3,002 research outputs found
Uniqueness and Non-uniqueness in the Einstein Constraints
The conformal thin sandwich (CTS) equations are a set of four of the Einstein
equations, which generalize the Laplace-Poisson equation of Newton's theory. We
examine numerically solutions of the CTS equations describing perturbed
Minkowski space, and find only one solution. However, we find {\em two}
distinct solutions, one even containing a black hole, when the lapse is
determined by a fifth elliptic equation through specification of the mean
curvature. While the relationship of the two systems and their solutions is a
fundamental property of general relativity, this fairly simple example of an
elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte
High power coupled CO2 waveguide laser array
A hollow-bore ridge waveguide technique for phase locking arrays of coupled CO2 rf excited waveguide lasers was demonstrated. Stable phase-locked operation of two- and three-channel arrays has been demonstrated at the 50 W output level. Preliminary experiments with a five-element array generated an output power of 95 W but phase-locked operation was not conclusively demonstrated
A new geometric invariant on initial data for Einstein equations
For a given asymptotically flat initial data set for Einstein equations a new
geometric invariant is constructed. This invariant measure the departure of the
data set from the stationary regime, it vanishes if and only if the data is
stationary. In vacuum, it can be interpreted as a measure of the total amount
of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the
non-time symmetric cas
The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach
We study the appearance of multiple solutions to certain decompositions of
Einstein's constraint equations. Pfeiffer and York recently reported the
existence of two branches of solutions for identical background data in the
extended conformal thin-sandwich decomposition. We show that the Hamiltonian
constraint alone, when expressed in a certain way, admits two branches of
solutions with properties very similar to those found by Pfeiffer and York. We
construct these two branches analytically for a constant-density star in
spherical symmetry, but argue that this behavior is more general. In the case
of the Hamiltonian constraint this non-uniqueness is well known to be related
to the sign of one particular term, and we argue that the extended conformal
thin-sandwich equations contain a similar term that causes the breakdown of
uniqueness.Comment: 9 pages, 1 figur
3+1 Approach to the Long Wavelength Iteration Scheme
Large-scale inhomogeneities and anisotropies are modeled using the Long
Wavelength Iteration Scheme. In this scheme solutions are obtained as
expansions in spatial gradients, which are taken to be small. It is shown that
the choice of foliation for spacetime can make the iteration scheme more
effective in two respects: (i) the shift vector can be chosen so as to dilute
the effect of anisotropy on the late-time value of the extrinsic curvature of
the spacelike hypersurfaces of the foliation; and (ii) pure gauge solutions
present in a similar calculation using the synchronous gauge vanish when the
spacelike hypersurfaces have extrinsic curvature with constant trace. We
furthermore verify the main conclusion of the synchronous gauge calculation
which is large-scale inhomogeneity decays if the matter--considered to be that
of a perfect-fluid with a barotropic equation of state--violates the
strong-energy condition. Finally, we obtain the solution for the lapse function
and discuss its late-time behaviour. It is found that the lapse function is
well-behaved when the matter violates the strong energy condition.Comment: 21 pages, TeX file, already publishe
On the existence of initial data containing isolated black holes
We present a general construction of initial data for Einstein's equations
containing an arbitrary number of black holes, each of which is instantaneously
in equilibrium. Each black hole is taken to be a marginally trapped surface and
plays the role of the inner boundary of the Cauchy surface. The black hole is
taken to be instantaneously isolated if its outgoing null rays are shear-free.
Starting from the choice of a conformal metric and the freely specifiable part
of the extrinsic curvature in the bulk, we give a prescription for choosing the
shape of the inner boundaries and the boundary conditions that must be imposed
there. We show rigorously that with these choices, the resulting non-linear
elliptic system always admits solutions.Comment: 11 pages, 2 figures, RevTeX
Counting Points on Genus 2 Curves with Real Multiplication
We present an accelerated Schoof-type point-counting algorithm for curves of
genus 2 equipped with an efficiently computable real multiplication
endomorphism. Our new algorithm reduces the complexity of genus 2 point
counting over a finite field (\F_{q}) of large characteristic from
(\widetilde{O}(\log^8 q)) to (\widetilde{O}(\log^5 q)). Using our algorithm we
compute a 256-bit prime-order Jacobian, suitable for cryptographic
applications, and also the order of a 1024-bit Jacobian
The influence of anesthetics, neurotransmitters and antibiotics on the relaxation processes in lipid membranes
In the proximity of melting transitions of artificial and biological
membranes fluctuations in enthalpy, area, volume and concentration are
enhanced. This results in domain formation, changes of the elastic constants,
changes in permeability and slowing down of relaxation processes. In this study
we used pressure perturbation calorimetry to investigate the relaxation time
scale after a jump into the melting transition regime of artificial lipid
membranes. This time corresponds to the characteristic rate of domain growth.
The studies were performed on single-component large unilamellar and
multilamellar vesicle systems with and without the addition of small molecules
such as general anesthetics, neurotransmitters and antibiotics. These drugs
interact with membranes and affect melting points and profiles. In all systems
we found that heat capacity and relaxation times are related to each other in a
simple manner. The maximum relaxation time depends on the cooperativity of the
heat capacity profile and decreases with a broadening of the transition. For
this reason the influence of a drug on the time scale of domain formation
processes can be understood on the basis of their influence on the heat
capacity profile. This allows estimations of the time scale of domain formation
processes in biological membranes.Comment: 12 pages, 6 figure
Testing Hardy nonlocality proof with genuine energy-time entanglement
We show two experimental realizations of Hardy ladder test of quantum
nonlocality using energy-time correlated photons, following the scheme proposed
by A. Cabello \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 040401 (2009)].
Unlike, previous energy-time Bell experiments, these tests require precise
tailored nonmaximally entangled states. One of them is equivalent to the
two-setting two-outcome Bell test requiring a minimum detection efficiency. The
reported experiments are still affected by the locality and detection
loopholes, but are free of the post-selection loophole of previous energy-time
and time-bin Bell tests.Comment: 5 pages, revtex4, 6 figure
Absorption spectrum in the wings of the potassium second resonance doublet broadened by helium
We have measured the reduced absorption coefficients occurring in the wings
of the potassium 4S-5P doublet lines at 404.414 nm and at 404.720 nm broadened
by helium gas at pressures of several hundred Torr. At the experimental
temperature of 900 K, we have detected a shoulder-like broadening feature on
the blue wing of the doublet which is relatively flat between 401.8 nm and
402.8 nm and which drops off rapidly for shorter wavelengths, corresponding to
absorption from the X doublet Sigma+ state to the C doublet Sigma+ state of the
K-He quasimolecule. The accurate measurements of the line profiles in the
present work will sharply constrain future calculations of potential energy
surfaces and transition dipole moments correlating to the asymptotes He-K(5p),
He-K(5s), and He-K(3d).Comment: 2 figure
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