Revisiting the generalized pseudospectral method: Radial expectation values,fine structure,and hyperfine splitting of confined atom

This paper revisits the generalized pseudospectral (GPS) method on the calculation of various radial expectation values of atomic systems, especially on the spatially confined hydrogen atom and harmonic oscillator. As one of the collocation methods based on global functions, the powerfulness and robustness of the GPS method has been well established in solving the radial Schrödinger equation with high accuracy. However, in our recent work, it was found that the previous calculations based on the GPS method for the radial expectation values of confined systems show significant discrepancies with other theoretical methods. In this work we have tackled such a problem by tracing its source to the GPS method and found that the method itself may not be able to obtain the system wave function at the origin. Combined with an extrapolation method developed here, the GPS method can fully reproduce the radial quantities obtained by other theoretical methods, but with more flexibility, efficiency, and accuracy. We apply the GPS-extrapolation method to investigate the relatievistic fine structure and hyperfine splitting of confined hydrogen atom in s-wave states where the zero-point wave function dominates. Good agreement with previous predictions is obtained for confined hydrogen in low-lying states, and benchmark results are obtained for high-lying excited states. The perturbation treatment of the fine and hyperfine interactions is validated in the confining environment.     

Completely p-summing maps on the operator Hilbert space OH

We prove the completely p-summing ideals of OH are all equal as sets for 1?p<2. A phase transition then occurs at p=2 as we also show for p?2, the completely p-summing ideals of OH turn out as sets to be Schatten ideal classes with the limiting case being the Schatten 4-class ideal S₄ when p→∞.     

Identification of protein domains on major pilin MrkA that affects the mechanical properties of Klebsiella pneumoniae type 3 fimbriae

The Klebsiella pneumoniae type 3 fimbriae are mainly composed of MrkA pilins that assemble into a helixlike filament. This study determined the biomechanical properties of the fimbriae and analyzed 11 site-directed MrkA mutants to identify domains that are critical for the properties. Escherichia coli strains expressing type 3 fimbriae with an Ala substitution at either F34, V45, C87, G189, T196, or Y197 resulted in a significant reduction in biofilm formation. The E. coli strain expressing MrkAG189A remained capable of producing a normal number of fimbriae. Although F34A, V45A, T196A, and Y197A substitutions expressed on E. coli strains produced sparse quantities of fimbriae, no fimbriae were observed on the cells expressing MrkAC87A. Further investigations of the mechanical properties of the MrkAG189A fimbriae with optical tweezers revealed that, unlike the wild-type fimbriae, the uncoiling force for MrkAG189A fimbriae was not constant. The MrkAG189A fimbriae also exhibited a lower enthalpy in the differential scanning calorimetry analysis. Together, these findings indicate that the mutant fimbriae are less stable than the wild-type. This study has demonstrated that the C-terminal β strands of MrkA are required for the assembly and structural stability of fimbriae.     

Metal-oxide-semiconductor characteristics of lanthanum cerium oxide film on Si

Metal-organic decomposed lanthanum cerium oxide (La _x Ce _y O _z ) film had been spin-coated on n-type Si substrate. Effects of post-deposition annealing temperature and time on the metal-oxide-semiconductor (MOS) properties of the film were studied. As temperature increased from 400 to 1000°C for 15 minutes dwell time, La _x Ce _y O _z demonstrated a decrease in interface trap density (D _it) and total interface trap density (D _total), which were related to the formation of SiO _x /silicates interfacial layer (IL). The lowest leakage current density and highest dielectric breakdown voltage (V _B) was obtained in 1000°C-annealed sample. When longer annealing times (30–120 minutes) were studied on the 1000°C-annealed sample, the sample annealed at 1000°C for 120 min showed the best MOS characteristics with V _B of 30 V. Reasons contributing to such observation were discussed.     

Inequalities for M and N0-matrices

In this paper, we study inequalities for two M or N₀-matrices A,B with A≤B. Necessary and sufficient conditions are given for positive linear combination of A and B to be an N₀-matrix.     

