72,391 research outputs found
An Introduction to Conformal Ricci Flow
We introduce a variation of the classical Ricci flow equation that modifies
the unit volume constraint of that equation to a scalar curvature constraint.
The resulting equations are named the Conformal Ricci Flow Equations because of
the role that conformal geometry plays in constraining the scalar curvature.
These equations are analogous to the incompressible Navier-Stokes equations of
fluid mechanics inasmuch as a conformal pressure arises as a Lagrange
multiplier to conformally deform the metric flow so as to maintain the scalar
curvature constraint. The equilibrium points are Einstein metrics with a
negative Einstein constant and the conformal pressue is shown to be zero at an
equilibrium point and strictly positive otherwise. The geometry of the
conformal Ricci flow is discussed as well as the remarkable analytic fact that
the constraint force does not lose derivatives and thus analytically the
conformal Ricci equation is a bounded perturbation of the classical
unnormalized Ricci equation. That the constraint force does not lose
derivatives is exactly analogous to the fact that the real physical pressure
force that occurs in the Navier-Stokes equations is a bounded function of the
velocity. Using a nonlinear Trotter product formula, existence and uniqueness
of solutions to the conformal Ricci flow equations is proven. Lastly, we
discuss potential applications to Perelman's proposed implementation of
Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur
Outflanking and securely using the PIN/TAN-System
The PIN/TAN-system is an authentication and authorization scheme used in
e-business. Like other similar schemes it is successfully attacked by
criminals. After shortly classifying the various kinds of attacks we accomplish
malicious code attacks on real World Wide Web transaction systems. In doing so
we find that it is really easy to outflank these systems. This is even
supported by the users' behavior. We give a few simple behavior rules to
improve this situation. But their impact is limited. Also the providers support
the attacks by having implementation flaws in their installations. Finally we
show that the PIN/TAN-system is not suitable for usage in highly secure
applications.Comment: 7 pages; 2 figures; IEEE style; final versio
Speed Limits in General Relativity
Some standard results on the initial value problem of general relativity in
matter are reviewed. These results are applied first to show that in a well
defined sense, finite perturbations in the gravitational field travel no faster
than light, and second to show that it is impossible to construct a warp drive
as considered by Alcubierre (1994) in the absence of exotic matter.Comment: 7 pages; AMS-LaTeX; accepted for publication by Classical and Quantum
Gravit
Modeling Spatial Autocorrelation in Spatial Interaction Data: A Comparison of Spatial Econometric and Spatial Filtering Specifications
The need to account for spatial autocorrelation is well known in spatial analysis. Many spatial statistics and spatial econometric texts detail the way spatial autocorrelation can be identified and modelled in the case of object and field data. The literature on spatial autocorrelation is much less developed in the case of spatial interaction data. The focus of interest in this paper is on the problem of spatial autocorrelation in a spatial interaction context. The paper aims to illustrate that eigenfunction-based spatial filtering offers a powerful methodology that can efficiently account for spatial autocorrelation effects within a Poisson spatial interaction model context that serves the purpose to identify and measure spatial separation effects to interregional knowledge spillovers as captured by patent citations among high-technology-firms in Europe.
Gd(III)-Gd(III) Relaxation-Induced Dipolar Modulation Enhancement for In-Cell Electron Paramagnetic Resonance Distance Determination
In-cell distance determination by electron paramagnetic resonance (EPR) spectroscopy reveals essential structural information about biomacromolecules under native conditions. We demonstrate that the pulsed EPR technique RIDME (relaxation induced dipolar modulation enhancement) can be utilized for such distance determination. The performance of in-cell RIDME has been assessed at Q-band using stiff molecular rulers labeled with Gd(III)-PyMTA and microinjected into Xenopus laevis oocytes. The overtone coefficients are determined to be the same for protonated aqueous solutions and inside cells. As compared to in-cell DEER (double electron-electron resonance, also abbreviated as PELDOR), in-cell RIDME features approximately 5 times larger modulation depth and does not show artificial broadening in the distance distributions due to the effect of pseudosecular terms
Perturbations of Spatially Closed Bianchi III Spacetimes
Motivated by the recent interest in dynamical properties of topologically
nontrivial spacetimes, we study linear perturbations of spatially closed
Bianchi III vacuum spacetimes, whose spatial topology is the direct product of
a higher genus surface and the circle. We first develop necessary mode
functions, vectors, and tensors, and then perform separations of (perturbation)
variables. The perturbation equations decouple in a way that is similar to but
a generalization of those of the Regge--Wheeler spherically symmetric case. We
further achieve a decoupling of each set of perturbation equations into
gauge-dependent and independent parts, by which we obtain wave equations for
the gauge-invariant variables. We then discuss choices of gauge and stability
properties. Details of the compactification of Bianchi III manifolds and
spacetimes are presented in an appendix. In the other appendices we study
scalar field and electromagnetic equations on the same background to compare
asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear
in Class. Quant. Gravi
Electroweak and finite width corrections to top quark decays into transverse and longitudinal -bosons
We calculate the electroweak and finite width corrections to the decay of an
unpolarized top quark into a bottom quark and a -gauge boson where the
helicities of the are specified as longitudinal, transverse-plus and
transverse-minus. Together with the corrections these
corrections may become relevant for the determination of the mass of the top
quark through angular decay measurements.Comment: 4 pages, 7 postscript figures adde
Hybridization and spin decoherence in heavy-hole quantum dots
We theoretically investigate the spin dynamics of a heavy hole confined to an
unstrained III-V semiconductor quantum dot and interacting with a narrowed
nuclear-spin bath. We show that band hybridization leads to an exponential
decay of hole-spin superpositions due to hyperfine-mediated nuclear pair flips,
and that the accordant single-hole-spin decoherence time T2 can be tuned over
many orders of magnitude by changing external parameters. In particular, we
show that, under experimentally accessible conditions, it is possible to
suppress hyperfine-mediated nuclear-pair-flip processes so strongly that
hole-spin quantum dots may be operated beyond the `ultimate limitation' set by
the hyperfine interaction which is present in other spin-qubit candidate
systems.Comment: 7 pages, 3 figure
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