基于微区LIBS菊石化石中钙元素分布的研究

化石的研究可帮助科学家了解生物的演化进程，并帮助地质学家确定地层年代等地质信息，其中不同年代地层地质元素的变化是地质研究的热门课题。为研究不同年代地层地质元素的变化，搭建了一套微区LIBS实验系统，研究菊石化石中Ca元素的分布情况。采用非对称最小二乘法去除光谱数据的基线，并确定了最优的拟合参数。采用平均值归一化算法以减小光谱强度的相对标准偏差，多元线性回归算法计算模型的回归方程。首先，通过前期实验确定微区LIBS实验系统的最佳测试参数：激光波长为1 064 nm，激光脉冲频率为30 Hz，光谱仪采集延时为700 ns。其次，选取12块经过定量标定的天然岩石样品，从中随机抽取9块样品（闪长岩、闪长玢岩、辉长辉绿岩、粗玄岩、碱长粗面岩、角闪闪长岩、黑色浮岩、斑状角闪石花岗岩、玄武玻璃）作为测试集，其余3块样品（辉石闪长岩、辉石岩、斜长花岗岩）作为预测集。选取Ca Ⅱ 393.186 nm，Ca Ⅰ 422.856 nm，Ca Ⅰ 445.572 nm，Ca Ⅱ 559.031 nm，Ca Ⅰ 616.61 nm五个特征峰的谱线强度作为自变量，测试样品的实际Ca元素含量为因变量，利用多元线性回归算法建立Ca元素的定量分析模型，经预测集检验后得平均预测精度为92.9%。对表面经打磨的菊石化石进行5×5点阵扫描，得到一系列原子光谱数据。根据Ca元素的定量分析模型，计算后得到菊石化石Ca元素的横向分布图，其横向分辨率优于100 μm。作为纵向对比，选取每个测试点的第6，11和16组光谱数据进行处理，分别得到Ca元素的横向分布图。对比可以得到菊石化石Ca元素的纵向分布情况，结果表明菊石化石在平面和空间内均呈现不均匀分布的状态, 推测实验所选取的菊石化石在形成的过程中所处周围地层地质的元素及其含量是动态变化的。菊石化石不仅可以作为判定地层年代的证据，还可以通过对菊石化石的元素分布及含量的研究推测该化石所处地层的元素信息。研究工作对于浅海地层地质的演变、环境的变化具有一定指导意义。     

一种考虑界面相物性影响的界面单元法

界面是由复杂的界面相简化而成的,界面破坏实际是界面相材料的破坏。数值计算为了方便,如经典模型和内聚力模型等,都把很薄的界面相作无厚度化处理。导致只能考虑界面的面力,而无法考虑界面相内的应力(平行于界面方向的应力)。使界面失效准则先天性地排除了界面相内部应力的影响,从界面相材料失效机理的角度来看这是不够严谨的。本文将界面相材料等效为一种弹性连续体,由界面本构关系推导得到了一种新的界面单元。该单元具有界面参数易确定、对界面相物性可以进行等效描述等优点。通过商用有限元软件ABAQUS和用户子程序UEL实现了数值分析,并与直接物理模型的数值模拟结果进行对比,证明了本方法的简便及准确性。通过对不同界面相厚度结构的进一步分析,探讨了本文方法的可行范围。     

Conical Kakeya and Nikodym sets in finite fields

A Kakeya set contains a line in each direction. Dvir proved a lower bound on the size of any Kakeya set in a finite field using the polynomial method. We prove analogues of Dvir's result for non-degenerate conics, that is, parabolae and hyperbolae (but not ellipses which do not have a direction). We also study so-called conical Nikodym sets where a small variation of the proof provides a lower bound on their sizes. (Here ellipses are included.)Note that the bound on conical Kakeya sets has been known before, however, without an explicitly given constant which is included in our result and close to being best possible.     

Method validation for direct determination of some trace and toxic elements in soft drinks by inductively coupled plasma mass spectrometry

