An Introduction to Hyperbolic Barycentric Coordinates and their Applications

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.Comment: 66 pages, 3 figure

Emergency Tenant Protection in New York: Ten Years of Rent Stabilization

New York City\u27s rent stabilization system was designed as an alternative to the rent control system. Rent stabilization looked to the owners for supervision as a way to benefit not only the system but tenants through an informed and experienced administration. Unfortunately, the system has had its fair share of shortcomings as rules have become technical, complex, and ill equipped to address the concerns of tenants. This comment examines the stabilization system\u27s history and its current status. Though the current system has flaws, the flaws can be fixed and must be to protect NYC tenants and owners

Panel loss factors due to gas-pumping at structural joints

High frequency structural damping due to riveted joints associated with gas pumping between overlapping surface

Quantum kinetic equations for the ultrafast spin dynamics of excitons in diluted magnetic semiconductor quantum wells after optical excitation

Quantum kinetic equations of motion for the description of the exciton spin dynamics in II-VI diluted magnetic semiconductor quantum wells with laser driving are derived. The model includes the magnetic as well as the nonmagnetic carrier-impurity interaction, the Coulomb interaction, Zeeman terms, and the light-matter coupling, allowing for an explicit treatment of arbitrary excitation pulses. Based on a dynamics-controlled truncation scheme, contributions to the equations of motion up to second order in the generating laser field are taken into account. The correlations between the carrier and the impurity subsystems are treated within the framework of a correlation expansion. For vanishing magnetic field, the Markov limit of the quantum kinetic equations formulated in the exciton basis agrees with existing theories based on Fermi's golden rule. For narrow quantum wells excited at the $1s$ exciton resonance, numerical quantum kinetic simulations reveal pronounced deviations from the Markovian behavior. In particular, the spin decays initially with approximately half the Markovian rate and a non-monotonic decay in the form of an overshoot of up to $10\,\%$ of the initial spin polarization is predicted.Comment: 17 pages, 3 figures, typographical errors corrected (Erratum published in Phys. Rev. B 96, 239904

Comment on "Minimal size of a barchan dune"

It is now an accepted fact that the size at which dunes form from a flat sand bed as well as their `minimal size' scales on the flux saturation length. This length is by definition the relaxation length of the slowest mode toward equilibrium transport. The model presented by Parteli, Duran and Herrmann [Phys. Rev. E 75, 011301 (2007)] predicts that the saturation length decreases to zero as the inverse of the wind shear stress far from the threshold. We first show that their model is not self-consistent: even under large wind, the relaxation rate is limited by grain inertia and thus can not decrease to zero. A key argument presented by these authors comes from the discussion of the typical dune wavelength on Mars (650 m) on the basis of which they refute the scaling of the dune size with the drag length evidenced by Claudin and Andreotti [Earth Pla. Sci. Lett. 252, 30 (2006)]. They instead propose that Martian dunes, composed of large grains (500 micrometers), were formed in the past under very strong winds. We show that this saltating grain size, estimated from thermal diffusion measurements, is not reliable. Moreover, the microscopic photographs taken by the rovers on Martian aeolian bedforms show a grain size of 87 plus or minus 25 micrometers together with hematite spherules at millimetre scale. As those so-called ``blueberries'' can not be entrained by reasonable winds, we conclude that the saltating grains on Mars are the small ones, which gives a second strong argument against the model of Parteli et al.Comment: A six page comment on ``Minimal size of a barchan dune'' by Parteli, Duran and Herrmann [Phys. Rev. E 75, 011301 (2007) arXiv:0705.1778