4种等温物态方程适用性的比较研究

 通过分析现有文献,认为4种两参数的物态方程在高压物理研究中较为流行,它们是Vinet、Baonza、Morse和Born-Meyer（BM）方程。将这4种方程用于拟合50种材料的实验压缩数据,得出了零压下压缩模量及其一阶压力导数的优化取值,并计算了4种方程的平均压力误差。结果表明,Morse方程的精度最高,对50种材料的平均拟合误差为0.557 6%;BM方程次之,平均误差为0.615 1%;Vinet和Baonza方程的误差大一些,分别为0.788 9%和0.833 3%。对8种典型材料计算了压力误差随压强变化的曲线,所得结果与平均误差的趋势一致,也是Morse方程的精度最高。在宽广压力范围的高压物态方程研究中,推荐使用Morse方程。     

应用于金属固体的四参数通用状态方程

提出一种能精确考虑固体结合能的四参数通用状态方程, 并且在高压和膨胀区域都具有正确的行为, 不会出现物理上不正确的振荡现象. 新方程可以将Vinet方程和普遍化Lennard-Jones (GLJ) 方程作为特例包括于其中. 将新方程与文献中的典型方程应用于32种金属固体, 结果表明新方程在给出正确结合能数据的同时, 能够很好的拟合实验压缩数据. 结果还表明, 多数金属的相互作用具有短程相互作用的性质, 但是结合能较大相互作用的强度较强.     

用冲击压缩数据计算物态方程的一种方法——Grüneisen系数最优化

 本文给出了一种用冲击压缩数据计算Grüneisen物态方程参数的方法。它使Grüneisen系数沿实验冲击绝热线的计算值与晶格振动理论的计算值达到最优拟合，给出了23种金属的冷能，冷压公式中的ρ_0K、Q和q以及Grüneisen系数的结果。用这些参数算得的冲击绝热线与实验冲击绝热线之间的平均相对偏差在1%以内。     

On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler function, a function with three-parameter which generalizes the classical ones, appear in the fractional telegraph equation. Here we introduce some integral transforms associated with this generalized Mittag-Leffler function. As particular cases some recent results are recovered.     

Equation of state of the alpha and epsilon phases of iron

An empirical equation of state that is thermodynamically consistent is found for the alpha (body-centered-cubic) and epsilon (hexagonal-close-packed) phases of iron. It is fit to all available types of experimental data-calorimetic, thermal expansion, acoustic, static compression, and shock data. All thermodynamic identities are satisfied, since expressions for all observables are derived from a thermodynamic potential. No specific theoretical assumptions are made, but the Helmholtz potential is formulated in terms of a number of adjustable functions of single variables by applying some general considerations of lattice vibrations, conduction electrons, and ferromagnetic exchange interaction. The effective Gruneisen parameter depends on temperature as well as volume. Ultrasonic and shock data for the alpha phase are found to be consistent with X-ray determinations of compression based on the sodium chloride standard. The Slater and Dugdale-MacDonald relations are tested against the fit at low pressure and are found to be in error. At high pressure not enough different types of data exist to establish a unique fit without theoretical assumptions.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Some new solitary and travelling wave solutions of certain nonlinear diffusion-reaction equations using auxiliary equation method

Attempts are made to look for the soliton content in the exact solutions of certain types of nonlinear diffusion-reaction (DR) equations with the quadratic and cubic nonlinearities. Such equations may arise in a variety of contexts in physical problems. In this Letter using the auxiliary equation method, some new solitary and travelling wave solutions of such nonlinear DR equations are obtained in a very general form. Several interesting special cases of these general solutions are also discussed.     

应用于碱卤化物固体的通用状态方程

提出一种能精确考虑固体结合能的通用状态方程,并且在高压和膨胀区域都具有正确的行为,不会出现物理上不正确的振荡现象.将新方程与文献中的典型方程应用于15种碱金属卤化物和一种碱土金属氧化物,结果表明新方程在给出正确结合能数据的同时,能够很好地拟合实验压缩数据.由Vinet方程和Morse方程定出的参数随数据范围变化很明显,新方程定出的参数随数据范围变化不明显.新方程的通用性优于Vinet方程和Morse方程. 关键词： 固体 通用状态方程 结合能 碱金属卤化物     

LaBaCu2O5-δ氧化物超导体的压缩特性

本文对La-Ba-Cu-O超导体的压缩特性进行了实验测量及理论计算,并利用所获实验数据写出了其Bridgman状态方程。 关键词：     

A study on the correlations of supercritical temperature of fluid alkali metals based on the generalised van der Waals equation of state

The supercritical temperature, the inversion temperature and the critical compressibility factor of caesium, rubidium and potassium are correlated through the generalised van der Waals equation of state. This three-parameter equation differs from the known van der Waals equation of state by the introduction of a third parameter in the expression for molecular pressure. For caesium, rubidium and potassium, the ratios of the supercritical temperature to the inversion temperature are estimated. The results of estimation are in agreement with the results from other equations which are based on experimental data. It has been established that caesium, rubidium and potassium obey the single-parameter law of corresponding states with the ratio of the supercritical temperature to the inversion temperature as the thermodynamic similarity parameter.     

