Applied Fluid Mechanics Colloquium
Date: Mon, Jan 20 2025
Hour: 12:00 - 13:00
Location: Maryam Mirzakhani Seminar Room at BCAM
Speakers: Prof. Tommaso Ruggeri (Università di Bologna and Accademia Nazionale dei Lincei (Italy))
Title: Rational Extended Thermodynamics: A Bridge between Mesoscopic and Macroscopic Scales
Abstract:
In many physical systems, phenomena occur across multiple scales—microscopic, mesoscopic, and macroscopic. A compelling mathematical challenge, closely related to the unsolved Sixth Hilbert Problem, is to rigorously establish connections between these scales. In this talk, we present a brief history of Rational Extended Thermodynamics (RET), a theory that bridges mesoscopic and
macroscopic descriptions. We begin with early approaches based on the closure of the moment hierarchy in the Boltzmann equation for monatomic rarefied gases and progress to recent developments for polyatomic and dense gases, gas mixtures, and new formulations addressing viscoelastic behavior and non-Newtonian fluids. RET is grounded in the universal principles of continuum mechanics, with particular emphasis on the compatibility of general hyperbolic systems with the entropy law governed by a convex entropy function. From a mathematical standpoint, the resulting system of partial differential equations is shown to be symmetric hyperbolic, ensuring the well-posedness of the Cauchy problem and favorable qualitative properties. Experimental results on
sound wave propagation, shock waves in polyatomic gases, and stress decay in viscoelastic materials are compared with the theoretical predictions of RET.
Confirmed speakers:
Prof. Tommaso Ruggeri is the 2025 G.I. Taylor Medalist for outstanding contribution to fluid mechanics and the development of the rational extended thermodynamics.
He is the author of over 275 publications, including six books and three monographs. His research spans Mathematical Physics, with a focus on non-linear wave propagation in hyperbolic systems, thermo-mechanics of continuous media (classical and relativistic), and hyperbolic formulations of general relativity. 2 He pioneered results on the symmetrization of hyperbolic balance laws with convex entropy and on the theory of acceleration and shock waves. In non-equilibrium thermodynamics, he is one of the founders of Extended Thermodynamics. Together with Ingo Müller, he co-authored the influential book Rational Extended Thermodynamics (Springer, 1993; 2nd ed. 1998). His more recent work develops new approaches to non-equilibrium thermodynamics, addressing polyatomic gases, moderately dense gases, and mixtures.
These advances are presented in two volumes co-authored with Masaru Sugiyama: Rational Extended Thermodynamics Beyond Monatomic Gas (Springer, 2015) and Classical and Relativistic Rational Extended Thermodynamics of Gases (Springer, 2021). In general relativity, in collaboration with Yvonne Choquet-Bruhat, he proved that the 3+1 decomposition of Einstein’s vacuum field equations (with suitable lapse and zero shift) forms a strictly hyperbolic system, ensuring the well-posedness of the initial value problem.