Entropy Optimization,Maxwell–Boltzmann,and Rayleigh Distributions

In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations.     

Dynamics of Ultracold Bosons in Artificial Gauge Fields—Angular Momentum,Fragmentation, and the Variance of Entropy

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge field, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well as the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schrödinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation—multiple macroscopic eigenvalues of the reduced one-body density matrix—emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.     

声纳信号宽容性检测指数的初步分析

自上世纪六十年代以来,信号的宽容性(Robust,Robustness)处理就开始在统计数学与信号处理领域受到关注。由于声纳使用的水声环境的特殊复杂性,从事声纳信号处理和声纳设计的学者对环境适应性处理和宽容性水声信号处理开展了大量的研究。主要的目的是探索水声环境效应以及对声纳信号处理的影响,企图寻求一种适应环境的宽容性信号处理方法。本文初步探讨水声信号处理领域宽容性检测的基本概念,给出一种度量宽容性性能的数量指标。同时推导在不同声速剖面下声纳检测宽容性指标和所使用频率的关系。对文中所提出的理论方法与国内外实际海试的某些实例进行了分析比较。     

基于模糊PID参数自整定的细胞培养箱温度控制算法

针对细胞培养箱温度控制具有非线性、时滞性、易受干扰且难以建立精确的数学模型的特点,传统的PID控制方法对于快速维持系统箱内温度稳定存在一定的局限性。提出了以温度误差和误差变化率为控制输入,培养箱内温度为控制量的模糊PID参数自整定的温度控制算法,实现了对PID参数的实时在线修正。实验表明,该模糊PID参数自整定温度控制算法,温度从26℃上升到目标温度37℃,建立稳态的时间为2890s,温度超调极小。系统温度控制精度为±0.05℃,并在相同型号的细胞培养箱上同样得到验证。在控制稳定性方面获得了比传统PID控制更好的控温效果,稳定快,极小超调,温度控制精度高,能满足细胞培养箱温度控制的要求。     

磨矿机装载量直接测定方法

针对现有电耳侦听、轴承油压、振动间隙、负载功率、气压差等磨矿机装载量测量法不能真正解决磨矿机胀肚问题,创新地运用激光测距仪,在排浆口激光沿筒体轴线立面射向机内料面测距,根据机内矿料三维运动形态,设计获取静动态装载量与料高间稳定对应关系的测量方法,并设置过滤原则排除料雨干扰,实现磨矿机内料直接测量,为磨矿作业的节能降耗打下了基础。     

A theoretical study on the excited states of MC3 (M = Sc, V, and Cr)

The ground state structures of MC₃ (M = Sc, V, and Cr) and their anions have been investigated, employing the first-principles DFT at the B3LYP level. The calculations predict that the equilibrium geometries of both neutral MC₃ and their anions are cyclic structures with C_2v symmetry. The Mulliken charge and spin populations of MC₃ and their anions have also been calculated, and it is found the electron charge changes mainly take place on the M atoms from anions to neutral molecules. The low-lying excited states for the clusters are calculated with time-dependent DFT to assign the features of the photoelectron spectra. Our results agree well with the available experimental and theoretical data.     

Some mathematical aspects of Anderson localization: boundary effect,multimodality, and bifurcation

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach, and further investigate some mathematical aspects of Anderson localization that are rarely discussed before. First, we observe that under the Neumann boundary condition, the low energy quantum states are localized on the boundary of the domain with high probability. We provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional case. Second, we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary conditions. Finally, we examine a bifurcation phenomenon of the localization subregion as the strength of disorder varies. The critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.     

Pressure-induced phase transitions in the ZrXY (X= Si,Ge, Sn;Y= S,Se, Te) family compounds

Pressure is an effective and clean way to modify the electronic structures of materials, cause structural phase transitions and even induce the emergence of superconductivity. Here, we predicted several new phases of the ZrXY family at high pressures using the crystal structures search method together with first-principle calculations. In particular, the ZrGeS compound undergoes an isosymmetric phase transition from P4/nmm-I to P4/nmm-II at approximately 82 GPa. Electronic band structures show that all the high-pressure phases are metallic. Among these new structures, P4/nmm-II ZrGeS and P4/mmm ZrGeSe can be quenched to ambient pressure with superconducting critical temperatures of approximately 8.1 K and 8.0 K, respectively. Our study provides a way to tune the structure, electronic properties, and superconducting behavior of topological materials through pressure.     

