Full rate constant matrix contraction method for obtaining branching ratio of unimolecular decomposition

The branching ratio of unimolecular decomposition can be evaluated by solving the rate equations. Recent advances in automated reaction path search methods have enabled efficient construction of the rate equations based on quantum chemical calculations. However, it is still difficult to solve the rate equations composed of hundreds or more elementary steps. This problem is especially serious when elementary steps that occur in highly different timescales coexist. In this article, we introduce an efficient approach to obtain the branching ratio from a given set of rate equations. It has been derived from a recently proposed rate constant matrix contraction (RCMC) method, and termed full‐RCMC (f‐RCMC). The f‐RCMC gives the branching ratio without solving the rate equations. Its performance was tested numerically for unimolecular decomposition of C₃H₅ and C₄H₅. Branching ratios obtained by the f‐RCMC precisely reproduced the values obtained by numerically solving the rate equations. It took about 95 h to solve the rate equations of C₄H₅ consisting of 234 elementary steps. In contrast, the f‐RCMC gave the branching ratio in less than 1 s. The f‐RCMC would thus be an efficient alternative of the conventional kinetic simulation approach. © 2016 Wiley Periodicals, Inc.     

On the free vibration response of rectangular plates,partially supported on elastic foundation

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind.     

On some Fermat rules for set-valued optimization problems

The aim of this article is to obtain necessary optimality conditions for Pareto minima in set-valued optimization problems. We employ a new method to derive generalized Fermat rules for set-valued optimization. This method is based on openness results for multifunctions and allows recovery of a large number of results and, at the same time, getting several new ones.     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

The solubility of bosentan in aqueous-2-propanol mixtures at several temperatures,measurement and data correlation

ABSTRACT

The solubilities of bosentan (BST) in binary aqueous mixtures of 2-propanol at temperatures ranging from 293.15 to 313.15 K were determined using a shake-flask method. The produced data were modelled with the Jouyban-Acree-van’t Hoff model and difference between the predicted data and experimental ones were illustrated by percent average relative deviations (%ARD). Moreover, the thermodynamic functions of dissolution for BST in the aqueous 2-propanol solutions were computed which suggest that the dissolution process is endothermic and not spontaneous.     

Bi-Hamiltonian structure of multi-component Novikov equation

In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure.     

Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems

In this article we give sufficient conditions on the scattering data of a defocusing or focusing Zakharov-Shabat system in order that its potential is square integrable. For a dense subset of integrable as well as square integrable potentials, we show that the scattering data actually satisfy these sufficient conditions.     

Model for spontaneous frequency sweeping of an Alfvén wave in a toroidal plasma

We study the frequency chirping signals arising from spontaneously excited toroidial Alfvén eigenmode (TAE) waves that are being driven by an inverted energetic particle distribution whose free energy is tapped from the generic particle/wave resonance interaction. Initially a wave is excited inside the Alfvén gap with a frequency determined from the linear tip model of Rosenbluth, Berk and Van dam (RBV) [1]. Hole/clumps structures are formed and are observed to chirp towards lower energy states. We find that the chirping signals from clump enter the Alfvén continuum which eventually produce more rapid chirping signals. The accuracy of the adiabatic approximation for the mode evolution is tested and verified by demonstrating that a WKB-like decomposition of the time response for the field phase and amplitude agree with the data. Plots of the phase space structure correlate well with the chirping dependent shape of the separatrix structure. A novel aspect of the simulation is that it performed close to the wave frame of the phase space structure, which enables the numerical time step to remain the same during the simulation, independent of the rest frame frequency.     

Linear wave dispersion relation of a magnetized relativistic rectilinear electron beam-dielectric system

A general dispersion relation is derived for a relativistic rectilinear electron beam of arbitrary momentum distributions interacting with a dielectric in a guide magnetic field, on the basis of Maxwell equations and the relativistic Vlasov equation. The instability occurs when the beam velocity exceeds the wave phase velocity in the medium. The linear wave dispersion relation, growth rate, spatial growth rate are studied analytically for delta and Lorentzian distributions of beam momentums in detail. The results are of importance for a new kind of high-power microwave generation or amplification devices based on anomalous Doppler effect.