High energy physics in the atmosphere: phenomenology of cosmic ray air showers

The properties of cosmic rays with energies above 10⁶ GeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review we summarize the phenomenology of these giant air showers. We describe the hadronic interaction models used to extrapolate results from collider data to ultra high energies, and discuss the prospects for insights into forward physics at the LHC. We also describe the main electromagnetic processes that govern the longitudinal shower evolution, as well as the lateral spread of particles. Armed with these two principal shower ingredients and motivation from the underlying physics, we provide an overview of some of the different methods proposed to distinguish primary species. The properties of neutrino interactions and the potential of forthcoming experiments to isolate deeply penetrating showers from baryonic cascades are also discussed. We finally venture into a terra incognita endowed with TeV-scale gravity and explore anomalous neutrino-induced showers.     

Submanifolds associated with graphs

In this paper we present an interesting relationship between graph theory and differential geometry by defining submanifolds of almost Hermitian manifolds associated with certain kinds of graphs. We show some results about the possibility of a graph being associated with a submanifold and we use them to characterize CR-submanifolds by means of trees. Finally, we characterize submanifolds associated with graphs in a four-dimensional almost Hermitian manifold.

     

Some Further Properties of the Accelerated Kerr-Schild Metrics

We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.     

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

X-ray diffraction study of some mesogenic copper, nickel and vanadyl complexes

We present a comparative study of various metallomesogenic complexes, using X-ray diffraction methods. For a given ligand linked to different metal atoms (Cu, Ni, VO), the nature of this central atom influences mainly the magnetic susceptibilities of the mesophases. With different ligands, which keep the close neighbourhood of the metal atom unchanged, the apparent length of the mesogenic unit is longer for short ligands than for longer ones. This unexpected behaviour is qualitatively well explained by taking into account the global shape of the different complexes.