Polynomial continuation in the design of deployable structures

Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers’ published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. iv Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage

Viscoelastic Effects in Metal-Polymer Laminate Inflatable Structures

A 1 m long inflatable-rigidizable mast was developed as a payload for InflateSail: a 3U CubeSat technology demonstration mission. The thin-walled cylindrical mast consists of an aluminum-polymer laminate, and long-term structural performance is ensured through strain-rigidization: the packaging creases are removed through plastic deformation of the aluminum plies. During ground tests it was observed that after rigidization the internal pressure dropped more rapidly than could be accounted for by leakage of inflation gas alone. It was hypothesized that viscoelastic behaviour of the laminate material causes a further, time-dependent (order of seconds), increase in cylinder diameter, with a corresponding drop in internal pressure. Additional experiments revealed an increase in diameter, including large visco-elastic shear in the adhesive of the lap joint. This was not found to be sufficient to fully account for the observed reduction in pressure. An increase in temperature of the gas during inflation, with subsequent cooling down to ambient is thought to cause the additional pressure drop

Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

A convolutional encoder-decoder-based transformer model has been developed to autoregressively train on spatio-temporal data of turbulent flows. It works by predicting future fluid flow fields from the previously predicted fluid flow field to ensure long-term predictions without diverging. The model exhibits significant agreements for \textit{a priori} assessments, and the \textit{a posterior} predictions, after a considerable number of simulation steps, exhibit predicted variances. Autoregressive training and prediction of \textit{a posteriori} states is the primary step towards the development of more complex data-driven turbulence models and simulations

A review on deep reinforcement learning for fluid mechanics: an update

In the past couple of years, the interest of the fluid mechanics community for deep reinforcement learning (DRL) techniques has increased at fast pace, leading to a growing bibliography on the topic. While the capabilities of DRL to solve complex decision-making problems make it a valuable tool for active flow control, recent publications also demonstrated applications to other fields, such as shape optimization or microfluidics. The present work aims at proposing an exhaustive review of the existing literature, and is a follow-up to our previous review on the topic. The contributions are regrouped by field of application, and are compared together regarding algorithmic and technical choices, such as state selection, reward design, time granularity, and more. Based on these comparisons, general conclusions are drawn regarding the current state-of-the-art in the domain, and perspectives for future improvements are sketched

First evidence for fin whale migration into the Pacific from Antarctic feeding grounds at Elephant Island

Funding: This work was funded by IWC-SORP and by the DFG within the priority programme SPP 1158 ‘Antarctic Research with comparative investigations in Arctic ice areas’ by grant HE5696/3-1. Additional funding from National Geographic / Disney+ supported field efforts by Hickmott.This study presents the first long-distance tracks of fin whales (Balaenoptera physalus) equipped with satellite transmitters off the Antarctic Peninsula. Southern Hemisphere fin whales were severely depleted by twentieth century industrial whaling, yet recently, they have returned to historical feeding grounds off the northern Antarctic Peninsula, forming large aggregations in austral summers. To date, our knowledge only extended to summer behaviour, while information regarding migration routes and the location of breeding and wintering grounds are lacking. During the austral autumn of 2021, we deployed nsatellite transmitters on four fin whales at Elephant Island. Two transmitters stopped working while the animals were still at the feeding grounds, while two continued to transmit during the transition from feeding activity to migration. Both migrating animals left the feeding ground on 15 April 2021, travelling northward into the Pacific and up along the Chilean coast. The most northerly position received before all tags stopped transmitting on 1 May 2021 was at 48°S. These tracks provide initial evidence of seasonal migratory routes and a first indication toward possible locations of winter destinations. This information, even if preliminary, is critical for investigations of population connectivity, population structure and the identification of breeding grounds of Southern Hemisphere fin whales.Publisher PDFPeer reviewe

Fitting experimental dispersion data with a simulated annealing method for nano-optics applications

International audienceA considerable amount of materials in nanophotonics are dispersive, enabling the propagation of so called surface plasmons at their interfaces with dielectrics. Hence, a reliable fit of frequency-dependent permittivity functions with an appropriate model is a first-order necessity for the accurate design of nano-optics devices with time-domain numerical methods, such as finite-difference time-domain (FDTD) or discontinuous Galerkin time-domain (DGTD). In this paper, we present the necessary ingredients to fit experimental permittivity functions using the simulated annealing (SA) method with a generalized second-order dispersion model implemented in the Diogenes software suite (see https://diogenes. inria.fr/). By scanning through different classes of materials, we come up with effective rules of thumb to make the fitting process fast and accurate

Review of inflatable booms for deployable space structures: Packing and rigidization

Inflatable structures offer the potential of compactly stowing lightweight structures, which assume a fully deployed state in space. An important category of space inflatables are cylindrical booms, which may form the structural members of trusses or the support structure for solar sails. Two critical and interdependent aspects of designing inflatable cylindrical booms for space applications are i) packaging methods that enable compact stowage and ensure reliable deployment, and ii) rigidization techniques that provide long-term structural ridigity after deployment. The vast literature in these two fields is summarized to establish the state of the art.The work described in this paper forms part of the DeployTech project; the authors gratefully acknowledge the funding from the European Commission Seventh Framework Programme (FP7).This is the accepted, peer-reviewed manuscript of an article originally published in the Journal of Spacecraft and Rockets. The final published version is available at http://arc.aiaa.org/doi/abs/10.2514/1.A32598

Efficient time-domain numerical analysis of waveguides with tailored wideband pulses

A simple procedure for the generation of accurate polychromatic sources in waveguides taking into account mode dispersion is presented. It allows for an efficient use of time-domain solvers in the analysis of guided modes, and can be used wether the mode dispersion and field distribution are known analytically or numerically. This method is implemented in the DIOGENES Discontinuous Galerkin Time-Domain (DGTD) solver (http://diogenes.inria.fr), and is validated on a waveguide mode converter