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.     

A study of peralkylated derivatives of bis(η6-benzene)chromium by gas-phase electronic absorption spectroscopy

The gas-phase electronic absorption spectra of (⁶-C₆R₆)₂Cr (R = Me (1) and Et (2)) reveal Rydberg structures, which disappear on going to the condensed phase. Each spectrum shows a Rydberg series converging to the ionization threshold. The first ionization potential determined as the series convergence limit is 4.662±0.008 eV for 1 and 4.667±0.019 eV for 2. The Rydberg bands are due to the transitions from the non-bonding MO 3d_z2 to the R4s and Rnp (n = 4—10) levels. The influence of methyl and ethyl substituents on the term values of the Rydberg transitions depends on the principal quantum number of the Rydberg MO.     

Kinetics of the Formation of Goethite in the Presence of Sulfates and Chlorides of Monovalent Cations

The synthesis of goethite by oxidation of Fe²⁺in presence of metallic iron was undertaken in an aqueous medium containing indifferent salts such as Na₂SO₄, (NH₄)₂SO₄, NaCl, and NH₄Cl. Temperature and bubbling air rate were maintained, respectively, at 70°C and 1 L/min. The influence of anions and cations on the kinetics of each step of the process has been followed distinctly, the iron dissolution rate has been determined by the variation of the medium acidity, and the precipitation of goethite has been determined by gravimetric measurements. With respect to Cl⁻, the SO₄²⁻anion decreases the rate of the two reactions. NH₄⁺acts as an inhibitor when it is present at low concentrations and as an accelerator for higher concentrations; the limit corresponding to the change of NH₄⁺behavior depends on the nature of the counter ion. The reaction product is composed of pure goethite in the presence of sulfate salts, whereas a mixture of goethite and lepidocrocite, respectively, 60–70 and 40–30%, was observed in the presence of chloride salts.     

Influences of Triton X-100 on Hemoglobin Behaviors in Hemoglobin/Acyclovir/Triton X-100/H2O System

The influences of Triton X-100 on hemoglobin （Hb） behaviors were studied by the methods of UV-Vis spectrum, fluorescence spectrum, HPLC, conductivity, zeta potential and negative-staining transmission electron microscope in Hb/acyclovir/Triton X-100/H2O system. With the increase of Triton X-100 concentration in the system, the percentage of the free acyclovir increased from 58%--63% to 90%--94%. The static quenching constant and the association number of acyclovir to Hb decreased. The fluorescence spectrum, conductivity, zeta potential, fluorescence polarization and negative-staining morphology of Hb tended to recover to those of the original state of Hb in the same concentration of Hb. The interaction between Triton X-100 and Hb is stronger than that between acyclovir and Hb. Most Triton-X-100 was associated with Hb at low Triton X-100 concentration. But the interaction of Triton X-100 with Hb was apparently dominant in high Triton X-100 concentration. The Hb structure was unfolded and finally denatured.     

THE SOLID STATE REACTIONS AND TRANSITIONS IN HIGH POLYMERIC SYSTEMS Ⅲ. THE BULK CRYSTALLIZATION OF LANTHANIDECATALYTICALLY POLYMERIZED POLYDIENES

For the mechanism of isothermal bulk crystallization of high polymers, beside the nucleation and growth steps, the unimpingement of growing crystal aggregates should be taken into account for the modification of the Avrami equation. Starting from Poisson distribution function of growing crystal aggregates, the probability of the unimpinging ones should be P(0)+P(1), then the Q-modified Avrami equation thus derived can be expressed aswhere V0 represents the volume fraction of crystal aggregates at crystallization time t at a given temperature, while the exponent n on t relates to the mode of nucleation and growth, and K_q is the corresponding shape factor. This Q-modified one is verified satisfactory by the isothermal bulk crystallization of lanthanidecatalytically polymerized polybutadiene (Ln-PB), polyisoprene (Ln-PIR) and their copolymers (LnPB/IR). Furthermore, the proposed mechanism is well identified by the change of morphological state during the course of crystallization of the corresponding east film of Ln-PB TR (92/8) at-60°(Fig. 1).Upon examination of the influence of the number of entanglement on crystallization rate, it reveals the existence of two stages of entanglementation, the primary and the secondary ones (Fig. 19)The equation for dependence of molecular weight and entanglement on bulk crystallization rate has been derived as Eq. 13 or 18 for Ln-PB, and verified by the experimental rate data of well fractionated Ln-PB samples crystallized at -9.1 to -15℃(Fig.20).     

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.     

基于直线运动机构的大变倍比红外变焦成像系统

针对同时兼顾大范围搜索和精确识别目标的迫切需求,研制了一种大变倍比红外变焦成像系统,设计两片独立运动的变倍镜及一片补偿镜,通过两个变倍镜级联的方式获得大变倍比。结合系统运动镜片多及变焦曲线复杂的特点,采用直线运动机构实现镜片变焦运动,使用集成编码器及螺纹丝杆的直线电机作为驱动。通过有限元仿真开展了系统力学分析,所设计镜片最大位移为3.04×10^-3 mm。成像系统适用于中波红外制冷式640×512焦平面阵列探测器,变倍比达到55倍。实验室成像及外场实景成像的结果表明,系统在焦距由6 mm至330 mm连续变化的过程中成像清晰、像质良好,验证了系统的连续变焦成像性能,该设计合理可靠。研究成果在搜索、跟踪、侦察、监视等方面有广阔的应用前景。     

Real-time 3D multi-pedestrian detection and tracking using 3D LiDAR point cloud for mobile robot

Mobile robots are used in modern life; however, object recognition is still insufficient to realize robot navigation in crowded environments. Mobile robots must rapidly and accurately recognize the movements and shapes of pedestrians to navigate safely in pedestrian-rich spaces. This study proposes real-time, accurate, three-dimensional (3D) multi-pedestrian detection and tracking using a 3D light detection and ranging (LiDAR) point cloud in crowded environments. The pedestrian detection quickly segments a sparse 3D point cloud into individual pedestrians using a lightweight convolutional autoencoder and connected-component algorithm. The multi-pedestrian tracking identifies the same pedestrians considering motion and appearance cues in continuing frames. In addition, it estimates pedestrians' dynamic movements with various patterns by adaptively mixing heterogeneous motion models. We evaluate the computational speed and accuracy of each module using the KITTI dataset. We demonstrate that our integrated system, which rapidly and accurately recognizes pedestrian movement and appearance using a sparse 3D LiDAR, is applicable for robot navigation in crowded spaces.     

Bahadur efficiency and robustness of studentized score tests

We derive the exact Bahadur slopes of studentized score tests for a simple null hypothesis in a one-parameter family of distributions. The Student's t-test is included as a special case for which a recent result of Rukhin (1993, Sankhy Ser. A, 55, 159–163) was improved upon. It is shown that locally optimal Bahadur efficiency for one-sample location models with a known or estimated scale parameter is attained within the class of studentized score tests. The studentized test has an asymptotic null distribution free of the scale parameter, and the optimality of likelihood scores does not depend on the existence of a moment generating function. We also consider the influence function and breakdown point of such tests as part of our robustness investigation. The influence of any studentized score test is bounded from above, indicating certain degree of robustness of validity, but a bounded score function is needed to cap the influence from below and to ensure a high power breakdown point. We find that the standard Huber-type score tests are not only locally minimax in Bahadur efficiency, but also very competitive in global efficiency at a variety of location models.