Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m

In this paper, we study the explicit expansion of the first order Melnikov function near a double homoclinic loop passing through a nilpotent saddle of order m in a near-Hamiltonian system. For any positive integer $m(m\ge 1)$, we derive the formulas of the coefficients in the expansion, which can be used to study the limit cycle bifurcations for near-Hamiltonian systems. In particular, for $m=2$, we use the coefficients to consider the limit cycle bifurcations of general near-Hamiltonian systems and give the existence conditions for 10, 11, 13, 15 and 16 (11, 13 and 16, respectively) limit cycles in the case that the homoclinic loop is of cuspidal type (smooth type, respectively) and their distributions. As an application, we consider a near-Hamiltonian system with a nilpotent saddle of order 2 and obtain the lower bounds of the maximal number of limit cycles.     

基于氧化石墨烯的长周期光纤光栅的全光控制

实验验证了一种通过将氧化石墨烯分散液沉积在长周期光纤光栅的全光控制的相关研究。通过外加的垂直泵浦光的作用,氧化石墨烯吸收泵浦光产生热量,改变长周期光纤光栅的包层模式的相位差,由于热膨胀的作用改变了氧化石墨烯所覆盖部分的光栅周期,使得谐振谱发生了移动,其最大调制深度可达10.6 dB,谐振谱最大可红移12.8 nm。通过实验发现,沉积相同浓度氧化石墨烯分散液的次数影响实验结果,通过在相同光栅的相同位置分别沉积三次,发现沉积三次可以在光纤表面获得更加均匀的氧化石墨烯膜,进行了时间响应的测试,其中沉积三次后的长周期光纤光栅的响应速度可达0.61 ms,沉积多次氧化石墨烯分散液可以在光纤表面沉积得更加平整均匀,从而获得更大的导热性能。     

Analytical and numerical studies for Seiches in a closed basin with bottom friction

A standing wave oscillation in a closed basin, known as a seiche, could cause destruction when its period matches the period of another wave generated by external forces such as wind, quakes, or abrupt changes in atmospheric pressure. It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy, resulting in damages around the area. One condition that might restrict the resonance from occurring is when the bottom friction is present. Therefore, a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena. The study will be conducted for several closed basin shapes. The model will be solved analytically and numerically in order to determine the natural resonant period of the basin, which is the period that can generate a resonance. The computational scheme proposed to solve the model is developed using the staggered grid finite volume method. The numerical scheme will be validated by comparing its results with the analytical solutions. As a result of the comparison, a rather excellent compatibility between the two results is achieved. Furthermore, the impacts that the friction coefficient has on the resonance phenomena are evaluated. It is observed that in the prevention of resonances, the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin. In addition, non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.     

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

新郑西亚斯东周玉器材料属性与加工工艺的科技分析

中国玉文化源远流长，治玉工艺经过各个时代的不断发展和完善，在一定程度上能反映古代社会生产力发展水平及文化、贸易、技术交流等信息。利用能量色散型X射线荧光光谱（EDXRF）、激光拉曼光谱（LRS）、超景深光学显微系统（OM）等分析技术，结合硅胶覆膜微痕复制技术，对河南省新郑西亚斯东周墓地出土的一批玉器进行科技分析。首先利用化学成分和物相结构分析技术确定了玉器材质的矿物属性，其次利用显微分析技术表征了玉器表面及穿孔内部和印模的加工痕迹，特别是阴刻纹饰和穿孔微痕特征，最后探讨了玉器样品的材料属性和加工工艺两者之间的联系。化学成分和物相结构分析结果表明，所分析的西亚斯东周玉器材质丰富，主要矿物组成有滑石、透闪石、水晶、云母等。玉器表面纹饰微痕特征分析表明，所分析玉器阴刻工艺采用了两种加工工具，分别是砣具和手持硬质工具。穿孔微痕分析特征表明，钻孔包括单面钻孔和双面/多面钻孔两种方式，钻孔工艺则有实心钻、管钻等。部分玉器钻孔形状和内部微痕特征表明，尽管均采用了实心钻工艺，但所采用的实心钻头在形状上存在差异，同时，也存在是否配合解玉砂进行钻孔的差异。不同材料属性的玉器采用了不同的加工工艺。滑石质玉器，莫氏硬度1，器型主要为玉片饰，其表面阴刻纹饰主要采用手持硬质工具进行刻画，钻孔主要采用了双面钻孔方式，并使用了实心钻头未添加解玉砂进行加工，钻头形状可能为圆锥状；云母质玉器，莫氏硬度2~3，器型主要为玉玦片饰，纹饰采用了砣具添加解玉砂的加工工艺，钻孔方式为单面钻孔，采用了管钻工艺。透闪石型玉器，莫氏硬度5~6，器型主要为玉片饰，表面纹饰采用砣具配合解玉砂砣刻，以双面钻孔的方式为主，钻孔工艺为实心钻头配合解玉砂工艺，钻头形状与滑石类样品一致，为圆锥状。水晶质玉器，莫氏硬度7，均为珠饰，表面无纹饰，钻孔方式为双面/多面钻孔，钻孔工艺为实心钻配合解玉砂工艺，且钻头可能为圆柱形。研究结果表明，玉器表面纹饰所采用的阴刻工艺和钻孔工艺，与玉器本身的材料属性、器型等存在密切关系。     

