Derivation of the multisymplectic Crank–Nicolson scheme for the nonlinear Schrödinger equation

The Crank–Nicolson scheme as well as its modified schemes is widely used in numerical simulations for the nonlinear Schrödinger equation. In this paper, we prove the multisymplecticity and symplecticity of this scheme. Firstly, we reconstruct the scheme by the concatenating method and present the corresponding discrete multisymplectic conservation law. Based on the discrete variational principle, we derive a new variational integrator which is equivalent to the Crank–Nicolson scheme. Therefore, we prove the multisymplecticity again from the Lagrangian framework. Symplecticity comes from the proper discrete Hamiltonian structure and symplectic integration in time. We also analyze this scheme on stability and convergence including the discrete mass conservation law. Numerical experiments are presented to verify the efficiency and invariant-preserving property of this scheme. Comparisons with the multisymplectic Preissmann scheme are made to show the superiority of this scheme.     

强化环保设计,促进水泥工业的可持续发展

从烟(粉)尘排放总量控制、大气污染物排放标准、清洁生产、中水回用、环境绿化和加强环境法制观念等方面,提出强化水泥建设项目环保设计和建设、促进水泥工业可持续发展的想法和建议。     

Pressure drop for single and two‐phase flow of non‐newtonian liquids in helical coils

New experimental results on pressure loss for the single and two‐phase gas‐liquid flow with non‐Newtonian liquids in helical coils are reported. For a constant value of the curvature ratio, the value of the helix angle of the coils is varied from 2.56° to 9.37°. For single phase flow, the effect of helix angle on pressure loss is found to be negligible in laminar flow regime but pressure loss increases with the increasing value of helix angle in turbulent flow conditions. On the other hand, for the two‐phase flow, the well‐known Lockhart‐Martinelli method correlates the present results for all values of helix angle (2.56‐9.37°) satisfactorily under turbulent/laminar and turbulent/turbulent conditions over the following ranges of variables as: 0.57 ≤ n′ ≤ 1; Re′ < 4000; Re_l < 4000; Re_g < 8000; 8 ≤ x ≤ 1000 and 0.2 ≤ De′ ≤ 1000.     

跨境共享水资源的国际法思考

除了政治和外交努力之外,运用国际法的手段来解决因国际河流的利用导致的冲突已成为各国的共识。文章试图梳理现有跨境共享水资源的国际规则,分析跨境共享水资源过程中的各种国家利益冲突,并为跨境共享水资源管理提出一个新的框架,以期通过国际法的手段预防和解决跨境共享水资源利用(主要集中在国际河流利用)引发的国际冲突。     

湘桂石膏矿岩层移动的反演分析

为了研究湘桂石膏矿的岩体变形规律,对该矿东采区顶板岩孔多点位移计观测和钻孔锚杆应力计检测的结果进行综合反演分析,提出了水下矿区开挖后采场岩层的变形规律,为采取有效措施控制岩层移动提供了依据.     

高产小麦磷钾效应和适宜氮磷钾配比研究

黄泛冲积石灰性土壤在适宜施氮水平下磷钾不同用量及配比对小麦生长的影响表现为:(1)磷肥以中量施用水平(每公顷施用P2O5120kg)增产效果最好,分别比未施磷、低量施用水平(每公顷用P2O548kg)增产30.82%、20.27%,高量施用水平(每公顷施用P2O5192kg),虽然比中量施用水平表现出增产,但增产幅度很小,只有2.85%;(2)钾肥对小麦的增产效应小于磷肥,只有在施用磷肥的基础上配施钾肥,才能使钾的效应得到充分发挥;(3)小麦全生育期氮磷钾施用比例1∶0.5∶0.5为最佳,每公顷施用N240kg、P2O5120kg、K2O120kg效益最高。     

Rheological properties and compatibility of NR/EPDM and NR/brominated EPDM blends

Ethylene–propylene–diene terpolymer (EPDM) was modified by bromination reaction. Blending the resulting brominated EPDM with natural rubber (STR5L) and blending the unmodified EPDM with STR5L at various compositions were carried out. The rheological properties of the blends were investigated using a capillary extrusion. Shear flow curves of the pure rubbers and their blends illustrated the pseudoplastic property as shear thinning behavior with a power law index n < 1. True shear viscosity of all blends showed the negative deviation in relation to their additive values. Rheological behavior and two T_g's found from the DSC thermograms at all blend compositions indicated blend incompatibility for both sets of blends. The incompatibility of the vulcanized blends was also found by measuring the spin–spin relaxation time T₂ by pulsed NMR. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 837–847, 2003     

Teeth segmentation of dental periapical radiographs based on local singularity analysis

Teeth segmentation for periapical raidographs is one of the most critical tasks for effective periapical lesion or periodontitis detection, as both types of anomalies usually occur around tooth boundaries and dental radiographs are often subject to noise, low contrast, and uneven illumination. In this paper, we propose an effective scheme to segment each tooth in periapical radiographs. The method consists of four stages: image enhancement using adaptive power law transformation, local singularity analysis using Hölder exponent, tooth recognition using Otsu's thresholding and connected component analysis, and tooth delineation using snake boundary tracking and morphological operations. Experimental results of 28 periapical radiographs containing 106 teeth in total and 75 useful for dental examination demonstrate that 105 teeth are successfully isolated and segmented, and the overall mean segmentation accuracy of all 75 useful teeth in terms of (TP, FP) is (0.8959, 0.0093) with standard deviation (0.0737, 0.0096), respectively.     

4-(α-吡啶甲酰基)-PMP的合成与谱学特性研究

合成了新吡唑啉酮类试剂1-苯基-3-甲基-4-(α-吡啶甲酰基)-吡唑啉-5-酮(简称4-(α-吡啶甲酰基)-PMP,下同)。在表征分子结构的同时,对其红外、紫外吸收光谱,核磁共振氢谱、碳谱,质谱等谱学特性和质谱裂解规律进行了分析与研究。     

Kinetics of the hydroformylation of soybean oil by ligand-modified homogeneous rhodium catalysis

The kinetics and mechanism of the hydroformylation of soybean oil by homogeneous ligand-modified rhodium catalysts were investigated at 70–130°C and 4000–11,000 kPa. The effects of reaction rates on systematic variations in reaction parameters were evaluated in order to develop an industrial process to convert vegetable oils to polyaldehydes. The activation energies in the presence of triphenylphosphine (Ph₃P) (61.1±0.8 kJ/mol) (mean±SD) and triphenyl phosphite [(PhO)₃P] (77.4±5.0 kJ/mol) were determined. The catalyst was deactivated at temperatures higher than 100°C. An evaluation of the effects of the reaction parameters on initial rates yielded the rate laws for Ph₃P {rate=k [olefin][Rh(CO)₂Acac]^1.1 [Ph₃P]^−0.5 (pH₂+pCO)^1.4, where Rh(CO)₂Acac is (acetylacetonato)dicarbonylrhodium (I)} and (PhO)₃P {rate=[olefin] [Rh(CO)₂Acac]^1.2 [(PhO)₃P]^−0.8 (pH₂+pCO)^0.9 at total pressures lower than 7000 kPa, and rate =[olefin] [Rh(CO)₂Acac]^1.2 [(PhO)₃P]^−0.8(pH₂+pCO)^1.7 at total pressures higher than 7000 kPa}.