Vectorial interpolation using radial-basis-like functions

AbstractThis paper deals with vector field interpolation, i.e., the data are R3 values located in scattered R3 points, while the interpolating function is a function from R3 into R3. In order to take into account possible connections between the components of the interpolant, we derive it by solving a variational spline problem involving the rotational and the divergence of the interpolant, and depending on a parameter ρ significative of the balance of the rotational part and of the divergence part, and on the order m of derivatives of the rotational and divergence involved in the minimized seminorm. We so obtain interpolants whose expression is σ(x) = Σni=1 Φ(x − xi)ai + pm−1(x), where Φ is some 3 × 3 matrix function, pm−1 is a degree m − 1 vectorial polynomial, and where the ai are R3-vectors. Besides, the ai meet a relation generalizing the usual orthogonality to all polynomials of degree at most m − 1. For ρ = 1, we find the usual m-harmonic splines in each component of σ. Numerical examples show the interest of the method, and we compare the so-obtained functions with the ones obtained by Matlab's procedures

The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths

We present the Planck Sky Model (PSM), a parametric model for the generation of all-sky, few arcminute resolution maps of sky emission at submillimetre to centimetre wavelengths, in both intensity and polarisation. Several options are implemented to model the cosmic microwave background, Galactic diffuse emission (synchrotron, free-free, thermal and spinning dust, CO lines), Galactic H-II regions, extragalactic radio sources, dusty galaxies, and thermal and kinetic Sunyaev-Zeldovich signals from clusters of galaxies. Each component is simulated by means of educated interpolations/extrapolations of data sets available at the time of the launch of the Planck mission, complemented by state-of-the-art models of the emission. Distinctive features of the simulations are: spatially varying spectral properties of synchrotron and dust; different spectral parameters for each point source; modeling of the clustering properties of extragalactic sources and of the power spectrum of fluctuations in the cosmic infrared background. The PSM enables the production of random realizations of the sky emission, constrained to match observational data within their uncertainties, and is implemented in a software package that is regularly updated with incoming information from observations. The model is expected to serve as a useful tool for optimizing planned microwave and sub-millimetre surveys and to test data processing and analysis pipelines. It is, in particular, used for the development and validation of data analysis pipelines within the planck collaboration. A version of the software that can be used for simulating the observations for a variety of experiments is made available on a dedicated website.Comment: 35 pages, 31 figure

Velocity Measurements within High Velocity Air-Water Jets

High velocity turbulent jets are often used in hydraulic structures to dissipate energy and to induce or enhance air entrainment. Examples include ski jumps and bottom aeration devices. This article presents new air concentration and velocity measurements performed in the flow development region of high velocity water jets. The measurements were obtained using a two-tips conductivity probe. The data are compared with analytical air concentration profiles derived from the diffusion equation, and theoretical velocity profiles of turbulent shear layers. The results highlight that the lower jet interface defined as C = 90% coincides with the streamline of maximum velocity gradient

Utilisation du Cloud StratusLab : tests de performance des clusters virtuels

Cloud computing offers IT resources on demand. This recent infrastructure in computing framework recovers three services named IaaS (Infrastructure-as-a-Service), PaaS (Platform-as-a-Service) and SaaS (Software-as-a-Service). In this work, we have focused on the IaaS layer which allows to provide virtual machine, cluster and storage on demand. We have tested the performance of the StratusLab Cloud (european research project) to determine advantages and disadvantages of Cloud computing for numerical simulation and data analysis. The academic StratusLab Cloud is a public open-source Cloud and it provides full Cloud solution: OpenNebula virtual infrastructure manager, computing resources and end-user client to instantiate and manage virtual machines. We have used classical benchmarks usually performed on supercomputers and we have compared our results with previous studies made on public paying Cloud like Amazon EC2, GoGrid and IBM. We have run benchmarks on memory bandwidth, I/O access, MPI communications, scientific applications-like and weak scalability. Furthermore, we have tested file transfer abilities with IRODS (Integrated Rule-Oriented Data System) software and we have run a numerical code to study strong scalability by measuring speedup, efficiency and Karp-Flatt metric. We have concluded that the virtual cluster of the StratusLab Cloud does not allow high performance in MPI involving tests. The slow inter-node communication is due to low virtual network i.e. virtualization layer overhead and Gigabit interconnection as shown in previous studies performed on equivalent paying Cloud. However, the non-MPI results of performed benchmarks are in agreement with classical cluster performances. Thus, the Cloud computing is an interesting solution for prototyping high performance computing applications and for running other types of scientific applications because it provides an easy and quick access to any kind of platform with reasonable resources and performances

Pseudo-polyharmonic vectorial approximation for div-curl and elastic semi-norms

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