Non-Equilibrium Dynamics of Dyson’s Model with an Infinite Number of Particles

Dyson’s model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant β/2. We give sufficient conditions for initial configurations so that Dyson’s model with β = 2 and an infinite number of particles is well defined in the sense that any multitime correlation function is given by a determinant with a continuous kernel. The class of infinite-dimensional configurations satisfying our conditions is large enough to study non-equilibrium dynamics. For example, we obtain the relaxation process starting from a configuration, in which every point of \mathbbZ{\mathbb{Z}} is occupied by one particle, to the stationary state, which is the determinantal point process with the sine kernel.     

New limits on coupling of fundamental constants to gravity using 87Sr optical lattice clocks

The 1S0-3P0 clock transition frequency nuSr in neutral 87Sr has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the 1 x 10(-15) level makes nuSr the best agreed-upon optical atomic frequency. We combine periodic variations in the 87Sr clock frequency with 199Hg+ and H-maser data to test local position invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant alpha, electron-proton mass ratio mu, and light quark mass. Furthermore, after 199Hg+, 171Yb+, and H, we add 87Sr as the fourth optical atomic clock species to enhance constraints on yearly drifts of alpha and mu.     

M1 states in 58Ni observed by proton inelastic scattering at 65 MeV

Inelastic proton scattering at 65 MeV was used to study 1⁺ states in ⁵⁸Ni. A new 1⁺ state was found at an excitation of 5.166 MeV. The angular distributions for the 1⁺ states at 2.903 and 5.166 MeV were well reproduced by a DWBA calculation under the assumptions of pure $\text{v(}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}\text{and}\text{v(}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ configurations, respectively. The angular distribution for the previously suggested 1⁺ state at 7.721 MeV was not well discribed by the DWBA calculation with the isoscalar $\text{(}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ wave function. The shape of the angular distribution for the 10.672 MeV, 1⁺ state was well reproduced by the DWBA calculation with the isovector $\text{(}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}$ wave function.     

Dimethylisopropylsilyl ether derivatives in gas chromatography-mass spectrometry of some prostanoids. Application to the microdetermination of 15-ketoprostaglandin F2 alpha formed by enzymatic conversion of PGF2 alpha in vitro

Treatment of 15-ketoprostaglandin F2 alpha (15-keto-PGF2 alpha) with ethereal diazomethane at -78 degrees C provided only the expected methyl ester (ME), without the formation of the pyrazoline adduct. The electron-ionization mass spectrum of the dimethylisopropylsilyl (DMiPS) ether derivative of 15-keto-PGF2 alpha ME showed the molecular ion, and the characteristic fragment ion of [M-43]+ was of high abundance. The appearance of these ions in the high-mass region made it possible to determine trace amounts of 15-keto-PGF2 alpha in biological specimens without any interference from endogenous substances. The detection limit for the DMiPS ether derivatives of 15-keto-PGF2 alpha ME was 12 pg (signal-to-noise ratio = 10). The method was applied to the analysis of 15-keto-PGF2 alpha obtained by the enzymatic conversion of PGF2 alpha with 15-hydroxyprostaglandin dehydrogenase in vitro.     

Mechanism of aerobic decomposition of Angeli's salt (sodium trioxodinitrate) at physiological pH

The recent determination that Angeli's salt may have clinical application as a nitrogen oxide donor for treatment of cardiovascular diseases such as heart failure has led to renewed interest in the mechanism and products of thermal decomposition of Angeli's salt under physiological conditions. In this report, several mechanisms are evaluated experimentally and by quantum mechanical calculations to determine whether HNO is in fact released from Angeli's salt in neutral, aerobic solution. The mechanism of product autoxidation is also considered.     

Analysis of the order parameter for uniform nearest particle system

The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space . The rigorous upper bound ^(mf) = ( – 1)/ for the order parameter ₂, is given by the correlation identity and the FKG inequality. Then an improvement of this bound ^(mf) is shown in a similar fashion; C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value _c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense.     

Determinantal Process Starting from an Orthogonal Symmetry is a Pfaffian Process

When the number of particles N is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index ν>−1 (BESQ^(ν)) are determinantal processes for arbitrary fixed initial configurations. In the present paper we prove that, if initial configurations are distributed with orthogonal symmetry, they are Pfaffian processes in the sense that any multitime correlation functions are expressed by Pfaffians. The 2×2 skew-symmetric matrix-valued correlation kernels of the Pfaffians processes are explicitly obtained by the equivalence between the noncolliding BM and an appropriate dilatation of a time reversal of the temporally inhomogeneous version of noncolliding BM with finite duration in which all particles start from the origin, Nδ ₀, and by the equivalence between the noncolliding BESQ^(ν) and that of the noncolliding squared generalized meander starting from Nδ ₀.     

Influence of 4‐fluorophenyl pendants in thieno[3,4‐b]thiophene‐benzo[1,2‐b:4,5‐b′]dithiophene‐based polymers on the performance of photovoltaics

Polymers consisting of benzo[1,2‐b:4,5‐b′]dithiophene and thieno[3,4‐b]thiophene units (PTB‐based polymers), either fully or partially containing 4‐fluorophenyl pendants, are synthesized as electron donor materials for inverted‐type polymer solar cells (PSCs). The influence of the 4‐fluorophenyl pendant content on the thermal and optical properties, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), the hole mobilities, and photovoltaic performances are investigated. As the 4‐fluorophenyl pendant content increased, the HOMO and LUMO of the polymers were deepened proportionally and the open‐circuit voltages of the PSCs improved. Incorporation of 4‐fluorophenyl pendants into the polymers also affected the crystallinity, orientation, and compatibility with [6,6]‐phenyl‐C₆₁‐butyric acid methyl ester in the active layers, leading to nonlinearities in the short‐circuit current densities, and fill factors. The incorporation of an appropriate number of 4‐fluorophenyl pendants enhanced the power conversion efficiencies of the PSC devices from 2.25 to 3.96% for identical device configurations. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1586–1593