Statistical energy analysis computer program, user's guide

A high frequency random vibration analysis, (statistical energy analysis (SEA) method) is examined. The SEA method accomplishes high frequency prediction of arbitrary structural configurations. A general SEA computer program is described. A summary of SEA theory, example problems of SEA program application, and complete program listing are presented

Fields in Nonaffine Bundles. I. The general bitensorially covariant differentiation procedure

The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the usual requirement that the base space should be flat or endowed with its own linear connection, and that there should be an ordinary gauge connection on the bundle, it is necessary to require also that there should be an intrinsic, bundle-group invariant connection on the fibre space. The procedure is based on the use of an appropriate primary-field (i.e. section) independent connector that is constructed in terms of the natural fibre-tangent-vector realisation of the gauge connection. The application to gauged harmonic mappings will be described in a following article.Comment: 17 page Latex file with some minor misprint corrections and added color for article originally published in black and whit

On h h -transforms of one-dimensional diffusions stopped upon hitting zero

For a one-dimensional diffusion on an interval for which 0 is the regular-reflecting left boundary, three kinds of conditionings to avoid zero are studied. The limit processes are $h$-transforms of the process stopped upon hitting zero, where $h$'s are the ground state, the scale function, and the renormalized zero-resolvent. Several properties of the $h$-transforms are investigated

Measures of gravitational entropy I. Self-similar spacetimes

We examine the possibility that the gravitational contribution to the entropy of a system can be identified with some measure of the Weyl curvature. In this paper we consider homothetically self-similar spacetimes. These are believed to play an important role in describing the asymptotic properties of more general models. By exploiting their symmetry properties we are able to impose significant restrictions on measures of the Weyl curvature which could reflect the gravitational entropy of a system. In particular, we are able to show, by way of a more general relation, that the most widely used "dimensionless" scalar is \textit{not} a candidate for this measure along homothetic trajectories.Comment: revtex, minor clarifications, to appear in Physical Review

Statistical energy analysis of complex structures, phase 2

A method for estimating the structural vibration properties of complex systems in high frequency environments was investigated. The structure analyzed was the Materials Experiment Assembly, (MEA), which is a portion of the OST-2A payload for the space transportation system. Statistical energy analysis (SEA) techniques were used to model the structure and predict the structural element response to acoustic excitation. A comparison of the intial response predictions and measured acoustic test data is presented. The conclusions indicate that: the SEA predicted the response of primary structure to acoustic excitation over a wide range of frequencies; and the contribution of mechanically induced random vibration to the total MEA is not significant

Navigation in Curved Space-Time

A covariant and invariant theory of navigation in curved space-time with respect to electromagnetic beacons is written in terms of J. L. Synge's two-point invariant world function. Explicit equations are given for navigation in space-time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer's coordinate time when their spatial position is known is also considered

Almost-stationary motions and gauge conditions in General Relativity

An almost-stationary gauge condition is proposed with a view to Numerical Relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is derived by a variational principle, by minimizing the deviations from isometry. The corresponding almost-stationary gauge condition allows one to put the field equations in hyperbolic form, both in the free-evolution ADM and in the Z4 formalisms.Comment: Talk presented at the Spanish Relativity Meeting, September 6-10 2005 Revised versio

Routh's procedure for non-Abelian symmetry groups

We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum in velocity phase space. We present a new method of analysis based on the use of quasi-velocities. We discuss the reconstruction of solutions of the full Euler-Lagrange equations from those of the reduced equations.Comment: 30 pages, to appear in J Math Phy

Generalized Farey trees, transfer Operators and phase transitions

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral analysis of generalized transfer operators. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.Comment: 39 pages, 10 figure