On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.     

Context-free grammars for triangular arrays

We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers.     

Solvation Rule for Solid‐Electrolyte Interphase Enabler in Lithium‐Metal Batteries

Despite the exceptionally high energy density of lithium metal anodes, the practical application of lithium‐metal batteries (LMBs) is still impeded by the instability of the interphase between the lithium metal and the electrolyte. To formulate a functional electrolyte system that can stabilize the lithium‐metal anode, the solvation behavior of the solvent molecules must be understood because the electrochemical properties of a solvent can be heavily influenced by its solvation status. We unambiguously demonstrated the solvation rule for the solid‐electrolyte interphase (SEI) enabler in an electrolyte system. In this study, fluoroethylene carbonate was used as the SEI enabler due to its ability to form a robust SEI on the lithium metal surface, allowing relatively stable LMB cycling. The results revealed that the solvation number of fluoroethylene carbonate must be ≥1 to ensure the formation of a stable SEI in which the sacrificial reduction of the SEI enabler subsequently leads to the stable cycling of LMBs.     

随机变量序列的大数定律及常返性定理

对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律.     

Along the Lines of Nonadditive Entropies: q-Prime Numbers and q-Zeta Functions

The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n−s=∏pprime11−p−s, Gauss, who estimated the rate at which prime numbers increase, and Riemann, who extended ζ(s) to the complex plane z and conjectured that all nontrivial zeros are in the R(z)=1/2 axis. The nonadditive entropy Sq=k∑ipilnq(1/pi)(q∈R;S1=SBG≡−k∑ipilnpi, where BG stands for Boltzmann-Gibbs) on which nonextensive statistical mechanics is based, involves the function lnqz≡z1−q−11−q(ln1z=lnz). It is already known that this function paves the way for the emergence of a q-generalized algebra, using q-numbers defined as 〈x〉q≡elnqx, which recover the number x for q=1. The q-prime numbers are then defined as the q-natural numbers 〈n〉q≡elnqn(n=1,2,3,⋯), where n is a prime number p=2,3,5,7,⋯ We show that, for any value of q, infinitely many q-prime numbers exist; for q≤1 they diverge for increasing prime number, whereas they converge for q>1; the standard prime numbers are recovered for q=1. For q≤1, we generalize the ζ(s) function as follows: ζq(s)≡〈ζ(s)〉q (s∈R). We show that this function appears to diverge at s=1+0, ∀q. Also, we alternatively define, for q≤1, ζq∑(s)≡∑n=1∞1〈n〉qs=1+1〈2〉qs+⋯ and ζq∏(s)≡∏pprime11−〈p〉q−s=11−〈2〉q−s11−〈3〉q−s11−〈5〉q−s⋯, which, for q<1, generically satisfy ζq∑(s)<ζq∏(s), in variance with the q=1 case, where of course ζ1∑(s)=ζ1∏(s).     

吸收峰混叠的太赫兹光谱区间组合特征提取算法

太赫兹光谱是物质识别的前沿方法之一。由于不同物质的分子组成或结构各异,许多物质的太赫兹吸收谱会在特定频率上出现吸收峰,可以作为混合物成分检测的重要特征。有效准确地提取这些吸收峰的参数,是提高识别率的关键。多峰拟合算法将光谱曲线拟合成若干个标准峰函数之和,能够同时提取到吸收峰的频率、峰高、峰宽等信息。但是该算法以寻峰算法结果为基础确定吸收峰的大致位置和数量,寻峰结果不一定是最优的拟合结果,而且很难准确识别定位混叠状态的吸收峰。为了提高混叠光谱中吸收峰的识别定位精度,提出以大幅度平滑后的曲线波谷为分界点,将预处理后的光谱分成若干个子区间。然后将子区间组合起来进行多峰拟合,通过遗传算法得到最优的拟合子区间组合和吸收峰频率近似值,拟合时每个子区间中通过峰数递增最优化方法确定拟合的吸收峰数,最后微调优化得到最优的吸收峰频率、峰高值。为了实现物质的识别,通过密度聚类算法得到同一类纯净物在多次测量中的共同吸收峰,以此作为标准数据,通过提出的基于吸收峰特征的光谱匹配算法实现了纯净物和不同含量混合物的快速识别。对10类纯净物的实际光谱数据进行拟合聚类,得到其吸收峰参数,结果与太赫兹光谱数据库一致。通过识别算法对纯净物测试集进行识别的识别率为100%,证明了特征提取和物质识别算法的有效性。对于含有混叠峰的混合物光谱,二阶导数法对葡萄糖-乳糖混合物光谱中被掩盖吸收峰(1.280 THz)的识别率仅为70%,提取到的频率平均值为1.316 THz;而该算法提高识别率至95%,频率平均值为1.281 THz,该算法提高了对混叠峰的分辨能力,能够精确定位混叠峰。对10类纯净物构成的6类不同程度混叠的二元混合物前二、三识别率分别达到90.8%和98.3%,提取到的特征能够有效应用于混合物的成分检测。该算法能够以纯净物数据为标准数据实现成分各异的混合物成分检测,对于太赫兹光谱混合物成分检测有重要意义。     

