Berry phase magnification in optical microcoil resonators

We have studied the effects of the Berry phase on the linear transmission properties of optical microcoil resonators and analyzed the resonant behavior for different input polarizations and coil geometries. Contrary to previous expectations, we find that on resonance the size of the Berry phase shift can be magnified significantly, leading to a measurable polarization rotation for some geometries. Our model also considers other polarization effects including elasto-optic bend birefringence and the polarization dependent coupling coefficients, which were also previously neglected, and we still find that observable Berry phase effects persist. For example, in a three turn microcoil with a diameter of 0.2 mm, close to 100% of an initially x polarized light will be coupled into the orthogonal y polarization, due to the optical activity arising from the cumulative effects of Berry phase on resonance. More generally, the cross-polarization coupling also significantly influences the resonance extinction ratio and quality factor.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Wavelength-tunable high-power picosecond pulses from a fiber-pumped diode-seeded high-gain parametric amplifier

We describe a high-gain optical parametric amplifier (OPA) and optical parametric generator (OPG) system pumped by a fiber chirped-pulse amplification source based on novel large-mode-area fiber components. 45-nJ OPG thresholds and 34% pump-signal conversion efficiencies are obtained for ~4-ps pulses. OPA gains in excess of 75 dB and pump-signal conversion efficiencies of ~39% (external) are demonstrated. Furthermore, we show that injection seeding of such high-gain parametric devices by use of a low-power continuous-wave beam results in high-power (>18-kW) picosecond pulses with a time-bandwidth produce of ~0.65, some ten times less than from a free-running OPG. Using such an approach, we obtain 2.7-ps 50-nJ pulses at 1.310 mum .     

Structural and free‐volume analysis for alkyl‐substituted palladium‐catalyzed poly(norbornene): A combined experimental and Monte Carlo investigation

Increasing the length of an alkyl side chain on a rigid polynorbornene (PNB) backbone is shown to decrease the glass‐transition temperature of the resultant polymer, decrease the density of the bulk polymer, decrease the number and average free‐volume element size present, and decrease the permeability of gases through the polymer. Methyl‐, butyl‐, and hexyl‐substituted PNBs were investigated. Experimental results were compared with predictions based on molecular modeling. By using models that provided good agreement between the experimental and simulated wide‐angle diffraction patterns, the distributions of free‐volume elements were predicted. These predictions clearly indicate that the number of large free‐volume elements decreases as the length of the side chain increases, suggesting that the flexible aliphatic side chains can be largely accommodated within the free volume between the rigid PNB backbones. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 215–233, 2006     

Impact of average free‐volume element size on transport in stereoisomers of polynorbornene. II. Impact of temperature on solubility

This article evaluates the influence of temperature on the sorption of gases in two isomers of polynorbornene. The subject polymers were stereoisomers with nearly identical bulk density and total free volume. Because of differences in the mobility of the polymer backbone, the isomers packed differently resulting in differences in the average free‐volume element size within the matrix. The influence of these differences on free‐volume element size was characterized by the heat of sorption of gases in the matrix. The most pronounced differences were observed in the isosteric heats of sorption of condensable carbon dioxide and methane in the polymer isomers. This analysis suggests that the relative space available for sorption into free‐volume elements is higher in the methyl II isomer relative to methyl III. These conclusions support the physical characterizations reported in Part I of this series suggesting that the methyl II isomer has larger average free‐volume elements but fewer of them than the methyl III isomer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1939–1946, 2003     

Application of principal component analysis to a full profile correlative analysis of FTIR spectra

We have demonstrated an informatics methodology for finding correlations between the full profile Fourier transform infrared spectra of polycrystalline 3C‐silicon carbide (poly‐SiC) films and their growth conditions, thereby developing high‐throughput structure‐process relationships. Because SiC films are a structural element in photonic sensors, this paper focuses on the interpretation of their optical response, the multivariate tracking of critical processing pathways, and the identification of controlling processing mechanisms. Using principal component analysis, we have developed a data analysis tool to aid in the assessment of the relative contributions of experimental parameters in low‐pressure chemical vapor deposition processes to optical responses on the basis of the size of eigenvalues of the spectral data set. The applied methodology for identifying spectral relationships of stoichiometry, dopant chemistry, and microstructure of poly‐SiC provides more effective guidelines to manipulate optical responses by controlling multiple experimental parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

Secondary structure analysis of peptides with relevance to iron–sulfur cluster nesting

Peptides coordinated to iron–sulfur clusters, referred to as maquettes, represent a synthetic strategy for constructing biomimetic models of iron–sulfur metalloproteins. These maquettes have been successfully employed as building blocks of engineered heme-containing proteins with electron-transfer functionality; however, they have yet to be explored in reactivity studies. The concept of iron–sulfur nesting in peptides is a leading hypothesis in Origins-of-Life research as a plausible path to bridge the discontinuity between prebiotic chemical transformations and extant enzyme catalysis. Based on past biomimetic and biochemical research, we put forward a mechanism of maquette reconstitution that guides our development of computational tools and methodologies. In this study, we examined a key feature of the first stage of maquette formation, which is the secondary structure of aqueous peptide models using molecular dynamics simulations based on the AMBER99SB empirical force field. We compared and contrasted S…S distances, [2Fe-2S] and [4Fe-4S] nests, and peptide conformations via Ramachandran plots for dissolved Cys and Gly amino acids, the CGGCGGC 7-mer, and the GGCGGGCGGCGGW 16-mer peptide. Analytical tools were developed for following the evolution of secondary structural features related to [Fe-S] cluster nesting along 100 ns trajectories. Simulations demonstrated the omnipresence of peptide nests for preformed [2Fe-2S] clusters; however, [4Fe-4S] cluster nests were observed only for the 16-mer peptide with lifetimes of a few nanoseconds. The origin of the [4Fe-4S] nest and its stability was linked to a “kinked-ribbon” peptide conformation. Our computational approach lays the foundation for transitioning into subsequent stages of maquette reconstitution, those being the formation of iron ion/iron–sulfur coordinated peptides. © 2018 Wiley Periodicals, Inc.