弹性薄壁桿件的平衡与稳定的一般理论

In this paper a theory of equilibrium and stability of elastic thin-walled cylinders is proposed. The theory is based on the following assumptions: 1) The cross section of the cylinder is uncleformable. 2) The cylinder is under a system of initial stresses σ_z⁰=- P⁰/F-M_y⁰/I_xx x + M_x⁰/I_yyy. This theory may be regarded as a generalization of V. Z. Vlasoff's theory of stability of thin-walled rods, and includes the theory of Karman-Chien and Adaduroff as a special case. For cases of simply supported cylinders and cantilever cylinders, a method of solution using trigonometric series is proposed which is much simpler than the methods used by Karman-Chien and Adaduroff.     

论弹性体力学与受范性体力学中的一般变分原理

In this paper, some general variational principles in the theory of elasticity and the theory of plasticity are established. Consider an elastic body in equilibrium with small displacement. By regarding u, v, w, e_x, e_y, e_z, y_yz, y_xz, y_xy, σ_{x,σy, σz,τyz,τxz,τxy as fifteen independent functions, and letting their variations be free from any restriction, we establish two variational principles, called the principle of generalized complementary energy and the principle of generalized potential energy. Each principle is equivalent to the four sets o?fundamental equations of the theory of elasticity, namely, the equations of equilibrium, the stress strain relations, the strain displacement relations and the appropriate boundary conditions. Special cases of these principles are examined. These principles are next expressed in other forms, where u, v, w, σx,σy, σz,τyz,τxz,τxy are regarded as nine independent functions with their variations free from any restrictions. Next we consider the bending of a thin elastic plate with supported edges under large deflection. By regarding Mx, My, Mxy, Nx, Ny, Nxy, u, v, w as nine independent functions with the restriction that w should vanish along the contour of the plate, we establish a variational principle, called the principle of generalized potential energy, which is equivalent to the three sets of fundamental equations in the theory of bending of thin plate, namely, the equations of equilibrium, the displacement stress relations (strain stress relations) and the appropriate boundary conditions. This principle is next expressed in another form which is more convenient for application. As an illustration, von Kármán's equations for the large deflection of thin plate are derived from this principle. In von Kármán's equations, one unknown is the deflection and the other unknown is the membrane stress function. Therefore it is impossible to derive von Karman's equations either from the principle of minimum potential energy or from the principle of complementary energy. Finally we consider the equilibrium of a plastic body with small displacement. In the case of the deformation type of stress strain relations, we establish two variational principles, each of which is equivalent to the equations of equilibrium, a certain type of stress strain relations and the appropriate boundary conditions. In these variational principles, u, v, w and their variations are free from any restriction, and σx,σy, σz,τyz,τxz,τxy and their variations satisfy a certain yield condition. In the case of the flow type of stress strain relations, we get two similar variational principles, in which u, v, w and their variations are free from any restriction, σx,σy, σz, τyz,τxz,τxy and their variations satisfy a certain yield condition and σx,σy, σz, τyz,τxz,τxy have no variations.}     

CRYSTAL STRUCTURE AND MAGNETIC PROPERTIES OF La1.2Sr1.8-xCaxMn2O7

The effect of divalent cation substitution on the structure and magnetic properties of La_1.2Sr_1.8-xCa_xMn₂O₇ (x = 0－0.900) is investigated in this paper. Partly replacing divalent cation Sr²⁺ by Ca²⁺ ions results in the weakening and then disappearance of long-range ferromagnetic ordering, and the formation of spin canting and low-temperature spin-glass. Based on structural analysis by Rietveld profile fitting, we suggest that this variation of magnetic property be related to a Jahn－Teller-type attice distortion of MnO₆ octahedra due to the introduction of the smaller sized Ca²⁺ ions.     