近红外光谱结合共识模型快速检测果酒的总酚含量

果酒发酵中的多酚是引起果酒口感、颜色变化的重要因素。为保证果酒品质,有必要开发一种快速监测发酵过程中多酚含量变化的技术。收集不同批次成熟期的蓝莓、桑葚为原料,分别碾压成汁,同时按比例混合二者,于小型发酵罐进行发酵。通过离线收集不同发酵时段的发酵液于离心管,高速离心后取上清液置于棕色瓶保存,共计得到48个果酒发酵样本。将上清液置于三个平行样比色皿,以傅里叶快速变换近红外光谱仪(FT-NIR)采集其透射光谱,取平均值作为该样本的光谱信号。然后将棕色瓶内的发酵液以国标法(即以标准液的吸光度值制定标准曲线)测定各样品的总酚含量,以duplex法计算样本光谱之间的距离且按2∶1的比例划分为训练集和预测集。采用间隔偏最小二乘法(iPLS)将训练集样本的透射光谱与总酚含量之间构建定量模型,间隔数从2依次变化到60个。该研究创新之处是使用共识方法融合多个已构建好的iPLS成员模型,按一定的共识规则分配权系数。通过各成员模型交互验证的残差及其残差之间的相关性来优化各成员模型的线性组合,以拉格朗日乘数法求解各成员模型的权系数,使间隔偏最小二乘-共识模型(consensual iPLS,CiPLS)的交互验证均方根误差最小。相比于全局PLS模型、划分不同间隔数量时的iPLS模型,CiPLS均具有较小的预测误差。当划分39个间隔时由三个iPLS成员模型(即14th,16th,18th)组成的共识模型误差最小为124.2,交互验证相关系数为0.944,对预测集样本的预测均方根误差为163.4,预测相关系数为0.931,预测性能均优于PLS和iPLS模型。另外,作为对比选用连续投影算法与无信息变量剔除法来优化光谱模型,其预测性能均不及本文提出的共识模型。分析各iPLS模型预测残差之间的相关性,发现共识模型主要是融合那些具有较高预测性能且模型间较低相关性的成员模型。结果表明,光谱分析结合共识方法可提高回归模型的预测精度、减少建模所需变量数,能够用于果酒总酚含量的离线快速检测。     

KINETIC ANALYSIS OF CO-CONDENSATION POLYMERIZATION OF AB2 AND AB MONOMERS

This work deals with the kinetics of co-condensation polymerization of AB2 and AB monomers, giving expressions of the two-dimensional molecular weight distribution function and the number/weight average molecular weights of the resulting copolymers. The two-dimensional molecular weight distribution depends on two indices, n and l, which are the respective numbers of AB2 and AB units in a copolymer species. The evolution of the two-dimensional weight and z distributions during the co-condensation polymerization has been evaluated systematically. Finally, the two-dimensional distribution was transformed into a one-dimensional molecular weight distribution with only one variable (the molecular weight of the products instead of the degree of polymerization). The calculated results show that the highly branched copolymer has a very broad molecular weight distribution when the co-condensation polymerization approaches completion.     

NOD随机变量序列加权乘积和的强大数律

利用乘积和的一表示定理和NOD（negatively orthant dependent）随机变量的性质,在较一般的条件下,得到了不同分布的NOD随机变量序列加权乘积和的强大数律,推广和改进了已知的一些文献中相应的结论.