A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

Padé approximations of quantized-vortex solutions of the Gross–Pitaevskii equation

Quantized vortices are important topological excitations in Bose–Einstein condensates. The Gross–Pitaevskii equation is a widely accepted theoretical tool. High accuracy quantized-vortex solutions are desirable in many numerical and analytical studies. We successfully derive the Padéapproximate solutions for quantized vortices with winding numbers ω = 1, 2, 3, 4, 5, 6 in the context of the Gross–Pitaevskii equation for a uniform condensate. Compared with the numerical solutions, we find that(1) they approximate the entire solutions quite well from the core to infinity;(2) higher-order Padé approximate solutions have higher accuracy;(3) Padé approximate solutions for larger winding numbers have lower accuracy. The healing lengths of the quantized vortices are calculated and found to increase almost linearly with the winding number. Based on experiments performed with ~(87)Rb cold atoms, the healing lengths of quantized vortices and the number of particles within the healing lengths are calculated, and they may be checked by experiment. Our results show that the Gross–Pitaevskii equation is capable of describing the structure of quantized vortices and physics at length scales smaller than the healing length.     

Linear superposition of Wronskian rational solutions to the KdV equation

A linear superposition is studied for Wronskian rational solutions to the Kd V equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.     

Antisolvent crystallization of aqueous ammonium dihydrogen phosphate solutions by addition of acetone at different rates

Results of an investigation of in situ measurements of laser‐beam intensity I_s and I_m transmitted through aqueous ammonium dihydrogen phosphate (ADP) solutions saturated at 30 °C and water, respectively, and temperature T_s of solution and T_m of water during feeding of antisolvent acetone at different rates R_A, using an indigenously designed experimental setup, are presented and discussed. It was found that: (1) for the measurement of MSZW, defined as the maximum volume fraction of acetone content Δx_max in the solution, obtained from temperature measurements are more reliable than transmitted laser‐beam intensity measurements for solutions, (2) two minima ΔT_min1 and ΔT_min2 associated with endothermic reactions, separated by a maximum ΔT_max due to exothermic reactions appear in the plots of temperature difference ΔT = T_s−T_m against acetone feeding time t, and (3) in the ΔT(t) plots there are time intervals Δt of constant rates R_T of increase in ΔT of aqueous ADP solutions, and these values of R_T increase linearly with acetone feeding time rate R_A. The experimental data on the observed dependence of MSZW on antisolvent feeding rate R_A, the appearance of minima ΔT_min1 and ΔT_min2 and maximum ΔT_max and their dependence on R_A, and the relationship between R_T and R_A are discussed from consideration of processes of nucleation and growth of crystallites.     

Green and mild laccase-catalyzed aerobic oxidative coupling of benzenediol derivatives with various sodium benzenesulfinates

The oxidative coupling reaction between hydroquinone or catechols and various sodium benzenesulfinates was investigated using the laccase from Trametes versicolor, in the presence of O₂ in a phosphate buffer solution at room temperature to afford sulfonyl benzenediols in 75–95% yield.     

Zero‐Valent Aluminum as Reducer in Sodium Carbonate Solution for Degradation of Imidacloprid

Imidacloprid (IMI ) was reduced by zero‐valent aluminum (ZVAl ) in sodium carbonate solution and tested by high‐performance liquid chromatography (HPLC ). The IMI degradation rate was heavily dependent on Na₂CO₃ concentration and reaction time but only slightly on temperature, reaching 99.4% in 0.5 mol/L Na₂CO₃ solution with 5 g/L ZVAl in 60 min. The degradation of IMI follows first‐order kinetics. We used high‐performance liquid chromatography‐mass spectrometry (HPLC‐MS ) for analyzing the transformation products, and found that IMI disintegrated into IMI urea, IMI guanidine, IMI nitrosamine, and 1‐choloro‐5‐methcyclohea‐1,4‐diene.     

Ion association in lithium metaborate solution: a Raman and ab initio insight

Ion association and hydration clusters in aqueous lithium borate solution are extremely important to understand some extraordinary properties of lithium borates. In the present work, polyborate distribution in aqueous LiBO₂ solution was investigated through Raman and thermodynamics equilibrium analysis. Geometry and stability of hydrated clusters LiB(OH)₄(H₂O)_n up to n = 8 were calculated at the B3LYP/aug-cc-pVDZ level. Three different types of ion association, namely, contact ion pairs (CIP), solvent-shared ion pairs (SIP) and solvent separated ion pairs (SSIP) were obtained; characteristics of all of these stable configurations were determined, and the most stable hydrated clusters were chosen. Then the mechanisms of ion aggregation and crystal nuclei formation in the LiB(OH)₄ solution were proposed. The tight four-hydrated sphere of Li⁺ makes it difficult for the dehydrated form of its first hydration sphere to from a CIP, which is the passible reason that lithium borate always has a large super-saturation degree.     

A novel colorimetric chemosensor based on quinoline for the sequential detection of Fe3+ and PPi in aqueous solution

A novel quinoline-functionalized Schiff-base derivative PY was designed and synthesized. Sensor PY displayed highly selective and sensitive fluorescence enhancement and naked-eye color change to Fe³⁺ in the presence of other competing cations. The mechanisms have been supported by Job’s plot evaluation, FT-MS and theoretical calculations. The in situ generated PY-Fe³⁺ complex solution exhibited a high selectivity toward PPi via Fe³⁺ displacement approach. The detection limits of sensor PY to Fe³⁺ and PY-Fe³⁺ complex to PPi were estimated to be 4.24 × 10^?8 M and 8.18 × 10^?8 M, respectively. This successive recognition feature of sensor PY makes it has a potential utility for Fe³⁺ and PPi detection in aqueous solution. A B3LYP/6-31G(d,p) basis set was employed for optimization of PY and PY-Fe³⁺ complex.     

ZnCl_2溶液中微波辅助SnCl_4催化纤维素制备5-HMF

将纤维素溶解在ZnCl_2溶液中,以SnCl_4为催化剂,微波下使纤维素降解成5-羟甲基糠醛(5-HMF)。实验考察了微波功率、纤维素的质量、ZnCl_2溶液浓度、反应时间及催化剂与纤维素物质的量比等对5-HMF产率的影响。结果表明,以SnCl_4为催化剂,在优化条件:1.0 g纤维素溶解在100 m L 70%ZnCl_2溶液中,微波功率为420 W,降解反应9 min,SnCl_4与纤维素物质的量比2∶1下,5-HMF的产率达到39.4%。     

Mg/Al物质的量比对Ce-La/MgAl2O4-x催化剂催化CO还原NO性能的影响

采用初始浸渍法制备了不同Mg/Al物质的量比的Ce-La/MgAl₂O₄-x催化剂,并通过低温N₂-吸附脱附、XRD、H₂-TPR和CO-TPR等手段对其进行了表征。结果表明,在Mg/Al物质的量比为0.5时,催化剂催化CO还原NO的性能最好。这主要是因为适量Mg的添加促进了CeO₂的分散和Ce-O-La固溶体的形成,从而使得表面Ce³⁺和氧空穴增加。两者的协同作用使得Ce-La/MgAl₂O₄-0.5表现出最佳的催化性能。另外,适量Mg的引入可以抑制Ce（SO₄）₂和Ce₂（SO₄）₃的形成,从而提高了Ce-La/MgAl₂O₄-0.5催化剂抗硫中毒能力。