Sebastiano Pennisi - Academia.edu (original) (raw)
Papers by Sebastiano Pennisi
Entropy, 2021
A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new... more A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bul...
Journal of Mathematical Physics, 2018
Recently Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] proposed a casual hyperbolic model for ... more Recently Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] proposed a casual hyperbolic model for a dissipative relativistic gas with internal structure. In this paper, we consider the particular case of the model when dissipation is negligible (Eulerian gas). We study in particular the energy behavior in comparison with the Synge energy which is valid for monatomic gas and we evaluate the characteristic velocities proving the hyperbolicity of the differential system. The second part of the paper is devoted to the ultra-relativistic limit of the model and we prove that there exists a critical value of the degree of freedom such that for smaller values of this quantity the ultra-relativistic limit of the energy of a gas with structure is the same as the Synge energy, while for larger degrees of freedom the energy increases with the degree of freedom itself.
International Journal of Non-Linear Mechanics, 2021
International Journal of Pure and Apllied Mathematics, 2016
Journal of Computational and Theoretical Transport, 2016
ABSTRACT Extended Thermodynamics of dense gases with an arbitrary but fixed number of moments has... more ABSTRACT Extended Thermodynamics of dense gases with an arbitrary but fixed number of moments has been recently studied in literature. As usual in Extended Thermodynamics, in the field equations some unknown functions appear; restriction on their generalities is obtained by imposing the entropy principle, the Galilean relativity principle, and some symmetry conditions. The solution of these conditions has been obtained by using a Taylor expansion around equilibrium, without proving its convergence but only assuming it. In this article, we find an exact solution without Taylor’ s expansion so avoiding the problem of proving convergence. It will be found through a kinetic type approach. It is not a pure kinetic approach because we do not know the distribution function, but the techniques that are used are similar. If we expand this exact solution around equilibrium, we find the most significative part of the closure previously obtained with the macroscopic approach.
Ricerche di Matematica, 2015
Extended thermodynamics (ET) developed up to now fails when a gas is very dense and is composed o... more Extended thermodynamics (ET) developed up to now fails when a gas is very dense and is composed of molecules with small internal degrees of freedom because the condition of convexity (stability) is violated. The aim of this paper is to explore a possible approach to construct an ET theory that is valid for any dense gas with the condition that it reduces to the usual ET theory when a gas is sufficiently rarefied. We restrict our study, for simplicity, within the simplest case in which the dissipation is only due to the dynamic pressure. Therefore the basic system of equations is the simplest variant of the Euler system, that is, the system composed of the equations for the conservation laws and an equation for the dynamic pressure (6-field theory).
Ricerche di Matematica, 2015
Waves and Stability in Continuous Media, 2006
International Journal of Pure and Apllied Mathematics, 2014
In a 4-dimensional Euclidean space, representation theorems have been recently obtained for isotr... more In a 4-dimensional Euclidean space, representation theorems have been recently obtained for isotropic functions depending on an arbitrary number of scalars, skew-symmetric second order tensors and symmetric second order tensors; the cases has been treated where at least one of these last ones has an eigenvalue with multiplicity 1 or two distinct eigenvalues with multiplicity 2. The case with at least a non null vector, among the independent variables, was already treated in literature. There remain the case where every symmetric tensor has an eigenvalue with multiplicity 4; but, in this case, it plays a role only through its trace. Consequently, it remains the case where the independent variables, besides scalars, are skew-symmetric tensors. This case is treated in the present paper. As in the other cases, the result is a finite set of scalar valued isotropic functions such that every other scalar function of the same variables can be expressed as a function of the elements of this set. Similarly, a set of tensor valued isotropic functions is found such that every other tensor valued function of the same variables can be expressed as a linear combination, trough scalar coefficients, of the elements of this set. This result is achieved both for symmetric functions , and for skew-symmetric functions.
Acta Applicandae Mathematicae, 2014
Ricerche di Matematica, 2006
In extended thermodynamic the entropy principle and the Galilean invariance dictate respectively ... more In extended thermodynamic the entropy principle and the Galilean invariance dictate respectively constraints for the constitutive equations and the velocity dependence. The entropy principle in particular requires the existence of a privileged field, the main field u′, such that the original system becomes symmetric hyperbolic and is generated by four potentials. It is not easy to solve the restrictions of
Ricerche di Matematica, 2010
In this article we aim to furnish arguments for further considerations on some procedures commonl... more In this article we aim to furnish arguments for further considerations on some procedures commonly used in Extended Thermodynamics, such as the Taylor’s expansions around equilibrium or the transition to subsystems. The initial impulse for these considerations lies in the fact that we have found, for a 14 moments model, the exact closure to the conditions arising from the entropy
Meccanica, 2012
An exact macroscopic extended model for ultrarelativistic gases, with an arbitrary number of mome... more An exact macroscopic extended model for ultrarelativistic gases, with an arbitrary number of moments, is present in literature. Here we exploit equations determining wave speeds for the model with 30 independent fields. We find interesting results; for example, the whole system for their determination can be split in some independent subsystems, some wave speeds are expressed by square roots of rational numbers, but not all of them. Moreover these wave speeds for the macroscopic model are the same of those in the kinetic model.
