# Mathematical Physics group

The main subject of my research activity is kinetic theory, not only for rarefied gases, but also for physical situations involving non-conservative interactions.

1) Kinetic theory for chemically reacting mixtures: kinetic models and hydrodynamic equations.

2) Kinetic theory for granular media: effects due to collision inelasticity.

3) Kinetic theory for socio-economic sciences: description of the interactions among agents, and of taxation and redistribution of the collected wealth.

My primary research activity deals with the kinetic theory of gases, in particular the dynamics of gas mixtures in the presence of non-conservative interactions, like chemical reactions, absorption, generations, inelastic scattering, presence of background host media (extended kinetic theory,generalized integro-differential equations of Boltzmann type). My present research activity includes also mathematical models in biomathematics, in particular the qualitative analysis of differential models in population dynamics and epidemiology (equilibria, stability, limit cycles, bifurcations).

Geometric Techniques in Impulsive Mechanics. Mechanical systems subject to unilateral positional constraints and permanent and/or instantaneous kinetic constraints. Ideal and non ideal constitutive characterizations for unilateral constraints. Feasibility of the pure rolling constraint. Internal impulsive reactions for permanent constraints and break of kinetic permanent constraints acting on impulsive systems. Collisions between free or constrained rigid bodies. Computability and explicit implementation of the algorithm for impact problems of system with high number of degrees of freedom.

**Giampiero Spiga** (retired starting from November 1rt, 2018)

Transport theory, kinetic theory, evolution problems, stability, non-conservative interactions in gas dynamics, exact solutions of the Boltzmann equation, entropy functionals, discrete and semidiscrete kinetic models, relaxation time approximations, chemically reactive gas mixtures, granular flows, hydrodynamic limits. Publications: about 200 scientific papers in International Journals, about 50 Congress communications.

**Giuseppe Stracquadanio** (University of Parma, XXVII cycle)**Giorgio Martalò** (University of Milan, XXVII cycle)**Elena Bonacini** (Universities of Ferrara, Modena-Reggio Emilia, Parma, XXIX cycle)**Cinzia Soresina **(University of Milan, XXIX cycle)

**Bruno Buonomo **(February 2017)**Ana Jacinta Soares** (January 2017)**Roberto Monaco** (January 2017)**Alexander Bobylev** (May 2011, June 2012, and November 2016) **Fiammetta Conforto** (short visits from November 2011 up to July 2016) **Tommaso Ruggeri **(March 2016)**Vladimir Aristov** (November 2015)**Laurent Desvillettes **(March 2015)**Niclas Bernhoff** (May 2012, and November 2013)**Gabriella Puppo** (October 2012)**Irina Potapenko** (June 2012)**Giovanni Russo** (April 2012)**Giuseppe Buffoni** (short visits from November 2011 up to now)**Stéphane Brull** (October 2010)**Giuseppe Alì** (September 2010)**Isabella Torcicollo **(September 2010)

**Kazuo Aoki** (National Taiwan University, Taipei, and National Cheng Kung University, Tainan, Taiwan)**Alexander Bobylev** (Russian Academy of Sciences)**Luca Bolzoni** (IZSLER Parma – Italy)**Giuseppe Buffoni** (CNR-Imati – Italy)**Stephane Brull** (University of Bordeaux – France)**Maria Josè Caceres** (University of Granada – Spain)**Josè Alfredo Canizo** (University of Granada - Spain)**Josè Antonio Carrillo** (Imperial College of London – UK)**Fiammetta Conforto** (University of Messina – Italy)**Giulio De Leo **(Hopkins Marine Station – Stanford University - USA)**Laurent Desvillettes** (University Paris Diderot – France)**Bertrand Lods** (University of Turin – Italy)**Silvia Lorenzani** (Politecnico of Milan – Italy)**Roberto Monaco **(Politecnico of Turin – Italy)**Giovanni Naldi** (University of Milan – Italy)**Sergej Rjasanow** (University of Saarbruecken – Germany)**Alberto Rossani** (Politecnico of Turin – Italy)**Tommaso Ruggeri** (University of Bologna – Italy)**Giovanni Russo** (University of Catania – Italy)**Ferdinand Schuerrer** (University of Graz – Austria)**Ana Jacinta Soares** (University of Minho – Portugal)**Giuseppe Toscani** (University of Pavia – Italy)

