Is nonrelativistic gravity possible?

We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Einstein gravity and IR limit of Horava gravity are locally identical.Comment: 4 pages, v2, typos corrected, published in Physical Review

Adjustable tension wire guide Patent

Adjustable spiral wire winding devic

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

Testing of pear trees on their own roots in comparison with important used rootstocks under organic farming conditions with special regard to fire blight (E. amylovora)

Pear trees on their own roots are tested in comparison to grafted trees in growth and yield characteristics and with special regard to the tolerance to diseases, above all fire blight (Erwinia amylovora). In spring 2004 15 randomized trees of the cultivar 'Williams' from three variants (self rooted in vitro, self rooted long cuttings, grafted on Quince A) were planted in a pear orchard, which was heavily infected with fire blight (Erwinia amylovora) the previous years. The trees were left untreated. Growth and yield characteristics, plant diseases and tree losses were observed. After four years the in vitro self rooted trees were significantly more vigorous in growth than those grafted on quince A. The self rooted long cuttings were comparable in growth with grafts on quince, but showed high tree losses probably due to frost damages in the first winter one year after planting. However no infections with Erwinia amylovora could be observed so far. In a field trial with more cultivars and rootstock variants planted in 2006 at two organically managed sites more significant effects are expected in the next years

Microscopic model for Bose-Einstein condensation and quasiparticle decay

Sufficiently dimerized quantum antiferromagnets display elementary S=1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J1=-2.3meV, J2=1.2meV, J3=2.9meV and J4=-0.3meV. These couplings determine IPA-CuCl3 as system of coupled asymmetric S=1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.Comment: 6 pages, 5 figure

Predicting the frequencies of diverse exo-planetary systems

Extrasolar planetary systems range from hot Jupiters out to icy comet belts more distant than Pluto. We explain this diversity in a model where the mass of solids in the primordial circumstellar disk dictates the outcome. The star retains measures of the initial heavy-element (metal) abundance that can be used to map solid masses onto outcomes, and the frequencies of all classes are correctly predicted. The differing dependences on metallicity for forming massive planets and low-mass cometary bodies are also explained. By extrapolation, around two-thirds of stars have enough solids to form Earth-like planets, and a high rate is supported by the first detections of low-mass exo-planets.Comment: 5 pages, 2 figures; accepted by MNRA

The Spectator Electromagnetic Effect on Charged Pion Spectra in Peripheral Ultrarelativistic Heavy-Ion Collisions

We estimate the electromagnetic effect of the spectator charge on the momentum spectra of $\pi^+$ and $\pi^-$ produced in peripheral Pb+Pb collisions at SPS energies. We find that the effect is large and results in strongly varying structures in the $x_F$ dependence of the $\pi^+/\pi^-$ ratio, especially at low transverse momenta where a deep valley in the above ratio is predicted at $x_F \sim$ 0.15 -- 0.20. It appears that the effect depends on initial conditions. Thus, it provides new information on the space and time evolution of the non-perturbative pion creation process.Comment: 20 pages and 8 figure