Hamiltonian formulation of generalized quantum dynamics

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations. Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph. D. Directing Programme of Chinese University, and the Chinese Academy of Sciences.     

对薄层柱壳爆炸膨胀断裂过程的研究

 本文提出了一个用于描述动态破坏发展过程的损伤度函数。从这个损伤度函数出发,把材料特征性方程取为强化粘塑性本构方程形式,导出了薄层柱壳爆炸膨胀运动在两种近似下（恒定膨胀速度近似合恒定应变速率近似）断裂判据的解析表达式。结果分析表明,在上述条件下,存在着一个动态断裂“塑性峰”,在这个峰值条件的应变率下,柱壳出现贯穿断裂时刻的应变最大。以软钢为算例,本断裂判据可以比较好地解释Иванов和陈大年等给出的实验结果。这时,动态断裂“塑性峰”对应的应变率为4×10⁴ s^-1,相应的应变约为60%~80%。     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Gas chromatographic trace analysis of underivatized nitrophenols

Summary A method for the gas chromatographic trace analysis of underivatized nitrophenols in ground-water is presented. Using a highly de-activated separation system a satisfactory precision for their quantitative GC analysis could be achieved by avoiding condensation of the solvent and by fast injection of the sample. The reproducibility of the peak areas of eleven nitrophenols in ethylacetate was <5 % RSD. Using a nitrogen-phosphorus detector detection limits were in a range from 10 to 30 pg. Within the concentration range from 0.1 to 10 ng μl⁻¹ the calibrations were linear with correlation coefficients >0.992. The approach described was applied to the analysis of nitrophenols in ground-water near a former ammunition plant, after preconcentration by continuous liquid/liquid extraction with ethylacetate. Using a GC-MS technique and retention times various nitrophenols were identified and then quantified in the μg/L-range by applying NPD.     

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.     

Effects of irradiation on trans fatty acids formation in ground beef

In order to give the consumer the assurance that meat processed by irradiation is a safe product, a great deal of research has been developed in the world. The effect of irradiation on the hygienic quality of meat and meat products is considered as related to the control of meat-borne parasites of humans; elimination of pathogens from fresh meat and poultry; and elimination of pathogens from processed meat. Lipid oxidation and associated changes are the major causes of the quality deterioration of meat during storage. Irradiation of lipids induces the production of free radicals, which react with oxygen, leading to the formation of carbonyls, responsible for alterations in food nutritional and sensorial characteristics. Trans fatty acids are present in ground beef and can also be formed during its processing. Interestingly, the trans fatty acids, due to their chemical and physical characteristics, show more resistance to the oxidizing process. This property motivated us to investigate the level of the trans fatty acids, as well as the level of oxidation in irradiated ground beef. Irradiation of ground beef was performed by gamma rays from a ⁶⁰Co source. The applied radiation doses were 0; 1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0 and 8.0 kGy. Lipid peroxidation in terms of TBA number and carbonyl content was monitored during storage. The sample characteristics and trans fatty acids composition were measured, following irradiation and after 60 and 90 days of storage at –10°C.     

水中矿物元素的ICP-MS分析

用ICP－MS对地下水、地表水和饮用水中的矿物元素进行了分析测定，实验证明用ICP－MS可以同时测定地下水，地表水和饮用水中矿物元素；该法灵敏度、精密度和准确度都能满足有关标准的要求，具有多元素同时分析，样品前处理简单，干扰少，测定快速，省事省力等优点。     

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.