Creation of helicopter dynamic systems digital twin using multibody simulations

International audienceThis paper presents a new approach to develop digital twins of helicopter dynamic systems. Helicopter industries attach growing attention to the development of digital twins to be more predictive of mechanical parts lifetime. The number of sensors available to measure loads during flights is limited. Complementary simulations are necessary to compute all the loads that the mechanical parts undergo. A new process is described to build these simulations fed with flights data records. Complexity of helicopters dynamics systems leads to create several local models of subsystems using a multibody dynamic formalism. A study focused on a swashplate rotor assembly is presented to illustrate this approach, including a new model of bearing and its validation based on bench tests

Random Dirac operators with time-reversal symmetry

Quasi-one-dimensional stochastic Dirac operators with an odd number of channels, time reversal symmetry but otherwise efficiently coupled randomness are shown to have one conducting channel and absolutely continuous spectrum of multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and Goldsheid-Margulis to the analysis of random products of matrices in the group SO$^*(2L)$, and then a version of Kotani theory for these operators. Absence of singular spectrum can be shown by adapting an argument of Jaksic-Last if the potential contains random Dirac peaks with absolutely continuous distribution.Comment: parts of introduction made more precise, corrections as follow-up on referee report

On compression of Bruhat-Tits buildings

We obtain an analog of the compression of angles theorem in symmetric spaces for Bruhat--Tits buildings of the type $A$. More precisely, consider a $p$-adic linear space $V$ and the set $Lat(V)$ of all lattices in $V$. The complex distance in $Lat(V)$ is a complete system of invariants of a pair of points of $Lat(V)$ under the action of the complete linear group. An element of a Nazarov semigroup is a lattice in the duplicated linear space $V\oplus V$. We investigate behavior of the complex distance under the action of the Nazarov semigroup on the set $Lat(V)$.Comment: 6 page

Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian

Annex III: Scenarios and modelling methods

The use of scenarios and modelling methods are pillars in IPCC Working Group III (WGIII) Assessment Reports. Past WGIII assessment report cycles identified knowledge gaps about the integration of modelling across scales and disciplines, mainly between global integrated assessment modelling methods and bottom-up modelling insights of mitigation responses. The need to improve the transparency of model assumptions and enhance the communication of scenario results was also recognised. This annex on Scenarios and Modelling Methods aims to address some of these gaps by detailing the modelling frameworks applied in the WGIII Sixth Assessment Report (AR6) chapters and disclose scenario assumptions and its key parameters. It has been explicitly included in the Scoping Meeting Report of the WGIII contribution to the AR6 and approved by the IPCC Panel at the 46th Session of the Panel