Elastic and thermal properties of Zr z Nb1 − z C x N y solid solutions

The temperature and concentration dependences of the elastic moduli and the thermal linear expansion coefficient of Zr _z Nb_{1 ? z} C _x N _y solid solutions containing from 3 to 8 at % of structural vacancies in a nonmetallic sublattice have been found. The temperature dependences of the Debye temperature Θ_D(T) have been calculated using the elastic data and the data on the heat capacity. It has been shown, using carbide NbC_0.97 as an example, that the Θ_D(T) dependences found from the elastic properties and the heat capacity coincide in the temperature range ～220–300 K. By analogy with the niobium carbide, the heat capacity C _p (300) of Zr _z Nb_{1 ? z} C _x N _y solid solutions of various compositions is calculated based on the values of Θ_D(300) determined from the elastic properties.     

Spin-glass-like behavior in ZnxCryAlzSe4

The magnetic and electrical properties of the Al-doped polycrystalline spinels Zn_xCr_yAl_zSe₄ (0.13≤z≤0.55) with the antiferromagnetic (AFM) order and semiconducting behavior were investigated. A complex antiferromagnetic structure below a Néel temperature T_N≈23 K for the samples with z up to 0.4 contrasting with the strong ferromagnetic (FM) interactions evidenced by a large positive Curie-Weiss temperature θ_CW decreasing from 62.2 K for z=0.13 to 37.5 K for z=0.55 was observed. Detailed investigations revealed a divergence between the zero-field-cooling (ZFC) and field-cooling (FC) susceptibilities at temperature less than T_N suggesting bond frustration due to competing ferromagnetic and antiferromagnetic exchange interactions in the compositional range 0.13≤z≤0.4. Meanwhile, for z=0.55 a spin-glass-like behavior of cluster type with randomly oriented magnetic moments is observed as the ZFC-FC splitting goes up to the freezing temperature T_f=11.5 K and the critical fields connected both with a transformation of the antiferromagnetic spin spiral via conical magnetic structure into ferromagnetic phase disappear.     

Noncommutative Geometry¶and Gauge Theory on Fuzzy Sphere

The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is identified with the left U(N+1) transformation of the field, where a field is a bimodule over the quantized algebra . The interaction with a complex scalar field is also given. Received: 21 January 1998 / Accepted: 4 February 2000     

Central charges and Lorentz and internal symmetries in massive supersymmetric quantum field theory

The properties of central charges in the framework of the massive supersymmetric quantum field theory related to internal symmetries, Lorentz covariance and locality of the fields are investigated. It is shown that in the presence of z central charges the largest semisimple part of the internal symmetry algebra is a direct sum of z compact symplectic group algebras and possibly an additional term representing the unimodular unitary group algebra. Next it is shown that 4j ? N + K, where j is the highest spin value of the underlying fields, N is the number of spinorial charges and K the number of these spinorial charges which are not linked to other spinorial charges by a central charge. It is further demonstrated that, in general, the central charge can not be redefined in such a way that it is at the same time real and preserves the locality principle. The discussion of the obtained results concludes the paper.     

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level T _z (z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and T _z (z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.     

The magnetic structures of LaTiO3 and CeTiO3

The basic features of the magnetic structures of LaTiO₃ and CeTiO₃ were determined by powder neutron diffraction. LaTiO₃ (T_N = 125 K) is a type G antiferromagnet with a moment on Ti (III) of 0.45(5)μ_B at 10 K. As bulk magnetic measurements indicate a weak ferromagnetic moment, a G_zF_x or G_xF_z configuration is implied. CeTiO₃ (T_N) = 116 K) shows more complex behaviour. At 81 K only G and F type reflections are observed. The most consistent interpretation is to assign G-type configuration to Ti(III) and an induced F_z on Ce(III). Moments are 0.36μ_B on Ti(III) and 0.4(1)μ_B on Ce(III). It is also possible to assign both G and F components to Ti(III). This demands a “canting angle” of 34° to explain the F moment. Below 80 K a C-type component develops. A model assuming a G_zF_x configuration for Ti(III) and a C_yF_x configuration for Ce(III) provides a good fit to the data. This assignment is consistent with Bertaut's symmetry considerations. Other models which violate Bertaut's rules also fit the data.     

