麦克斯韦速率分布的特色推导方法

大学物理教学的一个基本点是培养学生的空间想象力.麦克斯韦速率分布律是气体分子运动论的中心内容,是大学物理气体运动理论中讲授的一个难点,其公式抽象、繁难,学生不易理解.本文根据速度空间概念,给出速度球的表面积相当于气体分子微观状态数的观点,利用拉郎格日函数,推导理想气体平衡态下气体分子的速率分布函数.这种推导方法相对比较简单、易学,便于学生理解和培养学生的空间想象力.     

On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).     

Maximum Entropy Approach to Reliability of Multi-Component Systems with Non-Repairable or Repairable Components

The degradation and recovery processes are multi-scale phenomena in many physical, engineering, biological, and social systems, and determine the aging of the entire system. Therefore, understanding the interplay between the two processes at the component level is the key to evaluate the reliability of the system. Based on the principle of maximum entropy, an approach is proposed to model and infer the processes at the component level, and is applied to repairable and non-repairable systems. By incorporating the reliability block diagram, this approach allows for integrating the information of network connectivity and statistical moments to infer the hazard or recovery rates of the degradation or recovery processes. The overall approach is demonstrated with numerical examples.     

有限深水域中三维频域自由面格林函数及其导数的计算方法

三维频域自由面格林函数及其偏导数的数值计算是海洋结构物水动力分析的难点。本文对有限水深格林函数及其偏导数的数值算法作出两点改进：①对原函数的级数表达式进行变形,提出适用于数值计算的形式,解决高频率情况下级数解的计算失真问题;②对Gauss-Laguerre积分法作出改进,解决高频率大水深情况下积分解的数值溢出问题。计算结果表明：本文提出的改进算法可以有效提高有限水深格林函数及其偏导数的数值精度,对于研究较大吃水的浮体或潜体的高频垂荡问题具有重要意义。     

降雪对地表附近自由空间量子信道的影响及参数仿真

量子通信具有覆盖面广、安全保密的优势,是当前通信领域国内外的研究热点.在自由空间量子通信过程中,光量子信号需要在地表上空一定高度进行传输,因此各种环境因素,例如降雪、沙尘暴、降雨、雾霾、浮尘等,不可避免地会影响量子通信性能.然而,迄今为止,降雪对地表附近自由空间量子信道影响的研究尚未展开.为此,根据降雪的强度,将降雪分为小雪(S1)、中雪(S2)、大雪(S3)和暴雪(S4)四个等级.由于空中正在飘落雪花对光量子信号具有能量吸收作用,称为消光效应,不同强度的降雪,其消光效应对自由空间光量子信号的影响不同.本文首先建立了不同等级降雪对光量子信号消光效应的数学模型;然后建立了因降雪导致的自由空间消光衰减定量关系,信道极限生存函数、不同降雪强度下的信道容量和量子误码率等性能参数受降雪影响的变化情况;最后建立了降雪强度、传输距离与链路衰减、幅值阻尼信道容量、信道生存函数以及信道误码率的数学模型.仿真结果表明,当降雪强度为2.1 mm/d(S1),传输距离为2.2 km时,通信链路衰减为0.0362,信道容量为0.7745,信道生存函数为0.2329,信道误码率为0.0105.当降雪强度为3.8 mm/d(S2)。传输距离为3.5 km时,通信链路衰减为0.1326,信道容量为0.4922,信道生存函数为0.2099,信道误码率为0.019.由此可见,降雪对量子通信性能有不同程度的影响.所以在实际应用中应根据降雪强度大小,自适应调节量子通信相关参数,提高量子通信的可靠性.     

