Prof. Tommaso Ruggeri

Emeritus Professor of Mathematical Physics – University of Bologna

Department of Mathematics and Alma Mater Research Center on Applied Mathematics – AM²

National Member of the Accademia Nazionale dei Lincei

MAE – Member of the Academia Europaea

Member of the European Academy of Sciences and Arts

Member of the European Academy of Sciences (EurASc)

Accademico Benedettino of the Accademia delle Scienze dell’Istituto di Bologna

National Member of the Accademia di Scienze Fisiche e Matematiche di Napoli

Member of the Accademia Peloritana dei Pericolanti

G. I. Taylor Medal, Society of Engineering Science, 2025

Curriculum Vitae

tel: +39 051 209 3973 – e-mail: tommaso.ruggeri@unibo.it

Teaching Activity

Scientific Activity

Matlab and Mathematical Physics

Maple and Calculus

Teaching Activity

Office Hours: Thursday 11:30–13:00, AM² Center (formerly CIRAM).

Courses:

Mathematical Physics and Statistical Treatment of Observations M

Educational Software:

Development and use of mathematical software for research and teaching in Mathematical Physics, including Matlab, Maple, Mathematica
Matlab and Mathematical Physics
Maple and Calculus

Teaching Publications:

Richiami di Calcolo Vettoriale e Matriciale. Ed. Pitagora, Bologna (1989).
Laboratorio di Matematica – Primo Corso [with software]. In collaboration with S. Matarasso. Ed. Esculapio, Bologna (1990).
Laboratorio di Meccanica Razionale [with software]. In collaboration with A. Muracchini and L. Seccia. Ed. Esculapio, Bologna (1991).
Didattica Matematica con L’Ausilio del Personal Computer. Edited by R. Guidorzi and T. Ruggeri. Computing Center of the Faculty of Engineering and Interdepartmental Center for Research and Applications of Mathematics. University of Bologna. Ed. Tecnoprint (1992).
Lecture Notes on Mathematical Analysis II with the Use of Mathematical Software. Vol. 1. With software. In collaboration with S. Matarasso. Ed. Esculapio, Bologna (1993).
Lecture Notes on Mathematical Analysis II with the Use of Mathematical Software. Vol. 5. With software. In collaboration with S. Matarasso. Ed. Esculapio, Bologna (1994).
Some Experiences with MATLAB in Research and Teaching in Mathematical Physics. Proceedings of the Conference “MATLAB: Il mondo numerico incontra il mondo reale”, Bologna, 14 October 1994. Teoresi (1995).
Mathematical Analysis 2: Differential Calculus. Second Edition. In collaboration with S. Matarasso. Ed. Esculapio, Bologna (1996).
Exercises and Exam Problems in Rational Mechanics. Second Edition. In collaboration with A. Muracchini and L. Seccia. Ed. Esculapio, Bologna (1997).
Exercises and Exam Problems in Rational Mechanics for Three-Year Degree Courses in Engineering. In collaboration with A. Muracchini and L. Seccia. Ed. Esculapio, Bologna (2005).
Rational Mechanics for Engineering. In collaboration with P. Biscari, G. Saccomandi, M. Vianello. Ed. Monduzzi, Bologna (2005) [table of contents].
Introduction to Thermomechanics of Continua. Ed. Monduzzi (2007) [preface] [table of contents] [errata corrige].
Exercises and Exam Problems in Rational Mechanics. In collaboration with F. Brini, A. Muracchini and L. Seccia. Ed. Esculapio, Bologna (2019).
Rational Mechanics. In collaboration with P. Biscari, G. Saccomandi, M. Vianello. Springer, 4th edition (2022).

NEW BOOKS

A. Muracchini, T. Ruggeri and L. Seccia

Muracchini
Ruggeri Seccia

Scientific Activity

Main fields of interest:

Non-Linear Wave Propagation and Hyperbolic Systems
Non-Equilibrium Thermodynamics

Books:

Extended Thermodynamics. Jointly with I. Müller. Springer Tracts in Natural Philosophy, Vol. 37, pp. 231. Springer Verlag (1993).
Rational Extended Thermodynamics. Jointly with I. Müller. Springer Tracts in Natural Philosophy, Vol. 37, 2nd Edition, pp. 393. Springer Verlag (1998).
Rational Extended Thermodynamics beyond the Monatomic Gas. Jointly with M. Sugiyama. Springer Verlag (2015).
Classical and Relativistic Rational Extended Thermodynamics of Gases. Jointly with M. Sugiyama. Springer Verlag (2021).
Introduction to the Thermodynamics of Continua and Hyperbolic Systems. Springer (2024).
Rational Mechanics. Springer (2026).

