 |
Nader Masmoudi (born 1974 in Sfax) is a Tunisian mathematician.
|
Nader Masmoudi (born 1974 in Sfax) is a Tunisian mathematician.
He studied in Tunis and then at the École normale supérieure in Paris with a diploma in 1996; In 1999 he received his doctorate from the University of Paris-Dauphine with Pierre-Louis Lions (Problemes asymptotiques en mecanique des fluides). [1] He then went to the Courant Institute at New York University, where he became a professor in 2008.
Masmoudi is particularly concerned with nonlinear partial differential equations of hydrodynamics (Euler equation, Navier-Stokes equation, surface waves, gravity waves, capillary waves, acoustic waves, boundary layer equations and qualitative behavior of boundary layers, Couette flow, non-Newtonian fluids, nonlinear Schrödinger equations for waves and others dispersive systems, etc.), hydrodynamic limit value of the Boltzmann equation, limit behavior to incompressibility, chemotaxis (Keller-Segel equations), the Ginsburg-Landau equation, Landau damping, behavior of mixtures, general long-term behavior of semilinear systems of partial differential equations and stability problems in hydrodynamics . In 2013, together with his post-doctoral student Jacob Bedrossian, he strictly demonstrated the stability of the shear flow according to Couette for the two-dimensional Euler equations, i.e. in the non-linear case. The stability in linear approximation was already proven by Lord Kelvin in 1887 and more precisely by William McFadden Orr in 1907. He also obtained similar stability results in the viscous case for the boundary layer formation according to Prandtl in the two-dimensional Navier-Stokes equations (the linear theory is named here after Orr and Arnold Sommerfeld: Orr-Sommerfeld equations). [2] He built on the work on a similar problem by Cédric Villani, who dealt with Landau damping, the damping of plasma waves, which in a strictly mathematical treatment also results from non-viscous phenomena (strong smoothness properties and mixing, sometimes non-viscous damping called (inviscid damping), technically so-called Gevrey regularity) resulted. Possible instabilities also result from non-linear resonances between different waves in the plasma (non-linear build-up with the “echoes” of the waves) and must be “mathematically controlled” in order to prove stability. The behavior of plasmas and non-viscous liquids described by the Euler equation is similar.
In 1992 he received a gold medal at the International Mathematical Olympiad (as the first African or Arab at all). For 2017 he received the Fermat Prize. [3] In 2018 he was invited speaker at the International Congress of Mathematicians in Rio de Janeiro. In 2021 Masmoudi was elected to the American Academy of Arts and Sciences. In 2022 he was awarded the International King Faisal Prize [4] jointly with Martin Hairer.
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.
The Navier–Stokes equations are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector.
In fluid dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular, they correspond to the Navier–Stokes equations with zero viscosity and zero thermal conductivity.
In fluid dynamics, d'Alembert's paradox is a paradox discovered in 1752 by French mathematician Jean le Rond d'Alembert. d'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to the fluid. Zero drag is in direct contradiction to the observation of substantial drag on bodies moving relative to fluids, such as air and water; especially at high velocities corresponding with high Reynolds numbers. It is a particular example of the reversibility paradox.
Aeroacoustics is a branch of acoustics that studies noise generation via either turbulent fluid motion or aerodynamic forces interacting with surfaces. Noise generation can also be associated with periodically varying flows. A notable example of this phenomenon is the Aeolian tones produced by wind blowing over fixed objects.
Fluid mechanics is the branch of physics concerned with the mechanics of fluids and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
In fluid dynamics, inviscid flow is the flow of an inviscid fluid which is a fluid with zero viscosity.
Bram van Leer is Arthur B. Modine Emeritus Professor of aerospace engineering at the University of Michigan, in Ann Arbor. He specializes in Computational fluid dynamics (CFD), fluid dynamics, and numerical analysis. His most influential work lies in CFD, a field he helped modernize from 1970 onwards. An appraisal of his early work has been given by C. Hirsch (1979)
In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence. The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows.
In applied mathematics, the name finite pointset method is a general approach for the numerical solution of problems in continuum mechanics, such as the simulation of fluid flows. In this approach the medium is represented by a finite set of points, each endowed with the relevant local properties of the medium such as density, velocity, pressure, and temperature.
Laure Saint-Raymond is a French mathematician, and a professor of mathematics at Institut des Hautes Études Scientifiques (IHES). She was previously a professor at École Normale Supérieure de Lyon. She is known for her work in partial differential equations, and in particular for her contributions to the mathematically rigorous study of the connections between interacting particle systems, the Boltzmann equation, and fluid mechanics. In 2008 she was awarded the European Mathematical Society Prize, with her citation reading:
Saint-Raymond is well known for her outstanding results on nonlinear partial differential equations in the dynamics of gases and plasmas and also in fluid dynamics. [...] Saint-Raymond is at the origin of several outstanding and difficult results in the field of nonlinear partial differential equations of mathematical physics. She is one of the most brilliant young mathematicians in her generation.
The Darrieus–Landau instability or hydrodynamic instability is an instrinsic flame instability that occurs in premixed flames, caused by the density variation due to the thermal expansion of the gas produced by the combustion process. In simple terms, the stability inquires whether a steadily propagating plane sheet with a discontinuous jump in density is stable or not. It was predicted independently by Georges Jean Marie Darrieus and Lev Landau. Yakov Zeldovich notes that Lev Landau generously suggested this problem to him to investigate and Zeldovich however made error in calculations which led Landau himself to complete the work.
In fluid dynamics, Squire's theorem states that of all the perturbations that may be applied to a shear flow, the perturbations which are least stable are two-dimensional, i.e. of the form , rather than the three-dimensional disturbances. This applies to incompressible flows which are governed by the Navier–Stokes equations. The theorem is named after Herbert Squire, who proved the theorem in 1933.
In fluid dynamics, Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible and inviscid shear flow. The equation is:
François Golse is a French mathematician.
Walter Alexander Strauss is an American applied mathematician, specializing in partial differential equations and nonlinear waves. His research interests include partial differential equations, mathematical physics, stability theory, solitary waves, kinetic theory of plasmas, scattering theory, water waves, and dispersive waves.
Eduard Feireisl is a Czech mathematician.
This timeline describes the major developments, both experimental and theoretical understanding of fluid mechanics and continuum mechanics. This timeline includes developments in:
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
