Complex bounds for multimodal maps: bounded combinatorics

We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps.Comment: 20 pages, 3 figure

Development of a telescope for medium-energy gamma-ray astronomy

The Advanced Energetic Pair Telescope (AdEPT) is being developed at GSFC as a future NASA MIDEX mission to explore the medium-energy (5–200 MeV) gamma-ray range. The enabling technology for AdEPT is the Three- Dimensional Track Imager (3-DTI), a gaseous time projection chamber. The high spatial resolution 3-D electron tracking of 3-DTI enables AdEPT to achieve high angular resolution gamma-ray imaging via pair production and triplet production (pair production on electrons) in the medium-energy range. The low density and high spatial resolution of 3-DTI allows the electron positron track directions to be measured before they are dominated by Coulomb scattering. Further, the significant reduction of Coulomb scattering allows AdEPT to be the first medium-energy gamma-ray telescope to have high gamma-ray polarization sensitivity. We review the science goals that can be addressed with a medium-energy pair telescope, how these goals drive the telescope design, and the realization of this design with AdEPT. The AdEPT telescope for a future MIDEX mission is envisioned as a 8 m3 active volume filled with argon at 2 atm. The design and performance of the 3-DTI detectors for the AdEPT telescope are described as well as the outstanding instrument challenges that need to be met for the AdEPT mission

Doubly Special Relativity and de Sitter space

In this paper we recall the construction of Doubly Special Relativity (DSR) as a theory with energy-momentum space being the four dimensional de Sitter space. Then the bases of the DSR theory can be understood as different coordinate systems on this space. We investigate the emerging geometrical picture of Doubly Special Relativity by presenting the basis independent features of DSR that include the non-commutative structure of space-time and the phase space algebra. Next we investigate the relation between our geometric formulation and the one based on quantum $\kappa$-deformations of the Poincar\'e algebra. Finally we re-derive the five-dimensional differential calculus using the geometric method, and use it to write down the deformed Klein-Gordon equation and to analyze its plane wave solutions.Comment: 26 pages, one formula (67) corrected; some remarks adde

Roughness Signature of Tribological Contact Calculated by a New Method of Peaks Curvature Radius Estimation on Fractal Surfaces

This paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to fractal profiles of the Nowicki's method [Nowicki B. Wear Vol.102, p.161-176, 1985] by introducing a fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of fractal curves such as those described by Brownian motions. A new fractal function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process

Non-universal equilibrium crystal shape results from sticky steps

The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z=z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) using the Monte Carlo method, where p=(dz/dx, dz/dy)$, and represents the thermal averag |p| dependence of , we derive a |p|-expanded expression for the non-universal surface free energy f_{eff}(p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f_{eff}(p).Comment: 31 pages, 21 figure

Study on the Implications of Asynchronous GMO Approvals for EU Imports of Animal Feed Products

The aim of this study is to understand the implications of asynchronous approvals for genetically modified organisms (GMOs) that are imported to the European Union for use within animal feed products, specifically with regard to the EU livestock sector, as well as upon the upstream and downstream economic industries related to it. Asynchronous approval refers to the situation in which there is a delay in the moment when a genetically modified (GM) event – modifying a specific trait of a plant or animal – is allowed to be used in one country in comparison to another country. In the perspective of this study, the asynchronous GMO approvals concern the use of GM varieties of plants that are approved in the countries which supply them to the EU, in one form or another of feed material, before these are approved by the EU

Planetary Geochemistry Techniques: Probing In-Situ with Neutron and Gamma Rays (PING) Instrument

The Probing In situ with Neutrons and Gamma rays (PING) instrument is a promising planetary science application of the active neutron-gamma ray technology so successfully used in oil field well logging and mineral exploration on Earth. The objective of our technology development program at NASA Goddard Space Flight Center's (NASA/GSFC) Astrochemistry Laboratory is to extend the application of neutron interrogation techniques to landed in situ planetary composition measurements by using a 14 MeV Pulsed Neutron Generator (PNG) combined with neutron and gamma ray detectors, to probe the surface and subsurface of planetary bodies without the need to drill. We are thus working to bring the PING instrument to the point where it can be flown on a variety of surface lander or rover missions to the Moon, Mars, Venus, asteroids, comets and the satellites of the outer planets

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic