To the Question of Validity Grüneisen Solid State Equation

The first justified theory of solid state was proposed by Grüneisen in the year 1912 and was based on the virial theorem. The forces of interaction between two atoms were assumed as changing with distance between them according to inverse power laws. But only virial theorem is insufficient to deduce the equation of state, so this author has introduced some relations, which are correct, when the forces linearly depend on displacement of atoms. But with such law of interaction the phase transitions cannot take place. Debye received Grüneisen equation in another way. He deduced the expression for thermocapacity, using Plank formula for energy of harmonic vibrator. Taking into account the dependence of atomic vibration frequency from distance between atoms, when the forces of interaction are anharmonic, he received the equation of state, which in classical limit turns to Grüneisen equation. The question, formulated by Debye is—How can we come to phase transitions, when Plank formula for harmonic vibrator was used? Debye solved this question not perfectly, because he was born to small anharmonicity. In the presented work a chain of atoms is considered, and their movement is analysed by means of relations, equivalent to virial theorem and theorem of Lucas (disappearing of mean force). Both are the results of variation principle of Hamilton. The Grüneisen equation for low temperature (not very low, where quantum expression for energy is essential) was obtained, and a family of isotherms and isobars are drown, which show the existence of spinodals, where phase transitions occur. So, Grüneisen equation is an equation of state for low temperatures.

Fractional Difference Approximations for Time-Fractional Telegraph Equation

In this paper, we approximate the solution to time-fractional telegraph equation by two kinds of difference methods: the Grünwald formula and Caputo fractional difference.

Determination of Grüneisen EOS of MSN Alloy Steel Under High Pressure

Dynamic mechanical performances of 30CrMnSiNi2A alloy steel under high pressure of 1-15 GPa are studied with a one stage light gas gun. With the particle velocity ranging from 150 m/s to 300 m/s, the Hugoniot curve of 30CrMnSiNi2A alloy steel is analyzed and obtained based on the experimental data and the parameters of equation of state are obtained by calculating. The Grüneisen equation of state can be determined through these parameters.

Grüneisen参数体积相关性的理论研究

根据常用势模型运用关于Grüneisen参数体积相关性的Slater公式、Dugdale-McDonald公式和Vaschenko-Zubarev公式,计算了NaCl在0-30GPa压强范围内的Grüneisen参数,通过计算结果与实验数据的比较与分析,提出了对Grüneisen参数经验值一种新的修正方法,修正后的数据在整个压强范围内与实验值吻合得较好.

Grüneisen系数与铝的状态方程

基于GRAY三相状态方程模型，分别采用ργ=常数、GRAY、GRIZZLY的Grüneisen系数模型和从头算给出的Grüneisen系数计算了铝的熔化曲线、等熵压缩线、等温压缩线和等熵卸载线。计算结果与实验数据比较发现，GRIZZLY的Grüneisen系数模型对铝是最合适的。

用PVDF压力计研究未反应JB-9014钝感炸药的Grüneisen参数

为了获得未反应JB-9014炸药的Grüneisen参数Γ,在火炮加载平台上对JB-9014炸药进行一维平面冲击实验。实验中,将炸药样品安装于两个铜板之间,两个PVDF压力计分别安装在炸药样品前表面和中部,记录两个位置处的压力随时间的变化历程;将圆形铜板作为飞片安装于弹托前表面,利用火炮加速弹托,使飞片以一定速度撞击样品装置前铜板,前铜板中产生右行冲击波对炸药样品形成一次压缩;随后冲击波在炸药样品/后铜板交界面发生反射,产生左行冲击波对炸药样品形成二次压缩。假设炸药样品的Grüneisen参数Γ为常数,计算不同Γ值下炸药样品前表面和中部压力随时间的变化历程,将不同Γ下的计算值与实验值进行对比,获得了JB-9014钝感炸药Grüneisen参数的最优值,为1.7。

快速增压法研究温度对铝和氯化钠Grüneisen参数的影响

根据Grüneisen状态方程导出的偏导关系式γ=(K_S/T)(T/p)S(其中KS是绝热体积弹性模量),采用快速增压方法结合中值定理分别在297~494K和312~608K温度范围内研究了铝和氯化钠的Grüneisen参数γ随温度的变化关系。在平面对顶压砧模具上设计了内加热的样品组装方式,测量了不同温度下快速增压过程中样品的温升曲线和压力变化曲线,并对温升曲线进行了温度修正,使所得结果更接近绝热压缩过程。实验结果表明:铝和氯化钠在实验温度范围内、压力分别为2.17GPa和1.46GPa下,其ΔT/Δp值随着温度的升高而增大;γ值随着温度的升高表现为波动的变化趋势,与温度没有明显的变化关系。

Dispersive Property of Mode Grüneisen Parameter:Corundum andα-Quartz as Examples

The dispersive property of the mode Grüneisen parameter in solids is found theoretically.Such a property should appear in a reciprocal relationship to the mode frequency.This phenomenon is also confirmed experimentally in the cases of corundum andα-quartz.