Applying Ant System for solving Unequal Area Facility Layout Problems

Ant Colony Optimization (ACO) is a young metaheuristic algorithm which has shown promising results in solving many optimization problems. To date, a formal ACO-based metaheuristic has not been applied for solving Unequal Area Facility Layout Problems (UA-FLPs). This paper proposes an Ant System (AS) (one of the ACO variants) to solve them. As a discrete optimization algorithm, the proposed algorithm uses slicing tree representation to easily represent the problems without too restricting the solution space. It uses several types of local search to improve its search performance. It is then tested using several case problems with different size and setting. Overall, the proposed algorithm shows encouraging results in solving UA-FLPs.     

Fractional Gouy phase

In general, the total Gouy phase shift has the form n pi, where n need not be an integer. As a result of the Fourier transforming property of a lens, the Gouy phase is found to be related to the types of discontinuities at the upper or lower range of the pupil function Q(c) resulting from the asymptotic order of the Fourier transform. The sign of the Gouy phase is also related to the slope of the pupil function. The oscillations of the Gouy phase shift arise from the strength of the nondominant discontinuity.     

Multiple Solitary Waves Due to Second-Harmonic Generation in Quadratic Media

Summary. A detailed mathematical analysis is undertaken of solitary-wave solutions of a system of coupled nonlinear Schr?dinger equations describing second-harmonic generation in optical materials with χ ⁽²⁾ nonlinearity. The so-called bright-bright case is studied exclusively. The system depends on a single dimensionless parameter α that includes both wave and material properties. Using methods from the calculus of variations, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive α . Recently, bound states (multipulsed solitary waves) have been found numerically. Using numerical continuation, the region of existence of these solutions is revealed to be α ∈ (0,1), and the bifurcations occurring at the two extremes of this interval are uncovered. Received February 12, 1997; second revision received September 22, 1997     

Nanoenergetic Composites with Fluoropolymers: Transition from Powders to Structures

Over the years, nanoenergetic materials have attracted enormous research interest due to their overall better combustion characteristics compared to their micron-sized counterparts. Aluminum, boron, and their respective alloys are the most extensively studied nanoenergetic materials. The majority of the research work related to this topic is confined to the respective powders. However, for practical applications, the powders need to be consolidated into reactive structures. Processing the nanoenergetic materials with polymeric binders to prepare structured composites is a possible route for the conversion of powders to structures. Most of the binders, including the energetic ones, when mixed with nanoenergetic materials even in small quantities, adversely affects the ignitability and combustion performance of the corresponding composites. The passivating effect induced by the polymeric binder is considered unfavorable for ignitability. Fluoropolymers, with their ability to induce pre-ignition reactions with the nascent oxide shell around aluminum and boron, are recognized to sustain the ignitability of the composites. Initial research efforts have been focused on surface functionalizing approaches using fluoropolymers to activate them further for energy release, and to improve the safety and storage properties. With the combined advent of more advanced chemistry and manufacturing techniques, fluoropolymers are recently being investigated as binders to process nanoenergetic materials to reactive structures. This review focuses on the major research developments in this area that have significantly assisted in the transitioning of nanoenergetic powders to structures using fluoropolymers as binders.     

Benchmark calculations of Rényi,Tsallis entropies,and Onicescu information energy for ground state helium using correlated Hylleraas wave functions

Accurate values of physical quantities serve as the stepping stone for further researches. Consequently, we provide benchmark values of Shannon, Rényi, Tsallis entropies, and Onicescu information energy for ground state helium. With the highly correlated Hylleraas wave functions, our calculations fully considered the effect of electron correlation. Presented numerical results converge with increasing size of basis set, fulfill analytic relations between the quantities, and satisfactorily agree with those in the literature. In particular, we present these information-theoretic quantities with high accuracy, and it is believed that the reported data would be a valuable reference for further research on information-theoretic quantities of atomic and molecular systems.