Eigenmode Analysis of Boundary Conditions for the One-Dimensional Preconditioned Euler Equations

The effect of local preconditioning on boundary conditions is analyzed for the subsonic, one-dimensional Euler equations. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions and different preconditioners whose intent is to accelerate low Mach number computations. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective when used with preconditioning, and asymptotically, at low Mach numbers, initial disturbances do not decay. Other boundary conditions are shown to be perfectly non-reflective in conjunction with preconditioning. Two-dimensional numerical results confirm the trends predicted by the one-dimensional analysis

Multigrid Renormalization

We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for solving partial differential equations. When the solution on a grid of $N$ points is sought, our MGR method has a computational cost scaling as $\mathcal{O}(\log(N))$, as opposed to $\mathcal{O}(N)$ for the best standard MG method. Therefore MGR can exponentially speed up standard MG computations. To illustrate our method, we develop a novel algorithm for the ground state computation of the nonlinear Schr\"{o}dinger equation. Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem. We compare several different methods for the nonlinear tensor update and find that the Newton method is the most efficient as well as precise. The combination of MGR with our nonlinear ground state algorithm produces accurate results for the nonlinear Schr\"{o}dinger equation on $N = 10^{18}$ grid points in three spatial dimensions.Comment: 18 pages, 17 figures, accepted versio

The Influence of Unstructured Mesh Type on the Prediction of Convoluted Shear Layers

Lobed mixers are used in gas turbine engines to enhance mixing between hot and cold streams and to reduce noise. Computational modelling of such systems has previously been carried out on structured meshes, although mesh generation difficulties have encouraged the use of unstructured tetrahedral meshes. However, the ability of numerical schemes to predict the mixing behaviour correctly on tetrahedral meshes has not been studied and is the subject of this work. Three different mesh types for the mixing region resolution have been studied: purely hexahedral, purely tetrahedral, and a mixed mesh combining hexahedra, tetrahedra and pyramids. Results are presented for the evolution of both a planar and a convoluted turbulent shear layer. In regions of high shear, misalignment of control volume faces has a major influence on spurious numerical spreading of the shear layer. For the tetrahedral mesh, there is an initial rapid mixing, followed by a reduction in mixing rate. The smoothing terms present are triggered by the combination of a high gradient across a control volume face and a velocity normal to that face; this occurs on the diagonal edges of tetrahedral meshes. The magnitude of the spurious smoothing is diminished by increasing the aspect ratio of the cells. For lobed mixer predictions, a mixed mesh with aligned high aspect ratio hexahedral elements in the shear layer region and pyramids and tetrahedra linking to the outer domain provides a good compromise between ease of mesh generation and quality of solution.\ud \ud The authors would like to acknowledge funding from the Engineering and Physical Sciences Research Council (UK), Grant No. GR/L17863. Financial assistance and technical review monitoring was also provided by Rolls-Royce and DERA; the authors would like to thank in particular Dr Leigh Lapworth (RR), Dr Jens-Dominik Müller (Oxford University) and Prof Mike Giles (Oxford University)

Variational quantum algorithms for nonlinear problems

We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schr\"{o}dinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.Comment: 8 pages, 3 figures + Supplemental Material (7 pages, 7 figures), accepted versio

Eigenmode Analysis for Turbomachinery Applications

This paper discusses the numerical computation of unsteady eigenmodes superimposed upon an annular mean ow which is uniform axially and circumferentially, but non-uniform in the radial direction. Both inviscid and viscous ows are considered, and attention is paid to the separation of the eigenmodes into acoustic, entropy and vorticity modes. The numerical computations are validated by comparison to analytic test cases, and results are presented for more realistic engineering applications, showing the utility of the approach for post-processing and for the construction of non-reecting boundary condition

Autofertilité: Définition

National audienceAutofertility defines a soil able to preserve its own fertility, i.e. how easy it is for a plant to benefit, in sufficient quantity, through its roots and in the soil, from different factors of plant growth. A soil’s autofertility depends on its biological activity, impacting the physical and chemical self-fertility...L’autofertilité définit un sol capable de maintenir de lui-même sa fertilité, c’est à dire la facilité avec laquelle une plante, via ses racines, peut bénéficier dans ce sol des différents facteurs de croissance végétale, en quantité suffisante. L’autofertilité d’un sol dépend de son activité biologique, impactant l’autofertilité physique et chimique..

Geotechnologies as tools for managing cultural heritage: the need to train future professionals

International audienceTerritories and towns change sometimes slowly, sometimes abruptly. For example, landscapes can be transfigured. Buildings or entire neighbourhoods can be demolished. Nevertheless, History, memory, events that took place there, remain immutable. Most often, inhabitants can have difficulties to imagine the exact context where these events occurred. Furthermore, managers need to be able to analyze and to understand the past the best way, but also enhance cultural heritage, especially for the general public. So, cultural heritage experts need to use efficient tools. Methods Geotechnologies appear as important tools to explain and understand the past. The digitizationof archival records, the creation of new data, the construction of geographic database... The creation of geographic information systems (GIS) or 3D GIS make the archiving of memories possible. They provide methods of analysis, understanding, preservation and management of cultural heritage. They are effective tools against oblivion. Results Using two different examples which mobilize two different kinds of cultural heritages, we will show that it is possible to acquire, archive, analyze and enhance cultural heritages. The first example focuses on the 3D geovisualization which allows restoring the visibility of sunken heritage sites, in a context of large reservoir dams. The second one deals with an interactive 3D map showing locations of the resistance and collaborationism movements in a town, during World War II. Conclusion Students of cultural heritage curriculum will be the next generation of professionals and experts. In this regard, it is essential to train them or at least to make them aware of geotechnologies. Especially since the methodologies developed in these contexts providing two important other skills: transdisciplinarity and teamwork

Proteome analysis of Rickettsia felis highlights the expression profile of intracellular bacteria.

The proteome of Rickettsia felis, an obligate intracellular bacterium responsible for spotted fever, was analyzed using two complementary proteomic approaches: 2-DE coupled with MALDI-TOF, and SDS-PAGE with nanoLC-MS/MS. This strategy allowed identification of 165 proteins and helped to answer some questions raised by the genome sequence of this bacterium. We successfully identified potential virulence factors including two putative adhesins, four proteins of the type IV secretion system, four Sca autotransporters, four components of ABC transporters, some R. felis-specific proteins, and one antitoxin of the toxin-antitoxin system. Notably, the antitoxin was the first to be identified in intracellular bacteria. Only one protein containing rickettsia palindromic repeats was found, whereas none of the split genes, transposases, or tetratricopeptide/ankyrin repeats were detectably expressed. Comparison of the protein expression profiles of R. felis and 23 other bacterial species according to functional categories showed that intracellular bacteria express more proteins related to translation, especially ribosomal proteins. However, the remaining bacteria express more proteins related to energy production and carbohydrate/amino acid metabolism. In conclusion, this study reveals R. felis virulence factor expression and highlights the unique protein expression profile of intracellular bacteria