On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems

For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the angle between the subspace and the desired eigenvector converges to zero. We prove that there is a Ritz value that converges to the desired eigenvalue unconditionally but the Ritz vector converges conditionally and may fail to converge. To remedy the drawback of possible non-convergence of the Ritz vector, we propose a refined Ritz vector that is mathematically different from the Ritz vector and is proved to converge unconditionally. We construct examples to illustrate our theory.Comment: 20 page

BRDFs acquired by directional radiative measurements during EAGLE and AGRISAR

Radiation is the driving force for all processes and interactions between earth surface and atmosphere. The amount of measured radiation reflected by vegetation depends on its structure, the viewing angle and the solar angle. This angular dependence is usually expressed in the Bi-directional Reflectance Distribution Function (BRDF). This BRDF is not only different for different types of vegetation, but also different for different stages of the growth. The BRDF therefore has to be measured at ground level before any satellite imagery can be used the calculate surface-atmosphere interaction. The objective of this research is to acquire the BRDFs for agricultural crop types. A goniometric system is used to acquire the BRDFs. This is a mechanical device capable of a complete hemispherical rotation. The radiative directional measurements are performed with different sensors that can be attached to this system. The BRDFs are calculated from the measured radiation. In the periods 10 June - 18 June 2006 and 2 July - 10 July 2006 directional radiative measurements were performed at three sites: Speulderbos site, in the Netherlands, the Cabauw site, in the Netherlands, and an agricultural test site in Goermin, Germany. The measurements were performed over eight different crops: forest, grass, pine tree, corn, wheat, sugar beat and barley. The sensors covered the spectrum from the optical to the thermal domain. The measured radiance is used to calculate the BRDFs or directional thermal signature. This contribution describes the measurements and calculation of the BRDFs of forest, grassland, young corn, mature corn, wheat, sugar beat and barley during the EAGLE2006 and AGRISAR 2006 fieldcampaigns. Optical BRDF have been acquired for all crops except barley. Thermal angular signatures are acquired for all the crop

Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator

The dependence of quantum correlation of twin beams on the pump finesse of an optical parametric oscillator is studied with a semi-classical analysis. It is found that the phase-sum correlation of the output signal and idler beams from an optical parametric oscillator operating above threshold depends on the finesse of the pump field when the spurious pump phase noise generated inside the optical cavity and the excess noise of the input pump field are involved in the Langevin equations. The theoretical calculations can explain the previously experimental results, quantitatively.Comment: 27 pages, 8 figure

Hall Effect in the coma of 67P/Churyumov-Gerasimenko

Magnetohydrodynamics simulations have been carried out in studying the solar wind and cometary plasma interactions for decades. Various plasma boundaries have been simulated and compared well with observations for comet 1P/Halley. The Rosetta mission, which studies comet 67P/Churyumov-Gerasimenko, challenges our understanding of the solar wind and comet interactions. The Rosetta Plasma Consortium observed regions of very weak magnetic field outside the predicted diamagnetic cavity. In this paper, we simulate the inner coma with the Hall magnetohydrodynamics equations and show that the Hall effect is important in the inner coma environment. The magnetic field topology becomes complex and magnetic reconnection occurs on the dayside when the Hall effect is taken into account. The magnetic reconnection on the dayside can generate weak magnetic filed regions outside the global diamagnetic cavity, which may explain the Rosetta Plasma Consortium observations. We conclude that the substantial change in the inner coma environment is due to the fact that the ion inertial length (or gyro radius) is not much smaller than the size of the diamagnetic cavity.Comment: 23 pages, 6 figur

Variant Supercurrents and Linearized Supergravity

In this paper the variant supercurrents based on consistency and completion in off-shell N=1 supergravity are studied. We formulate the embedding relations for supersymmetric current and energy tensor into supercurrent multiplet. Corresponding linearized supergravity is obtained with appropriate choice of Wess-Zumino gauge in each gravity supermultiplet.Comment: v1: 9 pp; v2: minor changes; v3: 10 pp, published versio

Application and research of wireless laser methane sensor in drainage pipeline monitoring

Laser methane sensor has been widely promoted and successfully applied in coal mines as a new and effective technology building on the approach of laser-based absorption detection. Compared with the traditional catalytic methane sensor, the laser methane sensor discussed offers the important advantages of a long calibration period, high detection precision, the absence of zero drift and low power consumption, all of which are significant advantages for use in coal mining applications. By compensating for the temperature and pressure of the gases present, the accuracy of the methane sensor is evident across a wide range of temperatures and pressures, making it suitable for gas detection, including methane, in pipelines as well. The wireless laser approach which is incorporated into the methane sensor allows wireless transmission and data uploading to a cloud server through NB-IoT. This tackles the problem in gas pipeline monitoring of the length of many pipelines and thus the wide distribution of the sensors, avoiding complicated wiring and thus high associated cost. Further, remote data management can then be achieved, all of which greatly improves the flexibility and security of the management of the pipeline and the data generated

Quasispecies distribution of Eigen model

We study sharp peak landscapes (SPL) of Eigen model from a new perspective about how the quasispecies distribute in the sequence space. To analyze the distribution more carefully, we bring forth two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how the configuration of the distribution varies with copying fidelity $q$ in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance $d_{0}$, by which we can get a visual and in-depth result about how the sequences distribute. We find that there are several local optima around the center (global optimum) in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient $C(k)$ follows lognormal distribution and the curve of clustering coefficient $C$ of the network versus $d_{0}$ appears as linear behavior near the threshold.Comment: 13 pages, 6 figure

Non-Hermitian coherent coupling of nanomagnets by exchange spin waves

Non-Hermitian physics has recently attracted much attention in optics and photonics. Less explored is non-Hermitian magnonics that provides opportunities to take advantage of the inevitable dissipation of magnons or spin waves in magnetic systems. Here we demonstrate non-Hermitian coherent coupling of two distant nanomagnets by fast spin waves with sub-50 nm wavelengths. Magnons in two nanomagnets are unidirectionally phase-locked with phase shifts controlled by magnon spin torque and spin-wave propagation. Our results are attractive for analog neuromorphic computing that requires unidirectional information transmission