Transition between Airy1 and Airy2 processes and TASEP fluctuations

We consider the totally asymmetric simple exclusion process, a model in the KPZ universality class. We focus on the fluctuations of particle positions, starting with certain deterministic initial conditions. For large time t, one has regions with constant and linearly decreasing density. The fluctuations on these two regions are given by the Airy₁ and Airy₂ processes, whose one‐point distributions are the GOE and GUE Tracy‐Widom distributions of random matrix theory. In this paper we analyze the transition region between these two regimes and obtain the transition process. Its one‐point distribution is a new interpolation between GOE and GUE edge distributions. © 2007 Wiley Periodicals, Inc.     

Non-minimal pp-wave Einstein–Yang–Mills–Higgs model: color cross-effects induced by curvature

Non-minimal interactions in the pp-wave Einstein–Yang–Mills–Higgs (EYMH) model are shown to give rise to color cross-effects analogous to the magneto-electricity in the Maxwell theory. In order to illustrate the significance of these color cross-effects, we reconstruct the effective (associated, color, and color-acoustic) metrics for the pp-wave non-minimal seven-parameter EYMH model with parallel gauge and scalar background fields. Then these metrics are used as hints for obtaining explicit exact solutions of the non-minimally extended Yang–Mills and Higgs equations for the test fields propagating in the vacuum interacting with curvature. The influence of the non-minimal coupling on the test particle motion is interpreted in terms of the so-called trapped surfaces, introduced in the Analog Gravity theory.     

Kinetic study on the living/controlled cationic polymerization of p‐methoxystyrene coinitiated by tris(pentafluorophenyl)borane

A kinetic study of the living cationic polymerization of p‐methoxystyrene using 1‐(4‐methoxyphenyl)ethanol ( 1 )/B(C₆F₅)₃ initiating system in a mixture of CH₃CN with CH₂Cl₂ 1:1 (v/v) at room temperature was carried out utilizing a wide variety of conditions. The polymerization proceeded in a living fashion even in the presence of a large amount of water ([H₂O]/[B(C₆F₅)₃] ratio up to 20) to afford polymers whose M_n increased in direct proportion to monomer conversion with fairly narrow MWDs (M_w/M_n ≤ 1.3). The investigation revealed that the rate of polymerization was first‐order in B(C₆F₅)₃ concentration, while a negative order in H₂O concentration close to ?2 was obtained. It was also found that the rate of polymerization decreased with lowering temperature, which could be attributed to a decreased concentration in free Lewis acid, the true coinitiator of polymerization. A mechanistic scheme to explain the kinetic behavior of living p‐methoxystyrene polymerization is proposed, which has been validated by PREDICI simulation on multiple‐data curves obtained by ¹H NMR in situ polymerization experiment. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6928–6939, 2008     

Glycosyl alkoxythioimidates as complementary building blocks for chemical glycosylation

It is reported that S-glycosyl O-methyl phenylcarbamothioates (SNea carbamothioates) have a fully orthogonal character in comparison to S-benzoxazolyl (SBox) glycosides. This complete orthogonality was revealed by performing competitive glycosylation experiments in the presence of various promoters. The results obtained indicate that SNea carbamothioates have a very similar reactivity profile to that of glycosyl thiocyanates, yet are significantly more stable and tolerate selected protecting group manipulations. These features make the SNea carbamothioates new promising building blocks for further utilization in oligosaccharide synthesis.     

Analysis of the radiative transfer equation with highly assymetric phase function

This paper considers a scalar radiative transfer problem with high scattering anisotropy. Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal, which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2+ is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.     

An electrochemical study on the substituted spinel LiMn1.95Cr0.05O4

Cyclic voltammetry, galvanostatic charge?Cdischarge technique, potentiostatic intermittent titration technique (PITT), and electrochemical impedance spectroscopy (EIS) were used to study the behavior of a LiMn_1.95Cr_0.05O₄ (substituted lithium?Cmanganese spinel) electrode in nonaqueous electrolytes at 25 °C. Quantitative and qualitative changes of the electrode transport parameters as functions of lithium concentration were analyzed. Several equivalent circuits are discussed; the results obtained by different methods are compared. The PITT and EIS results are in good agreement; the chemical diffusion coefficient D varies within 10^?14?C10^?9 cm² s^?1 depending on the lithium content in the Li_xMn_1.95Cr_0.05O₄ electrode.     

Resonances for Dirac operators on the half-line

We consider the 1D Dirac operator on the half-line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: (1) asymptotics of counting function, (2) estimates on the resonances and the forbidden domain.     

Elliptic solutions of the Toda chain and a generalization of the Stieltjes–Carlitz polynomials

We construct new elliptic solutions of the restricted Toda chain. These solutions give rise to a new explicit class of orthogonal polynomials, which can be considered as a generalization of the Stieltjes–Carlitz elliptic polynomials. Relations between characteristic (i.e., positive definite) functions, Toda chain, and orthogonal polynomials are developed in order to derive the main properties of these polynomials. Explicit expressions are found for the recurrence coefficients and the weight function for these polynomials. In the degenerate cases of the elliptic functions, the modified Meixner polynomials and the Krall–Laguerre polynomials appear.