纵横载荷作用下功能梯度梁的弯曲和过屈曲

基于一阶非线性梁理论和物理中面概念,导出了纵横向载荷作用下功能梯度材料(FGM)梁非线性弯曲和过屈曲问题的控制方程,并获得了该问题的精确解;据此解研究了梯度材料性质、外载荷、横向剪切变形以及边界条件等因素对功能梯度材料梁非线性力学行为的影响,分析中假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。结果表明:纵横载荷共同作用下,功能梯度梁的弯曲构形将有无限多个;随着梯度指数的增大,梁的变形减小,临界载荷升高;随着长高比的增大,横向剪切变形的影响减小。     

Enhanced electronic and nonlinear optical responses of C24N24 cavernous nitride fullerene by decoration with first row transition metals; A computational investigation

The electronic (energy gap and work function) as well as electrical properties (dipole moment, polarizability, and first hyperpolarizabilities) of the first-row transition metals decorated C₂₄N₂₄ cavernous nitride fullerene were explored using DFT calculations. The transition metals are decorated at N4 cavity of C₂₄N₂₄ fullerene. According to our spin polarized computations, the most stable spin state monotonically increases to sextet for Mn@C₂₄N₂₄ and thereafter dropped off gradually to singlet state for Zn@C₂₄N₂₄ system. The findings demonstrate that transition metals can remarkably decrease the HOMO-LUMO energy gap and work function values up to 63% and 21% of bare C₂₄N₂₄, respectively. As can be seen, when the Sc and Ti metals are located above the N4 cavity of fullerene, systems of enhanced static hyperpolarizabilities (β₀) are delivered. These findings might provide an effective strategy to design high performance eletcro-optical materials based on carbon- nitride fullerene.     

Deposition pattern of drying droplets

The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.     

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.     

Central Sets Theorem along filters and some combinatorial consequences

The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the algebra of Stone–?ech compactification of arbitrary semigroup, say $\beta S$. It can be proved that every closed subsemigroup of $\beta S$ is generated by a filter. We will show that, under some restrictions, one can derive the Central Sets Theorem for any closed subsemigroup of $\beta S$. We will derive this theorem using the corresponding filter and its algebra. Later we will also deal with how the notions of largeness along filters are preserved under some well behaved homomorphisms and give some consequences.     

卡罗琳·露丝·贝尔托西——诺贝尔化学奖史上第八位女性得主

卡罗琳·露丝·贝尔托西因开创了生物正交化学而获得2022年诺贝尔化学奖,该反应使科学家能够在不破坏细胞正常化学功能的情况下探索细胞、跟踪生物过程并实现了多种应用,提高了人类探索生命运动的能力和医学药物治疗的发展水平。通过回顾贝尔托西的研究背景以及相关的科研历程,提出了重视自主研究能力,在实践探索中收获无限可能;关注跨学科知识生产,在交叉领域开拓学科前沿;发挥科研“她”力量,更加多元与开放包容的思考与启示。     

Cu-Doped MoSi2N4 Monolayer as a Potential NH3 Sensor

Cu doped MoSi₂N₄ monolayer (Cu-MoSi₂N₄) was firstly proposed to analyze adsorption performances of common gas molecules including O₂, N₂, CO, NO, NO₂, CO₂, SO₂, H₂O, NH₃ and CH₄ via density functional theory (DFT) combining with non-equilibrium Green's function (NEGF). The electronic transport calculations indicate that Cu-MoSi₂N₄ monolayer has high sensitivity for CO, NO, NO₂ and NH₃ molecules. However, only NH₃ molecule adsorbs on the Cu-MoSi₂N₄ monolayer with moderate strength (−0.55 eV) and desorbs at room temperature (2.36×10⁻³ s). Thus, Cu-MoSi₂N₄ monolayer is demonstrated as a potential NH₃ sensor.     

重量法测定土壤水溶性盐总量的优化

土壤水溶性盐是表征土壤盐碱化程度的重要指标,也是评价耕地地力的重要参数,被纳入第三次全国土壤普查（“三普”）监测指标体系中。重量法是测定土壤水溶性盐总量的最常用方法,其测定过程易受多种因素影响,导致其测定结果不准。鉴于此,本文设计试验分别验证了水溶性盐浸提和浸提液固液分离这两个过程对测定结果的影响,结果表明浸提液固液分离是影响土壤水溶性盐总量测定准确度和精密度的主要因素。基于此进一步探究4种不同固液分离方式（布氏漏斗过滤、滤膜真空抽滤、离心、滤纸组合过滤）对测定结果的影响,结果表明相较于其它方式,滤纸组合过滤测定结果准确度高,适用于土壤水溶性盐总量的测定。对改进后的重量法测定土壤水溶性盐总量进行方法学确认,结果表明其检出限为0.01 g/kg,测定下限为0.04 g/kg;方法的准确度和精密度、适用范围等均符合相关要求。本文推荐的土壤水溶性盐总量测定方法为：土壤样品采用1:5土水比浸提,180 r/min振荡3 min,浸提液采用滤纸组合自然过滤;其测定结果的准确度和精密度符合相关要求。本文旨在为“三普”内业检测提供参考和借鉴,为全面摸清不同区域土壤水溶性盐含量水平及土壤盐渍化程度提供技术支撑。     

氧化环境和比例对改性Hummers法制备GO的影响

以鳞片石墨(GR)为原料,采用改性Hummers法液相氧化方法制备氧化石墨,通过超声剥离的方法剥离出片状的氧化石墨烯(GO),探讨了H₂SO₄环境与H₂SO₄+H₃PO₄混酸环境和KMnO₄与GR的比例对GO制备的影响。采用FTIR、UV、TG、XRD、SEM和XPS等分析手段对制备的GO进行分析。结果表明：GO外貌是呈褶皱片状,在片层上主要有C=O、C-OH、-COOH和C-O-C等官能团,以共价键形式存在石墨层间;通过TG与XPS数据分析表明在H₂SO₄ H₃PO₄混酸环境下制备的GO含氧官能团较多,并且(KMnO₄)与鳞片石墨的最佳比例是1:4。     

Theoretical study of the structural,elastic, electronic and optical properties of XCaF3 (X = K and Rb)

The PLANE WAVE pseudo-potential method within density functional theory (DFT) has been used to investigate the structural, elastic, electronic and optical properties of XCaF₃ (X = K and Rb) insulating. The studied compounds show a weak resistance to shear deformation compared to the resistance to the unidirectional compression. KCaF₃ and RbCaF₃ are considered ductile. The elastic constants and related parameters were predicted. The stiffness is more important in KCaF₃, whereas, the lateral expansion is more important in RbCaF₃. KCaF₃ and RbCaF₃ have R- Г indirect band gap. The main peaks in the imaginary part of the dielectric function correspond to the transition from the occupied state F₋p to the unoccupied states Ca: s or K, Rb: p. At lower energies, KCaF₃ and RbCaF₃ show the same optical properties. Under pressure effect, the peaks of imaginary part of dielectric function were shifted toward high energy.