New book Springer new

NEW BOOKS

Monographs:

Wave Propagation (Propagazione Ondosa). Lecture Notes of the VI Summer School in Mathematical Physics (CNR), Ravello, September 1981. Internal Report of the Applied Mathematical Institute, University of Bologna (1981).
Heat Propagation and Constitutive Equations (Propagazione del Calore ed Equazioni Costitutive). Lecture Notes of the 8th Summer School in Mathematical Physics (CNR), Ravello, September 1983. Jointly with A. Morro. Quaderno C.N.R., p. 166. Pitagora-Tecnoprint, Bologna (1984).
Recent Results on Wave Propagation in Continuum Models. In Stability and Wave Propagation in Fluids and Solids, G.P. Galdi, Ed. CISM Course and Lectures n. 344, pp. 105–154. Springer-Verlag (1995).

Chapters in Books:

Straughan Book Lecture notes Choquet-Bruhat book Wilmanski book Bologna
Engelbrecht book Giovine book Godunov Dreyer

Scientific Editor:

Lecture Notes of the Italian–Polish Meeting on Selected Problems of Modern Continuum Theory. Bologna, 3–6 June 1987. T. Manacorda, A. Morro, W. Kosinski and T. Ruggeri Eds. Pitagora Tecnoprint, Bologna (1987).
ISIMM Symposium on Kinetic Theory and Extended Thermodynamics. Bologna (May 1987). Ed. I. Müller and T. Ruggeri. Pitagora Tecnoprint (1987).
7th Conference on Waves and Stability in Continuous Media. S. Rionero and T. Ruggeri Eds. Series in Advances in Mathematics for Applied Sciences, Vol. 23, pp. 429. World Scientific, Singapore (1994).
Recent Mathematical Methods in Nonlinear Wave Propagation. CIME Course 1994, T. Ruggeri Ed. Lecture Notes in Mathematics Vol. 1640. Springer-Verlag (1996).
Proceedings of the 12th Conference on Waves and Stability in Continuous Media (WASCOM 2003). Eds. R. Monaco, S. Pennisi, S. Rionero, T. Ruggeri. World Scientific, Singapore (2004).
Proceedings of the International Conference in Honour of Y. Choquet-Bruhat: Analysis, Manifolds and Geometric Structures in Physics. Elba (Italy), June 24–26, 2004 (2005).
Proceedings of the 13th Conference on Waves and Stability in Continuous Media (WASCOM 2005). Eds. R. Monaco, G. Mulone, S. Rionero, T. Ruggeri. World Scientific, Singapore (2006).
Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, n. 78, “Non-Linear Hyperbolic Fields and Waves – A Tribute to Guy Boillat” (2006).
Proceedings of the Workshop “Asymptotic Methods in Non-linear Wave Phenomena – In Honor of the 65th Birthday of Antonio Greco” (2007).
Proceedings of the 15th Conference on Waves and Stability in Continuous Media (WASCOM 2009). Eds. A.M. Greco, S. Rionero, T. Ruggeri. World Scientific, Singapore (2010).

Associate Editor:

Continuum Mechanics and Thermodynamics – Springer Verlag (1989–2006)
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali – Rendiconti Lincei: Matematica e Applicazioni – European Mathematical Society (EMS) (since 1999)
Ricerche di Matematica – Springer Verlag (since 2005)
Bollettino dell’Unione Matematica Italiana (BUMI) (2007–2013)
Le Matematiche (since 2016)
International Journal of Non-Linear Mechanics (2011–2018 and since 2022)
Entropy (since 2020)
Philosophical Transactions of the Royal Society A (since 2023)

Recent Papers (click here for the full Bibliography):

