5,378 research outputs found
Free Turbulence on R^3 and T^3
The hydrodynamics of Newtonian fluids has been the subject of a tremendous
amount of work over the past eighty years, both in physics and mathematics.
Sadly, however, a mutual feeling of incomprehension has often hindered
scientific contacts. This article provides a dictionary that allows
mathematicians to define and study the spectral properties of Kolmogorov-Obukov
turbulence in a simple deterministic manner. In other words, this approach fits
turbulence into the mathematical framework of studying the qualitative
properties of solutions of PDEs, independently from any a-priori model of the
structure of the flow. To check that this new approach is correct, this article
proves some of the classical statements that can be found in physics textbooks.
This is followed by an investigation of the compatibility between turbulence
and the smoothness of solutions of Navier-Stokes in 3D, which was the initial
motivation of this study.Comment: 47 pages, 6 figure
JuliBootS: a hands-on guide to the conformal bootstrap
We introduce {\tt JuliBootS}, a package for numerical conformal bootstrap
computations coded in {\tt Julia}. The centre-piece of {\tt JuliBootS} is an
implementation of Dantzig's simplex method capable of handling arbitrary
precision linear programming problems with continuous search spaces. Current
supported features include conformal dimension bounds, OPE bounds, and
bootstrap with or without global symmetries. The code is trivially
parallelizable on one or multiple machines. We exemplify usage extensively with
several real-world applications. In passing we give a pedagogical introduction
to the numerical bootstrap methods.Comment: 29 page
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