Giorgio Gentili
University of Bologna
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Featured researches published by Giorgio Gentili.
International Journal of Engineering Science | 1998
Mauro Fabrizio; Giorgio Gentili; David W. Reynolds
Abstract This paper studies a theory of linear rigid heat conductors with memory within the framework proposed by Gurtin and Pipkin. An approximate theory of thermodynamics is developed for this model. In such a context a new thermodynamic potential, called the free pseudoenergy, is introduced and used to define a new norm on a reduced state space. This norm is appropriate for stating a stability property and a domain of dependence inequality for solutions of the energy equation.
Mathematical Models and Methods in Applied Sciences | 1999
Pierluigi Colli; Giorgio Gentili; Claudio Giorgi
This paper is devoted to analyzing solutions of a nonlinear evolution system describing the phase transition in a rigid heat conductor in the presence of phase relaxation. First, in a general framework, a rate type constitutive law for the phase variable is considered and matched with the Helmholtz free energy involving the state of the material. Thermodynamic compatibility of the resulting models is scrutinized. Moreover, a comparison with a different phase change modelling is performed. Under proper assumptions, a nonlinear system in the (absolute) temperature and phase variable is achieved. For it, existence and uniqueness of the solution is proved and positivity of temperature is recovered.
International Journal of Engineering Science | 1995
Giorgio Gentili
Within the linear description of the electromagnetism in the ionosphere we find some thermodynamic potentials. They may be expressed in terms of Fourier transforms and induce suitable norms in the state functional space. In particular, we find even the maximal free enthalpy and the maximal free energy. For each thermodynamic potential we give several representations depending on the choice of the state variables. Finally, we give an application in stability problems.
Journal of Non-Equilibrium Thermodynamics | 1999
Valeria Berti; Giorgio Gentili
Abstract The minimum free energy for a rigid dielectric with linear memory is found under isothermal conditions. The resulting expression is given in the frequency domain, i.e., in terms of the Fourier transform of the variables. By means of such a thermodynamic potential and of the Clausius-Duhem inequality an explicit formula of the dissipation is obtained. Thus the minimum free energy restores the customary relation between the dissipativity and the Clausius-Duhem inequality, that had been proved to fail when memory effects occur. Finally, by virtue of some of its properties, the minimum free energy is viewed as the square of a norm in a suitable space of the variables.
International Journal of Engineering Science | 2001
Giorgio Gentili; Claudio Giorgi
Abstract A one-dimensional memory-based model of magnetic materials exhibiting hysteresis loops is proposed here. Mainly, we suggest a modification of the Duhem model investigated by Coleman and Hodgdon in connection with isoperms in order to better fit their real behaviour. Many properties fulfilled by the original model are preserved here. For instance, the presence of the major loop, bounding all hysteresis paths, the existence and uniqueness of asymptotically stable periodic solutions (primitive loops), the existence of a “universal” demagnetisation process (a suitable alternating magnetic field, with slowly decreasing amplitude, reproducing the “virgin state”). On the other hand, a few mathematical features are common to the Preisach model and allow the corresponding hysteretic functional to avoid effects, like self-magnetisation, which are typical of the Duhem models but physically unsound. In particular, equilibrium states are stable with respect to noises of small amplitude (static vibro-stability).
Quarterly of Applied Mathematics | 1996
Carlo Alberto Bosello; Giorgio Gentili
We study the quasi-static behaviour of a linearly viscoelastic body which is subject to boundary forces respectively of elastic type and of viscous type. The ensuing problems exhibit dynamic boundary conditions. We impose on the memory kernel only those restrictions deriving from thermodynamics and, making use of the Fourier transform method, we show existence and uniqueness of the solution to each problem.
Quarterly of Applied Mathematics | 1993
Claudio Giorgi; Giorgio Gentili
Quarterly of Applied Mathematics | 2002
Giorgio Gentili
Advances in Differential Equations | 2002
Mauro Fabrizio; Giorgio Gentili; John Murrough Golden
Archive | 2006
Giorgio Gentili; Claudio Giorgi