On stability of second-order quasi-polynomials with a single delay

In this note the stability of a second-order quasi-polynomial with a single delay is studied. Although there is a vast literature on this problem, most available solutions are limited to some particular cases. Moreover, some published results on this subject appear to contain imprecise, or even wrong, conditions. The purpose of this note is to show that by accurate application of known theories, a complete explicit characterization of stability regions can be derived in a most general case. As a byproduct of the proposed analysis, we show that in the high-order case the quasi-polynomial is delay-independent unstable whenever its delay-free version has an odd number of unstable roots (or, equivalently, a negative static gain).     

The effect of heat treatment on the microfibrillar network of poly(p-phenylene benzobisthiazole)

Materials exhibiting exceptional mechanical properties can be fabricated from rigid polymers. In a spinning process, an oriented solution is solidified by the action of a nonsolvent, which induces crystallization of an oriented rigid polymer. Drying and heat treatment result in the final material having the desired properties. The effect of heat treatment on the morphology of poly(p-phenylene benzobisthiazole) (PBZT) films was studied by measurements of small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD). Films were formed by coagulation in water. The wet films were dried with supercritical CO₂ to maintain an open network structure. Coagulation in water resulted in formation of microfibrils having diameter of ∼9 nm. Heat-treatment at 600°C caused significant coalescence of microfibrils. The crystallite size was increased by heat treatment from a value that is smaller than the microfibrillar diameter indicating defects in chain packing, to a value comparable to the microfibrillar diameter.     

Symmetry properties of the reciprocity gap functional in the linear elasticity

The reciprocity gap functional for a linear elastic body with an embedded defect is considered. The functional is a bilinear functional depending on two stress states—in an elastic body with a defect and without it. It is shown that for various types of boundary conditions the functional is a symmetric one in a certain sense. Some corollaries of the symmetry properties of the functional are obtained.     

Effect of terbium gallium garnet crystal orientation on the isolation ratio of a Faraday isolator at high average power

We present a comprehensive and systematic investigation of the fundamental physical limitations of Faraday isolation performance at high average powers that are due to thermally induced birefringence. First, the operation of various Faraday isolator designs by use of arbitrary orientation of cubic magneto-optic crystals is studied theoretically. It is shown that, for different Faraday isolator designs, different crystal orientations can optimize the isolation ratio. Second, thermo-optic and photoelastic constants for terbium gallium garnet crystals grown by different manufacturers were measured. Measurements of self-induced depolarization are made for various orientations of crystallographic axes. The measurements are in good agreement with our theoretical predictions. Based on our results, it is possible to select a crystal orientation that optimizes isolation performance at high average powers, resulting in a 5-dB enhancement over nonoptimized orientations.     

Gas Pressure and Temperature Dependences of Thermal Conductivity of Porous Ceramic Materials: Part 1, Refractories and Ceramics with Porosity below 30%

A review of experimental results and theoretical models for thermal conductivities of ceramic materials with porosity less than 30% is given. It is shown that the abnormal non-monotonic pressure and temperature dependences of thermal conductivity arise from the effects of microcracks and porous grain boundaries, characterizing many industrial refractories, and from the competitive influences of classical and novel mechanisms of heat transfer in composite multiphase materials. The latter mechanisms include segregation and surface diffusion of impurities and defects in crystal structure, and the mechanism arising from chemical conversion and gas emission, occurring within pores of ceramic materials. A fractal model of porous materials' structure is proposed and used for analysis, explanation, and classification of thermophysical properties of ceramic materials measured in various thermodynamic conditions.     

