Salvatore Rionero

Tommaso Ruggeri

Roberto Monaco

Giuseppe Mulone

The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications. The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss. Contents: On Whitham Equations for Camassa-Holm (S Abenda et al.); An Operational Description of Stock Markets (F Bagarello); Vortex Layers in the Small Viscosity Limit (R E Caflisch & M Sammartino); Integration of Partially Integrable Equations (R Conte); Waves and Vibrations in a Solid of Second Grade (M Destrade & G Saccomandi); Multicomponent Reactive Flows (V Giovangigli); Singularities for Prandtl''s Equations (G Lo Bosco et al.); Stability of Solitons of the ZakharovOCoRubenchik Equation (F Oliveira); Plain Waves and Vibrations in the Elastic Mixtures (M Svanadze); Extended Thermodynamics with Consistent Order (W Weiss); and other papers. Readership: Academics, researchers and post-graduates in mathematics and physics."

13th Conference on Waves and Stability in Continuous Media : Catania, Italy, 19-25 June 2005

Proceedings, "WASCOM 2005"

Ingo Müller

Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.

Extended Thermodynamics

Alessandra Celletti

Elisabetta Strickland

Ugo Locatelli

In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

Mathematical Models and Methods for Planet Earth

Sebastiano Pennisi

This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Chaos in Some Linear Kinetic Models (J Banasiak)Inverse Problems in Photon Transport. Part I: Determination of Physical and Geometrical Features of an Interstellar Cloud (A Belleni-Morante et al.)Inverse Problems in Photon Transport. Part II: Features of a Source Inside an Interstellar Cloud (A Belleni-Morante & R Riganti)The Riemann Problem for a Binary Non-Reacting Mixture of Euler Fluids (F Brini & T Ruggeri)Rate of Convergence toward the Equilibrium in Degenerate Settings (L Desvillettes & C Villani)Asymptotic and Other Properties of Positive Definite Integral Measures for Nonlinear Diffusion (J N Flavin)Thermocapillary Fluid and Adiabatic Waves Near its Critical Point (H Gouin)Constitutive Models for Atactic Elastomers (C O Horgan & G Saccomandi)Considerations about the Gibbs Paradox (I Müller)Transport Coefficients in Stochastic Models of the Revised Enskog and Square-Well Kinetic Theories (J Polewczak & G Stell)Some Recent Mathematical Results in Mixtures Theory of Euler Fluids (T Ruggeri)From Kinetic Systems to Diffusion Equations (F Salvarani & J L Vázquez)Non-Boussinesq Convection in Porous Media (B Straughan)and other papers Readership: Researchers, academics and graduate students working in the fields of continuum mechanics, wave propagation, stability in fluids, kinetic theory and computational fluid dynamics. Keywords:Discontinuity and Shock Waves;Stability in Fluid Mechanics;Small Parameter Problem;Kinetic Theories Towards Continuum Models;Non-Equilibrium Thermodynamics;Numerical Applications

Waves and Stability in Continuous Media

Masaru Sugiyama

This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule’s internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena.

Rational Extended Thermodynamics beyond the Monatomic Gas

Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book "Rational Extended Thermodynamics beyond the Monatomic Gas" by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. The book represents a valuable resource for applied mathematicians, physicists, and engineers, offering powerful models for many potential applications such as reentering satellites into the atmosphere, semiconductors, and nanoscale phenomena.

Classical and Relativistic Rational Extended Thermodynamics of Gases

Antonio Maria Greco

This book contains recent contributions in the field of waves propagation and stability in continuous media. The volume is the sixth in a series published by World Scientific since 1999.

Tommaso Ruggeri

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