2017

A thermodynamically consistent model for emergent behavior in flocks and comparison with multi-temperature mixture of fluids. In coll. with S-Y. Ha. Arch. Rational Mech. Anal. 223, 1397–1425 (2017).
Relativistic Extended Thermodynamics of Rarefied Polyatomic Gases. In coll. with S. Pennisi. Annals of Physics 373, 414–445 (2017).
Duality Principle from rarefied to dense gas and Extended Thermodynamics with 6 fields. In coll. with T. Arima, M. Sugiyama. Physical Review Fluids 2, 013401 (2017).
Symmetric form for the hyperbolic-parabolic system of fourth-gradient model for fluids. In coll. with H. Gouin. Ricerche di Matematica. DOI 10.1007/s11587-016-0315-7 (2017).
Galilean Invariance and Entropy Principle for a System of Balance Laws of Mixture Type. In coll. with T. Arima, M. Sugiyama and S. Taniguchi. Rend. Lincei Mat. Appl. 28, 495–513 (2017).
Rational Extended Thermodynamics of a Rarefied Polyatomic Gas with Molecular Relaxation Processes. In coll. with T. Arima, M. Sugiyama. Phys. Rev. E 96, 042143 (2017).
New Frontiers in Non-Equilibrium Thermodynamics. Lecture Notes Frontiere. Accademia Nazionale dei Lincei (29–30 January 2015). Atti dei Convegni Lincei 314, 49–71. Bardi Edizione (2017).

2018

Dynamical pressure in a polyatomic gas: interplay between kinetic theory and extended thermodynamics. In coll. with M. Bisi and G. Spiga. Kinetic and Related Models 11(1), 71–95 (2018).
On the sub-shock formation in extended thermodynamics. In coll. with S. Taniguchi. Int. J. Non-Linear Mechanics 99, 69–78 (2018).
A Global Existence of Classical Solutions to the Hydrodynamic Cucker-Smale Model in the Presence of a Temperature Field. In coll. with S-Y. Ha, J. Kim, C. Ho Min and X. Zhang. Analysis and Applications (2018).
Emergent Behaviors of Thermodynamic Cucker-Smale Particles. In coll. with S-Y. Ha and J. Kim. SIAM J. Math. Anal. (2018).
Extended Thermodynamics of Rarefied Polyatomic Gases: 15-Field Theory Incorporating Relaxation Processes of Molecular Rotation and Vibration. In coll. with T. Arima, M. Sugiyama. Entropy 20, 301 (2018).
Shock wave structure in rarefied polyatomic gases with large relaxation time for the dynamic pressure. In coll. with T. Arima, M. Sugiyama and S. Taniguchi. J. Phys.: Conf. Ser. 1035, 012009 (2018).
A New BGK Model for Relativistic Kinetic Theory of Monatomic and Polyatomic Gases. In coll. with S. Pennisi. J. Phys.: Conf. Ser. 1035, 012005 (2018).
Ultrarelativistic limit of a Rarefied Gas with Internal Structure. In coll. with S. Pennisi. J. Mathematical Physics 59, 043102 (2018).
Monatomic Limit of Relativistic Extended Thermodynamics of Polyatomic Gas. In coll. with M.C. Carrisi and S. Pennisi. Continuum Mech. Thermodyn. (2018).
Fluid Mixtures in Nanotubes. In coll. with H. Gouin and A. Muracchini. Physical Review E 97, 062152 (2018).
Uniform Stability and Mean-Field Limit of Thermodynamic Cucker-Smale Model. In coll. with S-Y. Ha, J. Kim, C. Ho Min and X. Zhang. Quarterly of Applied Mathematics (2018).
Molecular Extended Thermodynamics of a Rarefied Polyatomic Gas. In Trends in Applications of Mathematics to Mechanics, Editors E. Rocca et al. Springer INDAM Series 27, 265–287 (2018).

2019

Integrability properties for relativistic extended thermodynamics of polyatomic gas. In coll. with M.C. Carrisi and S. Pennisi. Ricerche di Matematica 68, 57–73 (2019).
A 2×2 simple model in which the sub-shock exists when the shock velocity is slower than the maximum characteristic velocity. In coll. with S. Taniguchi. Ricerche di Matematica 68, 119–129 (2019).
Second Order Approximation of Extended Thermodynamics of a Monatomic Gas and Hyperbolicity Region. In coll. with F. Brini. Continuum Mech. Thermodyn. (2019).
Production Terms in Relativistic Extended Thermodynamics of Gas with Internal Structure via a New BGK Model. In coll. with M.C. Carrisi and S. Pennisi. Annals of Physics 405, 298–307 (2019).
Similarity Solution of Strong Spherical Shock Waves in a Rarefied Polyatomic Gas based on Extended Thermodynamics. In coll. with R. Nagaoka and S. Taniguchi. AIP Conf. Proc. 2153, 020014 (2019).
Shock Waves in Hyperbolic Systems of Non-Equilibrium Thermodynamics. In coll. with S. Taniguchi. Applied Wave Mathematics II, Mathematics of Planet Earth 6, Chapter 8, 167–186. Springer (2019).