**Galileo project 2014**(financed by Università Italo Francese/*Université Franco Italienne*(UIF/UFI)): “Kinetic modelling and numerical simulations of reactive gas mixtures and plasmas for nuclear fusion”, coordinators: F. Salvarani (Italy) and F. Charles (France).**Junior Project GNFM, 2013**: “Damping forces exerted by multi-component gas mixtures in MEMS devices vibrating at high frequencies according to kinetic theory”, coordinator: S. Lorenzani (Politecnico of Milan).**ESA Working Group on Kinetic Theory, 2011**; coordinator: D. Giordano (ESA, Nordwijk (NL)).**PRIN 2009**(financed by Italian MIUR): “Mathematical problems in kinetic theories and applications”, national coordinator: Prof. M. Pulvirenti (University “La Sapienza” - Roma).

- March 9, 2017: Dr.
**Cinzia Soresina**(IMATI-CNR, Milan), A*bout predator-prey reaction-cross diffusion systems involving the Holling-type II and the Beddington-De Angelis functional responses* - February 27, 2017: Prof.
**Bruno Buonomo**(University of Napols “Federico II”)*Vaccination modeling in behavioral change frameworks* - November 15, 2016: Prof.
**Alexander V. Bobylev**(Russian Academy of Sciences),*Maxwellian bounds for solutions of the spatially homogeneous Boltzmann equation*(Colloquium of the Department of Mathematics and Computer Science, University of Parma) - December 3, 2015: Prof.
**Vincenzo Capasso**(University of Milan),*Controllo regionale per una classe di modelli epidemici a struttura spaziale: think globally - act locally!* - November 30, 2015: Prof.
**Vladimir V. Aristov**(Russian Academy of Sciences),*Nonequilibrium flows with chemical reactions simulated by the kinetic approach* - March 17, 2015: Prof.
**Laurent Desvillettes**(ENS Cachan - France),*About the use of entropy methods for PDEs: the example of the Landau equation*(Colloquium of the Department of Mathematics and Computer Science, University of Parma) - October 21, 2014: Prof.
**Giuseppe Saccomandi**(University of Perugia),*Matematica e meccanica delle onde di taglio*(Colloquium of the Department of Mathematics and Computer Science, University of Parma) - May 28, 2014: Prof.
**Giuseppe Toscani**(University of Pavia),*Distribuzione di ricchezza e conoscenza collettiva. Un approccio cinetico*(Colloquium of the Department of Mathematics and Computer Science, University of Parma) - November 13, 2013: Prof.
**Niclas Bernhoff**(University of Karlstad – Sweden),*Half-space problem for a non-linear system of ODEs* - October 8, 2012: Prof.
**Gabriella Puppo**(University of Insubria),*Microscopically implicit, macroscopically explicit schemes for the BGK model* - June 12, 2012: Prof.
**Alexander V. Bobylev**(University of Karlstad – Sweden),*Boltzmann equation and hydrodynamics beyond the Navier-Stokes level* - May 17, 2012: Prof.
**Niclas Bernhoff**(University of Karlstad – Sweden),*Halfspace problem for the discrete Boltzmann equation: Condensing vapor flow in the presence of a non-condensable gas* - November 9, 2011: Prof.
**Giuseppe Buffoni**(IMATI CNR – Milan),*Sistema preda-predatore: effetti del sotto/sovraffollamento della preda* - May 17, 2011: Prof.
**Alexander V. Bobylev**(University of Karlstad – Sweden),*Kinetic modelling of economic games with large number of participants* - October 27, 2010: Prof.
**Stéphane Brull**(University of Bordeaux 1 - France),*Derivation of BGK models for mixtures*

