Non-Commutative Painlevé Equations and Hermite-Type Matrix Orthogonal Polynomials

We study double integral representations of Christoffel–Darboux kernels associated with two examples of Hermite-type matrix orthogonal polynomials. We show that the Fredholm determinants connected with these kernels are related through the Its–Izergin–Korepin–Slavnov (IIKS) theory with a certain Riemann-Hilbert problem. Using this Riemann-Hilbert problem we obtain a Lax pair whose compatibility conditions lead to a non-commutative version of the Painlevé IV differential equation for each family.     

Study of a dynamical system with a strange attractor and invariant tori

A simple three-dimensional time-reversible system of ODEs with quadratic nonlinearities is considered in a recent paper by Sprott (2014). The author finds in this system, that has no equilibria, the coexistence of a strange attractor and invariant tori. The goal of this letter is to justify theoretically the existence of infinite invariant tori and chaotic attractors. For this purpose we embed the original system in a one-parameter family of reversible systems. This allows to demonstrate the presence of a Hopf-zero bifurcation that implies the birth of an elliptic periodic orbit. Thus, the application of the KAM theory guarantees the existence of an extremely complex dynamics with periodic, quasiperiodic and chaotic motions. Our theoretical study is complemented with some numerical results. Several bifurcation diagrams make clear the rich dynamics organized around a so-called noose bifurcation where, among other scenarios, cascades of period-doubling bifurcations also originate chaotic attractors. Moreover, a cross section and other numerical simulations are also presented to illustrate the KAM dynamics exhibited by this system.     

Features of electrical discharges in air triggered by laser

A numerical study of laser-triggered discharges in air at atmospheric pressure is presented for an ultraviolet laser in small gaps. Two models, one for the ionization of the air by the laser pulse and the second for the streamer evolution have been computed. From results of numerical simulations the influence of the laser parameters such as energy, pulse duration and beam radius is analyzed and electron distributions are obtained for different small gaps. Electric field, streamer velocity and evolution of the ionized volume are calculated by means of streamer simulations. This paper shows the main features of the laser-triggered discharges and also the importance of using numerical simulations in a laser-triggered experiment.     

The mechanism of double proton transfer in dimers of uracil and 2-thiouracil--the reaction force perspective

The intermolecular double proton transfer in dimers of uracil and 2-thiouracil is studied through density functional theory calculations. The reaction force framework provides the basis for characterizing the mechanism that in all cases has been associated to a dynamic balance between polarization and charge transfer effects. It has been found that the barriers for proton transfer depend upon the nature of the acceptor atoms and its position within the seminal monomer. Actually, the change in the nature of the hydrogen bonds connecting the two monomers along the reaction coordinate may favor or disfavor the double-proton transfer.     

Nickel‐Catalyzed Cross‐Coupling of Alkyl Zinc Halides for the Formation of C(sp2)?C(sp3) Bonds: Scope and Mechanism

Optimal conditions for a general Ni‐catalysed Negishi cross‐coupling of alkyl zinc halides with aryl, heteroaryl and alkenyl halides have been determined. These conditions allow the reaction to take place smoothly, with low catalyst loading, and in the presence of a wide variety of functional groups to afford products in good yields at room temperature. DFT studies on the mechanism support the occurrence of a catalytic cycle involving transmetalation of the alkyl zinc halide to Ni^I followed by oxidative addition of the haloarene and C? C reductive elimination.