On 3 + 1 Lorentzian Einstein manifolds with one rotational isometry

We consider 3 + 1 rotationally symmetric Lorentzian Einstein spacetime manifolds with \(\varLambda >0\) and reduce the field equations to 2 + 1 Einstein’s equations coupled to ‘shifted’ wave maps. Subsequently, we prove various (explicit) positive mass-energy theorems. No smallness is assumed.     

Global Properties of Gravitational Lens Maps¶in a Lorentzian Manifold Setting

In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere of the observer (or on part of it) and it takes values in a two-dimensional manifold representing a two-parameter family of worldlines. In this article we use methods from differential topology to characterize global properties of the lens map. Among other things, we use the mapping degree (also known as Brouwer degree) of the lens map as a tool for characterizing the number of images in gravitational lensing situations. Finally, we illustrate the general results with gravitational lensing (a) by a static string, (b) by a spherically symmetric body, (c) in asymptotically simple and empty spacetimes, and (d) in weakly perturbed Robertson–Walker spacetimes. Received: 16 October 2000 / Accepted: 18 January 2001     

The effect of frenkel defects on the electronic structure of 1T−TiSe2

Using a tight binding formalism the wave vector resolved electronic density of states has been calculated in the coherent potential approximation for an 1 T–TiSe₂ crystal containing Frenkel defects. Additional structure originating from disorder is discussed. An extra peak in the A direction at 1.5 eV binding energy can be traced back to a resonance caused by titanium vacancies.     

Local structure of the superionic conducting α-AgI type AgI1−xBrx solid-solution

The local structures of the α-AgI type AgI_1−xBr_x solid-solution (0⩽×⩽0.4) at 573 K have been determined by EXAFS and XANES analyses. The AgI and AgBr distances in the solid-solution remain constant values of 2.76 Å and 2.69 Å, respectively. There are little changes in the Br K and Ag K edge XANES spectra in the solid-solution. It is concluded that only tetrahedral sites are occupied at equilibrium in the solid-solution though the α-AgI type structure has several kinds of sites among interstices of the b.c.c. lattice formed by anions. The AgI distance in α-AgI obtained by EXAFS is significantly shorter than that by diffraction experiments, indicating that the average volume of tetrahedra occupied by Ag ions is smaller than that of unoccupied tetrahedra. The effective one-particle potentials (O.P.P.) and the probability-density functions (P.D.F.) Ag and I atoms in α-AgI are calculated. The potentials along the Ag-I bond do not change appreciably through the βα phase transition. The widespread distribution obtained for both atoms in the P.D.F. maps exhibits that the periodicity is substantially disturbed by the large thermal motion of the atoms. The Ag ion can jump to the neighboring site with appreciable probability by the thermal motion, while the I ion is localized on the b.c.c. lattice. The diffusion path of the Ag ions is determined from the P.D.F. maps. The potential barrier along the diffusion path is evaluated to be 0.07 eV from the O.P.P..     

On a characteristic of the first eigenvalue of the Dirac operator on compact spin symmetric spaces with a Kähler or Quaternion-Kähler structure

It is shown that on a compact spin symmetric space with a Kähler or Quaternion-Kähler structure, the first eigenvalue of the Dirac operator is linked to a “lowest” action of the holonomy, given by the fiberwise action on spinors of the canonical forms characterized by this holonomy. The result is also verified for the symmetric space $F_4/{\mathrm{Spin}}_9$, proving that it is valid for all the “possible” holonomies in Berger’s list occurring in that context. The proof is based on a characterization of the first eigenvalue of the Dirac operator given in Milhorat (2005) and Milhorat (2006). By the way, we review an incorrect statement in the proof of the first lemma in Milhorat (2005).     

A class of Einstein–Weyl spaces associated to an integrable system of hydrodynamic type

HyperCR Einstein–Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can in principle be constructed from a twistor correspondence, thus establishing the integrability. Simple examples of solutions including the hydrodynamic reductions yield new Einstein–Weyl structures.     

Crystal structure and electrical transport properties of polycrystalline TbMn1−xFexO3

Polycrystalline TbMn_1−xFe_xO₃ (x=0, 0.1, 0.3, 0.5, 0.7, 0.9, 1) were synthesized by solid sintering method. The Rietveld refinement results based on the X-ray powder diffraction (XRD) data showed that all samples were identified as orthorhombic perovskite structure with space group Pbnm (62). The lattice parameters a and c increased, while the b decreased with increasing of Fe content, indicating the crystal unit cell shrinks in the ab-plane and extends along c-axis with increasing concentration of Fe. Temperature dependent resistance (R–T) was also measured. The transition temperature of TbMn_1−xFe_xO₃ samples increased monotonically with increase of x. The activation energy of TbMn_1−xFe_xO₃ decreased with increasing Fe content (x≤0.5) and increased with increasing Fe content when x>0.5, meaning that the TbMn_0.5Fe_0.5O₃ has the lowest activation energy. These results implied that the transition temperature and conductivity could be controlled by impuring different elements, especially to obtained better performance as for the semiconductor materials working at broad temperature.     

Electronic state of a CoO2 layer with hexagonal structure: a Kagomé lattice structure in a triangular lattice

The electronic state in layered cobalt oxides with a hexagonal structure is examined. We find that the electronic structure reflects the nature of the Kagomé lattice hidden in the CoO2 layer which consists of stacked triangular lattices of oxygen ions and of cobalt ions. A fundamental model for the electron system is proposed, and the mechanism of the unique transport and magnetic properties of the cobalt oxides are discussed in light of the model.     

