Essentially different distributions of current in the inverse problem for the Grad-Shafranov equation

The paper answers a question debated by physicists for many years. It is proved that, for almost equal gradients of the magnetic flux u at its zero-level curve ∂ω, which is the piecewise smooth boundary of a simply-connected domain ω ⋐ ℝ², the inverse problem for the Grad-Shafranov equation of plasma equilibrium in a tokamak (in the cylindrical approximation) admits essentially different profiles of distributions f _u : ω ∋ (x, y) ↦ f(u(x, y)) = u _xx (x, y) + u _yy (x, y) ⩾ 0 in the class of third-order polynomials f(u) = Σ _m=0³ a _m u ^m .     

Fermionization,Convergent Perturbation Theory,and Correlations in the Yang–Mills Quantum Field Theory in Four Dimensions

We show that the Yang–Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function E(x,y) of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as

On the Theory of Gravitational Field in Finsler Spaces

Some structural considerations are made on the Finslerian gravitational field: A Finslerian metrical structure such as g_λχ(x, y) = γ_λχ(x) + h_λχ(x, y) is proposed, where γ_λχ denotes the Riemann metric of Einstein's gravitational field, while hλχ the Finsler metric induced by the Riemann metric h_ij(y) of the internal field; The intrinsic behaviour of the internal variable y, which is expressed as ?ⁱ = K(x, y) y^j in the internal field, is grasped by the Finslerian parallelism δyⁱ (=0), which is reflected in the spatial structure of the external gravitational field by the mapping relation δy^χ = e(x) δyⁱ. The whole metrical Finsler connection D for g_λχ(i.e., Dg_λχ = 0) is determined by taking account of the intrinsic behaviour δy^χ.     

Effect of hydrogen doping on the magnetic properties of Gd2CuO4

We report the results of ac-susceptibility and dc-magnetization measurements for H_yGd₂CuO₄ (0y0.54). It is shown thatH doping lowers the weak ferromagnetic component in the material. The distinct hysteresis loops observed atT=77 K for both non- and hydrogenated samples change its shape withy. The magnetic ordering temperatures T _N ^Cu and T _N ^Gd , as determined from the temperature dependencies of ac-susceptibility, remain unchanged with sample's hydrogenation. This result seems to indicate that extra electrons are not doped onto the Cu-O planes of Gd₂CuO₄. The frequency dependencies ofx(, T) andx(, T) for bothy=0 andy=0.15 samples are analysed., The maximums ofx andx found at about 200K are considered in terms of susceptibility dependence on the spin-lattice relaxation time (). The anomalies in ac-susceptibility found recently in Gd₂CuO₄ atT _a=8 K andT _b=9.5 K decrease significantly withy. Results are discussed in the context of available data on 214T-type compounds.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Density functional study of ternary AuxAgyCuz and AuxAgyCuz+ clusters (x + y+z = 5, 6)

ABSTRACT

We report a theoretical investigation of neutral Au_xAg_yCu_z and cationic Au_xAg_yCu_z⁺ ternary clusters, for x?+?y+z?=?5 and 6. Our study is performed within density functional theory at the TPSSTPSS/SDD level. The geometries, chemical order, binding energy, mixing energy, second difference in the energy, adiabatic ionisation potential of these clusters are evaluated as a function of the whole concentration range. The most probable dissociation channels and the corresponding dissociation energies for the most stable clusters are also determined and discussed.     

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).     

A charged ellipsoidal bunch in a magnetic field

The states of a long rotating charged ellipsoidal bunch in a longitudinal uniform magnetic field are studied. The states are described using two integrals of motion that couple the transverse velocities [(x)\dot]\dot x and [(y)\dot]\dot y with the x and y coordinates; the frequency ω_H=eH/mc (where H is the total magnetic field); and the quantities ω₁ and ω₂, which characterize the Coulomb repulsion in the x and y directions. It is shown that equilibrium states with a high charge density per unit length (ν≳1) can exist.     

Mixed hyperfine interactions in Fe-Mg-O: magnetic behaviour

The complex Mössbauer spectra exhibited by Fe_xO (x0.91) and (Fe_1–y Mg _y )_xO (y=0.15–0.85) powder samples at liquid helium temperature have been analysed by a Hamiltonian treatment to allow for the significant electric field gradients present at the Fe²⁺ defect sites. The magnetic behaviour of the defect clusters are considered in terms of antiferromagnetic couplings, consistent with the spin glass-like behaviour reported recently for magnesiowüstite.     

Martensitic transformation in La1−x Yb x Ag1−y In y

The structural phase transformation of La_1–x Yb _x Ag_1–y In _y has been studied on single crystals by low temperature Laue-technique. The martensitic transformation in this pseudobinary intermetallic alloy has to be characterized as a weak orthorhtombic distortion of a single I centered unit cell (c/a1.04;a/b1.006) and a collective slipping or twinning of these cells that gives a fixed orientation between the remaining cubic room temperature structure and the martensitic phase. Above room temperature exists an order-disorder transformation from the CsCl-B2 structure to an at room temperature metastable W-A2 structure. There is no dramatic change in the physical properties of this alloy by substituting La by Yb, so we may approximate our results to LaAg_1–y In _y .This paper is dedicated to Prof. Dr. S. Methfessel on the occasion of his 60^th birthday     

Novel 1122 thallium cuprates showing high Tc superconductivity: TlCa1-xY,Ba2Cu2O y,T,1-xPb x CaSr2Cu2O y and TlCa0.5Ln0.5Sr2Cu2O y

Substitution of Ca by Y in TlCaBa₂Cu₂O _y does not favour superconductivity, but substitution of Tl by Pb or of Ca by Ln (Ln = Y or rare earth) in TlCaSr₂Cu₂O _y results in high T_c superconductivity (T_c π 60–90 K). TlCa_1-xLn _x Sr₂Cu₂O _y is a new series of high T_c superconductors, but the x = 0.0 composition does not exhibit bulk superconductivity.     

