标定X射线粉末照相指数的新图解法,推广于正交晶系与单斜晶系

本文叙述了X射线粉末照相指数的新图解法在正交晶系与单斜晶系中的应用。由于在这两个晶系中所须确定的原始参量多于2,所以不可能像在四方晶系或六角晶系的情形,一次用图解法在平面上求得晶胞的所有初基参量。本文分析了正交晶系与单斜晶系的一些特殊情形,可用新图解法对粉末照相上一些特殊情形下的衍射线指数进行标定。为方便起见,图解法是尽量用线坐标进行的。     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

Canonical superenergy tensors in general relativity

We present the concept of superenergy tensors in the framework of general relativity (GR). These tensors were introduced constructively by the author years ago and they were obtained by a suitable averaging of the energy-momentum tensors or pseudotensors. Because in GR the Einstein canonical energy-momentum pseudotensor_E t _i ^k of the gravitational field and the canonical energy-momentum complex , matter and gravitation,are physically distinguished, we confine this paper to thecanonical superenergy tensor ^g S _i ^k of the gravitational field Γ _kl ⁱ and to the canonical total superenergy tensorS _i ^k = ^g S _i ^k + ^m S _i ^k of matter and gravitation only. These superenergy tensors can be obtained by the above-mentioned averaging of the pseudotensor_E t _i ^k and complex_E K _i ^k . We give the analytic forms of these two canonical superenergy tensors and show some of their possible applications in GR. The canonical superenergy tensor ^g S _i ^k of the gravitational field Γ _kl ⁱ can be used as asubstitute for the nonexisting energy-momentum tensor of this field.     

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current (AC) and direct-current (DC) electric field E_app = E₀ (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function ε_i (r) = C_k r^k (r ≤ a), where r is the radius of the cylindrical inclusion, and C_k, k, a are parameters. In the dilute limit, the local potentials and the effective nonlinear responses at all harmonics are derived. Meanwhile, the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field. It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field. Moreover, the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable, and the maximum of the electric field inside the cylinder is at its center.     

High speed in spin‐torque‐based magnetic memory using magnetic nanocontacts

Magnetization switching by a spin‐polarized current in perpendicular anisotropy devices with magnetic nanocontact (NC) is investigated using a micromagnetic formalism. The critical switching current (i_cr) and switching time (τ₀) can be reduced when a soft layer is exchange coupled to the NC. The study reveals that devices with fewer NCs have smaller i_cr compared to those with a large number. Furthermore, τ₀ for nanoconstricted devices is almost constant with anisotropy field (H_k), in contrast to devices without NCs that show an exponential increase with H_k. This suggests that nanoconstricted devices could be used to improve thermal stability, while reducing i_cr and τ₀. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On gauge theories of mass

The classical Einstein–Hilbert action in general relativity extends naturally to a blow-up (in the sense of algebraic geometry) of the usual space of pseudo-Riemannian metrics; this presents the metric tensor _gik$g_{ik}$ as a kind of Goldstone boson associated to the real scalar field defined by its determinant. This seems to be quite compatible with the Higgs mechanism in the standard model of particle physics.     

Topological and physical effects of rotation and spin in the general relativistic theory of gravitation

Interrelations of the intrinsic momentum (spin), rotation of material distributions, and intrinsic momentum of the gravitational field are investigated in the context of the general relativistic theory of gravitation involving the general relativity theory (GRT) and the Einstein-Cartan theory. It is demonstrated that the spin density vector of the gravitational field s _g ⁱ is equal to the rotor of the tetrad reference point ωⁱ=ɛ^iklm e _k ^(a) e_(a)l,m/2 to within the factor 1/κ (s _g ⁱ =ω/κc). It is demonstrated that the vector s _g ⁱ is proportional to the spin density vector of the gravitating field sⁱ (ω)=jc(Ψγⁱγ₅Ψ)/2 as well as the pseudovector of space-time torsion Qⁱ in the Einstein-Cartan theory, which in both cases induces a cubic nonlinearity of the spinor field. An expression for the energy-momentum density tensor of the eddy gravitational field is derived. It is also demonstrated that the free eddy gravitational field with polarized spin can form “mole holes.” An ideal fast-rotating self-gravitating fluid can cause a similar effect. The corresponding exact solutions of joint systems of the Einstein and rotating ideal fluid equations are presented. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 57–60, October, 2007.     

