Comparison of Four Space Propulsion Methods for Reducing Transfer Times of Manned Mars Mission

We assess the possibility of reducing the travel time of a manned mission to Mars by examining four different propulsion methods, and keeping the mass at departure under 2,500 tonnes, for a fixed architecture. We evaluated representative systems of three different state of the art technologies (chemical, nuclear thermal, and electric), and one advance technology, the "Pure Electro-Magnetic Thrust" (PEMT) concept (proposed by Rubbia). A mission architecture mostly based on the Design Reference Architecture 5.0 is assumed in order to estimate the mass budget, that influences the performance of the propulsion system. Pareto curves of the duration of the mission and time of flight versus mass of mission are drawn. We conclude that the ion engine technology, combined with the classical chemical engine, yields the shortest mission times for this architecture with the lowest mass, and that chemical propulsion alone is the best to minimise travel time. The results obtained using the PEMT suggest that it could be a more suitable solution for farther destinations than Mars.Comment: Change in title, abstract and presentation so to clarify the main results. 14 pages, 7 figures and 2 table

General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas, let us say a, and the added s+1 is either independent of the former ones, or it is identical to one of the overlaps q(a,b), with b running among the first s replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical and General. Also available at http://rerumnatura.zool.su.se/stefano/ms/ghigu.p

Interpolating the Sherrington-Kirkpatrick replica trick

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally implemented into the cavity field technique, or its variants as the stochastic stability or the random overlap structures. However the first and most famous approach to mean field statistical mechanics with quenched disorder is the replica trick. Among the models where these methods have been used (namely, dealing with frustration and complexity), probably the best known is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to apply the interpolation scheme to the replica trick framework and test it directly to the cited paradigmatic model: interestingly this allows to obtain easily the replica-symmetric control and, synergically with the broken replica bounds, a description of the full RSB scenario, both coupled with several minor theorems. Furthermore, by treating the amount of replicas $n\in(0,1]$ as an interpolating parameter (far from its original interpretation) this can be though of as a quenching temperature close to the one introduce in off-equilibrium approaches and, within this viewpoint, the proof of the attended commutativity of the zero replica and the infinite volume limits can be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his seventieth birthda

Replica symmetry breaking in mean field spin glasses trough Hamilton-Jacobi technique

During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick spin glass model have been firmly established. In particular, it has been possible to prove the existence and uniqueness of the infinite volume limit for the free energy, and its Parisi expression, in terms of a variational principle, involving a functional order parameter. Even the expected property of ultrametricity, for the infinite volume states, seems to be near to a complete proof. The main structural feature of this model, and related models, is the deep phenomenon of spontaneous replica symmetry breaking (RSB), discovered by Parisi many years ago. By expanding on our previous work, the aim of this paper is to investigate a general frame, where replica symmetry breaking is embedded in a kind of mechanical scheme of the Hamilton-Jacobi type. Here, the analog of the "time" variable is a parameter characterizing the strength of the interaction, while the "space" variables rule out quantitatively the broken replica symmetry pattern. Starting from the simple cases, where annealing is assumed, or replica symmetry, we build up a progression of dynamical systems, with an increasing number of space variables, which allow to weaken the effect of the potential in the Hamilton-Jacobi equation, as the level of symmetry braking is increased. This new machinery allows to work out mechanically the general K-step RSB solutions, in a different interpretation with respect to the replica trick, and lightens easily their properties as existence or uniqueness.Comment: 24 pages, no figure

Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses

We study the low-temperature spin-glass phases of the Sherrington-Kirkpatrick (SK) model and of the 3-dimensional short range Ising spin glass (3dISG). For the SK model, evidence for ultrametricity becomes clearer as the system size increases, while for the short-range case our results indicate the opposite, i.e. lack of ultrametricity. Our results are obtained by a recently proposed method that uses clustering to focus on the relevant parts of phase space and reduce finite size effects. Evidence that the mean field solution does not apply in detail to the 3dISG is also found by another method which does not rely on clustering

Relación angular radiológica de las superficies articulares de la tibia en sujetos asintomáticos

Se efectuó un estudio radiológico para determinar la relación angular existente entre las superficies articulares proximal y distal de 108 tibias correspondientes a 54 pacientes asintomáticos, de edades entre 14 y 72 años (media: 29,8). La medición se llevó a cabo con un «cobbometro» de Oxford en proyección anteroposterior y lateral. El ángulo medio entre ambas superficies fue de 3,3 ± 2,6° (intervalo de confianza al 95%: 2,8-3,8°) en proyección anteroposterior y de 5,5 ± 3,9° (intervalo de confianza: 4,7-6,3°) en proyección lateral. Cuando se consideró para cada paciente, la diferencia media de esta relación angular entre las tibias derechas e izquierdas fue inferior a 0,5° en ambas proyecciones.The angular relationship between proximal and distal articular surfaces was determined, through an Oxford Cobbometer, in 108 tibiae of 54 asymptomalic patients aging 14 to 72 years (mean: 30). Mean angle between both surfaces was 3.3 ± 2.6° (95% confidence interval: 2.8-3.8°) for the anteroposterior view and 5.5 ± 3.9° (95% confidence interval: 4.7-6.3°) for the lateral view. When considered individually for each patient, mean difference of this angular relationship among right and left tibiae was lesser than 0.5° for both projections

How glassy are neural networks?

In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: Critical line, behavior of the principal thermodynamic observables and their fluctuations as well as overlap fluctuations are obtained and discussed. Then, we move further, extending such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and we show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two quenched spin-glass free energies even in the replica symmetric framework