Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation

This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in the highest weight Virasoro module and commute for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q(λ) contains the “dual” nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system. Received: 2 December 1996 / Accepted: 11 March 1997     

The distribution of liberated energy and injected charge under normal incidence of a fast electron beam on a target

Formulas for the distributions of the liberated energy and injected charge are derived within the diffusion model of the kinetic equation for an electron beam normally incident on the target. The theory does not involve empirical adjustable parameters. The calculation of the liberated energy for the case of a planar directional electron source in an infinite medium (C, Al, Sn, and Pb) correlates well with the Spencer data, obtained from the exact solution of the Bethe equation, which is also used as the basis in the diffusion model.     

Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.     

TR-LII for sizing of carbon particles forming at room temperature

Time-resolved laser-induced incandescence (TR-LII) was applied for the determination of particle sizes during carbon-particle formation from supersaturated atomic carbon vapor that was generated by laser photolysis of carbon suboxide (C₃O₂) at room temperature. Thus, the solid carbon particles were formed under hydrogen-free conditions. The TR-LII technique was used for in situ size measurement of growing carbon particles and samples of final particles were analyzed by transmission electron microscopy (TEM). It was found that the particles grow to a final size of 4–12 nm within 0.02–1 ms. The properties of the obtained particles depend on the initial conditions in the reaction volume, i.e. concentration of carbon suboxide, pressure and type of gas diluter, photolysis wavelength, and laser pulse energy. The comparison of TR-LII and TEM particle sizing results yields information about the effective thermal energy accommodation coefficients for He, Ar, CO, and C₃O₂ molecules on carbon particles. PACS 61.46.Df; 07.60.-j; 78.70.-g     

Mechanical endurance of polymer electrolyte membrane and PEM fuel cell durability

The life of proton exchange membrane fuel cells (PEMFC) is currently limited by the mechanical endurance of polymer electrolyte membranes and membrane electrode assemblies (MEAs). In this paper, the authors report recent experimental and modeling work toward understanding the mechanisms of delayed mechanical failures of polymer electrolyte membranes and MEAs under relevant PEMFC operating conditions. Mechanical breach of membranes/MEAs in the form of pinholes and tears has been frequently observed after long‐term or accelerated testing of PEMFC cells/stacks. Catastrophic failure of cell/stack due to rapid gas crossover shortly follows the mechanical breach. Ex situ mechanical characterizations were performed on MEAs after being subjected to the accelerated chemical aging and relative humidity (RH) cycling tests. The results showed significant reduction of MEA ductility manifested as drastically reduced strain‐to‐failure of the chemically aged and RH‐cycled MEAs. Postmortem analysis revealed the formation and growth of mechanical defects such as cracks and crazing in the membranes and MEAs. A finite element model was used to estimate stress/strain states of an edge‐constrained MEA under rapid RH variations. Damage metrics for accelerated testing and life prediction of PEMFCs are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2346–2357, 2006     

Application of Horner–Emmons Olefination to the Crown-Ether Derivatives

An effective synthetic approach to the preparation of a new crown-ether vinylogs involving the Horner–Emmons olefination of carbonyl precursors with the use of C₂- and C₅-phosphonates was proposed. The effects of the conjugation chain length and the nature of the terminal polar functions in the phosphonate reagent on the yield and process stereoselectivity were discussed.     

Luminescent Zn and Pd tetranaphthaloporphyrins

Zn and Pd complexes of meso-tetraphenyltetranaphthaloporphyrins (Ph(4)TNP) exhibit strong infrared absorption bands and luminesce in solutions at room temperature. S1 --> S0 fluorescence (lambda(max) = 732 nm, phi = 5.3%) is the predominant emission in the case of ZnPh(4)TNP (1). This emission is in part due to the delayed fluorescence (phi = 1.1%). Phosphorescence (T1 --> S0) of 1 (lambda(max) = 973 nm) is very weak (phi = 0.04%) and occurs with lifetime of about 440 micros in deoxygenated DMF. In the case of PdPh(4)TNP (2), almost no S1 --> S0 fluorescence could be observed, while the main emission detected was T1 --> S0 phosphorescence (lambda(max) = 938 nm). The phosphorescence of 2 occurs with lifetime of about 65 micros and (phi=6.5%) in deoxygenated DMF solution. Metalloporphyrins 1 and 2 are promising near infrared dyes biomedical applications.     

Kinetics and mechanism of the Co(II)-assisted oxidation of thioureas by dioxygen

Catalytic oxidation of N,N'-dimethylthiourea and thiourea by dioxygen in water using a new cobalt(II) complex of octasulfophenyltetrapyrazinoporphyrazine was performed under mild conditions. The reaction is shown to include the formation of an intermediate anionic five-coordinate complex followed by an unusual two-electron oxidation to produce the corresponding urea and elemental sulfur (S8). Kinetic and thermodynamic parameters for the different reaction steps of the process were determined. Drastic differences in catalytic activity of cobalt and iron octasulfophenyltetrapyrazinoporphyrazines were observed.     

Effective force field for liquid hydrogen fluoride from ab initio molecular dynamics simulation using the force-matching method

A recently developed force-matching method for obtaining effective force fields for condensed matter systems from ab initio molecular dynamics (MD) simulations has been applied to fit a simple nonpolarizable two-site pairwise force field for liquid hydrogen fluoride. The ab initio MD in this case was a Car-Parrinello (CP) MD simulation of 64 HF molecules at nearly ambient conditions within the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure included a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The performance of the force-match potential was examined for the gas-phase dimer and for the liquid phase at various temperatures. The model was able to reproduce correctly the bent structure and energetics of the gas-phase dimer, while the results for the structural properties, self-diffusion, vibrational spectra, density, and thermodynamic properties of liquid HF were compared to both experiment and the CP MD simulation. The force-matching model performs well in reproducing nearly all of the liquid properties as well as the aggregation behavior at different temperatures. The model is computationally cheap and compares favorably to many more computationally expensive potential energy functions for liquid HF.