Journal of Mathematical Physics, 2011
In the 1980s, Amendt and Weitzner proposed an interesting model capable to describe relativistic ... more In the 1980s, Amendt and Weitzner proposed an interesting model capable to describe relativistic electron beams. It concerned 14 independent variables and the closure was obtained by using the entropy and the Einstein relativity principles. As we know from literature, an extension to many moments allows to achieve an improvement in the results. Three years ago, we exhibited a macroscopic model with an arbitrary but fixed number of moments for relativistic extended thermodynamics. Such model was more general than those previously appeared in literature, so it was applicable even to materials different from an electron beam. Subsequently, we found the closure of such model consistent with the entropy and the Einstein relativity principles, up to whatever order with respect to equilibrium. The solution was determined in terms of a family of arbitrary single variable functions arising from integration. Those results have a very complex shape and are very difficult to handle so a simplif...
Entropy, 2013
The many moments model for dense gases and macromolecular fluids is considered here, where the up... more The many moments model for dense gases and macromolecular fluids is considered here, where the upper order moment is chosen in accordance to the suggestions of the non-relativistic limit of the corresponding relativistic model. The solutions of the restrictions imposed by the entropy principle and that of Galilean relativity were, until now, obtained in the literature by using Taylor expansions around equilibrium and without proving convergence. Here, an exact solution without using expansions is found. The particular case with only 14 moments has already been treated in the literature in a completely different way. Here, it is proven that this particular closure is included in the presently more general one.
ANNALI DELL'UNIVERSITA' DI FERRARA, 2007
An exact macroscopic extended model, with many moments, for ultrarelativistic gas has been recent... more An exact macroscopic extended model, with many moments, for ultrarelativistic gas has been recently proposed in literature. However, a further condition has not been imposed, even if it is evident in the case of a charged gas and when the electromagnetic field acts as an external force; in the present paper we exploit it and prove that it results in many identities and in residual conditions which allow to determine the arbitrary single variable functions present in the general theory. The result is that they are polynomials determined except for a corresponding number of constants. These are arbitrary constants, so that the macroscopic model remains still more general than the kinetic model.
International Journal of Engineering Science, 1987
Entropy, 2021
A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new... more A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann–Chernikov equation are derived, and the system for the first 15 equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with 14 and 6 moments are deduced as principal subsystems. Particularly interesting is the subsystem with 6 fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bul...
Journal of Mathematical Physics, 2018
Recently Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] proposed a casual hyperbolic model for ... more Recently Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] proposed a casual hyperbolic model for a dissipative relativistic gas with internal structure. In this paper, we consider the particular case of the model when dissipation is negligible (Eulerian gas). We study in particular the energy behavior in comparison with the Synge energy which is valid for monatomic gas and we evaluate the characteristic velocities proving the hyperbolicity of the differential system. The second part of the paper is devoted to the ultra-relativistic limit of the model and we prove that there exists a critical value of the degree of freedom such that for smaller values of this quantity the ultra-relativistic limit of the energy of a gas with structure is the same as the Synge energy, while for larger degrees of freedom the energy increases with the degree of freedom itself.
International Journal of Non-Linear Mechanics, 2021
International Journal of Pure and Apllied Mathematics, 2016
Journal of Computational and Theoretical Transport, 2016
ABSTRACT Extended Thermodynamics of dense gases with an arbitrary but fixed number of moments has... more ABSTRACT Extended Thermodynamics of dense gases with an arbitrary but fixed number of moments has been recently studied in literature. As usual in Extended Thermodynamics, in the field equations some unknown functions appear; restriction on their generalities is obtained by imposing the entropy principle, the Galilean relativity principle, and some symmetry conditions. The solution of these conditions has been obtained by using a Taylor expansion around equilibrium, without proving its convergence but only assuming it. In this article, we find an exact solution without Taylor’ s expansion so avoiding the problem of proving convergence. It will be found through a kinetic type approach. It is not a pure kinetic approach because we do not know the distribution function, but the techniques that are used are similar. If we expand this exact solution around equilibrium, we find the most significative part of the closure previously obtained with the macroscopic approach.
Ricerche di Matematica, 2015
Extended thermodynamics (ET) developed up to now fails when a gas is very dense and is composed o... more Extended thermodynamics (ET) developed up to now fails when a gas is very dense and is composed of molecules with small internal degrees of freedom because the condition of convexity (stability) is violated. The aim of this paper is to explore a possible approach to construct an ET theory that is valid for any dense gas with the condition that it reduces to the usual ET theory when a gas is sufficiently rarefied. We restrict our study, for simplicity, within the simplest case in which the dissipation is only due to the dynamic pressure. Therefore the basic system of equations is the simplest variant of the Euler system, that is, the system composed of the equations for the conservation laws and an equation for the dynamic pressure (6-field theory).