Liquid crystalline properties of dissymmetric molecules IV. The substituent effect on thermal properties of nematic and smectic A phases in three aromatic ring systems with ester linkages

This paper describes the effect of substituent and ester linkage on smectic properties for some derivatives of 4-R -phenyl 4-(4-octyloxybenzoyloxy)benzoates (1), 4-octyloxyphenyl 4-(4-R-benzyloxy)benzoates (2), 4-(4-octyloxybenzoyloxy)phenyl 4- R -benzoates (3), and 4-R-phenyl 4-octyloxyphenyl terephthalates (4) where R = OCH₃, CH₃, OC₈H₁₇, C8H17, halogens, CF₃, OCF₃, CN, NO2, etc. The thermal properties are discussed in terms of the electrostatic nature of the substituents and the relative orientation of the ester groups with respect to both terminal substituents. The substituent effect on the layer structure of the smectic A phase is also examined by means of a small angle X-ray analysis.     

ClF-分子离子的结构与势能函数

采用单、双取代包括三重激发的二次组态相互作用[QCISD(T)]方法和单、双取代包括非迭代三重激发的耦合簇理论[CCSD(T)]方法, 结合相关一致基组aug-cc-pVXZ (X=D, T, Q, 5)对基态³⁵ClF^-和³⁷ClF^- (X²Σ⁺)分子离子进行了结构优化计算. 对CCSD(T)方法的计算结果用四种方法分别外推至基组极限, 得到了体系在基组极限的平衡结构常数. 在CCSD(T)/aug-cc-pVXZ (X=D, T, Q, 5)理论水平进行了单点能扫描. 对扫描计算结果进行基组外推并用Murrell-Sorbie 势能函数拟合得到了体系的解析势能函数表达式, 并进一步得到了³⁵ClF^-和³⁷ClF^-的光谱常数. 拟合所得势能曲线准确地再现了其离解能和平衡结构特征. 对ClF 中性自由基采用完全相同的理论方法进行了计算. 所得结果与有关文献中的实验结果符合得很好, 而且在一定程度上证明了将该理论方法应用于ClF^-分子离子的计算是合适而可靠的. ClF 自由基的优化计算结果还被用于计算其电子亲和能.ClF^-的垂直解离能也同时计算得出. 基于ClF^-的结构优化和单点能扫描计算结果, 通过求解核运动的径向薛定谔方程, 得到了无转动³⁵ClF^-和³⁷ClF^-(X²Σ⁺)的全部振动态及相应的分子常数.     

An analytical depth resolution function for the MRI model

The mixing roughness information depth model is frequently used for the quantification of sputter depth profiles. In general, the solution of the convolution integral for any kind of in‐depth distributions is achieved by numerical methods. For a thin delta layer, an analytical depth resolution function is presented, which enables a simple and user‐friendly quantification of measured delta layer profiles in AES, XPS and SIMS. Copyright © 2013 John Wiley & Sons, Ltd.     

Water PMF for predicting the properties of water molecules in protein binding site

Water is an important component in living systems and deserves better understanding in chemistry and biology. However, due to the difficulty of investigating the water functions in protein structures, it is usually ignored in computational modeling, especially in the field of computer‐aided drug design. Here, using the potential of mean forces (PMFs) approach, we constructed a water PMF (wPMF) based on 3946 non‐redundant high resolution crystal structures. The extracted wPMF potential was first used to investigate the structure pattern of water and analyze the residue hydrophilicity. Then, the relationship between wPMF score and the B factor value of crystal waters was studied. It was found that wPMF agrees well with some previously reported experimental observations. In addition, the wPMF score was also tested in parallel with 3D‐RISM to measure the ability of retrieving experimentally observed waters, and showed comparable performance but with much less computational cost. In the end, we proposed a grid‐based clustering scheme together with a distance weighted wPMF score to further extend wPMF to predict the potential hydration sites of protein structure. From the test, this approach can predict the hydration site at the accuracy about 80% when the calculated score lower than ?4.0. It also allows the assessment of whether or not a given water molecule should be targeted for displacement in ligand design. Overall, the wPMF presented here provides an optional solution to many water related computational modeling problems, some of which can be highly valuable as part of a rational drug design strategy. © 2012 Wiley Periodicals, Inc.