The quantum 2-sphere as a complex quantum manifold

We describe the quantum sphere of Podles for c = 0 by means of a stereographic projection which is analogous to that which exibits the classical sphere as a complex manifold. We show that the algebra of functions and the differential calculus on the sphere are covariant under the coaction of fractional transformations with SU _q(2) coefficients as well as under the action of SU _q(2) vector fields. Going to the classical limit we obtain the Poisson sphere. Finally, we study the invariant integration of functions on the sphere and find its relation with the translationally invariant integration on the complex quantum plane.     

A bicovariant differential algebra of a quantum group

A bicovariant differential algebra of four basic objects (coordinate functions, differential 1-forms, Lie derivatives and inner derivations) within a differential calculus on a quantum group is shown to be produced by a direct application of the cross-product construction to the Woronowicz differential complex, whose Hopf algebra properties account for the bicovariance of the algebra. A correspondence with classical differential calculus, including Cartan identity, and some other useful relations are considered. An explicit construction of a bicovariant differential algebra on GL_q(N) is given and its (co)module properties are discussed.     

Temperature measurements in small holes drilled in superconducting bulk during pulsed field magnetization

The time dependence of the temperatures T(z, t) has been measured along the thickness direction z in several drilled holes in a superconducting bulk during pulsed field magnetization (PFM) and the heat generation and heat transfer in the bulk have been discussed. In the previous paper [H. Fujishiro, S. Kawaguchi, K. Kakehata, A. Fujiwara, T. Tateiwa, T. Oka, Supercond. Sci. Technol. 19 (2006) S540], we calculated the T(z, t) profiles in the bulk by solving a three-dimensional heat-diffusion equation to reproduce the measured T(t) on the bulk surface; the heat generation took place adiabatically and the calculated T(z, t) was isothermal along the z direction. In this study, the measured T(z, t) at the top surface was higher than that at the bottom surface just after the pulse field application at t < 0.5 s, and then became isothermal with increasing time. These results suggest that the magnetic flux intrudes inhomogeneously into the bulk from the edge of the top surface and the periphery at the early stage. The inhomogeneous magnetic flux intrusion and the flux trap during PFM change depending on the strength of the pulsed field and the pulse number in the successive pulse field application.     

A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere

The current paper establishes the computational efficiency and accuracy of the RBF-FD method for large-scale geoscience modeling with comparisons to state-of-the-art methods as high-order discontinuous Galerkin and spherical harmonics, the latter using expansions with close to 300,000 bases. The test cases are demanding fluid flow problems on the sphere that exhibit numerical challenges, such as Gibbs phenomena, sharp gradients, and complex vortical dynamics with rapid energy transfer from large to small scales over short time periods. The computations were possible as well as very competitive due to the implementation of hyperviscosity on large RBF stencil sizes (corresponding roughly to 6th to 9th order methods) with up to O(10⁵) nodes on the sphere. The RBF-FD method scaled as O(N) per time step, where N is the total number of nodes on the sphere. In Appendix A, guidelines are given on how to chose parameters when using RBF-FD to solve hyperbolic PDEs.     

Higher Dimensional Cosmological Models Filled with Perfect Fluid in f(R,T) Theory of Gravity

The new class of higher dimensional cosmological model of the early universe filled with perfect fluid source in the framework of f(R,T) theory of gravity (Harko et al. in Phys. Rev. D 84, 024020, 2011) is considered. A cosmological model with an appropriate choice of the function f(T) has been constructed. The physical behavior of the model is studied. The well known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with redshift are discussed.     