Lithium ion conductivity of the B-site substitution in Li3xLa0.67−xRE y III Ti1−2yPyO3 system (REIII=Sc3+, Y3+, Nd3+, Sm3+, Eu3+, Yb3+)

The B-site substituted perovskite solid solution systems Li_3xLa_0.67−xRE_yTi_1−2yP_yO₃ (RE=Sc, Y, Nd, Sm, Eu, Yb) have been investigated. Perovskite solid solutions formed in the range of x=0.10, y<0.10 for RE=Sc³⁺, Y³⁺, Yb³⁺, x=0.10, y≤0.05 for RE=Nd³⁺, Sm³⁺, Eu³⁺. Li_0.3La_0.57Nd_0.05Ti_0.9P_0.05O₃ has the highest bulk conductivity of 4.31×10⁻⁴ S·cm⁻¹ and the highest total conductivity of 2.52×10⁻⁴ S·cm⁻¹ at room temperature in all prepared compositions. The compositions have low activation energies of about 24–30 kJ/mol in the temperature ranges of 298–523 K. SEM studies showed that the sample made by solid-state reaction has a sphere-like morphology and a rough particle with particle size of about 50 μm. The research results also indicated that the reaction temperature decreases and the electrochemical stabilities of the titanate-based perovskite-type solid solutions are improved by using RE³⁺ and P⁵⁺ replaced Ti⁴⁺ on B-site in the Li_3xLa_0.67−xTiO₃ parent.     

高能电子对原子核C12的弹性散射

In this paper, we have calculated the elastic scattering of high energy electrons with nuclei C¹² by phase shift calculation.We take the charge distribution of the nucleus C¹² as following:(1) exponential distribution:ρ(x)=ρ₀θ^-x/a, (2) gaussian distribution:ρ(x)=ρ₀e^(-x2/a2),(3) uniform distribution: ρ(x) ={ρ₀ when 0kR, where a and b are the parameters, and the constant R is the radius of the nucleus C¹². The energy of the electrons is 187 Mev.The result of the calculation shows that the gaussian distribution confirms the experimental result better than the other two kinds of distributions, and gives R=(12)^1/3r₀, where r₀=1.35×10^-13 cm.     

Energy level of an electron in a saddle-potential quantum dot under a uniform magnetic field obtained by the invariant eigenoperator method

We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field. The Landau diamagnetism decreases with the value ω_y² - ω_x² due to the existence of the saddle potential.     

Energy level of an electron in a saddle-potential quantum dot under a uniform magnetic field obtained by the invariant eigenoperator method

We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field. The Landau diamagnetism decreases with the value ω_y² - ω_x² due to the existence of the saddle potential.     

Reference electrodes for low-temperature gas sensors

The behavior of sodium oxide bronzes in contact with sodium-conducting solid electrolytes in atmospheres of oxygen, carbon dioxide, hydrogen sulfide, and humid air was investigated. The exchange currents at the Na_xCoO_y/NASICON interface was determined. It is shown that among the sodium-cobalt oxide bronzes the β-phase of the composition Na_0.6CoO₂ is the most reversible one (exchange current 236 μA/cm²). Paper presented at the 1st Euroconference on Solid State Ionics, Zakynthos, Greece, 11–18 Sept. 1994     

TEMPERATURE-DEPENDENT ANISOTROPY IN La1.86Sr0.14CuO4

Based on the scaling rule: R(T, H, θ) = R(T, h), where h = H(sin²θ+cos²θ/γ²)^1/2 and θ is field angle with respect to the ab-plane, the scaling approach is performed to examine the c-axis resistances of single crystalline La_1.86Sr_0.14CuO₄ as functions of field and its orientation at different temperatures. The anisotropy parameter γ of the system is extracted from the scaling approach, but shows an unusual temperature-dependent behavior, which is not expected by conventional theory. A phenomenological explanation of this temperature dependence is presented.     

Sn-based type-VIII single-crystal clathrates with a large figure of merit

Single-crystal samples of type-VIII Ba₈Ga_{16 - x}Cu_xSn₃₀ (x=0, 0.03, 0.06, 0.15) clathrates were prepared using the Sn-flux method. At room temperature the carrier density, n, is 3.5-5×10¹⁹ cm^-3 for all the samples, the carrier mobility, μ_H, increases to more than twice that of Ba₈Ga₁₆Sn₃₀ for all the Cu doping samples, and consequently the electrical conductivity is enhanced distinctly from 1.90×10⁴ S/m to 4.40×10⁴ S/m, with the Cu composition increasing from x=0 to x=0.15. The Seebeck coefficient, α , decreases slightly with the increases in Cu composition. The κ values are about 0.72 W/mK at 300 K and are almost invariant with temperature up to 500 K for the samples with x=0 and x=0.03. The lattice thermal conductivity, κ_L, decreases from 0.59 W/mK for x=0 to 0.50 W/mK for x=0.03 at 300 K. The figure of merit for x=0.03 reaches 1.35 at 540 K.     