Ricerche di Matematica, 2015
Waves and Stability in Continuous Media, 2006
International Journal of Pure and Apllied Mathematics, 2014
In a 4-dimensional Euclidean space, representation theorems have been recently obtained for isotr... more In a 4-dimensional Euclidean space, representation theorems have been recently obtained for isotropic functions depending on an arbitrary number of scalars, skew-symmetric second order tensors and symmetric second order tensors; the cases has been treated where at least one of these last ones has an eigenvalue with multiplicity 1 or two distinct eigenvalues with multiplicity 2. The case with at least a non null vector, among the independent variables, was already treated in literature. There remain the case where every symmetric tensor has an eigenvalue with multiplicity 4; but, in this case, it plays a role only through its trace. Consequently, it remains the case where the independent variables, besides scalars, are skew-symmetric tensors. This case is treated in the present paper. As in the other cases, the result is a finite set of scalar valued isotropic functions such that every other scalar function of the same variables can be expressed as a function of the elements of this set. Similarly, a set of tensor valued isotropic functions is found such that every other tensor valued function of the same variables can be expressed as a linear combination, trough scalar coefficients, of the elements of this set. This result is achieved both for symmetric functions , and for skew-symmetric functions.
Acta Applicandae Mathematicae, 2014
Ricerche di Matematica, 2006
In extended thermodynamic the entropy principle and the Galilean invariance dictate respectively ... more In extended thermodynamic the entropy principle and the Galilean invariance dictate respectively constraints for the constitutive equations and the velocity dependence. The entropy principle in particular requires the existence of a privileged field, the main field u′, such that the original system becomes symmetric hyperbolic and is generated by four potentials. It is not easy to solve the restrictions of
Ricerche di Matematica, 2010
In this article we aim to furnish arguments for further considerations on some procedures commonl... more In this article we aim to furnish arguments for further considerations on some procedures commonly used in Extended Thermodynamics, such as the Taylor’s expansions around equilibrium or the transition to subsystems. The initial impulse for these considerations lies in the fact that we have found, for a 14 moments model, the exact closure to the conditions arising from the entropy
Meccanica, 2012
An exact macroscopic extended model for ultrarelativistic gases, with an arbitrary number of mome... more An exact macroscopic extended model for ultrarelativistic gases, with an arbitrary number of moments, is present in literature. Here we exploit equations determining wave speeds for the model with 30 independent fields. We find interesting results; for example, the whole system for their determination can be split in some independent subsystems, some wave speeds are expressed by square roots of rational numbers, but not all of them. Moreover these wave speeds for the macroscopic model are the same of those in the kinetic model.
Journal of Mathematical Physics, 2011
In the 1980s, Amendt and Weitzner proposed an interesting model capable to describe relativistic ... more In the 1980s, Amendt and Weitzner proposed an interesting model capable to describe relativistic electron beams. It concerned 14 independent variables and the closure was obtained by using the entropy and the Einstein relativity principles. As we know from literature, an extension to many moments allows to achieve an improvement in the results. Three years ago, we exhibited a macroscopic model with an arbitrary but fixed number of moments for relativistic extended thermodynamics. Such model was more general than those previously appeared in literature, so it was applicable even to materials different from an electron beam. Subsequently, we found the closure of such model consistent with the entropy and the Einstein relativity principles, up to whatever order with respect to equilibrium. The solution was determined in terms of a family of arbitrary single variable functions arising from integration. Those results have a very complex shape and are very difficult to handle so a simplif...
Entropy, 2013
The many moments model for dense gases and macromolecular fluids is considered here, where the up... more The many moments model for dense gases and macromolecular fluids is considered here, where the upper order moment is chosen in accordance to the suggestions of the non-relativistic limit of the corresponding relativistic model. The solutions of the restrictions imposed by the entropy principle and that of Galilean relativity were, until now, obtained in the literature by using Taylor expansions around equilibrium and without proving convergence. Here, an exact solution without using expansions is found. The particular case with only 14 moments has already been treated in the literature in a completely different way. Here, it is proven that this particular closure is included in the presently more general one.
ANNALI DELL'UNIVERSITA' DI FERRARA, 2007
An exact macroscopic extended model, with many moments, for ultrarelativistic gas has been recent... more An exact macroscopic extended model, with many moments, for ultrarelativistic gas has been recently proposed in literature. However, a further condition has not been imposed, even if it is evident in the case of a charged gas and when the electromagnetic field acts as an external force; in the present paper we exploit it and prove that it results in many identities and in residual conditions which allow to determine the arbitrary single variable functions present in the general theory. The result is that they are polynomials determined except for a corresponding number of constants. These are arbitrary constants, so that the macroscopic model remains still more general than the kinetic model.
International Journal of Engineering Science, 1987