Connection Considerations of Gravitational Field in Finsler Spaces

Some alternative connection structures of the Finslerian gravitational field are considered by modifying the independent variables (x,y) (x: point and y: vector) in various ways. For example, (x ^k ,y ⁱ ) (k,i = 1,2,3,4) are changed to (x ^k ,y ⁰) (y ⁰: scalar) or (x ⁰,y ⁱ ) (x ⁰: time axis); (x ^k ,y ⁱ ) are generalized to (x ^k ,y ⁱ ,p _i ) (p _i : covector dual to y ⁱ ) or (x ^k ,y ⁱ ,q _a ) (q _a : covector different from p _i ); (x ^k ,y ⁱ ) are further generalized to (x ^k ,y ^(a)i ) (a = 1,2,…,m), (y ^(a): (a)th vector), etc.     

Calculation of Tc and the ratio 2Δ(0)/kBTc of MgB2 within a two-band model of superconductivity

Superconductivity in the MgB₂ superconductor is described within the framework of a two-band Eliashberg formalism. Different gaps are assumed to open on the different parts of the Fermi surface of this compound. Separation of the order parameter (OP) into two components is achieved by taking the Fourier transform of the OP using the momentum states of the σ- and π-bands of MgB₂. Expressions for the T_c and the ratio 2Δ_σ(0)/k_BT_c for this superconductor are obtained. Numerical values for these two properties are obtained for a range of values of the cut-off frequency of the phonons responsible for the superconductivity and for a range of values of the ratio between the two energy gaps. This was done for various values of the normalized partial densities of states on the σ-sheet of the Fermi surface.     

Vacuum polarization around an Aharonov-Bohm solenoid

The quantisation of a charged scalar field in an externally specified electromagnetic field, described by the vector potentialA _i=∂_if withf(t,r,θ,z)=Bθ is discussed. The electromagnetic field is zero everywhere except at the origin; a singular magnetic field (Aharonov-Bohm field) exists at the origin. The vacuum polarization around such a magnetic field is computed and the non-local behaviour is discussed.     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.     

Dynamics of a neural network model with finite connectivity and cycle stored patterns

The spatiotemporal evolution and memory retrieval properties of a Hopfield-like neural network with cycle-stored patterns and finite connectivity are studied. The analytical studies on a mean-field version show that, given the number of stored patterns p, there is a critical connectivity k_c such that the retrieval states are stable fixed points if and only if k > k_c. The dependence of k_c on the number of stored patterns is also present. The numerical simulations are applied to the short-ranged model with local interaction. It is revealed that, given p, the memory retrieval function is kept if the connectivity is high enough while the dynamics of the system is in the frozen phase. However when the connectivity k is less than a critical value k_c the system is in the chaotic phase and loses its memory retrieval ability. The critical points of both the dynamical phase transition and memory-loss phase transition are obtained by simulation data.     

Growing random networks with fitness

Three models of growing random networks with fitness-dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes of connectivity k and random additive fitness η, with rate (k−1)+η. For η>0 we find the connectivity distribution is power law with exponent γ=〈η〉+2. In the second model (B), the network is built by connecting nodes to nodes of connectivity k, random additive fitness η and random multiplicative fitness ζ with rate ζ(k−1)+η. This model also has a power law connectivity distribution, but with an exponent which depends on the multiplicative fitness at each node. In the third model (C), a directed graph is considered and is built by the addition of nodes and the creation of links. A node with fitness (α,β), i incoming links and j outgoing links gains a new incoming link with rate α(i+1), and a new outgoing link with rate β(j+1). The distributions of the number of incoming and outgoing links both scale as power laws, with inverse logarithmic corrections.     

Theory of Gravitational-Inertial Field of Universe. I. Gravitational-Inertial Field Equations

In the series of present articles the original proposition is a generalization of the real world tensor by the introduction of a inertial field tensor. From this generalization it follows, particularly, that ?_ig_lm ? g_lm;i ≠ 0. This allows to use as a Lagrangian density of the field the expression A_g = k₁ g_lm;ig^lm _;kg^ik. On the basis of variational equations a system of more general covariant equations of the gravitational-inertial field is obtained. In the Einstein approximation these equations reduce to the field equations of Einstein. The solution of fundamental problems in the general theory of relativity by means of the new equations gives the same results as the solution by means of Einstein's equations. However, application of these equations to the cosmologic problem gives a result different from that obtained by Friedmann's theory. In particular, the solution gives the Hubble law as the law of motion of a free body in the inertial field - in contrast to Galileo-Newton's law.     