- RGD 31 – 31st International Symposium on “Rarefied Gas Dynamics” – Glasgow (UK), July 23-27, 2018.
- Summer School on “Methods and Models of Kinetic Theory” (M&MKT 2018), 9th edition - Porto Ercole (GR, Italy), June 11–16, 2018.
- Workshop "Numerical aspects of hyperbolic balance laws and related problems", University of Ferrara, April 16-18, 2018.
- SIAM Conference on “Analysis of Partial Differential Equations” – Baltimore, Maryland (USA), December 9-12, 2017.
- “Advance in Mathematics for Technology 2017” (AMATH2017) Catania, Villa Citelli, October 9-11, 2017.
- SigmaPhi2017 - International Conference on “Statistical Physics” - Corfù (Greece), July 10-14, 2017.
- 7th Workshop on “Kinetic Theory and Applications” – Karlstad (Sweden), June 19-21, 2017.
- WASCOM 2017 - XIX International Conference on “Waves and Stability in Continuous Media” - Bologna (Italy), June 12-16, 2017.
- Conference “Continuum physics: a ‘rational’ approach” – Brescia (Italy), May 25-27, 2017.
- Conference “PSPDE V - Particle Systems and Partial Differential Equations” - Braga (Portugal), November 28-30, 2016.
- Meeting “SEMODAY - Mathematical Models for Quantum and Classical Mechanics” – Firenze (Italy), November 17-18, 2016.
- XIII SIMAI Biannual Congress – Milano (Italy), September 13-16, 2016.
- Summer School on “Methods and Models of Kinetic Theory” (M&MKT 2016), 8th edition - Porto Ercole (GR, Italy), June 5–11, 2016.
- Workshop “Numerical aspects of hyperbolic balance laws and related problems” - University of Ferrara (Italy), December 17-19, 2015.
- Workshop on “Kinetic Models and Methods for Rarefied Gas Dynamics” - Bordeaux (France), October 8-9, 2015.
- Workshop - Recent advances in kinetic equations and applications, Parma (Italy), October 1-2, 2015.
- XL Summer School on Mathematical Physics – Ravello (SA, Italy), September 14-26, 2015.
- XX Congresso dell'Unione Matematica Italiana – Siena (Italy), September 7-12, 2015.
- ICTT 2015 – 24th International Conference on “Transport Theory” – Taormina (CT, Italy), September 7-11, 2015.
- 17th EWM General Meeting – Cortona (AR, Italy), August 31- September 4, 2015
- Erice MathCompEpi 2015 – “Mathematical and Computational Epidemiology of Infectious diseases” – Erice (TP, Italy), August 30 – September 5, 2015.
- Ph.D. School-Conference on “Mathematical Modeling of Complex Systems” – Patrasso (Greece), July 20-30, 2015.
- XX Convegno Nazionale di Fisica Statistica e dei Sistemi Complessi – Parma (Italy), June 29 – July 1, 2015.
- “Calcolo Scientifico e Modelli Matematici” – Genova (Italy), June 3-5, 2015.
- WASCOM 2015 - XVIII International Conference on “Waves and Stability in Continuous Media” - Cetraro (CS, Italy), June 1-5, 2015.
- Workshop “Statistical physics methods in social and economic systems” – IHP Paris (France), January 26-30, 2015.
- Conference "Problems on Kinetic Theory and PDE's" – Novi Sad (Serbia), September 25-27, 2014.
- XXXIX Summer School on Mathematical Physics – Ravello (SA, Italy), September 15-27, 2014.
- Workshop on “PDEs: Modelling, Analysis and Numerical Simulation” (PDE-MANS 2014) – Granada (Spain), September 15-19, 2014.
- 10th AIMS Conference on “Dynamical Systems, Differential Equations and Applications” – Madrid (Spain), July 7-11, 2014.
- SIMAI National Conference 2014 – Taormina (CT, Italy), July 7-10, 2014.
- School BIOMAT 2014 – “Complexity and emergence in social and biological systems” – Granada (Spain), June 25-27, 2014.
- Summer School on “Methods and Models of Kinetic Theory” (M&MKT 2014), 7th edition - Porto Ercole (GR, Italy), June 8–14, 2014.
- 9th SICC International Tutorial Workshop “Topics in Nonlinear Dynamics” – “Modelling and analysis of innovation and competition processes” – Politecnico of Milan (Italy), May 26-30, 2013.
- Assemblea Scientifica GNFM 2014 - Montecatini Terme (PT, Italy), May 15-17, 2014.
- NumHyp2013 – “Numerical approximations of hyperbolic systems with source terms and applications” – Aachen (Germany), September 23-27, 2013.
- XXXVIII Summer School on Mathematical Physics – Ravello (SA, Italy), September 16-28, 2013.
- WASCOM 2013 - XVII International Conference on “Waves and Stability in Continuous Media” - Levico (TN), June 17-21, 2013.
- Workshop “Kinetic days” - Toulouse (France), April 5-6, 2013.

*Pubblicato*Monday, 23 June, 2014 - 14:16 |

*ultima modifica*Tuesday, 13 November, 2018 - 12:21