Monte Carlo model of the uncertainty of SEA loss factors

Finite Element Methods are widely used to model vibro-acoustic systems, but as the modal density becomes higher this type of model becomes inaccurate and impractical. This is why in the high modal density region the use of Statistical Energy Analysis (SEA) models has become increasingly popular. SEA has some obvious advantages such as its simple formal expression, being based on linear equation systems or the reduced number of variables involved. But SEA has drawbacks as well, such as the absence of local information or the necessity of frequency averaging. A key quantity in SEA models is the loss factor. This takes into account the energy dissipated within a given subsystem or when power flows from one subsystem to another. Even though analytical expressions exist for a number of subsystems of differing nature, the measurement of the loss factor is still advisable and a necessity for a large number of cases. The most commonly used method of measuring loss factors is the Power Injection Method. This method is based on the injection of power into every single subsystem in sequence while the energy in each subsystem is measured. In spite of its simplicity, there remain a number of problems where the accuracy of the results is influenced by various practical issues. In this paper, a Monte Carlo model is used to describe the uncertainty of a two subsystemproblem consisting of two planar elements connected along one side. The influence of the input variables is studied and the conditioning of the coefficient matrix that model the system is also taken into accoun

Predictability in an unpredictable artificial cultural market

In social, economic and cultural situations in which the decisions of individuals are influenced directly by the decisions of others, there appears to be an inherently high level of ex ante unpredictability. In cultural markets such as films, songs and books, well-informed experts routinely make predictions which turn out to be incorrect. We examine the extent to which the existence of social influence may, somewhat paradoxically, increase the extent to which winners can be identified at a very early stage in the process. Once the process of choice has begun, only a very small number of decisions may be necessary to give a reasonable prospect of being able to identify the eventual winner. We illustrate this by an analysis of the music download experiments of Salganik et.al. (2006). We derive a rule for early identification of the eventual winner. Although not perfect, it gives considerable practical success. We validate the rule by applying it to similar data not used in the process of constructing the rule

Nuevas subespecies de la Subfamilia Onychiurinae de la Península Ibérica.

Se describen cinco nuevas especies de colémbolos Oniquiúridos, de las colecciones del Museo de Ciencias Naturales, Universidad Autónoma de Madrid y Universidad del País Vasco: Onychiurus gemae sp. n., Onychiurus selgae sp. n., Onychiurus vinuensis sp. n., Protaphorura florae n. sp. y Archaphorura alavensis sp.n

Air gap influence on the vibro-acoustic response of Solar Arrays during launch

One of the primary elements on the space missions is the electrical power subsystem, for which the critical component is the solar array. The behaviour of these elements during the ascent phase of the launch is critical for avoiding damages on the solar panels, which are the primary source of energy for the satellite in its final configuration. The vibro-acoustic response to the sound pressure depends on the solar array size, mass, stiffness and gap thickness. The stowed configuration of the solar array consists of a multiple system composed of structural elements and the air layers between panels. The effect of the air between panels on the behaviour of the system affects the frequency response of the system not only modifying the natural frequencies of the wings but also as interaction path between the wings of the array. The usual methods to analyze the vibro-acoustic response of structures are the FE and BE methods for the low frequency range and the SEA formulation for the high frequency range. The main issue in the latter method is, on one hand, selecting the appropriate subsystems, and, on the other, identifying the parameters of the energetic system: the internal and coupling loss factors. From the experimental point of view, the subsystems parameters can be identified by exciting each subsystem and measuring the energy of all the subsystems composing the Solar Array. Although theoretically possible, in practice it is difficult to apply loads on the air gaps. To analyse this situation, two different approaches can be studied depending on whether the air gaps between the panels are included explicitly in the problem or not. For a particular case of a solar array of three wings in stowed configuration both modelling philosophies are compared. This stowed configuration of a three wing solar arrays in stowed configuration has been tested in an acoustic chamber. The measured data on the solar wings allows, in general, determining the loss factors of the configuration. The paper presents a test description and measurements on the structure, in terms of the acceleration power spectral density. Finally, the performance of each modelling technique has been evaluated by comparison between simulations with experimental results on a spacecraft solar array and the influence on the apparent properties of the system in terms of the SEA loss factors has been analyse

LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of $d-$dimensional Anderson models on $l^2(\Z^d)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman-Molchanov to get exponential estimates on fractional moments of the matrix elements of $U_\omega(U_\omega -z)^{-1}$, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of $S$. Such estimates imply almost sure localization for $U_\omega$

Quantum interest in two dimensions

The quantum interest conjecture of Ford and Roman asserts that any negative-energy pulse must necessarily be followed by an over-compensating positive-energy one within a certain maximum time delay. Furthermore, the minimum amount of over-compensation increases with the separation between the pulses. In this paper, we first study the case of a negative-energy square pulse followed by a positive-energy one for a minimally coupled, massless scalar field in two-dimensional Minkowski space. We obtain explicit expressions for the maximum time delay and the amount of over-compensation needed, using a previously developed eigenvalue approach. These results are then used to give a proof of the quantum interest conjecture for massless scalar fields in two dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR

Localization for Random Unitary Operators

We consider unitary analogs of $1-$dimensional Anderson models on $l^2(\Z)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of $U_\omega$ is pure point almost surely for all values of the parameter of $S$. We provide similar results for unitary operators defined on $l^2(\N)$ together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunski coefficients of constant modulus and correlated random phases

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output