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General educational program FME - Grenoble INP - Master MFE - FME Master

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General educational program FME


Signal analysis, random signals and stochastic processes

Instructors: C.Baudet (Prof.UJF) and N. Mordant

In physics and more particularly in fluid mechanics, experimentalists and numericians are frequently faced to a wide variety of random signals. Both the qualitative and quantitative description of such random signals (as opposed to deterministic signals), like those encountered inturbulent situations, require a statistical approach relying on the definitionof proper (reliable) statistical estimators. This course is intended to give some basic knowledge about signal analysis  theory and the correspondingstatistical tools (eg : correlation, spectral estimation) allowing aproper description of both deterministic and random signals of various kinds.As an introduction, the course will start with a classification of signals anda presentation of some of their usual properties (eg : ergodicity,stationnarity). In a second part of the course will be devoted to the theory of  signal representation and decomposition. In a third part, areview of several type of noises (eg : Brownian motions, Poissonprocesses) will be given and their corresponding properties discussed. The effects of sampling and discretization in the conversion from analog to digitalsignals will be discussed in a fourth part of the course. The course will beconcluded by giving a flavour on several modern developments in signal analysis techniques like time-frequency distributions, wavelet decomposition,bi-spectral analysis.

: Random signals, Linear systems.

: Participants are expected to have a background in fluid mechanics and mathematics. None particular experience is required in the field of signal processing.


Numerical simulation and modelling of turbulent flows

: S.Tardu, G. Balarac (MCF INPG), G.-H. Cottet (Prof.UJF)

Turbulence: statistical approach and deterministicapproach. Direct simulation. Filtered equationsand large eddy simulation. Averaged equations and closure problems.
One point closure andtransport equations. Numerical methods for unsteady flows. Spectral methods and compact schemes. Velocity-vorticityformulation for incompressible flows. Vortexdynamics and vortex methods. Example of industrial applications of numericalcodes in complex geometries.

Microfluidics and Nanofluidics

: Laurent Davoust (20H, CR, CNRS)

This course is intended to provide the state-of-the-art information on channel microfluidics as well as on drop microfluidics. Lectures on the fundamentals of microfluidics are illustrated by modern applications of microfluidics (chips, digital lab-on-a-chip, electrophoretic cells...). Complementary lectures focus on the detailed coupling between physical mechanisms evident at small scale or at the vicinity of one interface (capillarity, rheology, physico-sorption and electrostatics at or along surfaces).

Detailed presentation: After a general introduction devoted to microfluidics applications, continuum transport equations (mass, momentum,energy, chemical species, electric potential) are briefly recalled for a fluid bulk whilst they are derived for a fluid interface after introducing Gibbs approach (surface excess quantities).
The course continues with details on the various physical mechanisms which could arise at a small length scale when a liquid is flowing at/along a fluid interface as well as a solid wall (electrokinetics,drop electrowetting, physico-sorption).
The presence of a fluid interface which delimitates a flow at a small scale (motion of a drop for instance) is also taken into account with the introduction of physico-chemical phenomena such as diffusion-limited aging (Ward & Tordai equation), sorption-limited aging, compositionnal Marangoni effect. Thermal or compositional Marangoni effects are typically presented as an efficient driver especially for a small fluid body. Electrohydrodynamics of Taylor-Melcher is presented as a way to promote mixing at the small scale of a drop. Special emphasis is given to competition between mechanical and Maxwell tensors at a liquid surface.This allows students to understand the origin of electrowetting as well as the origin of electrically-induced tangential motion at fluid surfaces.

Key-words: drop, microchannel, electrokinetics, electrowetting, bubble, Langmuir, surface rheology, surfactants, Marangoni effect

Pre-requisites: Participants are expected to demonstrate minimum background in fluid or continuum mechanics or in soft matter. No particular experience is required in the field of microfluidics.

Master MFE - FME Master
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