Investigation of YBa2Cu3O x , Bi(Pb)-HTSC and Nd(123)-Particles in a Running Magnetic Field Near the Superconducting Transition Temperature

A novel system of electromagnetic separation (EMS) employing an alternating magnetic field (RMF) of suspended HTSC-particles in liquid nitrogen is described (Broide in Supercond. Cryoelectron. Summer:33, [1998]; Broide in Superconductor Week 12, No. 21, [1998]; Broide in US Patent 5,919,737, [1999]; Broide et al. in International Conference, Barcelona, Spain, [1999]). The EMS method is realized at temperatures close to those of the HTSC transition by extracting particles of YBaCuO, BiSrCaCuO, BiPbSrCaCuO, and NdBaCuO with optimal physical properties from the powders, concentrating particles with a greater critical current at one side. This process has shown great promise in its ability to produce high quality superconducting materials, being also an effective method of testing and analyzing powders to determine if synthesis adjustments are necessary in order to achieve optimal materials properties. In addition, a correlation between the speed of YBa₂Cu₃O _x particles and the percentage of oxygen (O _x ) was discovered. Since the temperature of the superconducting (SC) transition (T _c ) practically has a linear dependence on the oxygen percentage, the knowledge of the speed of the HTSC-particles during the separation, one may immediately give (within 10 s) the percentage of the oxygen in the chemical structure of the new HTSC materials. The EMS method enables statistical improvement in the uniformity of HTSC powders by decreasing the quantity of defective zones in the separated powders, the number of nonvalid admixtures, and thus, an increase in T _c and I _c (critical current). At the same time, ΔT _c the width of the SC-transition is decreased. Three YBa₂Cu₃O _x thick films have been produced by the paint method on MgO substrates from the source material, the separated high-quality concentrate, and the low-quality remnant (tail). The films exhibit different structural and electrical properties, in particular, different I _c , and ΔT _c . For the film that was made from the high-quality concentrate, ΔT _c is decreased from 5–7 K to 1–2 K. I _c is increased by a factor of 2–5 from the I _c of the source material (before EMS) and T _c is changed from 89 K to 93 K. Thick films, which had been produced from low-quality remnant (tail) do not have SC transition down to 77 K.      

An assessment of a revised Olmo et al. model to predict solar global radiation on a tilted surface at Beer Sheva,Israel

A model to convert horizontal solar global radiation to that on a tilted surface is presented. It is based upon a relatively simple model proposed by [Olmo FJ, Vida J, Foyo I, Castro-Diez Y, Alados-Arboledas L. Prediction of global irradiance on inclined surfaces from horizontal global irradiance. Energy 24 (1999) 689–704]., which requires only measurements of horizontal solar radiation but was found to produce significant errors when tested with data from another site. The present model assumes the availability of databases for at least two of the three solar radiation types, viz., global, beam and diffuse. The horizontal global radiation is converted to that on a tilted surface by applying the Olmo model to the diffuse component, whereas the beam component is converted by using the geometrical relationship between the two surfaces. The original Olmo anisotropic radiation correction factor is now assumed to be a function of sky conditions. The solar radiation databases were converted to subsets corresponding to clear, partially cloudy and cloudy sky based upon clearness index values. The three anisotropic correction factors were determined by fitting to a 12-months database. The present model was then tested by applying it to a second database consisting of 24-months not involved in the model development. It was found to give better results than three highly regarded more complex models.     

Computational fluid dynamic simulations of coal-fired utility boilers: An engineering tool

The objective of this study was to develop an engineering tool by which the combustion behavior of coals in coal-fired utility boilers can be predicted. We presented in this paper that computational fluid dynamic (CFD) codes can successfully predict performance of- and emission from- full-scale pulverized-coal utility boilers of various types, provided that the model parameters required for the simulation are properly chosen and validated. For that purpose we developed a methodology combining measurements in a 50 kW pilot-scale test facility with CFD simulations using the same CFD code configured for both test and full-scale furnaces. In this method model parameters of the coal processes are extracted and validated. This paper presents the importance of the validation of the model parameters which are used in CFD codes. Our results show very good fit of CFD simulations with various parameters measured in a test furnace and several types of utility boilers. The results of this study demonstrate the viability of the present methodology as an effective tool for optimization coal burning in full-scale utility boilers.