Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

Note on the fractal dimension of hard sphere trajectories

Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations.     

Electrochemical detector with a 20 nl volume for micro-columns liquid chromatography

Summary A flow-through two electrode wall-jet cell with a platinum measuring electrode and a cell volume of 20 nl has been designed and evaluated. It has been used to detect phenols by reversed phase liquid chromatography using short micro bore columns. The linear dynamic range between the measured current and the concentration is greater than 10³ (1.5×10^–7–5×10^–4 mol/l) and the minimum analyzable amount was found to be 10 pg for pyrocatechol. A negligible broadening in the detector permits the use of micro columns down to 0.5 mm internal diameter, packed with 5 m particles, without any substantial distortion of eluted zones.Presented at the 14th International Symposium on Chromatography London, September, 1982     

气相法分析3-氯-2-羟丙基三甲基氯化铵中的微量有机杂质

 以氯仿为萃取剂 ,对 3 氯 2 羟丙基三甲基氯化铵 (CHPTMA)水溶液进行萃取 ,用气相法分析了CHPT MA溶液中的微量有机杂质环氧氯丙烷和 1 3 二氯丙醇。柱为 2m× 3mmi d 的不锈钢填充柱 ,固定相为10 %的PEG 2 0M ,载体为ChromosorbW/AW。环氧氯丙烷和 1,3 二氯丙醇的回收率分别为 97 5 %～ 10 5 0 %和93 3%～ 98 8% ,相对标准偏差分别为 11 5 %和 13 1% ,最低检测限分别为 5 0 μg/g和 10 0 μg/ g。     

The Sialons MLn[Si4−xAlxOxN7−x] with M = Eu,Sr, Ba and Ln = Ho‐Yb – Twelve Substitution Variants with the MYb[Si4N7] Structure Type

The oxonitridoalumosilicates (so‐called sialons) MLn[Si_4?xAl_xO_xN_7?x] with M = Eu, Sr, Ba and Ln =Ho, Er, Tm, Yb were obtained by the reaction of the respective lanthanoid metal, the alkaline earth carbonates or europium carbonate, resp., AlN, “Si(NH)₂” and MCl₂ as a flux in a radiofrequency furnace at temperatures around 2100 °C. The compounds MLn[Si_4?xAl_xO_xN_7?x] are relevant for the investigation of substitutional effects on the materials properties due to their ability of tolerating a comparatively large phase width up to x ≈ 2.0(5). The crystal structures of the twelve compounds were refined from X‐ray single crystal data and X‐ray powder data and are found to be isotypic to the MYb[Si₄N₇] structure type. The compounds crystallize in space group P6₃mc (no. 186, hexagonal) and are made up of chains of so‐called starlike units [N^[4](SiN₃)₄] or [N^[4]((Si,Al)(O,N)₃)₄], respectively. These units are formed by four (Si,Al)(N/O)₄ tetrahedra sharing a common central nitrogen atom. The structure refinement was performed utilizing an O/N‐distribution model according to Paulings rules, i.e. nitrogen was positioned on the four‐fold bridging site and nitrogen and oxygen were distributed equally on both of the two‐fold bridging sites, resulting in charge neutrality of the compound. The Si and Al atoms were distributed equally on their two crystallographic sites, referring to their elemental proportion in the compound, due to being poorly distinguishable by X‐ray methods. The chemical compositions of the compounds were derived from electron probe micro analyses (EPMA).     

空间机器人组装超大型结构的动力学分析北大核心CSCD

超大型航天结构具有超大柔性、超低固有频率的特点,空间机器人在轨组装时应尽可能避免激起超大型结构的柔性振动.空间机器人组装超大型结构模块的过程分成抓捕阶段、位姿调整与稳定阶段、安装阶段和爬行阶段.通过对安装阶段的动力学与控制研究,提出共线安装的轨迹规划方法,有效避免了柔性结构振动.首先,采用自然坐标法和绝对节点坐标法建立主结构-空间机器人-待组装结构的在轨组装系统动力学模型.然后,将共线安装的要求转化为空间机器人的轨迹规划约束,要求空间机器人质心到主结构/待组装结构的距离保持不变,实现共线安装的轨迹规划.数值仿真表明:提出的组装方法在组装过程中可有效避免超大型结构的横向运动,降低夹持力矩.最后,分析了系统参数对组装过程动力学响应的影响,为超大型航天器的在轨组装提供了参考.     

Impact Responses of Prismatic Lithium-Ion Battery Based on the Membrane Factor Method北大核心CSCD

Aimed at the internal short circuit problem due to large deformation of the prismatic lithium-ion battery cell under impact loadings, a simplified battery model was first established. Then the motion equations of velocity and displacement based on the membrane factor method were proposed. With the effects of the face-sheet thickness and the densification region on the normalized final deflection, impact response characteristics of prismatic battery cells were investigated in detail. The results show that, the improved motion equations involving the membrane factor can reflect the dynamic response mechanisms of the prismatic battery cell under impact loadings, and the large deflection under high-speed impact can be predicted. With the increase of the face-sheet thickness, the deflection of the battery cell’s lower part decreases obviously. However, the densification region expands with the face-sheet thickness. The deflection and the densification region of the cell’s lower part both increase with the inner core density of the battery. This proposed impact model provides a theoretical guidance for the multi-functional integrated dynamic design of prismatic battery cells. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Skew Brownian motion-type of extensions

We consider a class of possible extensions of a given symmetric Feller processZ _t fromR{0} to the entire real lineR, depending on a parameter [0, 1]. It is proved that the proposed extension exists if =1/2; for 1/2, exists if and only ifZ _t does not jump over 0 (e.g., ifZ _t is a diffusion).