Related papers: Lecture notes on variational models for incompress…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
The purpose of this note is to show how simple Optimal Transport arguments, on the real line, can be used in Superconcentration theory. This methodology is efficient to produce sharp non-asymptotic variance bounds for various functionals…
In this review, we examine the problem of designing interpretable and explainable machine learning models. Interpretability and explainability lie at the core of many machine learning and statistical applications in medicine, economics,…
Lecture notes of lectures delivered at the Hodge Theory Summer School in ICTP Trieste, June 2010.
This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the…
These notes closely correspond to a series of lectures given by the first author in Toulouse, on the recent extension of the theory of ODE well-posedness to abstract spaces, jointly obtained by the two authors. In the last part, we describe…
The Euler and Navier-Stokes fluid mechanics equations are derived using a modified statistical mechanical approach using theory taken from the Chapman-Enskog perturbation analysis used to support the lattice Boltzmann method. Additional…
These notes are an account of a series of lectures given at the Les Houches Summer School "Active Matter and Non-equilibrium Statistical Physics" during August and September 2018. The lectures can be viewed online at…
We show two new conserved quantities for the three-dimensional incompressible Euler equations. Due to professor Lin's comments, these quantities are deeply related to the concept of topological degree and not new. I will post a new version…
Transference numbers play an important role for understanding the dynamics of electrolytes and assessing their performance in batteries. Unfortunately, these transport parameters are difficult to measure in highly concentrated, liquid…
In this thesis I develop a variety of techniques to train, evaluate, and sample from intractable and high dimensional probabilistic models. Abstract exceeds arXiv space limitations -- see PDF.
This study focuses on the exact observability of a non-classical Euler-Bernoulli micro-beam equation. This non-classical model was derived based on the strain gradient elasticity theory, which is intended to explain the phenomenon of size…
An inviscid two-dimensional fluid model with nonlinear dispersion that arises simultaneously in coarse-grained descriptions of the dynamics of the Euler equation and in the description of non-Newtonian fluids of second grade is considered.…
This manuscript is a shorthand version of my talk given at Odessa Gamov School on Astronomy, Cosmology and Beyond (22-28 August 2011, Odessa, Ukraine). Within this note we very briefly review the main achievements, new results and open…
The debate on OPERA focused on two extremes: either "OPERA is wrong" or our formulation of the laws of physics needs a major overhaul. I here argue that some effort should be directed toward manifestations of laws that are already known,…
Lectures at the CRM-CAP Summer School 'Particles and Fields 94' August 16-24 1994, Banff, Alberta, Canada.
These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.
This is an adapatation by U. Frisch of an English translation by Thomas E. Burton of Euler's memoir `Principes g\'en\'eraux du mouvement des fluides' (Euler, 1775b). Burton's translation appeared in Fluid Dynamics, 34} (1999) pp. 801-82,…
Submitted by the authors for the June 27-29 Princeton Conference. Questions should be directed to: [email protected]
We derive a new version of the von K\'arm\'an energy and the corresponding Euler-Langrange equations, in the context of thin prestrained plates, under the condition of incompressibility relative to the given prestrain. Our derivation uses…