Radiative processes in external gravitational fields

Kinematically forbidden processes may be allowed in the presence of external gravitational fields. These ca be taken into account by introducing generalized particle momenta. The corresponding transition probabilities can then be calculated to all orders in the metric deviation from the field-free expressions by simply replacing the particle momenta with their generalized counterparts. The procedure applies to particles of any spin and to any gravitational fields. transition probabilities, emission power, and spectra are, to leading order, linear in the metric deviation. It is also shown how a small dissipation term in the particle wave equations can trigger a strong backreaction that introduces resonances in the radiative process and deeply affects the resulting gravitational background.Comment: 5 pages, 1 figur

Seven views on approximate convexity and the geometry of K-spaces

As in Hokusai's series of paintings "Thirty six views of mount Fuji" in which mount Fuji's is sometimes scarcely visible, the central topic of this paper is the geometry of $K$-spaces although in some of the seven views presented $K$-spaces are not easily visible. We study the interplay between the behaviour of approximately convex (and approximately affine) functions on the unit ball of a Banach space and the geometry of Banach K-spaces.Comment: 2 figure

Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited

Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retrieved, with modes growing independently on S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfven velocity. In the fully nonlinear stage we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfven speed from the X-point, and a fast reconnection rate at the predicted value R~(ln S)^-1.Comment: 14 pages, 9 figures, accepted for publication (MNRAS

Can Gravity Distinguish Between Dirac and Majorana Neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavour system, as shown explicitly for SN1987A.Comment: 4 pages, 2 figures; minor changes of text; typo corrected; accepted in Physical Review Letter

Some computations on the characteristic variety of a line arrangement

We find monodromy formulas for line arrangements which are fibered with respect to the projection from one point. We use them to find $0$-dimensional translated components in the first characteristic variety of the arrangement $\mathcal R(2n)$ determined by a regular $n$-polygon and its diagonals.Comment: 17 pages, 4 figure

Analysis of chattering phenomenon in industrial S6-high rolling mill

Chatter in rolling mills is the undesirable vibration observed in most of the rolling mills operating at high speed and rolling thin strip. In this work the authors discuss some problems relative to the vibrations occurring in a S6-high cold rolling mill. It can result in not good surface finish for some applications and, rare cases, in gauge variations in the rolled strip and it is considered to be the result of interaction between rolling mill structure and rolling-process. Three basic types of chatter can be classified in rolling mills: torsional, third-octave mode, and fifth-octave-mode chatter. S6-high rolling mill is an innovative mode to work the steel: it allows the use of very small work rolls laterally guided by individually adjustable side support rolls, which are supported by two rows of roller bearings mounted in cassettes. It has six rolls able to roll steel strip coming directly from hot rolling mill train. A proposed solution based on empirical observations, vibration analysis and considerations of a model is described with the aim to improve the quality of the product and increasing production