596 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
Continuous approximation of binomial lattices
A systematic analysis of a continuous version of a binomial lattice,
containing a real parameter and covering the Toda field equation as
, is carried out in the framework of group theory. The
symmetry algebra of the equation is derived. Reductions by one-dimensional and
two-dimensional subalgebras of the symmetry algebra and their corresponding
subgroups, yield notable field equations in lower dimensions whose solutions
allow to find exact solutions to the original equation. Some reduced equations
turn out to be related to potentials of physical interest, such as the
Fermi-Pasta-Ulam and the Killingbeck potentials, and others. An instanton-like
approximate solution is also obtained which reproduces the Eguchi-Hanson
instanton configuration for . Furthermore, the equation under
consideration is extended to --dimensions. A spherically symmetric form
of this equation, studied by means of the symmetry approach, provides
conformally invariant classes of field equations comprising remarkable special
cases. One of these enables us to establish a connection with the
Euclidean Yang-Mills equations, another appears in the context of Differential
Geometry in relation to the socalled Yamabe problem. All the properties of the
reduced equations are shared by the spherically symmetric generalized field
equation.Comment: 30 pages, LaTeX, no figures. Submitted to Annals of Physic
Boundary definition of a multiverse measure
We propose to regulate the infinities of eternal inflation by relating a late
time cut-off in the bulk to a short distance cut-off on the future boundary.
The light-cone time of an event is defined in terms of the volume of its future
light-cone on the boundary. We seek an intrinsic definition of boundary volumes
that makes no reference to bulk structures. This requires taming the fractal
geometry of the future boundary, and lifting the ambiguity of the conformal
factor. We propose to work in the conformal frame in which the boundary Ricci
scalar is constant. We explore this proposal in the FRW approximation for
bubble universes. Remarkably, we find that the future boundary becomes a round
three-sphere, with smooth metric on all scales. Our cut-off yields the same
relative probabilities as a previous proposal that defined boundary volumes by
projection into the bulk along timelike geodesics. Moreover, it is equivalent
to an ensemble of causal patches defined without reference to bulk geodesics.
It thus yields a holographically motivated and phenomenologically successful
measure for eternal inflation.Comment: 39 pages, 4 figures; v2: minor correction
Functional Integration Over Geometries
The geometric construction of the functional integral over coset spaces
is reviewed. The inner product on the cotangent space of
infinitesimal deformations of defines an invariant distance and volume
form, or functional integration measure on the full configuration space. Then,
by a simple change of coordinates parameterizing the gauge fiber , the
functional measure on the coset space is deduced. This
change of integration variables leads to a Jacobian which is entirely
equivalent to the Faddeev-Popov determinant of the more traditional gauge fixed
approach in non-abelian gauge theory. If the general construction is applied to
the case where is the group of coordinate reparametrizations of
spacetime, the continuum functional integral over geometries, {\it i.e.}
metrics modulo coordinate reparameterizations may be defined. The invariant
functional integration measure is used to derive the trace anomaly and
effective action for the conformal part of the metric in two and four
dimensional spacetime. In two dimensions this approach generates the
Polyakov-Liouville action of closed bosonic non-critical string theory. In four
dimensions the corresponding effective action leads to novel conclusions on the
importance of quantum effects in gravity in the far infrared, and in
particular, a dramatic modification of the classical Einstein theory at
cosmological distance scales, signaled first by the quantum instability of
classical de Sitter spacetime. Finite volume scaling relations for the
functional integral of quantum gravity in two and four dimensions are derived,
and comparison with the discretized dynamical triangulation approach to the
integration over geometries are discussed.Comment: 68 pages, Latex document using Revtex Macro package, Contribution to
the special issue of the Journal of Mathematical Physics on Functional
Integration, to be published July, 1995
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
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
Knaster's problem for -symmetric subsets of the sphere
We prove a Knaster-type result for orbits of the group in
, calculating the Euler class obstruction. Among the consequences
are: a result about inscribing skew crosspolytopes in hypersurfaces in , and a result about equipartition of a measures in
by -symmetric convex fans
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
- …