The collision energy effect on the stereodynamics of the Ca + HCl→CaCl + H reaction

Abstract

The stereodynamics of the reaction of Ca + HCl are calculated at three different collision energies based on the potential energy surface [Verbockhaven G et al. 2005 J. Chem. Phys. 122 204307] using quasi-classical trajectory theory. The polarization-dependent differential cross sections (PDDCSs) (2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), (2π/σ)(dσ21−/dωt) and the distributions of P(θr), P(φr), and P(θr,φr) are calculated. The results indicate that the rotational polarization of the CaCl product presents different characteristics for the different collision energies, and the effects of the collision energy on the vector potential, including the alignment, orientation, and PDDCSs, are not obvious.

Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback

“…In this section, the formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions of system (19) at τ 0 will be presented by employing the normal form method and the center manifold theorem. [30] For convenience, let t = sτ, y i (t) = x i (τt), and…”

“…Therefore, we have the following results. Theorem 2 The Hopf bifurcation of system (19) occurring at the origin when τ = τ 0 is supercritical (subcritical) if µ 2 > 0 (µ 2 < 0) and the bifurcating periodic solutions on the center manifold are stable (unstable) if δ < 0 (δ > 0).…”

“…In order to validate the above analysis, numerical simulations of system (19) have been carried out. The parameters are taken as τ 1 = τ 2 = τ, β 1 = β 2 = 1 and the rest of the parameters remain the same.…”

“…Many important advances have been made in neural network systems, [15][16][17] biological systems, [18] and control systems. [19][20][21] The time delay feedback control applied to suppress the vibration of the primary system was put forward by Olgac et al [22,23] The critical feature of the technique is the utilization of a controlled time delay in the feedback loop, which is traditionally looked upon as an undesirable element in dynamic controls. A novel active vibration absorption device, the centrifugal delayed resonator, was presented as an efficient way of eliminating undesired torsional oscillations in rotating mechanical structures.…”

Numerical Simulation of the Foundation of Wind Turbines about Different Reinforcement Types

“…Wind power generation is one of the energy technologies which our country supports especially, it is estimated that wind-power electricity generation will increase more than 30% every year in the future , wind energy will be utilized and paid attention to extensively day by day. The wind-powered electricity unit , as a kind of new-type towering structure, for its mass force , air motive force and operating loads, is always in complicated strength state [1][2][3] . As a special reinforced concrete structure, our country only imitates external experience in the design at present, have not formed the normal theoretical basis yet, leading to the fact that pertinence is insufficient and there are certain hidden dangers.…”