An Isosteric Triaza Analogue of a Polycyclic Aromatic Hydrocarbon Monkey Saddle

Since a few years, the interest in negatively-curved fused polycyclic aromatic hydrocarbons (PAHs) has significantly increased. Recently, the first chiral negatively-curved PAH with the topology of a monkey saddle was introduced. Herein the synthesis of its triaza congener is reported. The influence of this CH↔N exchange on photophysical and electrochemical properties is studied as well as the isomerization process of the enantiomers. The aza analogue has a significantly higher inversion barrier, which makes it easier to handle at room temperature. All experimental results are underpinned by theoretical DFT calculations.     

Rotation-Inversion Isomerization of Tertiary Carbamates: Potential Energy Surface Analysis of Multi-Paths Isomerization Using Boltzmann Statistics

Potential energy surface (PES) analyses at the SMD[MP2/6–311++G(d,p)] level and higher-level energies up to MP4(fc,SDTQ) are reported for the fluorinated tertiary carbamate N-ethyl-N-(2,2,2-trifluoroethyl) methyl carbamate ( VII ) and its parent system N,N-dimethyl methyl carbamate ( VI ). Emphasis is placed on the analysis of the rotational barrier about the CN carbamate bond and its interplay with the hybridization of the N-lone pair (NLP). All rotational transition state (TS) structures were found by computation of 1D relaxed rotational profiles but only 2D PES scans revealed the rotation-inversion paths in a compelling fashion. We found four unique chiral minima of VII , one pair each of E- and Z-rotamers, and we determined the eight unique rotational TS structures associated with every possible E/Z-isomerization path. It is a significant finding that all TS structures feature N-pyramidalization whereas the minima essentially contain sp²-hybridized nitrogen. We will show that the TS stabilities are affected by the synergetic interplay between NLP/CO₂ repulsion minimization, NLP→σ^*(CO) negative hyperconjugation, and two modes of intramolecular through-space electrostatic stabilization. We demonstrate how Boltzmann statistics must be applied to determine the predicted experimental rotational barrier based on the energetics of all eight rotamerization pathways. The computed barrier for VII is in complete agreement with the experimentally measured barrier of the very similar fluorinated carbamate N-Boc-N-(2,2,2-trifluoroethyl)-4-aminobutan-1-ol II . NMR properties of VII were calculated with a variety of density functional/basis set combinations and Boltzmann averaging over the E- and Z-rotamers at our best theoretical level results in good agreement with experimental chemical shifts δ(¹³C) and J(¹³C,¹⁹F) coupling constants of II (within 6 %).     

Trace 1300气相色谱仪故障排查与期间核查

使用赛默飞Trace 1300气相色谱仪进行环境样品分析过程中,出现了FID信号变弱、点火困难的现象,严重影响检测数据的准确性,干扰正常分析工作。从样品性质、仪器方法的设置、气路系统以及检测系统进行故障排查,确定故障原因为FID喷嘴堵塞,点火线圈锈蚀严重。对维修好后的气相色谱仪进行期间核查,核查结果:基线噪声为0.066 pA,基线漂移(30 min)为0.321 pA,FID检测限为0.094 1 ng/s,定性重复性为0.062%,定量重复性为1.41%,均满足技术指标要求。