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 W W -bosons

We calculate the electroweak and finite width corrections to the decay of an unpolarized top quark into a bottom quark and a $W$-gauge boson where the helicities of the $W$ are specified as longitudinal, transverse-plus and transverse-minus. Together with the $O(\alpha_s)$ 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