Properties of the Ising magnet confined in a corner geometry

The properties of Ising square lattices with nearest neighbor ferromagnetic exchange confined in a corner geometry, are studied by means of Monte Carlo simulations. Free boundary conditions at which boundary magnetic fields ±h are applied, i.e., at the two boundary rows ending at the lower left corner a field +h acts, while at the two boundary rows ending at the upper right corner a field −h acts. For temperatures T less than the critical temperature T_c of the bulk, this boundary condition leads to the formation of two domains with opposite orientation of the magnetization direction, separated by an interface which for T larger than the filling transition temperature T_f(h) runs from the upper left corner to the lower right corner, while for T<T_f(h) this interface is localized either close to the lower left corner or close to the upper right corner. It is shown that for T=T_f(h) the magnetization profile m(z) in the z-direction normal to the interface simply is linear and the interfacial width scales as w∝L, while for T>T_f(h) it scales as . The distribution P(?) of the interface position ? (measured along the z-direction from the corners) decays exponentially for T<T_f(h) from either corner, is essentially flat for T=T_f(h), and is a Gaussian centered at the middle of the diagonal for T>T_f(h). Unlike the findings for critical wetting in the thin film geometry of the Ising model, the Monte Carlo results for corner wetting are in very good agreement with the theoretical predictions.     

Magnetic properties of undoped YBa 2 Cu 3 O 6 + x system

In the present paper, we study the magnetic properties of bilayer cuprate antiferromagnets. In order to evaluate the expressions for spin-wave dispersion, sublattice magnetization, Néel temperature and the magnetic contribution to the specific heat, the double time Green's function technique has been employed in the random phase approximation (RPA). The spin wave dispersion curve for a bilayer antiferromagnetic system is found to consist of one acoustic and one optic branch. The “optical magnon gap” has been attributed solely to the intra-bilayer exchange coupling (J _⊥ ) as its magnitude does not change significantly with the inter-bilayer exchange coupling (J_z). However J_z is essential to obtain the acoustic mode contribution to the magnetization. The numerical calculations show that the Néel temperature (T _N ) of the bilayer antiferromagnetic system increases with the J_z and a small change in J_z gives rise to a large change in the Néel temperature of the system. The magnetic specific heat of the system follows a T² behaviour but in the presence of J_z it varies faster than T². Received 13 July 2000 and Received in final form 14 May 2001     

Critical properties of the biaxial Ising model with both the longitudinal crystal field and the transverse dilution crystal field

Within the effective field theory (EFT), the critical properties of the biaxial Ising model with both longitudinal crystal field and transverse dilution crystal field are investigated for a simple cubic lattice. The tricritical point (TCP) and its trajectory are discussed in T-D_x and T-D_z space. A new phenomenon of two TCPs is found in T-D_x space. There exists a second-order line between two first-order lines, separated by two TCPs. The change of dilution concentration leads to a complex relation of the trajectory of the TCP. The degenerate patterns at the ground state appear by changing the longitudinal crystal field. The range of the ordered phase for transition lines labelled as a positive or (negative) value of D_x/J becomes larger or (smaller) with the decrease of t_x in T-D_z space. Some results have not been revealed in previous works.     

Can the optical excitations of surface plasmons be used to study (liquid) metal surfaces?

The surface plasmon dispersion relation is obtained for a metal with a free electron density given by N(z) = N_b + (N_s ? N_b) exp $\text{(}\text{?z}\text{a}\text{)}$ for z ? 0 and N = 0 for z < 0. We have used a local theory which includes the effects of retarded fields and found the dispersion relation to be sensitive to the parameters $\text{(N}{}_{\mathrm{s}}\text{? N}{}_{\mathrm{b}}\text{)}\text{N}{}_{\mathrm{b}}$ and a, which characterize our density profile.     

Superconductivity of (Sn1−z Pbz)1−x InxTe alloys

The temperature dependences of the electrical resistivity of (Sn_1?z Pb_z)_1?x In_xTe alloys with different concentrations of lead (z=0–0.60) and indium (x=0.03–0.20) were studied at temperatures T=0.4–4.2 K in magnetic fields from zero to H=15 kOe. A resistivity drop of no less than three-four orders of magnitude was observed in this range of alloy compositions. Application of a magnetic field above a critical level resulted in a recovery of the sample resistivity to the original value. The observed resistivity drop is identified with a superconducting transition. The critical parameters of the superconducting transition (T _c and H _c2) were determined at the drop to one half the normal resistivity level. Experimental dependences of the critical supercon-ducting-transition temperature T _c and of the second critical magnetic field H _c2 on the contents of lead (z) and indium (x) were measured. The data obtained confirm a strong localization of the In impurity states and are evidence of the extrinsic nature of superconductivity in the class of materials under study. It was established that as the Pb content in (Sn_1?z Pb_z)_1?x In_xTe increases, T _c and H _c2 decrease as the Fermi level E _F (fixed in the In impurity resonance band) leaves the Δ extremum and the superconductivity breaks down when E _F leaves the LΣ saddle point in the valence-band energy spectrum.     

