464 research outputs found
S=1/2 Kagome antiferromagnets CsCu_{12}$ with M=Zr and Hf
Magnetization and specific heat measurements have been carried out on
CsCuZrF and CsCuHfF single crystals, in which
Cu ions with spin-1/2 form a regular Kagom\'{e} lattice. The
antiferromagnetic exchange interaction between neighboring Cu spins is
K and 540 K for CsCuZrF and
CsCuHfF, respectively. Structural phase transitions were
observed at K and 175 K for CsCuZrF and
CsCuHfF, respectively. The specific heat shows a small bend
anomaly indicative of magnetic ordering at K and 24.5 K in
CsCuZrF and CsCuHfF, respectively. Weak
ferromagnetic behavior was observed below . This weak
ferromagnetism should be ascribed to the antisymmetric interaction of the
Dzyaloshinsky-Moriya type that are generally allowed in the Kagom\'{e} lattice.Comment: 6 pages, 4 figure. Conference proceeding of Highly Frustrated
Magnetism 200
The constraint equations for the Einstein-scalar field system on compact manifolds
We study the constraint equations for the Einstein-scalar field system on
compact manifolds. Using the conformal method we reformulate these equations as
a determined system of nonlinear partial differential equations. By introducing
a new conformal invariant, which is sensitive to the presence of the initial
data for the scalar field, we are able to divide the set of free conformal data
into subclasses depending on the possible signs for the coefficients of terms
in the resulting Einstein-scalar field Lichnerowicz equation. For many of these
subclasses we determine whether or not a solution exists. In contrast to other
well studied field theories, there are certain cases, depending on the mean
curvature and the potential of the scalar field, for which we are unable to
resolve the question of existence of a solution. We consider this system in
such generality so as to include the vacuum constraint equations with an
arbitrary cosmological constant, the Yamabe equation and even (all cases of)
the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum
Gravit
Blow-up solutions for linear perturbations of the Yamabe equation
For a smooth, compact Riemannian manifold (M,g) of dimension N \geg 3, we
are interested in the critical equation where \Delta_g is the Laplace--Beltrami
operator, S_g is the Scalar curvature of (M,g), , and
is a small parameter
Quantitative and qualitative relationship between microstructural factors and fatigue lives under load- And strain-controlled conditions of Ti-5Al-2Sn-2Zr-4Cr-4Mo (Ti-17) fabricated using a 1500-ton forging simulator
The fatigue lives of forged Ti-17 using a 1500-ton forging simulator subjected to different solution treatments and a common aging treatment were evaluated under both load- and strain-controlled conditions: high and low cycle fatigue lives, respectively. Then, the tensile properties and microstructures were also examined. Finally, the relationships among fatigue lives and the microstructural factors and tensile properties were examined. The microstructure after solution treatment at 1203 K, which is more than the β transus temperature, and aging treatment exhibits equiaxed prior β grains composed of fine acicular ¡. On the other hand, the microstructures after solution treatment at temperatures of 1063, 1123, and 1143 K, which are less than the β transus temperature, and aging treatment exhibit elongated prior β grains composed of two different microstructural feature regions, which are acicular α and fine spheroidal α phase regions. The 0.2% proof stress, σ₀.₂, and tensile strength, σB, increase with increasing solution treatment temperature up to 1143 K within the (α + β) region, but decrease with further increasing solution treatment temperature to 1203 K within the β region. The elongation (EL) and reduction of area (RA) decrease with increasing solution treatment temperature, and it becomes nearly 0% corresponding to a solution treatment temperature of 1203 K. The high cycle fatigue limit increases with increasing solution treatment temperature up to 1143 K, corresponding to the (α + β) region. However, it decreases with further increase in the solution treatment temperature to 1203 K in the β region. The fatigue ratio in high cycle fatigue life region is increasing with decreasing solution treatment temperature, namely increasing the volume fraction of the primary α phase, and it relates well qualitatively with the volume fraction of the primary α phase when the solution treatment temperature is less than the β transus temperature. The low cycle fatigue life increases with decreasing solution treatment temperature, namely increasing the volume fraction of the primary α phase. The low cycle fatigue life relates well quantitatively with the tensile true strain at breaking of the specimen and the volume fraction of the primary α phase for each total strain range of low cycle fatigue testing.Niinomi M., Akahori T., Nakai M., et al. Quantitative and qualitative relationship between microstructural factors and fatigue lives under load- And strain-controlled conditions of Ti-5Al-2Sn-2Zr-4Cr-4Mo (Ti-17) fabricated using a 1500-ton forging simulator. Materials Transactions 60, 1740 (2019); https://doi.org/10.2320/matertrans.ME201904
A compactness theorem for scalar-flat metrics on manifolds with boundary
Let (M,g) be a compact Riemannian manifold with boundary. This paper is
concerned with the set of scalar-flat metrics which are in the conformal class
of g and have the boundary as a constant mean curvature hypersurface. We prove
that this set is compact for dimensions greater than or equal to 7 under the
generic condition that the trace-free 2nd fundamental form of the boundary is
nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential
Equation
Arithmeticity vs. non-linearity for irreducible lattices
We establish an arithmeticity vs. non-linearity alternative for irreducible
lattices in suitable product groups, such as for instance products of
topologically simple groups. This applies notably to a (large class of)
Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as
we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page
Nonlinear quantum gravity on the constant mean curvature foliation
A new approach to quantum gravity is presented based on a nonlinear
quantization scheme for canonical field theories with an implicitly defined
Hamiltonian. The constant mean curvature foliation is employed to eliminate the
momentum constraints in canonical general relativity. It is, however, argued
that the Hamiltonian constraint may be advantageously retained in the reduced
classical system to be quantized. This permits the Hamiltonian constraint
equation to be consistently turned into an expectation value equation on
quantization that describes the scale factor on each spatial hypersurface
characterized by a constant mean exterior curvature. This expectation value
equation augments the dynamical quantum evolution of the unconstrained
conformal three-geometry with a transverse traceless momentum tensor density.
The resulting quantum theory is inherently nonlinear. Nonetheless, it is
unitary and free from a nonlocal and implicit description of the Hamiltonian
operator. Finally, by imposing additional homogeneity symmetries, a broad class
of Bianchi cosmological models are analyzed as nonlinear quantum
minisuperspaces in the context of the proposed theory.Comment: 14 pages. Classical and Quantum Gravity (To appear
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