2020

From the Relativistic Mixture of Gases to the Relativistic Thermomechanical Cucker-Smale Flocking. In coll. with S-Y. Ha and J. Kim. Arch. Rational Mech. Anal. 235, 1661–1706 (2020).
Second Order Approximation of Extended Thermodynamics of a Monatomic Gas and Hyperbolicity Region. In coll. with F. Brini. Continuum Mech. Thermodyn. 32, 23–39 (2020).
On Invariance in 1+1-Dimensional Isentropic Relativistic Gasdynamics. In coll. with C. Rogers. Wave Motion 94, 102527 (2020).
Rational Extended Thermodynamics: a link between kinetic theory and continuum theory. In coll. with M. Sugiyama. Rendiconti Lincei. Scienze Fisiche e Naturali (2020).
Classical limit of relativistic moments associated with the Boltzmann-Chernikov equation: optimal choice of moments in classical theory. In coll. with S. Pennisi. J. Statistical Physics (2020).
Rational Extended Thermodynamics of Dense Polyatomic Gases Incorporating Molecular Rotation and Vibration. In coll. with T. Arima and M. Sugiyama. Phil. Trans. R. Soc. A 378, 20190176 (2020).
Classical and ultrarelativistic limits of the Riemann problem for the relativistic Euler fluid with Synge energy. In coll. with Q. Xiao. Ricerche di Matematica (2020).
Maximum Entropy Principle Closure for 14-Moment System for a Non-Polytropic Gas. Ricerche di Matematica (2020).
Hyperbolicity of first and second order extended thermodynamics theory of polyatomic rarefied gases. In coll. with F. Brini. Int. J. Non-Linear Mechanics 124, 103517 (2020).
Emergent Behaviors of the Thermodynamic Kuramoto Ensemble on a Ring Lattice. In coll. with S-Y. Ha, H. Park and W. Shim. J. Statistical Physics (2020).
The explicit closure for the ultrarelativistic limit of Extended Thermodynamics of Rarefied Polyatomic Gas. In coll. with S. Pennisi. Technium Vol. 2, Issue 5, pp. 11–42 (2020).
Multiscale Phenomena in Continuum Mechanics: Mesoscopic Justification of Rational Extended Thermodynamics of Gases with Internal Structure. In Views on Multiscale Modelling of Granular Materials, Birkhäuser (2020).
On relativistic gasdynamics. Invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections. In coll. with C. Rogers and W.K. Schief. Proc. Royal Society A (2020).

2021

Nonlinear Hyperbolic Waves in Relativistic Gases of Massive Particles with Synge Energy. In coll. with Q. Xiao and H. Zhao. ARMA 239, 1061–1109 (2021).
Shock Structure in Extended Thermodynamics with Second Order Maximum Entropy Principle Closure. In coll. with A. Mentrelli. Continuum Mech. Thermodyn. 33, 125–150 (2021).
Uniform Stability and Uniform-In-Time Mean-Field Limit of the Thermodynamic Kuramoto Model. In coll. with S-Y. Ha, M. Kang, H. Park and W. Shim. Quarterly of Applied Mathematics (2021).
Molecular Extended Thermodynamics of Rarefied Polyatomic Gases with a New Hierarchy of Moments. In coll. with T. Arima. Fluids 6, 62 (2021).
Maxwellian Iteration of a Causal Relativistic Model of Polyatomic Gases and Evaluation of Bulk, Shear Viscosity and Heat Conductivity. In coll. with M.C. Carrisi and S. Pennisi. Annals of Physics 428, 168477 (2021).
Emergent behaviors of the continuum thermodynamic Kuramoto model in a large coupling regime. In coll. with S-Y. Ha, M. Kang, H. Park and W. Shim. J. Differential Equations 300, 519–564 (2021).
Kinetic and Hydrodynamic Models for the Relativistic Cucker-Smale Ensemble and Emergent Dynamics. In coll. with S-Y. Ha and J. Kim. Communications in Mathematical Sciences (2021).
Shock Structure and Sub-shock Formation in a Binary Mixture of Polyatomic Eulerian Gas. In coll. with S. Taniguchi. Rendiconti Lincei Matematica e Applicazioni (2021).
Which moments are appropriate to describe gases with internal structure in Rational Extended Thermodynamics? In coll. with T. Arima, M.C. Carrisi and S. Pennisi. Int. J. Non-Linear Mechanics 137, 103820 (2021).