Spectral properties of a metal–dielectric sensor structure

Numerical analysis of the spectral characteristics of a two-layer structure is performed in the processes of fabrication, measurement, and application of this structure as a sensor of the refractive index of the external medium. The effect of environmental conditions and parameters of the metal and dielectric layers on the sensor sensitivity is discussed. The results of model calculations are confirmed by experimental studies.     

Spatial structure of a Bose–Einstein condensate in a combined trap

We study the spatial structure of a Bose–Einstein condensate(BEC) with a space-dependent s-wave scattering length in a combined trap. There exists a space-dependent nonlinear atomic current in the system. The atomic current has an important influence on the spatial structure of the BEC. Research findings reveal that a large chemical potential can effectively suppress the chaotic spatial structure in the BEC system. Due to the large chemical potential, a strong atomic current is necessary to make...     

On Spatially Homogeneous Solutions of a Modified Boltzmann Equation for Fermi–Dirac Particles

The paper considers a modified spatially homogeneous Boltzmann equation for Fermi–Dirac particles (BFD). We prove that for the BFD equation there are only two classes of equilibria: the first ones are Fermi–Dirac distributions, the second ones are characteristic functions of the Euclidean balls, and they can be simply classified in terms of temperatures: T>2/5T _F and T=2/5T _F , where T _F denotes the Fermi temperature. In general we show that the L ^∞-bound 0≤f≤ 1/ε derived from the equation for solutions implies the temperature inequality T≥2/5T _F , and if T>2/5T _F , then f trend towards Fermi–Dirac distributions; if T=2/5T _F , then f are the second equilibria. In order to study the long-time behavior, we also prove the conservation of energy and the entropy identity, and establish the moment production estimates for hard potentials.     

Wavelength switching in a mixed structure of a long-period and a Bragg fiber gratings

We built a numerical model for evaluating the coupling processes of a mixed structure of a Bragg fiber grat-ing and a long-period grating. From the numerical results, we not only confirmed the wavelength switchingphenomena observed in previously reported experiments, but also discovered a new coupling mechanism,which generated the reflection of a signal with its wavelength longer than the Bragg wavelength. Thedependencies of the wavelength switching behaviors on various parameters of the mixed grating structure     

Numerical study of homogeneous dynamo based on experimental von Kármán type flows

A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.     

Calculation of the structure properties and P–T phase diagram of hafnium

Abstract

The full-potential linear muffin-tin orbitals (FP-LMTO) method is used to calculate the total energy and equilibrium lattice properties for the observed phases of Hf. The temperature and pressure dependences of the Gibbs energy are found for these structures within the Debye model. A quantitative agreement with the experimental points of the P-T phase diagram is obtained.     

Relaxation of the magnetic state of a ferromagnetic–superconducting layered structure

We have proposed a real-time method of neutron reflectometry. The magnetic state of the Ta/V/FM/Nb/Si ferromagnetic–superconducting system has been analyzed. Relaxation of the inhomogeneous magnetic state with a characteristic time of several hours, which depends on the magnetic field magnitude and temperature, has been observed. The relaxation of the domain structure has changed upon a transition of the V and Nb layers to the superconducting state. It has been concluded that real-time reflectometry data for polarized neutrons are important for determining the origin of magnetism in ferromagnetic–superconducting layered structures.     

Clinical feasibility of 3D-QALAS – Single breath-hold 3D myocardial T1- and T2-mapping

PurposeTo investigate the in-vivo precision and clinical feasibility of 3D-QALAS - a novel method for simultaneous three-dimensional myocardial T1- and T2-mapping.MethodsTen healthy subjects and 23 patients with different cardiac pathologies underwent cardiovascular 3 T MRI examinations including 3D-QALAS, MOLLI and T2-GraSE acquisitions. Precision was investigated in the healthy subjects between independent scans, between dependent scans and as standard deviation of consecutive scans. Clinical feasibility of 3D-QALAS was investigated for native and contrast enhanced myocardium in patients. Data were analyzed using mean value and 95% confidence interval, Pearson correlation, Paired t-tests, intraclass correlation and Bland-Altman analysis.ResultsAverage myocardial relaxation time values and SD from eight repeated acquisitions within the group of healthy subjects were 1178 ± 18.5 ms (1.6%) for T1 with 3D-QALAS, 52.7 ± 1.2 ms (2.3%) for T2 with 3D-QALAS, 1145 ± 10.0 ms (0.9%) for T1 with MOLLI and 49.2 ± 0.8 ms (1.6%) for T2 with GraSE.Myocardial T1 and T2 relaxation times obtained with 3D-QALAS correlated very well with reference methods; MOLLI for T1 (r = 0.994) and T2-GraSE for T2 (r = 0.818) in the 23 patients. Average native/post-contrast myocardial T1 values from the patients were 1166.2 ms/411.8 ms for 3D-QALAS and 1174.4 ms/438.9 ms for MOLLI. Average native myocardial T2 values from the patients were 53.2 ms for 3D-QALAS and 54.4 ms for T2-GraSE.ConclusionsRepeated independent and dependent scans together with the intra-scan repeatability, demonstrated all a very good precision for the 3D-QALAS method in healthy volunteers. This study shows that 3D T1 and T2 mapping in the left ventricle is feasible in one breath hold for patients with different cardiac pathologies using 3D-QALAS.     

Positron generation upon decay of a π0-meson in constant homogeneous crossed fields

Simple expressions for decay probability are obtained. Significant acceleration of decay is predicted for field intensities in the ⁰-meson rest system of F 10¹¹-10¹² Oe. A simple method is presented for obtaining the probability asymptote relative to the external field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 34–39, October, 1989.In conclusion, the authors thank A. A. Grib for his valuable remarks.