Bifurcations of phase portraits of spherical pendulum with vibrating suspension point

We consider a spherical pendulum whose suspension point performs high-frequency oscillations. We derive the averaged over these oscillations Hamiltonian of the problem. We assume that these oscillations are such that the averaged Hamiltonian is invariant with respect to rotations about the vertical direction. Under this assumption we give complete description of bifurcations of phase portraits of the averaged system.Comment: arXiv admin note: text overlap with arXiv:1605.0944

Bifurcations of phase portraits of pendulum with vibrating suspension point

We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two parameters. We give complete description of bifurcations of phase portraits of this averaged system

Catalytic Dehydration of Ethanol to Ethylene over Alkali-Treated HZSM-5 Zeolites

The catalytic performance of alkali-treated HZSM-5 catalysts was investigated in a continuous fixed-bed microreactor. The properties of the parent and modified HZSM-5 catalysts were characterized by X-ray diffraction (XRD), inductively coupled plasma atomic emission spectroscopy (ICP-AES), N2 adsorption and temperature programmed desorption of NH3 (NH3-TPD). The results show that the alkali treatment is a suitable method to modify the HZSM-5 catalyst for ethanol dehydration to ethylene. The HZSM-5 catalyst with 0.4 mol L-1 NaOH shows high activity and good stability. The improved catalytic performances of alkali-treated catalysts are mainly attributed to the created mesopores and the decreased number of strong acid sites during the alkali treatment

Stability analysis of apsidal alignment in double-averaged restricted elliptic three-body problem

We are dealing with the averaged model used to study the secular effects in the motion of a body of the negligible mass in the context of a spatial restricted elliptic three-body problem. It admits a two-parameter family of equilibria (stationary solutions) corresponding to the motion of the third body in the plane of primaries’ motion, so that the apse line of the orbit of this body is aligned with the apse lines of the primaries’ orbits. The aim of our investigation is to analyze the stability of these equilibria. We show that they are stable in the linear approximation. The Arnold–Moser stability theorem provides sufficient conditions under which this means stability in a nonlinear sense too. These conditions are violated for parameters of the problem that belong to a set formed by a finite number of analytic curves in the parameters’ plane. As it turned out, in the system under consideration, violation of these conditions in some cases actually leads to an instability

Elucidating the strain–vacancy–activity relationship on structurally deformed Co@CoO nanosheets for aqueous phase reforming of formaldehyde

Lattice strain modulation and vacancy engineering are both effective approaches to control the catalytic properties of heterogeneous catalysts. Here, Co@CoO heterointerface catalysts are prepared via the controlled reduction of CoO nanosheets. The experimental quantifications of lattice strain and oxygen vacancy concentration on CoO, as well as the charge transfer across the Co-CoO interface are all linearly correlated to the catalytic activity toward the aqueous phase reforming of formaldehyde to produce hydrogen. Mechanistic investigations by spectroscopic measurements and density functional theory calculations elucidate the bifunctional nature of the oxygen-vacancy-rich Co-CoO interfaces, where the Co and the CoO sites are responsible for CH bond cleavage and OH activation, respectively. Optimal catalytic activity is achieved by the sample reduced at 350 °C, Co@CoO-350 which exhibits the maximum concentration of Co-CoO interfaces, the maximum concentration of oxygen vacancies, a lattice strain of 5.2% in CoO, and the highest aqueous phase formaldehyde reforming turnover frequency of 50.4 h-1 at room temperature. This work provides not only new insights into the strain-vacancy-activity relationship at bifunctional catalytic interfaces, but also a facile synthetic approach to prepare heterostructures with highly tunable catalytic activities.National Research Foundation (NRF)Submitted/Accepted versionThe authors are grateful for financial supports from the National Natural Science Foundation of China (Grant No. 21872123, and 22172143), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY18B030007), and the Excellent Postgraduate Thesis Program of Zhejiang Sci-Tech University (Grant No. 2019D05). W.L. acknowledges funding from the National Research Foundation of Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program

Ce³⁺, Pr³⁺ Co-Doped Lu₃Al₅O₁₂ Single Crystals and Ceramics: A Comparative Study

Ce3+, Pr3+ co-doped Lu3Al5O12 (Ce, Pr:LuAG) single crystals and ceramics were prepared using the optical floating zone (OFZ) and reactive vacuum sintering methods, respectively. The microstructure, photo- (λex = 450 nm), and radio-luminescence (under X-ray excitation) performance, as well as scintillation light yield (LY, under γ-ray, 137Cs source) of both materials, were investigated and compared. Ce, Pr:LuAG ceramics had an in-line transmittance of approximately 20% in the visible light range, while the analogous crystals were more transparent (~65%). The X-ray excited luminescent (XEL) spectra showed the characteristic Ce 3+ and Pr3+ emissions located at 310 nm, 380 nm, and 510 nm. The highest LY of the Ce, Pr:LuAG ceramics reached 34,112 pho/MeV at 2 μs time gate, which is higher than that of a single crystal. The ratio of LY values (LY2/LY0.75) between shaping times of 0.75 μs and 2 μs indicated a faster scintillation decay of ceramics regarding single crystals. It was ascribed to the lower effective concentration of luminescent activators in single crystals because of the coefficient segregation effect

Atomically Dispersed Dual Metal Sites Boost the Efficiency of Olefins Epoxidation in Tandem with CO₂ Cycloaddition

Tandem catalysis provides an economical and energy-efficient process for the production of fine chemicals. In this work, we demonstrate that a rationally synthesized carbon-based catalyst with atomically dispersed dual Fe–Al sites (ADD-Fe-Al) achieves superior catalytic activity for the one-pot oxidative carboxylation of olefins (conversion ∼97%, selectivity ∼91%), where the yield of target product over ADD-Fe-Al is at least 62% higher than that of monometallic counterparts. The kinetic results reveal that the excellent catalytic performance arises from the synergistic effect between Fe (oxidation site) and Al sites (cycloaddition site), where the efficient CO2 cycloaddition with epoxides in the presence of Al sites (3.91 wt %) positively shifts the oxidation equilibrium to olefin epoxidation over Fe sites (0.89 wt %). This work not only offers an advanced catalyst for oxidative carboxylation of olefins but also opens up an avenue for the rational design of multifunctional catalysts for tandem catalytic reactions in the future