2022

Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments. In coll. with T. Arima, M.C. Carrisi and S. Pennisi. Entropy 24, 43 (2022).
On a Relativistic BGK Model for Polyatomic Gases near Equilibrium. In coll. with B-H. Hwang and S-B. Yun. SIAM J. Math. Anal. 54(3), 2906–2947 (2022).
Relativistic Kinetic Theory of Polyatomic Gases: Classical Limit of a New Hierarchy of Moments and Qualitative Analysis. In coll. with T. Arima, M.C. Carrisi and S. Pennisi. Partial Differ. Equ. Appl. 3, 39 (2022).

2023

Navier-Stokes-Fourier equations as a parabolic limit of a general hyperbolic system of rational extended thermodynamics. In coll. with T. Arima and A. Mentrelli. Int. J. Non-Linear Mechanics 151, 104379 (2023).
Shock Structure and sub-shock formation in a mixture of polyatomic gases with large bulk viscosity. In coll. with S. Taniguchi. Ricerche di Matematica (2023).
Eckart equations, Maxwellian iteration and relativistic causal theories of divergence type. Phil. Trans. R. Soc. A 381, 20220371 (2023).
Effect of the dynamic pressure on the shock structure and sub-shocks formation in a mixture of polyatomic gases. In coll. with S. Taniguchi. Comm. Appl. Math. and Comp. (2023).

2024

A Nonlinear Approach to Viscoelasticity via Rational Extended Thermodynamics. IJNLM (2024).
Energy of a Non-linear Viscoelastic Model Compatible with Fractional Relaxation. In coll. with A. Giusti and A. Mentrelli. JNLM (2024).
Hyperbolicity Region of a Rational Extended Thermodynamics Model with 14 Moments for a Non-polytropic Gas. In coll. with F. Brini. Proc. HYP 2022 XVIII Int. Conf. on Hyperbolic Problems. Springer (2024).
Dispersion relation of linear waves propagating in three-dimensional space in Extended Thermodynamics of Polyatomic Gases. In coll. with T. Arima and M. Sugiyama. Rivista di Matematica di Parma 15 (2024).
A Novel ES-BGK Model for Non-Polytropic Gases with Internal State Density Independent of the Temperature. In coll. with T. Arima and A. Mentrelli. J. Stat. Phys. 191, 95 (2024).
On the Comparison Between Phenomenological and Kinetic Theories of Gas Mixtures with Applications to Flocking. In coll. with Gi-Chan Bae, Seung-Yeal Ha and Gyuyoung Hwang. Physica D 469, 134321 (2024).

2025

Stress Relaxation and Viscous Energy in Nonlinear Viscoelasticity: a Rational Extended Thermodynamics Framework. In coll. with M. Amabili and T. Arima. Journal of the Mechanics and Physics of Solids (2025).
The Taub Relativistic Gasdynamic System. Chaplygin–Kármán–Tsien Laws and Substitution Principle. In coll. with C. Rogers. Rend. Lincei Mat. Appl. 35, 447–457 (2025).
Flocking Dynamics and Optimal Classical Limit of the Relativistic Cucker–Smale Model with Infinite Particles. In coll. with S-Y. Ha, S. Lee, X. Wang and Q. Xiao (2025).
The Maximum Entropy Principle in Nonequilibrium Thermodynamics: A Brief History and the Contributions of Wolfgang Dreyer. In coll. with T. Arima. Springer Vol. dedicated to W. Dreyer (2025).
Rational Extended Thermodynamics for Non-Newtonian Fluids with Finite Relaxation Time. POF Letters (2025).
Fifty Years of Excellence: The Summer School of Mathematical Physics of the National Group of Mathematical Physics. In coll. with G. Saccomandi. arXiv:2509.17194 (2025).

2026