On Relativistic Perturbations of Second and Higher Order

We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit transformation rules at second order.Comment: 6 pages, latex, with special style included, Proceedings of the 12th Italian Conference on General Relativity and Gravitational Physic

Dynamics of Silent Universes

We investigate the local non--linear dynamics of irrotational dust with vanishing magnetic part of the Weyl tensor, $H_{ab}$. Once coded in the initial conditions, this dynamical restriction is respected by the relativistic evolution equations. Thus, the outcome of the latter are {\it exact solutions} for special initial conditions with $H_{ab}=0$, but with no symmetries: they describe inhomogeneous triaxial dynamics generalizing that of a fluid element in a Tolman--Bondi, Kantowski--Sachs or Szekeres geometry. A subset of these solutions may be seen as (special) perturbations of Friedmann models, in the sense that there are trajectories in phase--space that pass arbitrarily close to the isotropic ones. We find that the final fate of ever--expanding configurations is a spherical void, locally corresponding to a Milne universe. For collapsing configurations we find a whole family of triaxial attractors, with vanishing local density parameter $\Omega$. These attractors locally correspond to Kasner vacuum solutions: there is a single physical configuration collapsing to a degenerate {\it pancake}, while the generic configuration collapses to a triaxial {\it spindle} singularity. These {\it silent universe} models may provide a fair representation of the universe on super horizon scales. Moreover, one might conjecture that the non--local information carried by $H_{ab}$ becomes negligible during the late highly non--linear stages of collapse, so that the attractors we find may give all of the relevant expansion or collapse configurations of irrotational dust.Comment: 40 pages with 4 figures, compressed and uuencoded PostScript file, submitted to ApJ, SISSA preprint Ref. 85/94/

Integrating Dynamics and Wear Modelling to Predict Railway Wheel Profile Evolution

The aim of the work described was to predict wheel profile evolution by integrating multi-body dynamics simulations of a wheelset with a wear model. The wear modelling approach is based on a wear index commonly used in rail wear predictions. This assumes wear is proportional to Tγ, where T is tractive force and γ is slip at the wheel/rail interface. Twin disc testing of rail and wheel materials was carried out to generate wear coefficients for use in the model. The modelling code is interfaced with ADAMS/Rail, which produces multi-body dynamics simulations of a railway wheelset and contact conditions at the wheel/rail interface. Simplified theory of rolling contact is used to discretise the contact patches produced by ADAMS/Rail and calculate traction and slip within each. The wear model combines the simplified theory of rolling contact, ADAMS/Rail output and the wear coefficients to predict the wear and hence the change of wheel profile for given track layouts

General formulation of general-relativistic higher-order gauge-invariant perturbation theory

Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing the general framework of the second-order gauge-invariant perturbation theory, we show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant parts, which was the important premis of this general framework. This means that the development the higher-order gauge-invariant perturbation theory on generic background spacetime is possible. A remaining issue to be resolve is also disscussed.Comment: 4 pages, no figure. (v3) some explanations are added and a reference is adde

Nets, relations and linking diagrams

In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the composition of spans over appropriate categories of relations, and study the underlying algebraic structures.Comment: 15 pages, Proceedings of 5th Conference on Algebra and Coalgebra in Computer Science (CALCO), Warsaw, Poland, 3-6 September 201

Human-Automation Collaboration in Complex Multivariate Resource Allocation Decision Support Systems

In resource allocation problems for systems with moving planning horizons and significant uncertainty, typical of supervisory control environments, it is critical that some balance of human-automation collaboration be achieved. These systems typically require leveraging the computational power of automation, as well as the experience and judgment of human decision makers. Human-automation collaboration can occur through degrees of collaboration from automation-centric to human-centric, and such collaboration is inherently distinct from previously-discussed levels of automation. In the context of a command and control mission planning task, we show that across a number of metrics, there is no clear dominant human-automation collaboration scheme for resource allocation problems using three distinct instantiations of human-automation collaboration. Rather, the ultimate selection for the best resource allocation decision support system will depend on a cost-benefit approach that could include mitigation of workload, conformance to intended design characteristics, as well as the need to maximize overall mission performance

Cosmic no-hair: non-linear asymptotic stability of de Sitter universe

We study the asymptotic stability of de Sitter spacetime with respect to non-linear perturbations, by considering second order perturbations of a flat Robertson-Walker universe with dust and a positive cosmological constant. Using the synchronous comoving gauge we find that, as in the case of linear perturbations, the non-linear perturbations also tend to constants, asymptotically in time. Analysing curvature and other spacetime invariants we show, however, that these quantities asymptotically tend to their de Sitter values, thus demonstrating that the geometry is indeed locally asymptotically de Sitter, despite the fact that matter inhomogeneities tend to constants in time. Our results support the inflationary picture of frozen amplitude matter perturbations that are stretched outside the horizon, and demonstrate the validity of the cosmic no-hair conjecture in the nonlinear inhomogeneous settings considered here.Comment: 8 pages, REVTEX, submitted to Physical Review Lette

A new CAE procedure for railway wheel tribological design

New demands are being imposed on railway wheel wear and reliability to increase the time between wheel reprofiling, improve safety and reduce total wheelset lifecycle costs. In parallel with these requirements, changes in railway vehicle missions are also occurring. These have led to the need to operate rolling stock on track with low as well as high radius curves; increase speeds and axle loads; and contend with a decrease in track quality due to a reduction in maintenance. These changes are leading to an increase in the severity of the wheel/rail contact conditions, which may increase the likelihood of wear or damage occurring. The aim of this work was to develop a new CAE design methodology to deal with these demands. The model should integrate advanced numerical tools for modelling of railway vehicle dynamics and suitable models to predict wheelset durability under typical operating conditions. This will help in designing wheels for minimum wheel and rail wear; optimising railway vehicle suspensions and wheel profiles; maintenance scheduling and the evaluation of new wheel materials. This work was carried out as part of the project HIPERWheel, funded by the European Community within the Vth Framework Programme