Nuclear magnetic resonance studies of CePd2In and LaPd2In at low temperatures

We report on In nuclear magnetic resonance (NMR) and nuclear quadrupolar resonance (NQR) measurements on the new heavy-electron compound CePdZIn over a wide temperature range, from 45 mK up to 30 K. CePd₂In undergoes an antiferromagnetic (AF) phase transition at T _N = 1.23 K involving small localised Ce moments of 0.11 μ_B. In zero field, the spin-lattice relaxation rate T ₁ ^?1 (T) shows remarkable changes in its temperature dependence. Above 3 K, T ₁ ^?1 is constant and 850 sec^?1. Between T _N and 2T _N, (T ₁ T)^?1 = 330 (Ksec)^?1, but rapidly decreases below T _N. A Korringatype relaxation, characteristic for simple metals at low temperatures, with (T ₂ T)^?1 = 17(Ksec)¹ is resumed below 0.6 K. This value is an order of magnitude larger than (T ₁ T)^?1 for LaPd₂In and therefore is associated with low-energy excitations of the itinerant charge carriers with 4f symmetry. The T ₁ ^?1 data at various non-zero magnetic fields fall on a single curve when plotted as a function of (T/H) if H exceeds 3.5 T. Thus the AF ordering, the 4f moment fluctuations and the Kondo screening are drastically suppressed by the application of fields H of the order of 3.5 T.     

Kondo behaviour of the solid solution (Ce1−xLax)PtGa

The solid solution (Ce_1−xLa_x)PtGa has been studied through X-ray diffraction, magnetization (σ(B)), magnetic susceptibility (χ(T)), electrical resistivity (ρ(T)), magnetoresistivity (MR) and heat capacity (C_P(T)) measurements. The Néel temperature (T_N=3.3 K) for CePtGa is lowered upon La substitution as observed from χ(T) and ρ(T) measurements. The Kondo temperature T_K as calculated from MR measurements is comparable to T_N and also decreases with La substitution. The volume dependence of T_K is in accordance with the compressible Kondo lattice model and a Doniach diagram of the results is presented. C_P(T) measurements are presented for CePtGa, Ce_0.2La_0.8PtGa and LaPtGa and the results are discussed in terms of the electronic and magnetic properties. Other features of interest are anomalies in ρ(T) and C_P(T) due to crystalline electric field effects and metamagnetism as observed in σ(B) studies for samples with 0≤x≤ 0.3.     

Ising ferromagnet with biquadratic exchange

A spin one Ising system with biquadratic exchange, is investigated, using Green's function technique in random phase approximation (RPA). Transition temperature T_c and <(S^z)²> at T_c, are found to increase with biquadratic exchange parameter α for sc, bcc and fcc lattices. The variation of <(S^z)²> at T_c with α is found to be the same for the above lattices.     

Perturbative versus lattice QCD energy density correlators at high temperatures

Correlators of magnetic and electric field energy density are investigated for SU(N_c) gauge theory at high temperatures T. A separations z ⩽ 2/T the correlators are shown to be dominated by a power-law behavior even for finite gluon screening masses. This continuum behavior is well approximated on current 4 × 16³-lattices in the perturbative limit and leads to a considerable overestimate of screening masses deduced from fitting the lattice correlators with conventional exponential forms. The use of extended sources and sinks to enhance the signal improves the situation for screening masses m ⪢ T but leads to a largely uncontrolled error for masses less than T. In fact, we show that recent lattice QCD data of Grossmann et al., from which a magnetic screening mass m_M ∼ 2.9T was deduced, may even be consistent with a vanishing actual magnetic screening mass.