21,138 research outputs found
The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics
By combining the join construction from Sasakian geometry with the
Hamiltonian 2-form construction from K\"ahler geometry, we recover
Sasaki-Einstein metrics discovered by physicists. Our geometrical approach
allows us to give an algorithm for computing the topology of these
Sasaki-Einstein manifolds. In particular, we explicitly compute the cohomology
rings for several cases of interest and give a formula for homotopy equivalence
in one particular 7-dimensional case. We also show that our construction gives
at least a two dimensional cone of both Sasaki-Ricci solitons and extremal
Sasaki metrics.Comment: 38 pages, paragraph added to introduction and Proposition 4.1 added,
Proposition 4.15 corrected, Remark 5.5 added, and explanation for irregular
Sasaki-Einstein structures expanded. Reference adde
The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar Curvature
We describe a general procedure for constructing new Sasaki metrics of
constant scalar curvature from old ones. Explicitly, we begin with a regular
Sasaki metric of constant scalar curvature on a 2n+1-dimensional compact
manifold M and construct a sequence, depending on four integer parameters, of
rays of constant scalar curvature (CSC) Sasaki metrics on a compact Sasaki
manifold of dimension . We also give examples which show that the CSC
rays are often not unique on a fixed strictly pseudoconvex CR manifold or a
fixed contact manifold. Moreover, it is shown that when the first Chern class
of the contact bundle vanishes, there is a two dimensional subcone of Sasaki
Ricci solitons in the Sasaki cone, and a unique Sasaki-Einstein metric in each
of the two dimensional sub cones.Comment: 32 pages. A gap in the argument of applying the admissibility
conditions to irregular Sasakian structures is filled. Some minor corrections
and additions are also made. This is the final version which will appear in
the Journal of Geometric Analysis. It also encorporates much from our paper
arXiv:1309.706
An Improved Procedure for Laboratory Rearing of the Corn Earworm, \u3ci\u3eHeliothis Zea\u3c/i\u3e (Lepidoptera: Noctuidae)
An improved method for the laboratory rearing of the corn earworm. Heliothis zea, described. The rearing medium is a modification of the commonly used wheat germ An oviposition chamber, a feeder for adults, and a simple and inexpensive contrnlled humidity chamber are described
Covariant Uniform Acceleration
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only
partially covariant. To achieve full Lorentz covariance, we replace the
four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By
taking this tensor to be constant, we obtain a covariant definition of
uniformly accelerated motion. We compute explicit solutions for uniformly
accelerated motion which are divided into four types: null, linear, rotational,
and general. For null acceleration, the worldline is cubic in the time. Linear
acceleration covariantly extends 1D hyperbolic motion, while rotational
acceleration covariantly extends pure rotational motion.
We use Generalized Fermi-Walker transport to construct a uniformly
accelerated family of inertial frames which are instantaneously comoving to a
uniformly accelerated observer. We explain the connection between our approach
and that of Mashhoon. We show that our solutions of uniformly accelerated
motion have constant acceleration in the comoving frame. Assuming the Weak
Hypothesis of Locality, we obtain local spacetime transformations from a
uniformly accelerated frame K' to an inertial frame K. The spacetime
transformations between two uniformly accelerated frames with the same
acceleration are Lorentz. We compute the metric at an arbitrary point of a
uniformly accelerated frame.
We obtain velocity and acceleration transformations from a uniformly
accelerated system K' to an inertial frame K. We derive the general formula for
the time dilation between accelerated clocks. We obtain a formula for the
angular velocity of a uniformly accelerated object. Every rest point of K' is
uniformly accelerated, and its acceleration is a function of the observer's
acceleration and its position. We obtain an interpretation of the
Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page
Weak Localization Coexisting with a Magnetic Field in a Normal-Metal--Superconductor Microbridge
A random-matrix theory is presented which shows that breaking time-reversal
symmetry by itself does {\em not} suppress the weak-localization correction to
the conductance of a disordered metal wire attached to a superconductor.
Suppression of weak localization requires applying a magnetic field as well as
raising the voltage, to break both time-reversal symmetry and electron-hole
degeneracy. A magnetic-field dependent contact resistance obscured this anomaly
in previous numerical simulations.Comment: 8 pages, REVTeX-3.0, 1 figur
Structure and Response in the World Trade Network
We examine how the structure of the world trade network has been shaped by
globalization and recessions over the last 40 years. We show that by treating
the world trade network as an evolving system, theory predicts the trade
network is more sensitive to evolutionary shocks and recovers more slowly from
them now than it did 40 years ago, due to structural changes in the world trade
network induced by globalization. We also show that recession-induced change to
the world trade network leads to an \emph{increased} hierarchical structure of
the global trade network for a few years after the recession.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let
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