Mössbauer effect study of Ni1−xCuxMnyFe2−yO4 system

The Mössbauer effect technique has been employed for the study of magnetic properties of spinel series Ni_1?xCu_xMn_yFe_2?yO₄ with 0.0≤x≤1.0, and y=0.6. The substitution of Mn³⁺ and Cu²⁺ ions results in a slight decrease of the hyperfine field at B‐ as well as A‐sites. The area ratio of Fe³⁺ ions at the A‐ and B‐site at 77 K indicates that Cu²⁺, Ni²⁺ and Mn³⁺ ions occupy the octahedral sites in an evidence for complete inverse spinel in this system. The temperature dependence of the hyperfine parameters has been studied for composition with x=0.5 where Nèel point T_N and Debye temperature θ_D are found to be 650 and 679 K, respectively. The temperature dependence of the sublattice magnetization σ(T) obeys a one‐third‐power law in the range 0.5N<0.99.     

Post-Newtonian estimation in relativistic optics

A post-Newtonian analysis of the theory of gravity based on the metricg _ij(x,y)= _ij(x)+/c ²(1–1n ²)y _iy_j with the index of refractionn(x, y) is given. A generalized Lagrange space endowed with this metric is used for the study of gravitational phenomena. The index of refractionn(x, y) is expanded in integer powers of the gravitational potentialU=GM/rc ² andv ²/c ². It is shown that solar system tests impose a constraint on a combination of the constant, the post-Newtonian parameters defining the index of refractionn(x, y), and the post-Newtonian parameter associated to the Riemannian metric _ij(x).     

Energy levels of the Schrödinger equation for some rational potentials in two-dimensional space using the inner product technique

The energy levels of a two-dimensional system are calculated for the rational potential,V(x, y; λ, g)=x ²+y ²+λ[x ²/(1+gx ²)+y ²/(1+gy ²)+a _xxx⁴+a _xyx² y ²+a _yyy⁴] using the inner product technique over a wide range of values of the perturbation parameters (g, λ) and for various eigenstates.     

3∶29型Gd3(Fe1-xCox)29-yCry化合物的成相与结构

通过X射线衍射分析和磁测量研究了Gd-Fe-Co-Cr四元系中对应于化学式Gd₃(Fe,Co,Cr)₂₉且Gd含量为一定值的截面内富Fe,Co区的相关系,重点探索了高Co含量3∶29型化合物合成的可能性,研究了3∶29型Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的结构与磁性.研究结果表明,获得3∶29型单相Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的范围为:y=5,0≤x≤0.7;y=5.5,0.7≤x≤0.8和y=6,0.8≤x≤0.9.基于对Gd₃(Fe_1-xCo_x)_29-yCr_y化合物成相条件的研究,成功地合成了纯Co基Gd₃Co_29-yCr_y化合物,其固溶范围为6.5≤y≤7.3.3∶29型单相Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的晶体结构都属于单斜晶系,Nd₃(Fe,Ti)₂₉型结构,空间群为A2m.得到3∶29型单相Gd₃(Fe_1-xCo_x)_29-yCr_y化合物的固溶极限即Co含量的极大值与稳定元素Cr含量有关.Co原子的含量越高,所需稳定元素Cr的含量越大.值得注意的是,用Co原子替代Fe原子会导致Gd₃(Fe_1-xCo_x)_29-yCr_y化合物磁晶各向异性的显著改变.当x≥0.4时,化合物的磁晶各向异性从易面型转变为易轴型 关键词： 3(Fe_1-xCo_x)_29-yCr_y化合物')" href="#">Gd₃(Fe_1-xCo_x)_29-yCr_y化合物 相关系和相结构 X射线衍射 磁晶各向异性     

Low Temperature Properties for Correlation Functions in Classical N-Vector Spin Models

