Programas de Pós-Grad. Promovem Minicursos e Palestras

Olá leitor!

Segue abaixo uma nota postada hoje (21/09) no site do Instituto Nacional de Pesquisas Espaciais (INPE) destacando que programas de pós-graduação do INPE promoverão nos dias 24 e 25/09 Minicursos e Palestras nas áreas de Computação Aplicada e Geofísica Espacial.

Duda Falcão

Programas de Pós-Graduação Promovem

Minicursos e Palestras nas Áreas de

Computação Aplicada e Geofísica Espacial

Sexta-feira, 21 de Setembro de 2012

Nos dias 24 e 25 de setembro, pesquisadores e estudantes poderão participar de palestras e minicursos promovidos pelos programas de pós-graduação em Geofísica Espacial (GES) e Computação Aplicada (CAP) do Instituto Nacional de Pesquisas Espaciais (INPE), em São José dos Campos.

Aberta a todos os interessados, a programação é parte do Simpósio VI WWlet 2012 - Wavelets & Aplicações, que neste ano integra o Congresso Nacional de Computação e Matemática Aplicada (CNMAC 2012). O evento conta com o apoio da FAPESP, CAPES e CNPq.

Ministrados em inglês, os minicursos e palestras serão realizados no auditório do IAI, das 13h30 às 17h30, conforme a agenda abaixo:

Program

Monday (Sept. 24, 2012)

Wavelet-based density estimation for noise reduction in plasma simulations using particles

By : Romain Nguyen van yen (Freie University Berlin, Germany)  and  Kai Schneider (Aix-Marseille University, France)

A parallel fast wavelet transform and its application to turbulent flow analysis and computation.

By: Romain Nugyen van yen (Freie University Berlin, Germany)

Tuesday (Sept. 25, 2012)

D’Alembert’s paradox and the resistance of fluid flows in the fully-developed turbulent regime: still an open problem.

By: Marie Farge (ENS, Paris, France)

High dimensional covariance modelling based on wavelets. (Mini lecture on fractal and wavelets)

By: Olivier Pannekoucke (Meteo-France, France)

Content

Monday

1 - Wavelet-based density estimation for noise reduction in plasma simulations using particles

For given computational resources, the accuracy of plasma simulations using particles is mainly limited by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a nite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finnite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Moreover, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets involving different levels of collisionality and interaction with external and self-consistent fields. As perspective we also present a new numerical scheme called particle-in-wavelets for solving the Vlasov-Poisson equations. The method is tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. This work is joint work with Diego del-Castillo-Negrete, Marie Farge and Guangye Chen.

2 - A parallel fast wavelet transform and its application to turbulent flow analysis and computation

When fluids and plasmas are set into motion and start to flow, they carry their on momentum according to Newton’s first law of motion. Each region wants to continue to flow in its own direction, and overall the fluid develops complex patterns with many scales. These patterns are very sensitive to initial conditions and external perturbations, and often cannot be predicted exactly. But their partial prediction is crucial for many recent applications, in meteorology, engineering, fusion science, astrophysics, etc. Two ingredients are essential to achieve this partial prediction: − a representation of the flow which efficiently distinguishes what is predictable and what is not predictable, - efficient algorithms running on parallel computers. Even when the prediction is made, it can be highly uncertain, which places us under the threat of fake interpretation, wishful thinking, and misunderstandings between communities. The goal of this mini-course is to introduce a consistent way to think about these problems and solve them, based on wavelet theory, a major new mathematical tool developed since the 1980’s. We will work our way from the mathematical theory and computational implementation, to the physical interpretation. For the sake of brevity and clarity we will limit ourselves to 1D and 2D academic cases.

Topics

1. Introduction to the problem

(a) The 1D Vlasov equation

(b) The 2D Navier-Stokes equations

2. Mathematical wavelet theory

(a) Hilbert spaces of functions

(b) Multiresolution analysis

(c) Construction of the wavelet filter

(d) Examples

3. Implementation

Tuesday

3 - D’Alembert’s paradox and the resistance of fluid flows in the fully-developed turbulent regime: still an open problem.

When fluid flows reach the fully-developed turbulent regime, one observes that the dissipation rate becomes independent of the fluid viscosity. We conjecture that, when the Reynolds number Re tends to infinity, viscous dissipation becomes negligible and turbulent dissipation, triggered by the nonlinear flow dynamics, takes over. To study this, we consider the generic case of a jet hitting a wall and perform direct numerical simulations of the two-dimensional Navier-Stokes equations in the vanishing viscosity limit, using volume penalization method to take into account the wall.  We show that the energy dissipation first sets up within very thin vorticity sheets, which then detach from the wall and  roll up into spirals where dissipation is maximal. We thus propose a new explanation of the d'Alembert's paradox (1752) based on turbulent dissipation rather than on viscous dissipation. Our results are compatible with Kato's theorem (1984) which proves that for dissipation to occur, anywhere in the flow and at any time, at least some dissipation had to occur in the vanishing viscosity limit within very thin boundary layers whose thickness is proportional to Re^{-1}.

4 - High dimensional covariance modelling based on wavelets.

Data assimilation aims to provide an optimal estimation of the numerical representation of system knowing observations. From linear estimation theory, this optimum results as the combination of a prior state, called the background, and the observations. This implies to estimate and specify high dimensional covariance matrix, especially the background error covariance matrix. This talk describes several use of wavelets to estimate and to represent background error covariance matrix. A first use relies on the diagonal assumption in wavelets space (spherical wavelets, Kingsbury's wavelets) where wavelet functions are assumed to be principal directions of the covariance matrix. A second application concerns the use of deformation of simple correlations where the deformation is estimated from ensemble diagnosis by using wavelets.

5 - Mini-lecture program on fractal and wavelets:

In this mini-lecture we will describe what is called a fractal object while providing mathematical background to study it. This allows us to introduce the fractal dimension that enlarge classical integer dimensions. Some example of fractal set  will be presented and featured in term of dimension. The fractal dimension of a set of point associated to a given regularity will leads to notion of singularity spectrum and of multi-fractal signal. Estimation and construction of such signal is presented.

Fonte: Site do Instituto Nacional de Pesquisas Espaciais (INPE).