Conditional Probabilities and Density Operators in Quantum Modeling

Motivated by a recent proof of free choices in linking equations to the experiments they describe, I clarify some relations among purely mathematical entities featured in quantum mechanics (probabilities, density operators, partial traces, and operator-valued measures), thereby allowing applications of these entities to the modeling of a wider variety of physical situations. I relate conditional probabilities associated with projection-valued measures to conditional density operators identical, in some cases but not in others, to the usual reduced density operators. While a fatal obstacle precludes associating conditional density operators with general non-projective measures, tensor products of general positive operator-valued measures (POVMs) are associated with conditional density operators. This association together with the free choice of probe particles allows a postulate of state reductions to be replaced by a theorem. An application shows an equivalence between one form of quantum key distribution and another with respect to certain eavesdropping attacks.     

A two-sided estimate in the Hsu-Robbins-Erdös law of large numbers

Let X₁, X₂, … be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdös (1949, 1950) have proved that

,

if and only if E[X²₁] < ∞ and E[X₁] = 0. We prove that there are absolute constants C₁, C₂ (0, ∞) such that if X₁, X₂, … are independent identically distributed mean zero random variables, then

c₁λ⁻² E[X₁²·1_{|X1|λ}]S(λ)C₂λ⁻² E[X₁²·1_{|X1|λ}]

,

for every λ > 0.     

Exact L 2 Small Balls of Gaussian Processes

We prove a comparison theorem extending Li(6) and develop a complex-analytic approach to treat L ² small ball probabilities of Gaussian processes. We demonstrate the techniques for the m-times integrated Brownian motions and in examples where one can not apply Li comparison theorem.     

Absorbing Interface Conditions for the Simulation of Wave Propagation on Non-Uniform Meshes

We proposed absorbing interface conditions for the simulation of linear wave propagation on non-uniform meshes. Based on the superposition principle of second-order linear wave equations, we decompose the interface condition problem into two subproblems around the interface: for the first one the conventional artificial absorbing boundary conditions is applied, while for the second one, the local analytic solutions can be derived. The proposed interface conditions permit a two-way transmission of low-frequency waves across mesh interfaces which can be supported by both coarse and fine meshes, and perform a one-way absorption of high-frequency waves which can only be supported by fine meshes when they travel from fine mesh regions to coarse ones. Numerical examples are presented to illustrate the efficiency of the proposed absorbing interface conditions.     

特种泡沫塑料的动态力学性能研究

通过大尺寸分离式Hopkinson压杆对特种泡沫塑料进行了高应变率冲击实验，完整地给出了该材料在高应变率下的动态应力应变曲线，并将结果和理论上的Eyring模型进行了比较，指出了这种材料在一定的应变率范围内，具有明显的应变率效应，同时从应力应变曲线的特点来看，这种材料又有良好的吸能特性，最后通过对实验数据的拟合，提出了便于工程应用的动态本构方程。     

Review on underwater sound absorption materials and mechanisms

随着我国加速实施海洋强国战略,对先进水下吸声材料的需求日益迫切.与空气吸声不同,水下的高静水压力和复杂的海洋环境对水下吸声材料提出了更为苛刻的要求.吸声问题的本质是如何将弹性能高效地转化为热能或其他形式能量.本文综述了主要以聚合物分子内摩擦机制及界面耗能机制为基础的传统水下吸声材料.传统水下吸声材料面临的主要是其在低频及高静水压力下吸声性能差的问题.这是因为：一方面受质量密度定律的限制,有限厚度的水下吸声材料无法有效吸收水中传来的低频声波;另一方面,在高静水压力下,弹性材料如高分子聚合物会变“硬”,从而大大降低了声波弹性能的转换效率.随着局域共振理论及超材料概念的提出,发展出了一系列新型水下吸声材料,为解决水下吸声材料遇到的难题提供了新思路.局域共振理论的特点是可以用小尺度结构控制长波声波的传播,从而可以解决低频吸声问题.本文重点综述了局域共振理论,以及由此发展出的声子木堆、声子玻璃等新型水下吸声材料.声子玻璃材料在局域共振理论基础上,通过引入多孔金属骨架结构提高了材料的抗压性能,从而解决了高静水压力下材料吸声性能变差的问题.本文最后对水下吸声材料未来发展方向进行了展望.     

NZFO-PZT磁电复合纳米纤维的制备及其吸波性能

采用静电纺丝法制备(1-x)Ni_0.5Zn_0.5Fe₂O₄-(x)Pb(Zr_0.52Ti_0.48)O₃(简称为(1-x)NZFO-(x)PZT, x=0.1、0.2、0.3、0.4、0.5)磁电复合纳米纤维, 研究了PZT含量对复合纳米纤维结构、电磁特性及微波吸收性能的影响。所有样品均由尖晶石结构NZFO和钙钛矿结构PZT两相所组成。由于NZFO磁损耗与PZT介电损耗的协同效应及界面效应的加强, 适量PZT相的引入可改善复合纳米纤维吸波涂层的电磁阻抗匹配和衰减特性, 提高微波吸收性能。x=0.3和0.4的复合纳米纤维分别在低频和高频范围表现出最强的微波吸收能力。当涂层厚度为2.5~5.0 mm时, x=0.3样品的最小反射损耗在6.1 GHz处达-77.2 dB, 反射损耗小于-10 dB的有效吸收带宽为11.2 GHz(2.8~12.9和16.9~18 GHz);x=0.4样品的最小反射损耗位于18 GHz处为-37.6 dB, 有效吸收带宽达到12.5 GHz(3.3~12.5和14.7~18 GHz)。     

通用有限元系统实现无限域波动仿真方法

在有限元模型中加入人工边界,可以进行无限域波动仿真。本文将介绍一种改进的Higdon人工边界,并通过适当的变换形式,将其在通用有限元软件上实现。最后通过数值实验验证了这种方法具有良好的稳定性和计算精度,并且实施简单方便,其他人工边界条件可参照本文方法,通过变换形式在通用有限元程序中实现。     

Preparation and properties of water‐absorbent composites of chloroprene rubber,starch, and sodium acrylate

The effects of the amounts of starch, sodium acrylate (NaAA) and dicumyl peroxide (DCP) on the properties of chloroprene rubber (CR)/starch/NaAA composites prepared by melting method were investigated. The results showed that the addition of starch improved the mechanical properties, but decreased the water‐absorbing capacity of the composite, most likely due to the decrease in the local concentration of the main water‐absorbing material sodium polyacrylate and the increase in crosslinking density of the composite resulting from the reaction between starch and CR. This reaction was verified by the vulcanized curves, DSC curves, and the cut surface morphology. The as‐prepared composite demonstrated higher water‐absorbing capacity, resulting from the incorporation of NaAA. The mechanical properties decreased with increasing the DCP loading, and the water‐absorbing ratio is the maximum at 1.0 phr DCP. The tensile strength of the composite decreased significantly after water immersion, due to the absorbed water acting as a plasticizer. The extracted component from composites after water immersion is mainly sodium polyacrylate according to Fourier transform infrared (FT‐IR) spectroscopy analysis. The morphology of the composites before and after water immersion was observed by optical transmission microscopy (OTM). The results indicated that the starch exhibits a good dispersion state, and the water‐absorbing capacity results primarily from sodium polyacrylate. Copyright © 2010 John Wiley & Sons, Ltd.