Simulation of the required operation modes and analysis of their stability for multipurpose isochronous cyclotrons

A mathematical and computer simulation of the operation modes of multipurpose isochronous cyclotrons is based on a calculation of current values in trim coils correcting the main magnetic field (I _i , i = 1, 2, ..., n) for a certain current level in the main coil (I _mc). This calculation is performed for the given kinetic energy (E _k ) at a certain radius or for the particle orbital frequency (F ₀). The results of this calculation provide a formation with the necessary precision of the required magnetic field in the range from the ion source to the particle extraction system. A number of numerical and physical experiments on calculating the main operation mode of the multipurpose isochronous cyclotron AIC-144 (Institute of Nuclear Physics, Polish Academy of Sciences, Krakow) (p, E _k = 60 MeV, F ₀ = 26.25 MHz) proved the necessity of taking into account the estimate of the stability of the sought solution and the possibility of obtaining accelerated ion beams in the whole range of acceleration radii for small phase losses in the isochronization range of the required magnetic field.     

In-plane and out-of-plane anisotropic magnetoresistances in La1 − x Pb x MnO3 thin films

The temperature and field dependences of in-plane (IP) and out-of-plane (OP) anisotropic magnetoresistances (AMRs) have been measured in La_{1 ? x} Pb _x MnO₃ (LPMO) thin films having different microstructures, namely the single-crystal (SC), nanocrystalline (NC) and polycrystalline (PC) microstructures. The OP AMR, irrespective of the microstructure, is found to be considerably larger than the IP AMR. The magnetization data show that the larger OP AMR arises because magnetization is favoured in the film plane owing to strain anisotropy. In addition, the temperature and field dependences of both IP and OP AMRs are governed by the crystallinity of the films, indicating that the AMRs are strongly influenced by the magnetization process.     

Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an n×n matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let x _k denote eigenvalue number k. Under the condition that both k and n?k tend to infinity as n→∞, we show that x _k is normally distributed in the limit. We also consider the joint limit distribution of eigenvalues $(x_{k_{1}},\ldots,x_{k_{m}})$ from the GOE or GSE where k ₁, n?k _m and k _i+1?k _i , 1≤i≤m?1, tend to infinity with n. The result in each case is an m-dimensional normal distribution. Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments.     

Z(2) gauge neural network and its phase structure

We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable _Si=±1$S_i=\pm 1$ on the i$i$-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable _Jij=±1$J_{ij}=\pm 1$ describes a state of the synaptic connection between j$j$-th and i$i$-th neurons. The gauge symmetry allows for a self-coupling energy among _Jij$J_{ij}$’s such as _JijJjkJki$J_{ij}{J}_{jk}{J}_{ki}$, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of _Jij$J_{ij}$, (II) a quenched model with full connections where _Jij$J_{ij}$ is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III).     

Optical study of the antiferromagnetic-paramagnetic phase transition in chromium oxide Cr2O3

Abstract

Optical effects of the first and second order with respect to the order parameter (1 is antiferromagnetic vector) have been studied in Cr₂O₃ around its phase transition at T_N = 306 K from the antiferromagnetic to paramagnetic state. The magnetic linear birefringence is characterized by a rather large magnitude Δn _sp ? 10^?3 and by a large contribution of fluctuations of the order parameter to the birefringence. The study of the nonreciprocal optical rotation induced by an electric field has shown that the phase transition has a well defined first-order character. This result is also supported by the observation of a nonlinear (quadratic in the electric field) nonreciprocal rotation in a narrow temperature region ΔT = 0.15 K around T_N . The temperature variation of the order parameter l(T) below T_N is well described by a power low l where τ^β = (T_N - T)/T_N and β = 0.355. We also observed a very reproducible effect of the rotation of the optical indicatrix in opposite directions for two types of antiferromagnetic domains. The possible explanation of this effect could be related to the so-called gyrotropic birefringence, an effect related to k_il_i terms in the dielectric permeability.