A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

MEASUREMENT OF THE TEMPERATURE DEPENDENCE OF THE FLUORESCENCE QUANTUM YIELD OF ORGANIC MOLECULES IN SOLUTION

A DETAILED investigation of the temperature dependence of the fluorescence quantum yield φ_f can yield–directly or indirectly–significant information about behavior of excited states of organic molecules, such as the temperature effect on radiationless transitions and on photochemical reactivity. Variation of the temperature changes the viscosity of the solvent and, in conjunction with measurements of φ_f( T ), allows investigations of diffusion-controlled processes. For example, energy transfer and quenching processes as well as excimer or exciplex formation fall into this category. Recent review articles by Weller (1962) and Birks (1970) deal with this topic. Moreover, Huber and Mantulin (1972) have suggested that restraints placed upon geometric modifications of the excited molecule by temperature-induced changes in the solvent cage (variation of site structure) are reflected in a varying φ_f.
The purpose of this note is to describe and verify a simple procedure, accurate to about ± 5%, for measuring the relative fluorescence quantum yield as a function of temperature. A quantum yield study of 9,10-diphenylanthracene between room temperature and 77°K is employed to demonstrate the capabilities of this method. In addition, we consider an example of diffusion-controlled quenching by oxygen measured over a wide temperature range.     

Low temperature Mössbauer spectra and magnetic ordering of lithiated ferric molybdate: Li2Fe2(MoO4)3

Powder x-ray diffraction, variable temperature magnetic susceptibility, and zero field Mössbauer spectroscopy measurements were used to characterize the new phase Li₂Fe₂ (MoO₄)₃. This material is obtained topochemically simply by the mixing of solutions of lithium iodide in acetonitrile with solid Fe₂(MoO₄)₃ at ambient temperature. Li₂Fe₂(MoO₄)₃ possesses the high temperature orthorhombic ferric molybdate $$\begin{gathered} Fe_2 (MoO_4 )_3 + 2LiI\xrightarrow{{CH_3 CN}}Li_2 Fe_2 (MoO_4 )_3 + I_2 \hfill \\ (solid)(solution)(solid)(solution) \hfill \\ \end{gathered}$$ structure. Guinier photographs were completely indexed in space group Pnca. Magnetic hyperfine splitting of the zero field Mössbauer spectrum below 12.5 K indicates a three-dimensional magnetically ordered state which susceptibility results show to be weakly ferromagnetic owing to probable canting of antiferromagnetically coupled sublattices.     

Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.     

The difference between Newtonian and relativistic forces

This paper discusses a new turn in the 148-year old electrodynamic force law controversy between the 1822 Ampère force law of the Newtonian electrodynamics and Grassmann's 1845 law which has become the electrodynamic force law of relativistic electromagnetism. Faced with the infallibility of Ampère's empirical law, defenders of relativity theory now argue that Ampère's law is equivalent to the relativistic law. This paper demonstrates that, far from being equivalent, the laws require two different mechanics of solid bodies, disagree on internally generated stresses, and predict different force distributions.     

Spin-Dependent Electron Properties of a Triple-Terminal Quantum Dot Structure

Electron transport properties of a triple-terminal Aharonov-Bohm interferometer are theoretically studied. By applying a Rashba spin-orbit coupling to a quantum dot locally, we find that remarkable spin polarization comes about in the electron transport process with tuning the structure parameters, i.e., the magnetic flux or quantum dot levels. When the quantum dot levels are aligned with the Fermi level, there only appear spin polarization in this structure by the presence of an appropriate magnetic flux. However, in absence of magnetic flux spin polarization and spin separation can be simultaneously realized with the adjustment of quantum dot levels, namely, an incident electron from one terminal can select a specific terminal to depart from the quantum dots according to its spin state.     

High-bandwidth and low-loss photonic crystal power-splitter with parallel output based on the integration of Y-junction and waveguide bends

A 1×2 power-splitter with parallel output that exhibits high-bandwidth and low-loss splitting for TE-polarized light is designed based on a photonic crystal slab in a silicon-on-insulator (SOI) material. The high performance is achieved by the integration of a Y-junction and 60° waveguide bends, which is designed to ensure single-mode operation, and keep the output channels of the power-splitter be parallel to the input channel. With a three-dimensional finite-difference time-domain (3D-FDTD) technique, ultralow-loss output of the optimized power-splitter with normalized transmission above 45% (in the range 3.216±0.18 dB) is obtained in the high-bandwidth range 1472–1634 nm, which covers the entire C-band of optical communication. In addition, the simulation results demonstrate that when the manufacture error of the lattice shift (dx) is in the range of ±10 nm, the disturbance of the transmission and the bandwidth are 1.52% and 6.79%, respectively. Both the specific result and the general idea of integration design are promising in the optical integrated circuit (OIC) and integrated optical devices in the future.     

Effect of secondary phases evolution in the first sintering process on the critical current density of Bi-2223/Ag tapes

Effect of the evolution of the secondary phases in the first sintering process on the microstructure and critical current density of Bi-2223/Ag tapes has been studied. The amount and grain size of secondary phases were characterized by XRD and SEM/EDS. It has been found that both the microstructure and critical current of the fully reacted tapes depended strongly on the secondary phases formed in the first sintering process. The (Ca,Sr)₂CuO₃ and (Ca,Sr)₁₄Cu₂₄O₄₁ phases were easily formed and to be stable at higher temperature, however, at lower temperature, the CuO particles appeared easily and keeping stable with dwelling time. The best conversion to Bi-2223, together with the lowest amount of the total secondary phases was achieved when samples treated at 830 °C in 8.5% O₂. Samples with the lowest amount and minimum size of secondary phase produced in the first sintering process will obtain the best performance of the fully reacted tapes. The optimum sintering parameters are obtained by controlling the evolution of the secondary phases during the first sintering process.