Thermodynamic Formalism for Contracting Lorenz Flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential [^( j)]_t(x,y,z):=-tlogJ_(x,y,z)^cu\hat{ \varphi }_{t}(x,y,z):=-t\log J_{(x,y,z)}^{cu} for the contracting Lorenz flow and for t in an interval containing [0,1]. We also analyse the Lyapunov spectrum of the flow in terms of the pressure.     

Isotope effect and characteristic features of the phase diagram for cobaltites with spin-state transitions

The effect of ¹⁶O → ¹⁸O oxygen isotope substitution has been studied for (Pr_1−y Eu _y )_0.7Ca_0.3CoO₃ cobaltites (0.12 < y < 0.26). A pronounced isotope shift has been found for the spinstate transition temperature, which increases with the oxygen isotope mass. In contrast, the ferromagnetic transition temperature has slightly lower values for the samples with heavier oxygen. The observed phenomena and constructed phase diagram confirm the results reported previously for (Pr_{1 − y} Sm _y )_0.7Ca_0.3CoO₃ in [G. Y. Wang, X. H. Chen, T. Wu, et al., Phys. Rev. B 74, 165113 (2006)]. The measurements of the specific heat have been performed for (Pr_{1 − y} Eu _y )_0.7Ca_0.3CoO₃ with the main emphasis on the analysis of the isotope effect. The contributions to the isotope effect coming from the lattice and magnetic components of the specific heat have been separated. The mechanisms underlying the large isotope effect are discussed.     

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.     

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.     

Inequalities for a unified family of Voigt functions in several variables

The classical Voigt functions occur frequently in a wide variety of problems in astrophysical spectroscopy, emission, absorption and transfer of radiation in heated atmosphere, and plasma dispersion, and indeed also in the theory of neutron reactions. Here, in the present paper, by applying several known upper bounds for the first-kind Bessel function J _ν (x) given recently by (for example) Landau, Olenko and Krasikov, sharp bounding inequalities are obtained for the unified multivariable Voigt function V _μ,ν (x; y) in terms of the confluent Fox-Wright function ₁ψ₀ and its incomplete variant ₁ψ₀. Connections of the unified multivariable Voigt function V _μ,ν (x; y) with other unifications and generalizations of the classical Voigt function are also briefly pointed out.     

双合成反铁磁结构及其对自旋阀巨磁电阻效应的影响

用直流磁控溅射方法制备了双合成反铁磁结构Co₉₀Fe₁₀(5 nm)/Ru(x nm)/Co₉₀Fe₁₀(3 nm)/Ru(y nm)/Co₉₀Fe₁₀(5 nm)(x=0.45,0.45,1.00; y=0.45,1.00,1.00)的系列样品,并对样品的性能及其作为钉扎层对自旋阀巨磁电阻(GMR)效应的影响进行了研究 关键词： 双合成反铁磁 自旋阀 巨磁电阻     

Molecular orbital study of germanium,germanium-gallium and germanium-arsenic clusters

The quasirelativistic INDO/1 method has been used to generate molecular orbitals for some {Ge _x }, doped {Ge _x Ga _y } and {Ge _x As _y } clusters. These one-electron energy levels predefine the density of states (DOS) and/or hole functions. The effect of the cluster size (x=24, 56, 92) and that of dopants on the DOS profiles are discussed. The calculations are compared with those generated by periodic crystal orbitals of the EHT quality.     

Disorder-order phase transformations and electrical resistivity of nonstoichiometric titanium carbide

Phase transformations of the disorder-order type in the homogeneity region of nonstoichiometric titanium carbide TiC_y (0.5<y<1.0) have been studied. It has been established that, depending on the actual composition of TiC_y, there may form in it for T<980–1000 K a cubic or a trigonal ordered Ti₂C phase (space groups Fd3m and , respectively) and a rhombic ordered Ti₃C₂ phase (space group C222₁). The effect of ordering on the electrical resistivity of the nonstoichiometric carbide TiC_y was studied, and the temperatures of the reversible disorder-order equilibrium transitions determined. The ordering in titanium carbide is shown to be a first-order phase transition. Fiz. Tverd. Tela (St. Petersburg) 40, 1332–1340 (July 1998)     

Influence of Si on the magnetic properties of multilayer nanostructures with composite magnetic layers

The static and dynamic properties of multilayer structures [(Co₄₅Fe₄₅Zr₁₀) _m (Al₂O₃)_{100 − x} ] _x /(a-Si) _y with various magnetic phase concentrations and for different thicknesses x and y were measured. It was shown that for samples with comparatively thick composite layers and thin interlayers (x/y > 8), the silicides that form play no significant role and the magnetic properties are determined by the composites. With an increase in the thickness of the interlayers, more granules form silicides. This reduces the concentration of the magnetic phase, influencing the samples’ resonance fields and magnetization.