First-principles study of ground- and metastable-state properties of XO (X = Be,Mg, Ca,Sr, Ba,Zn and Cd)

The evolution of the local atomic order of an amorphous Ni₄₆Ti₅₄ alloy produced by mechanical alloying as a function of temperature was studied by synchrotron X-ray diffraction (XRD) and differential scanning calorimetry (DSC) techniques. XRD measurements at several temperatures (25 °C, 350 °C, 412 °C, 430 °C, 450 °C and 515 °C) were performed and analyzed using the reverse Monte Carlo (RMC) simulations method or the Rietveld refinement procedure. The experimental total structure factor for samples at 25 °C and 350 °C, which are amorphous in nature, were simulated by using the RMC method, and the local structures of the alloy at both temperatures were determined, indicating a decrease in its density as the temperature increases. At 412 °C, the XRD pattern shows a partially crystalline sample, indicating that the crystallization process is in progress. At 430 °C, 450 °C and 515 °C, the XRD measurements indicate the presence of two crystalline phases, NiTi and NiTi₂, whose structural parameters (lattice parameters, coherently diffracting domains (CDD) sizes, microstrains and relative amount of phases) were determined using the Rietveld refinement procedure. DSC measurements at different heating rates furnished the crystallization temperature, enthalpy and activation energy of the crystallization process, and these values are similar to those found in other amorphous alloys of the Ni-Ti system. They also showed the existence of a second exothermic process, which was related to diffusive processes in the crystalline phases, which could be associated with the changes in the CDD sizes happening from 450 °C to 515 °C.     

Interplay of electronic,magnetic and structural properties of surface-supported clusters

We present first theoretical evidence revealing the influence of structural changes on the spin-polarized surface states of large Co nanoislands grown on Cu(111). The minority density of electronic states possesses a pronounced peak whose energetic position depends sensitively on the Co layers stacking order. Our results suggest a way to deduce the stacking order of large Co nanoislands using scanning tunnelling microscopy/spectroscopy.     

YH,YD,YT分子基态的结构与势能函数

在Y的有效核势近似下, 对H分别选6-311++G(3df,2pd), AUG-cc-PVTZ, AUG-cc-PVQZ基组, 应用密度泛函理论的B3LYP方法, 优化计算了YH(D,T)分子基态的能量, 平衡结构, 和谐振频率.根据原子分子反应静力学原理, 导出了YH(D,T)分子基态的合理离解极限. 通过优化计算结果和已有的实验和理论数据对比, 得出LANL2TZ/AUG-cc-PVQZ混合基组为对体系进行计算的最优基组. 基于此, 在B3LYP/LANL2TZ/AUG-cc-PVQZ水平对YH(D,T)分子基态的势能面进行了单点能扫描. 并采用最小二乘法拟合得到了相应的Murrell-Sorbie势能函数. 计算出了这些分子的力常数(f₂, f₃, f₄)和光谱常数(B_e, α_e, ω_e, ω_eχ_e, D_e).结果与已有的实验数据符合得很好.     

Electron energy loss spectra of the silicon 2p, 2s, carbon 1s and valence shells of tetramethylsilane

Inner shell excitation spectra of tetramethylsilane, (CH₃)₄Si, have been measured in the silicon 2s, 2p (L_I,II,III-shell) and carbon is (K-shell) regions using electron energy-loss spectroscopy at an impact energy of 2.5 keV and a scattering angle of ~1°. The high-resolution valence shell spectrum has also been observed at an impact energy of 3 keV and a zero degree scattering angle. The silicon 2p spectra are compared and contrasted with published photoabsorption spectra of SiF₄, SiH₄, and other related Si-containing molecules with varying ligands.     