Analytical and Numerical Solutions of Riesz Space Fractional Advection-Dispersion Equations with Delay

In this paper,we propose numerical methods for the Riesz space fractional advection-dispersion equations with delay(RFADED).We utilize the fractional backward differential formulas method of second order(FBDF2)and weighted shifted Grünwald difference(WSGD)operators to approximate the Riesz fractional derivative and present the finite difference method for the RFADED.Firstly,the FBDF2 and the shifted Grünwald methods are introduced.Secondly,based on the FBDF2 method and the WSGD operators,the finite difference method is applied to the problem.We also show that our numerical schemes are conditionally stable and convergent with the accuracy of O(+h2)and O(2+h2)respectively.Thirdly we find the analytical solution for RFDED in terms Mittag-Leffler type functions.Finally,some numerical examples are given to show the efficacy of the numerical methods and the results are found to be in complete agreement with the analytical solution.

A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation

By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation,and then using the fractional-compact Grünwald–Letnikov tempered difference operator to approximate the Riemann–Liouville tempered fractional partial derivative,the fractional central difference operator to discritize the space Riesz fractional partial derivative,and the classical central difference formula to discretize the advection term,a numerical algorithm is constructed for solving the Caputo tempered fractional advection-diffusion equation.The stability and the convergence analysis of the numerical method are given.Numerical experiments show that the numerical method is effective.

Grtzsch环函数的几个不等式

建立了Ramanujan模方程中Grtzsch环函数μ(r)与第二类完全椭圆积分ε(r)及拟共形理论中的Hübner函数m(r)之间的关系,并通过研究μ(r)与某些初等函数及特殊函数组合的单调性,获得了μ(r)的几个不等式,利用这些结果给出了μ(r)+logr的上下界,从而改进了已知的此类估计,同时给出了μ(r)形如Landen恒等式的不等式形式。所得结果有助于研究Ramanujan模方程理论。

关于Grtzsch环函数的几个性质

揭示拟共形映照理论中平面Grotzsch环的模μ(r)和广义平面Grotzsch环函数μa(r)的若干性质,这些结果将被用于研究Ramanujan模方程及其解的性态.

基于Grüneisen弛豫非线性光声效应的单波长浓度解析方法

光声分子影像技术在生物医学中具有广泛的应用。实现分子探针浓度的准确解析,对于相关疾病的研究具有重要意义。然而,活体探测时,来源于生物组织的信号与探针的信号混叠,增加了准确解析的难度。当前改善的方法:或需要使用多波长进行探测,导致解析速度慢而且过程复杂;或使用单波长的方法,但需要依托于一类特殊探针的开关功能,导致普适性不足。鉴于此,提出了一种基于Grüneisen弛豫非线性光声效应的单波长浓度解析方法,并分别对色素染料与罗丹明6G探针两类样品开展了解析实验。结果表明,本文提出的方法获得的解析结果比线性单波长方法的解析结果误差更小,并且具有较好的普适性,为光声分子影像的浓度解析方法提供了新的思路。

Evaluating thermal expansion in fluorides and oxides:Machine learning predictions with connectivity descriptors

Open framework structures(e.g.,ScF_(3),Sc_(2)W_(3O)_(12),etc.)exhibit significant potential for thermal expansion tailoring owing to their high atomic vibrational degrees of freedom and diverse connectivity between polyhedral units,displaying positive/negative thermal expansion(PTE/NTE)coefficients at a certain temperature.Despite the proposal of several physical mechanisms to explain the origin of NTE,an accurate mapping relationship between the structural–compositional properties and thermal expansion behavior is still lacking.This deficiency impedes the rapid evaluation of thermal expansion properties and hinders the design and development of such materials.We developed an algorithm for identifying and characterizing the connection patterns of structural units in open-framework structures and constructed a descriptor set for the thermal expansion properties of this system,which is composed of connectivity and elemental information.Our developed descriptor,aided by machine learning(ML)algorithms,can effectively learn the thermal expansion behavior in small sample datasets collected from literature-reported experimental data(246 samples).The trained model can accurately distinguish the thermal expansion behavior(PTE/NTE),achieving an accuracy of 92%.Additionally,our model predicted six new thermodynamically stable NTE materials,which were validated through first-principles calculations.Our results demonstrate that developing effective descriptors closely related to thermal expansion properties enables ML models to make accurate predictions even on small sample datasets,providing a new perspective for understanding the relationship between connectivity and thermal expansion properties in the open framework structure.The datasets that were used to support these results are available on Science Data Bank,accessible via the link https://doi.org/10.57760/sciencedb.j00113.00100.