The consumption of soft drink beverages has increased in the last few years around the world and it is related to the diversity of brands and flavours available, increasing also the risk of ingestion of compounds considered non-beneficial to the health of consumers. In this study, fast, easy and simple method of analysis for direct determination of As, Pb, Cd, Sb, Hg, Cu, Zn, Fe, Al, Cr, Sn, Co, Mn and Ni in soft drink samples using quadrupole inductively coupled plasma mass spectrometry (Q-ICP–MS) was validated. The estimated detection limits, practical quantification limits, linearity (linear dynamic ranges and method linearity), accuracy (trueness and precision) and measurement uncertainty parameters were studied under optimised (Q-ICP–MS) conditions. The method showed that the estimated detection limits were varied between 0.02 and 2.403 µg/L, and the quantification limits were varied between 0.5 and 20 µg/L. The mean recoveries ± standard deviations at different spiking levels were varied between 75.03 ± 0.62% and 117.07 ± 2.83% and the coefficients of variation were varied between 0.49% and 9.79%. The method trueness was confirmed by using four different certified reference materials (soft drinks and treated water) purchased from FAPAS (Food Analysis Performance Assessment Scheme) and all obtained results were within satisfactory ranges and had acceptable recovery and Z-score values. The method precision, in terms of relative standard deviation, was below 4.88%. The method uncertainty expressed as expanded uncertainty of all validated elements was found to be ≤22.52%. The results obtained make the method suitable for accurate determination of validated elements in different kinds of soft drink samples at these low concentration values. Validated method was used for the determination of metallic contaminants in 40 commercial soft drink samples and the results were compared with the provisional guideline of the elements stated by Egyptian, WHO and European standards in drinking and potable bottled natural mineral water.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Next-generation NATO reference mobility model complex terramechanics – Part 2: Requirements and prototype

In part 2 of this paper, the Complex Terramechanics (CT) software tools requirements recommended by the NATO research task group RTG-248 are presented along with example simulations from a CT prototype software tool which attempts to satisfy the requirements.     

Lamb波频域逆散射全聚焦成像方法研究

Lamb波因其传播距离远、衰减小常被用于板状结构的无损检测中,在基于Lamb波损伤检测的诸多成像技术中,全聚焦方法(Total Focus Method,TFM)方法因其成像分辨率高、信噪比高而受青睐。然而Lamb波的频散效应导致时域延时量不能被准确计算,进而影响传统TFM方法对损伤定位及成像的精度;此外,既有的TFM方法仅以回波幅值作为成像指标,忽略了Lamb波与损伤的相互作用,故而不能通过损伤表面的物理参数增强成像质量。针对这两个问题,本文首先在时域TFM基础上发展了频域TFM,在计算中纳入频散关系以规避频散的影响;其次以包含明确的损伤特征参数--反射率为成像指标,结合频域TFM方法建立损伤逆散射模型,以实现对损伤的准确成像。仿真和实验结果表明:频域逆散射TFM成像方法能够实现对铝板结构中的损伤检测,在工程实践中具有应用价值。     

微区X射线荧光成像技术在岩心分析中的应用

微区X射线荧光（Micro-XRF）分析技术是通过微小的X射线光束照射样品，对样品进行原位成分观测的无损分析手段之一，具有灵敏度高、速度快和准确性高的特点。采用微区X射线荧光光谱仪（M6 JETSTREAM）对安徽铜陵冬瓜山铜矿床四段岩心样品进行面扫描，分析不同矿层共17种元素区域分布特征、空间分布规律及组合关系等，结果表明：（1）Cu和Fe两种成矿元素高值空间分布区域基本不重叠，S与Fe分布范围高度重叠，关系密切，微量元素Ni，Bi，Pb，Zn，Si，Na与Cu密切相关，而Ti，Al，K与Fe具有弱相关性；（2）垂向上，Fe元素含量随深度增加逐步增大，而Cu元素含量呈降低趋势，其他元素也随深度呈下降趋势；（3）元素分布受石炭纪中期海底喷流沉积成矿作用和岩浆热液成矿作用叠加改造作用明显；（4）该钻孔矿石矿物以磁黄铁矿、黄铜矿和黄铁矿为主，垂向上组合规律明显，脉石矿物以石英、石榴子石和透辉石为主。该技术通过分析元素空间分布规律、相关性以及矿物组合和分配关系等可对元素富集和运移以及对矿床的成矿机制、成因模式等地质环境和地质过程提供新认识和新证据。结合矿床地球化学特征的分布模式，微量元素可作为寻找主矿种的指示元素，为深部找矿提供依据。此外，该技术能作为预分析技术快速筛选出感兴趣的信息和位置，为后期各种更高精度的微区分析提供不同尺度、不同层次的元素分布信息。     

Modeling of metallic foam morphology using the Representative Volume Element approach: Development and experimental validation

This paper focuses on the development of an algorithm capable of generating morphologically-representative foam structures using the Representative Volume Element (RVE) approach. Stereology, a sampling method based on direct observations of the foam cross-sections, is used to characterize the pore size and shape distributions. Using the morphology generation algorithm, the smallest RVEs corresponding to the numerically-convergent foam morphologies are calculated for different foam porosities. To validate the foam generation algorithm, the pore size and shape distributions of the numerically-generated foams are compared to those of the titanium foams manufactured by the space holder method.