New isothermal equation of state of solids applied to high pressures

In the present paper, a new two-parameter inverted equation of state (EOS) is developed which is found to be working very well in the high-pressure region. To check its success and validity, this EOS has been applied in a number of solids. The computed volume compression is found to be in very good agreement with the experimental data in the whole range of pressure in all the solids. The minimum and the maximum pressure range used in the present study is 0–320 kbar and 0–3000 kbar, respectively.     

Applications of Lie Symmetries to Higher Dimensional Gravitating Fluids

We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein’s equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.     

关于原子核电荷半径的研究

结合原子核电荷半径实验数据, 对885个中子数N≥8和质子数Z≥8的核电荷半径做了系统的研究. 对于单参数核电荷半径公式, Z^1/3律公式计算的结果优于A^1/3律的结果, 而对于两参数和三参数公式, Z^1/3律和A^1/3律的结果基本相当. 考虑到壳效应及奇偶摆动现象, 在原有的三参数公式基础上提出了加入Casten因子项和δ项的核电荷半径新公式. 利用该公式计算得到的核电荷半径理论值和实验值符合得非常好, 均方根偏差仅为σ=0.0266 fm, 此值比常用的三参数公式的结果下降了近50%, 理论计算值能更好地反映出壳效应及核电荷半径奇偶摆动的变化趋势.     

Differentially Rotating Disks of Dust

We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer—Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspond to disks with angular velocities depending monotonically on the radial coordinate; both decreasing and increasing behaviour is exhibited. In general, the solutions are related mathematically to Jacobi's inversion problem and can be expressed in terms of Riemann theta functions. A particularly interesting two-parameter subfamily represents Bäcklund transformations to appropriate seed solutions of the Weyl class.     

Initial compression rate of the cylindrically symmetric Z-pinch in gas

Based on the experimental data and the energy balance of the cylindrically symmetric Z-pinch in gas, a nonlinear differential equation for the plasma filament (layer) radius was derived. From this equation, for the instant of the filament detachment from the discharge chamber wall, the dependence of the initial filament compression rate on the initial discharge and gas parameters was determined, which was compared with experimental data obtained by us and other researchers. It was shown that the dependence found is in agreement with experimental data within measurement error.     

On the determination of the nuclear matter equation of state from pion yield data

Attempts to derive the nuclear matter equation of state from pion yield data have shown that the data can be reproduced by quite different parametrisations of the equation of state. We investigate this ambiguity within the one-dimensional shock wave model by deriving equations of statenot restricted to a predefined functional form. The results show that while in principle the dependence of the pion yields on energy can be reproduced by widely differing equations of state, some of these equations of state do not allow for sufficiently high bombarding energies. Others may violate causality inside the experimentally studied energy range, so that the admissible range of equations of state may be narrowed down considerably. Suggestions for further improvement are made.     

Correction of errors caused by imperfect inversion pulses in MR imaging measurement of T1 relaxation times

Spin-lattice (T₁) relaxation times were measured by an inversion-recovery magnetic resonance imaging method with a slice-selective inversion pulse (SIP), a non-selective rectangular inversion pulse (RIP), or a B₁-insensitive adiabatic inversion pulse (AIP). Data analysis either assumed perfect inversion (two-parameter fit) or allowed for imperfect inversion (three-parameter fit). Imperfect inversion pulses caused low T₁ values in phantoms with a two-parameter fit, while three-parameter T₁ estimates were accurate over the range 430–2670 ms. A difference of ∼10% between two-parameter and three-parameter T₁ values in normal human brain tissue was attributed to B₁ inhomogeneity with the slice-selective inversion pulse and rectangular inversion pulse, to the slice profile with the slice-selective inversion pulse, and to T₂ effects for the adiabatic inversion pulse. Any T₁ method that relies on accurate flip angles may have a significant systematic error in vivo. Phantom accuracy does not ensure accuracy in vivo, because phantoms may have a more homogeneous B₁ field and a longer T₂ than do biological samples.     

Equation of state for inert gas solids

The equation of state is a fundamental relation to analyse the thermophysical properties of different class of solids and it plays a key role in basic and applied condensed matter physics research. A lot of work has been done in the field of ionic solids, minerals and metals but a very little work is done in the field of inert gas solids. Most of the equations of state failed to explain the properties of inert gas solid because of their abnormal behavior in the low temperature range. In the present paper, Singh-Gupta equation of state has been used to study the properties of these solids. The results obtained using these equations have shown a good agreement with available experimental results. Thus it is shown that these equations of states successfully explain the behavior of inert gas solids.