A model of nonlinear electrodynamics

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.     

Simultaneously Probing Two Ultrafast Condensed‐Phase Molecular Symmetry Breaking Events by Two‐Dimensional Infrared Spectroscopy

In condensed phases, a highly symmetric gas‐phase molecule lowers its symmetry under perturbation of the solvent, which is vital to a variety of structural chemistry related processes. However, the dynamical aspects of solvent‐mediated symmetry‐breaking events remain largely unknown. Herein, direct evidence for two types of solvent‐mediated symmetry‐breaking events that coexist on the picosecond timescale in a highly symmetric anion, namely, hexacyanocobaltate, is presented: 1) an equilibrium symmetry‐breaking event in which a solvent‐bound species having lowered symmetry undergoes a population exchange reaction with the symmetry‐retaining species; 2) a dynamic symmetry‐breaking event that is composed of many dynamic population‐exchange reactions under fluctuating solvent interactions. Ultrafast two‐dimensional infrared spectroscopy is used to simultaneously observe and dynamically characterize these two events. This work opens a new window into molecular symmetry and structural dynamics under equilibrium and non‐equilibrium conditions.     

Dimers linked by type‐I C—F...F—C contacts in (Z)‐3‐methyl‐4‐[2‐(4‐methylphenyl)hydrazinylidene]‐1‐(pentafluorophenyl)‐1H‐pyrazol‐5(4H)‐one

The title compound, C₁₇H₁₁F₅N₄O, is described and compared with two closely related analogues in the literature. There are two independent molecules in the asymmetric unit, linked by N—H...O hydrogen bonds and π–π interactions into dimeric entities, presenting a noticeable noncrystallographic C₂ symmetry. These dimers are in turn linked by a medium‐strength type‐I C—F...F—C interaction into elongated tetramers. Much weaker C—H...F contacts link the tetramers into broad two‐dimensional substructures parallel to (101).     

XPS of oxygen atoms on Ag(111) and Ag(110) surfaces: Accurate study with SAC/SAC‐CI combined with dipped adcluster model

O1s core‐electron binding energies (CEBE) of the atomic oxygens on different Ag surfaces were investigated by the symmetry adapted cluster‐configuration interaction (SAC‐CI) method combined with the dipped adcluster model, in which the electron exchange between bulk metal and adsorbate is taken into account properly. Electrophilic and nucleophilic oxygens (O_elec and O_nuc) that might be important for olefin epoxidation in a low‐oxygen coverage condition were focused here. We consider the O1s CEBE as a key property to distinguish the surface oxygen states, and series of calculation was carried out by the Hartree–Fock, Density functional theory, and SAC/SAC‐CI methods. The experimental information and our SAC/SAC‐CI results indicate that O_elec is the atomic oxygen adsorbed on the fcc site of Ag(111) and that O_nuc is the one on the reconstructed added‐row site of Ag(110) and that one‐ and two‐electron transfers occur, respectively, to the O_elec and O_nuc adclusters from the silver surface. © 2013 Wiley Periodicals, Inc.     

Existence of pulses in excitable media with nonlocal coupling

We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with finite-range, non-local coupling. Our approach replaces methods from geometric singular perturbation theory, that had been crucial in previous existence proofs, by a PDE oriented approach, relying on exponential weights, Fredholm theory, and commutator estimates.     

Q‐symmetry and conditional Q‐symmetries for Drinfel'd–Sokolov–Wilson system

We study in this paper the Q‐symmetry and conditional Q‐symmetries of Drinfel'd–Sokolov–Wilson equations. The solutions which we obtain in this paper take the form of convergent power series with easily computable components. Copyright © 2014 John Wiley & Sons, Ltd.     

Dirac reduction for nonholonomic mechanical systems and semidirect products

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange–Dirac and Hamilton–Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler–Poincaré–Suslov equations with advected parameters and the implicit Lie–Poisson–Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin–Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.     

Quantum McKay Correspondence for Disc Invariants of Toric Calabi–Yau 3-orbifolds

We announce a result on quantum McK ay correspondence for disc invariants of outer legs in toric Calabi–Yau 3-orbifolds, and illustrate our method in a special example [C3/Z5(1, 1, 3)].