Research


Mathematical Physics Group

Research

Interests

On account of the past experiences and competences, the main interest of the Group is addressed to the modeling of complex systems (physical, chemical, and biological) and materials of interest in applications, jointly with the study of differential integral and integrodifferential evolution equations governing their evolution.

Keywords

  • PE1_10 ODE and dynamical systems

  • PE1_11 Theoretical aspects of partial differential equations

  • PE1_12 Mathematical physics

  • PE1_20 Application of mathematics in sciences

  • PE1_21 Application of mathematics in industry and society

  • PE2_14 Thermodynamics

  • PE2_15 Non-linear physics

  • PE3_5 Physical properties of semiconductors and insulators.

Major Research Topics

The main research topics of the Group include: mathematical modeling of complex systems, dynamical systems and solvable models, properties and applications of special functions, controllability of solutions and analysis of contact and transmission problems, materials with memory (thermo-viscoelastic solids and fluids, hereditary heat conductors, ...), phase transition phenomena. In the framework of the national project, the members of this Group have specific knowledge to study:

    • compatibility of the model within the framework of non-classical thermodynamic theories (extended and irreversible thermodynamics, energy and entropy extra-flux assumptions, ...),

    • analysis of well-posedness, control and asymptotic behavior (in time) of solutions to nonlinear ODEs, PDEs and IPDEs arising in the modeling.

  1. Phase transition phenomena

    1. Modeling

      1. A phase-field model for non isochoric phase separation induced both by temperature and pressure.

      2. Non isothermal, anisotropic, phase-field models describing spontaneous magnetization in the paramagnetic-ferromagnetic transition.

      3. Non isothermal phase-field models describing the isotropic-nematic transition in liquid crystals.

      4. Thermodynamical models of vector-valued dynamics in ferromagnets and ferroelectrics

    2. Direct and control problems

      1. Well-posedness results and longtime behaviour of solutions for singular phase-field models in which the standard internal energy balance is replaced by an entropy balance with memory or more general laws.

      2. Analysis of well-posedness and global longtime behavior in the history space setting of a phase-field model with thermal memory (Coleman-Gurtin heat flux law) and a third order nonlinearity in the latent heat.

      3. Well-posedness and stability of solutions to a nonlinear system describing the non-isothermal, paramagnetic-ferromagnetic (vector) transition and involving a singular potential of the log type.

      4. Boundary controllability of solutions to a simple phase-field model with thermal memory (in the heat flux) describing a first order transition.

  1. Viscoelastic materials

    1. Modeling

      1. Thermo-viscoelatic beams and plates fixed at the boundary and involving a kinematic nonlinear term accounting for their extensibility (Woinovsky-Krieger, Berger, etc.) with different constitutive laws for the heat flux (Fourier, Coleman-Gurtin and Gurtin-Pipkin).

      2. Coupled suspension bridge equations when both the main cable and the road bed are composed of a viscoelastic material.

      3. Some viscoelastic models with nonlinear memory (cubic in some sense) having a special class of fourth-order free energy functionals.

      4. Analysis of the aging in viscoelasticity: viscoelastic solids with time-dependent memory kernels.

    2. Thermo-viscoelastic models: direct problems

      1. Steady-states analysis of some nonlinear problems in coupled structures (double-beam and string-beam systems).

      2. Longtime behavior and existence of the global attractor for the thermo-viscoelastic extensible beam (cf. the item 2.1.1).

      3. Steady states and longtime dynamics for an extensible elastic beam on a viscoelastic foundation, and for an extensible thermoelastic beam on an elastic foundation.

      4. Stationary solutions and well-posedness of the IBVP for the doubly nonlinear suspension bridge equation obtained from model 2.1.2 by keeping the main cable fixed.

      5. Control on the boundary for transmission problem in composite (elastic and thermo-viscoelatic) materials.

      6. Determination of constitutive parameters in a (elastic/viscoelastic/thermo-viscoelastic) multilayer through data associated with the reflected wave in a reflection-transmission process.

  1. Bäcklund transformations

      1. Construction of Bäcklund transformations for second order ODEs. Applications of the theory to problems of physical interests modeled by the Emden Fowler equation, the Ermakov Pinney equation and the Gross-Pitaevskii equation and its reductions.

  1. Thermodynamics.

      1. Study of equilibrium and non-equilibrium processes in heat and mass transfer, with applications to

        1. Extension and quantification of entropy, energy and mechanical work to non-equilibrium phenomena

        2. Thermal rectification devices

  1. Special functions and ODEs in the complex domain

1. Study of the properties of solutions of ODEs in the complex domain, in particular

        1. Distribution of poles and zeros, series expansions, connection formulae.

        2. Applications to the solutions of the Airy equation and Painlevé equations.

Major Research Project

  1. INFN/MMNLP

    1. Project name: Mathematical Methods of Nonlinear Physics

    2. Period : 2021-2023 (three years)

  2. GDRE CONEDP

    1. Project name: Gruppo di Ricerca Italo Francese sul Controllo delle Equazioni alle Derivate Parziali

    2. Period : 01/01/2010-31/12/2013 and 01/01/2014-31/12/2017

  3. MIUR/PRIN2005

    1. Project name: Mathematical Models and Methods in Continuum Physics

    2. Period (months): 24

  1. MIUR/PRIN2002

    1. Project name: Modelli Matematici per la Scienza dei Materiali

    2. Period (months): 24

  1. MIUR/PRIN2000

    1. Project name: Modelli Matematici per la Scienza dei Materiali

    2. Period (months): 24

Strategic collaborations