPLE therapy is more effective than either treatment strategy alone in controlling symptoms and exacerbations in patients with moderate-to-severe COPD. It will also help physicians to understand the GOLD recommendation work in Japan

Spin fluctuations and superconductivity in noncentrosymmetric heavy fermion systems CeRhSi3_3 and CeIrSi3_3

We study the normal and the superconducting properties in noncentrosymmetric heavy fermion superconductors CeRhSi$_3$ and CeIrSi$_3$. For the normal state, we show that experimentally observed linear temperature dependence of the resistivity is understood through the antiferromagnetic spin fluctuations near the quantum critical point (QCP) in three dimensions. For the superconducting state, we derive a general formula to calculate the upper critical field $H_{c2}$, with which we can treat the Pauli and the orbital depairing effect on an equal footing. The strong coupling effect for general electronic structures is also taken into account. We show that the experimentally observed features in $H_{c2}\parallel \hat{z}$, the huge value up to 30(T), the downward curvatures, and the strong pressure dependence, are naturally understood as an interplay of the Rashba spin-orbit interaction due to the lack of inversion symmetry and the spin fluctuations near the QCP. The large anisotropy between $H_{c2}\parallel \hat{z}$ and $H_{c2}\perp \hat{z}$ is explained in terms of the spin-orbit interaction. Furthermore, a possible realization of the Fulde-Ferrell- Larkin-Ovchinnikov state for $H\perp \hat{z}$ is studied. We also examine effects of spin-flip scattering processes in the pairing interaction and those of the applied magnetic field on the spin fluctuations. We find that the above mentioned results are robust against these effects. The consistency of our results strongly supports the scenario that the superconductivity in CeRhSi$_3$ and CeIrSi$_3$ is mediated by the spin fluctuations near the QCP.Comment: 21pages, 13figures, to be published in Phys. Rev.

Suprathermal electrons at Saturn's bow shock

The leading explanation for the origin of galactic cosmic rays is particle acceleration at the shocks surrounding young supernova remnants (SNRs), although crucial aspects of the acceleration process are unclear. The similar collisionless plasma shocks frequently encountered by spacecraft in the solar wind are generally far weaker (lower Mach number) than these SNR shocks. However, the Cassini spacecraft has shown that the shock standing in the solar wind sunward of Saturn (Saturn's bow shock) can occasionally reach this high-Mach number astrophysical regime. In this regime Cassini has provided the first in situ evidence for electron acceleration under quasi-parallel upstream magnetic conditions. Here we present the full picture of suprathermal electrons at Saturn's bow shock revealed by Cassini. The downstream thermal electron distribution is resolved in all data taken by the low-energy electron detector (CAPS-ELS, <28 keV) during shock crossings, but the higher energy channels were at (or close to) background. The high-energy electron detector (MIMI-LEMMS, >18 keV) measured a suprathermal electron signature at 31 of 508 crossings, where typically only the lowest energy channels (<100 keV) were above background. We show that these results are consistent with theory in which the "injection" of thermal electrons into an acceleration process involves interaction with whistler waves at the shock front, and becomes possible for all upstream magnetic field orientations at high Mach numbers like those of the strong shocks around young SNRs. A future dedicated study will analyze the rare crossings with evidence for relativistic electrons (up to ~1 MeV).Comment: 22 pages, 5 figures. Accepted for publication in Ap

Microscopic Mechanism and Pairing Symmetry of Superconductivity in the Noncentrosymmetric Heavy Fermion Systems CeRhSI3_3 and CeIrSi3_3

We study the pairing symmetry of the noncentrosymmetric heavy fermion superconductors CeRhSi$_3$ and CeIrSi$_3$ under pressures, which are both antiferromagnets at ambient pressure. We solve the Eliashberg equation by means of the random phase approximation and find that the mixed state of extended s-wave and p-wave rather than the $d+f$ wave state could be realized by enhanced antiferromagnetic spin fluctuations. It is elucidated that the gap function has line nodes on the Fermi surface and the resulting density of state in the superconducting state shows a similar character to that of usual d-wave superconductors, resulting in the NMR relaxation rate $1/(T_1T)$ that exhibits no coherence peak and behaves like $1/(T_1T)\propto T^2$ at low temperatures

Kinetic signatures of the region surrounding the X-line in asymmetric (magnetopause) reconnection

Kinetic particle-in-cell simulations are used to identify signatures of the electron diffusion region (EDR) and its surroundings during asymmetric magnetic reconnection. A "shoulder" in the sunward pointing normal electric field (EN > 0) at the reconnection magnetic field reversal is a good indicator of the EDR, and is caused by magnetosheath electron meandering orbits in the vicinity of the x-line. Earthward of the X-line, electrons accelerated by EN form strong currents and crescent-shaped distribution functions in the plane perpendicular to B. Just downstream of the X-line, parallel electric fields create field-aligned crescent electron distribution functions. In the immediate upstream magnetosheath, magnetic field strength, plasma density, and perpendicular electron temperatures are lower than the asymptotic state. In the magnetosphere inflow region, magnetosheath ions intrude resulting in an Earthward pointing electric field and parallel heating of magnetospheric particles. Many of the above properties persist with a guide field of at least unity.Comment: Submitted to Geophysical Research Letter

Non-dissipative thermal transport in the massive regimes of the XXZ chain

We present exact results on the thermal conductivity of the one-dimensional spin-1/2 XXZ model in the massive antiferromagnetic and ferromagnetic regimes. The thermal Drude weight is calculated by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy as well as analytical results in the low and high temperature limits are presented. At finite temperature, the thermal Drude weight is finite and hence there is non-dissipative thermal transport even in the massive regime. At low temperature, the thermal Drude weight behaves as $D(T)\sim \exp(-\delta/T)/\sqrt{T}$ where $\delta$ is the one-spinon (respectively one-magnon) excitation energy for the antiferromagnetic (respectively ferromagnetic) regime.Comment: 16 page