We obtain convergent multi-scale expansions for the one-and two-point correlation functions of the low temperature lattice classical N - vector spin model in d S 3 dimensions, N S 2. The Gibbs factor is taken as exp[-b(1/2 ||?f||² +l/8 || |f|² - 1 ||² + v/2||f- h||²)], \exp [-\beta (1/2 ||\partial \phi||^2 +\lambda/8 ||\, |\phi|^2 - 1 ||^2 + v/2||\phi - h||^2)], where f(x), h ? R^N\phi(x), h \in R^N, x ? Z^dx \in Z^d, |h|=1, b < ￥|h|=1, \beta < \infty, l 3 ￥\lambda \geq \infty are large and 0 < v h 1. In the thermodynamic and v ˉ 0v \downarrow 0 limits, with h = e₁, and j L ‘^½ ‘, the expansion gives áf₁(x)? = 1+0(1/b^1/2)\langle \phi_1(x)\rangle = 1+0(1/\beta^{1/2}) (spontaneous magnetization), áf₁(x)f_i(y)? = 0\langle \phi_1(x)\phi_i(y)\rangle=0, áf_i (x)f_i (y)? = c₀ D^-1(x,y)+R(x,y)\langle \phi_i (x)\phi_i (y)\rangle = c_0 \Delta^{-1}(x,y)+R(x,y) (Goldstone Bosons), i = 2, 3, ?, Ni= 2, 3,\,\ldots, N, and áf₁(x)f₁(y)?^T=R￠(x,y)\langle \phi_1(x)\phi_1(y)\rangle^T=R'(x,y), where |R(x,y)||R(x,y)|, |R￠(x,y)| < 0(1)(1+|x-y|)^d-2+r|R'(x,y)|< 0(1)(1+|x-y|)^{d-2+\rho} for some „ > 0, and c₀ is aprecisely determined constant.     

一种具有次近邻相互作用的Transverse XY模型

本文推广Transverse XY模型量子链至次近邻相互作用情况,考虑哈密顿量 H=g∑_nσ_n²-∑_n ((1+γ)/2σ_n^xσ_n+1^x+(1-γ)/2σ_n^yσ_n+1^y)-λ∑_n ((1+β)/2σ_n^xσ_n+2^x+(1-β)/2σ_n^yσ_n+2^y)。当β=0以及γ≠0时,证明在临界点附近它对应于一自由费密场,从而属伊辛普适类。 关键词：     

在BaF2-BiF3系统中的相组成和离子电导

用固相反应法、X射线粉末衍射技术和复平面阻抗谱测量研究了BaF₂-BiF₃系统的相组成和离子电导。在此系统中发现了两种类型的Ba_1-xBi_xF_2+x固溶体:萤石型(0s≈0.5(14^1/2)a_F,c_{s< 关键词：}     

Synthesis,Mössbauer studies and superconductivity of substituted Bi 2201 phase

We report X-ray diffraction, resistivity and Mössbauer studies on several substituted 2201 Bi cuprates, Bi₂Sr₂Cu_1?xFe_xO_y(O≤x≤1) and Bi₂Sr_1.6La_0.4Cu_1?xFe_xO_y and Bi_1.6Pb_0.4Sr_1.6La_0.4Cu_1?xFe_xO_y (O≤x≤0.04). The first series is not superconducting and a new phase appears for x=1. For La substituted samples, T_c increases up to 35K and decreases strongly with x. All Mössbauer spectra were fitted well with four quadrupole doublets, with relative population depending on samples.     

A new approach to Ermakov systems and applications in quantum physics

Milne–Pinney equation [(x)\ddot]=-w²(t)x+ k/x³\ddot x=-\omega^2(t)x+ k/{x^3} is usually studied together with the time-dependent harmonic oscillator [(y)\ddot]+w²(t) y=0\ddot y+\omega^2(t) y=0 and the system is called Ermakov system, and actually Pinney showed in a short paper that the general solution of the first equation can be written as a superposition of two solutions of the associated harmonic oscillator. A recent generalization of the concept of Lie systems for second order differential equations and the usual techniques of Lie systems will be used to study the Ermakov system. Several applications of Ermakov systems in Quantum Mechanics as the relation between Schroedinger and Milne equations or the use of Lewis–Riesenfeld invariant will be analysed from this geometric viewpoint.