ALIKHANOV LINEARIZED GALERKIN FINITE ELEMENT METHODS FOR NONLINEAR TIME-FRACTIONAL SCHRODINGER EQUATIONS

We present Alikhanov linearized Galerkin methods for solving the nonlinear time fractional Schrödinger equations.Unconditionally optimal estimates of the fully-discrete scheme are obtained by using the fractional time-spatial splitting argument.The convergence results indicate that the error estimates hold without any spatial-temporal stepsize restrictions.Numerical experiments are done to verify the theoretical results.

Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schr¨odinger Equations

A linearized transformed L1 Galerkin finite element method(FEM)is presented for numerically solving the multi-dimensional time fractional Schr¨odinger equations.Unconditionally optimal error estimates of the fully-discrete scheme are proved.Such error estimates are obtained by combining a new discrete fractional Gr¨onwall inequality,the corresponding Sobolev embedding theorems and some inverse inequalities.While the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting approaches.Numerical examples are presented to confirm the theoretical results.

The Principal Role of Antimatter

In a previous paper, we proposed that ud~du~ exotic mesons, comprised of even number of quarks and antiquarks, form a QCD gas that fills space and further proposed a method to determine the QCD gas effective mass based on a pseudo-first order β decay reaction kinetics. In a second paper, we proposed a method to determine if the QCD gas density on black hole ergospheres grows in time and hence their ergoregions act as matter reactors that break matter and antimatter symmetry by trapping antimatter particles. In this paper, we suggest that quark and antiquark pair exchange reactions between particles and the QCD gas may accelerate or decelerate particles and that the quarks and antiquarks numbers are strictly conserved in these pair exchange reactions. We further suggest that antimatter plays a principal role in the universe and is inseparable from both matter, via Dirac’ spinors, and space, via the quarks and antiquarks pair exchange reactions with the QCD gas;however with a singular exception, black hole ergospheres separate and black hole ergoregions trap antimatter particles.

Solving Multivariate Polynomial Matrix Diophantine Equations with Gr?bner Basis Method

Different from previous viewpoints,multivariate polynomial matrix Diophantine equations are studied from the perspective of modules in this paper,that is,regarding the columns of matrices as elements in modules.A necessary and sufficient condition of the existence for the solution of equations is derived.Using powerful features and theoretical foundation of Gr?bner bases for modules,the problem for determining and computing the solution of matrix Diophantine equations can be solved.Meanwhile,the authors make use of the extension on modules for the GVW algorithm that is a signature-based Gr?bner basis algorithm as a powerful tool for the computation of Gr?bner basis for module and the representation coefficients problem directly related to the particular solution of equations.As a consequence,a complete algorithm for solving multivariate polynomial matrix Diophantine equations by the Gr?bner basis method is presented and has been implemented on the computer algebra system Maple.

A Compact Difference Scheme on Graded Meshes for the Nonlinear Fractional Integro-differential Equation with Non-smooth Solutions

In this paper,a compact finite difference scheme for the nonlinear fractional integro-differential equation with weak singularity at the initial time is developed,with O(N^(-(2-α))+M^(-4))accuracy order,where N;M denote the numbers of grids in temporal and spatial direction,α ∈(0,1)is the fractional order.To recover the full accuracy based on the regularity requirement of the solution,we adopt the L1 method and the trapezoidal product integration(PI)rule with graded meshes to discretize the Caputo derivative and the Riemann-Liouville integral,respectively,further handle the nonlinear term carefully by the Newton linearized method.Based on the discrete fractional Gr¨onwall inequality and preserved discrete coefficients of Riemann-Liouville fractional integral,the stability and convergence of the proposed scheme are analyzed by the energy method.Theoretical results are also confirmed by a numerical example.

蓝柱石的高温X射线衍射、差热-热重分析、偏振红外光谱和高压拉曼光谱研究

通过高温X射线衍射(XRD)、差热-热重分析、偏振红外光谱和高压拉曼光谱研究了江西大余的蓝柱石的热膨胀行为、稳定性、羟基峰在(010)面上的强度变化及其常温高压拉曼光谱特征。结果表明,蓝柱石在1273K完全非晶化,其热膨胀系数αV为1.2(1)×10-5+0.16(1)T×10-9/K。蓝柱石在750K开始发生分解反应,最大的反应速率发生在1266K。在蓝柱石的(010)面上,羟基吸收峰在光的偏振方向与c轴夹角为70°和250°时最强,在光的偏振方向与c轴夹角为160°和340°时最弱。在常压至12.3GPa的压力范围内,蓝柱石没有发生相变。通过高压拉曼光谱计算得到了蓝柱石的mode Grüneisen参数的算术平均值为0.52(2)、thermal Grüneisen参数为0.64(2)。另外,根据Grüneisen关系式可以求得thermal Grüneisen参数,其值为0.70(6)。