Space Laser Power Transmission System Studies

Power transmission by laser technique is addressed. Space to Earth and space to space configurations are considered

Fluid-solid transition in hard hyper-sphere systems

In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D = 4, 5, 6 and 7. We have studied the changes of the Radial Distribution Function (RDF) as a function of density in the coexistence region. We started our simulations from crystalline states with densities above the melting point, and moved down to densities in the liquid state below the freezing point. For all the examined dimensions (including D = 3) it was observed that the height of the first minimum of the RDF changes in an almost continuous way around the freezing density and resembles a second order phase transition. With these results we propose a numerical method to estimate the freezing point as a function of the dimension D using numerical fits and semiempirical approaches. We find that the estimated values of the freezing point are very close to previously reported values from simulations and theoretical approaches up to D = 6 reinforcing the validity of the proposed method. This was also applied to numerical simulations for D = 7 giving new estimations of the freezing point for this dimensionality.Comment: 13 pages, 10 figure

Similar Sublattices and Coincidence Rotations of the Root Lattice A4 and its Dual

A natural way to describe the Penrose tiling employs the projection method on the basis of the root lattice A4 or its dual. Properties of these lattices are thus related to properties of the Penrose tiling. Moreover, the root lattice A4 appears in various other contexts such as sphere packings, efficient coding schemes and lattice quantizers. Here, the lattice A4 is considered within the icosian ring, whose rich arithmetic structure leads to parametrisations of the similar sublattices and the coincidence rotations of A4 and its dual lattice. These parametrisations, both in terms of a single icosian, imply an index formula for the corresponding sublattices. The results are encapsulated in Dirichlet series generating functions. For every index, they provide the number of distinct similar sublattices as well as the number of coincidence rotations of A4 and its dual.Comment: 8 pages, paper presented at ICQ10 (Zurich, Switzerland

Quaternionic Root Systems and Subgroups of the Aut(F4)Aut(F_{4})

Cayley-Dickson doubling procedure is used to construct the root systems of some celebrated Lie algebras in terms of the integer elements of the division algebras of real numbers, complex numbers, quaternions and octonions. Starting with the roots and weights of SU(2) expressed as the real numbers one can construct the root systems of the Lie algebras of SO(4),SP(2)= SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the division algebras. The roots themselves display the group structures besides the octonionic roots of E_{8} which form a closed octonion algebra. The automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the largest crystallographic group in 4-dimensional Euclidean space, is realized as the direct product of two binary octahedral group of quaternions preserving the quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192 with different conjugacy classes occur as maximal subgroups in the finite subgroups of the Lie group $G_{2}$ of orders 12096 and 1344 and proves to be useful in their constructions. The triality of SO(8) manifesting itself as the cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and F_{4} respectively

The RAG Model: a new paradigm for genetic risk stratification in multiple myeloma

Molecular studies have shown that multiple myeloma is a highly genetically heterogonous disease which may manifest itself as any number of diverse subtypes each with variable clinicopathological features and outcomes. Given this genetic heterogeneity, a universal approach to treatment of myeloma is unlikely to be successful for all patients and instead we should strive for the goal of personalised therapy using rationally informed targeted strategies. Current DNA sequencing technologies allow for whole genome and exome analysis of patient myeloma samples that yield vast amounts of genetic data and provide a mutational overview of the disease. However, the clinical utility of this information currently lags far behind the sequencing technology which is increasingly being incorporated into clinical practice. This paper attempts to address this shortcoming by proposing a novel genetically based “traffic-light” risk stratification system for myeloma, termed the RAG (Red, Amber, Green) model, which represents a simplified concept of how complex genetic data may be compressed into an aggregate risk score. The model aims to incorporate all known clinically important trisomies, translocations, and mutations in myeloma and utilise these to produce a score between 1.0 and 3.0 that can be incorporated into diagnostic, prognostic, and treatment algorithms for the patient

Preliminary observations of Rustaveli basin, Mercury

Rustaveli basin on Mercury (82.76° E, 52.39° N) is a 200.5 km diameter peak-ring basin. Since the approval of its name on April 24, 2012, it has not featured prominently in the literature. It is a large and important feature within the Hokusai (H5) quadrangle of which we are currently producing a 1:2M scale geological map. Here, we describe our first observations of Rustaveli

Preliminary findings from geological mapping of the Hokusai (H5) quadrangle of Mercury

Quadrangle geological maps from Mariner 10 data cover 45% of the surface of Mercury at 1:5M scale. Orbital MESSENGER data, which cover the entire planetary surface, can now be used to produce finer scale geological maps, including regions unseen by Mariner 10. Hokusai quadrangle (0–90° E; 22.5–66° N) is in the hemisphere unmapped by Mariner 10. It contains prominent features which are already being studied, including: Rachmaninoff basin, volcanic vents within and around Rachmaninoff, much of the Northern Plains and abundant wrinkle ridges. Its northern latitude makes it a prime candidate for regional geological mapping since compositional and topographical data, as well as Mercury Dual Imaging System (MDIS) data, are available for geological interpretation. This work aims to produce a map at 1:2M scale, compatible with other new quadrangle maps and to complement a global map now in progress