Lipid hydroperoxides in nutrition,health, and diseases

Research on lipid peroxidation in food degradation, oil and fat nutrition, and age-related diseases has gained significant international attention for the view of improvement of societal health and longevity. In order to promote basic studies on these topics, a chemiluminescence detection-high performance liquid chromatography instrument using a high-sensitivity single photon counter as a detector was developed. This instrument enabled us to selectively detect and quantify lipid hydroperoxides, a primary product of lipid peroxidation reactions, as hydroperoxide groups at the lipid class level. Furthermore, an analytical method using liquid chromatography–tandem mass spectrometry has been established to discriminate the position and stereoisomerization of hydroperoxide groups in lipid hydroperoxides. Using these two methods, the reaction mechanisms of lipid peroxidation in food and in the body have been confirmed.     

ELECTRICAL PROPERTIES, EQUATIONS OF STATE AND PHASE TRANSITION IN SOLID C60 AT HIGH PRESSURE

Electrical properties and equations of state in solid C₆₀ at room temperature and high pressure have been studied in a diamond anvil cell using capacitance and resistance measurements and a piston-cylinder type device using P-V measurements, respectively. Experimental results by capacitance and P-V measurements indicate that solid C₆₀ also undergoes a phase transition at room temperature and a lower pressure, about 2GPa. The phase transition may be from a face-centered-cubic to a simple-cubic structure.     

Geometries,stabilities, and electronic properties analysis in In_nNi~((0,±1)) clusters: Molecular modeling and DFT calculations

Density functional theory(DFT) with the B3 LYP method and the SDD basis set is selected to investigate In_nNi,In_nNi~-, and In_nNi~+ (n = 1–14) clusters. For neutral and charged systems, several isomers and different multiplicities are studied with the aim to confirm the most stable structures. The structural evolution of neutral, cationic, and anionic In_nNi clusters, which favors the three-dimensional structures for n = 3–14. The main configurations of the In_nNi isomers are not affected by adding or removing an electron, the order of their stabilities is also nearly not affected. The obtained binding energy exhibits that the Ni-doped In_(13) cluster is the most stable species of all different sized clusters. The calculated fragmentation energy and the second-order energy difference as a function of the cluster size exhibit a pronounced even–odd alternation phenomenon. The electronic properties including energy gap(E_g), adiabatic electron affinity(AEA), vertical electron detachment energy(VDE), adiabatic ionization potential energy(AIP), and vertical ionization potential energy(VIP) are studied. The total magnetic moments show that the different magnetic moments depend on the number of the In atoms for charged In_nNi. Additionally, the natural population analysis of In_nNi~((0,±1)clusters is also discussed.     

Microscopic noise,adaptation and survival in hostile environments

The survival of autocatalytic agents in hostile environments depends on their ability to adapt their spatial configuration to local fluctuations. A model of diffusive reactants that extract the advantage of spatio-temporal fluctuations associated with the stochastic wandering of diffusive catalysts is discussed. Two arguments are presented for the basic processes behind this extraordinary behavior. In the first, the local colonies that evolve around any spatially advantageous region overlap in space-time and an infinite directed percolation cluster emerges. The second argument is based on the return probability of a diffusive agent that is shown to yield finite density of active “oases" with an exponentially large contribution to the reactant population. The different range of applicability of these survival lower bounds to small systems is discussed.     

微波消解-ICP-AES测定香烟接装纸中的汞、砷、铅、铬、镉和硒

采用HNO3-HCl-HF-H2O2消解体系对香烟接装纸进行湿法消解和微波消解,去除有机成分,保留待测元素。结果表明:不同种类的接装纸中各元素含量也不尽相同,但是大量吸烟对身体的有害程度还是显而易见的。采用微波消解-电感耦合等离子体-原子发射光谱法测定香烟接装纸中的As、Cd、Cr、Hg、Pb、Se等的含量。重金属元素加标回收率为96.7%—104.8%,检出限在0.000075—0.1288μg/mL范围内。