arXiv subjects

Tommaso Ruggeri

Publications and source records attributed to Tommaso Ruggeri.

At least 37 records · Page 2Linked to original sources

arXiv2023

Effect of the dynamic pressure on the shock structure and sub-shocks formation in a mixture of polyatomic gases

We study the shock structure and the sub-shocks formation in a binary mixture of rarefied polyatomic gases, considering the dissipation only due to the dynamic pressure. We classify the regions depending on the concentration and the Mach number for which there may exist the sub-shock in the profile of shock structure in one or both constituents or not for prescribed values of the mass ratio of the constituents and the ratios of the specific heats. We compare the regions with the ones of the corresponding mixture of Eulerian gases and we perform the numerical calculations of the shock structure for typical cases previously classified and confirm whether sub-shocks emerge.

physics.flu-dyn↗

arXiv2023

Eckart equations, Maxwellian iteration and Relativistic Causal Theories of Divergence type

We consider a general causal relativistic theory of divergence type in the framework of Rational Extended Thermodynamics (RET) for a compressible, possibly dense, gas. We require that the system converges in the Maxwellian iteration's first step to the parabolic Eckart equations. This requirement implies a constraint between the two coefficients present in the triple tensor evaluated at equilibrium. Moreover, the production tensor is determined for prescript thermal and caloric state equations and given heat conductivity, shear, and bulk viscosities. In the second part, we prove that if the original hyperbolic system satisfies the universal principles of RET, as can be put in the symmetric form using the \emph{main field}, it always satisfies the previous compatibility condition. Therefore any causal system of divergence type that satisfies the entropy principle with a convex entropy converges to the Eckart system in the Maxwellian iteration also when we have no information at the mesoscopic scale from the kinetic theory. The obtained results are tested on the RET theories of rarefied monatomic and polyatomic gases.

math-ph↗

arXiv2022

A Complete Classification of Sub-Shocks in the Shock Structure of a Binary Mixture of Eulerian Gases with Different Degrees of Freedom

The shock structure in a binary mixture of polyatomic Eulerian gases with different degrees of freedom of a molecule is studied based on the multi-temperature model of rational extended thermodynamics. Since the system of field equations is hyperbolic, the shock-structure solution is not always regular, and discontinuous parts (sub-shocks) can be formed. For given values of the mass ratio and the specific heats of the constituents, we identify the possible sub-shocks as the Mach number $M_0$ of the shock wave and the concentration $c$ of the constituents change. In the plane $(c,M_0)$, we identify the possible regions for the sub-shock formation. The analysis is obtained to verify when the velocity of the shock wave meets a characteristic velocity in the unperturbed or perturbed equilibrium states that gives a necessary condition for the sub-shock formation. The condition becomes necessary and sufficient when the velocity of the shock becomes greater than the maximum characteristic velocity in the unperturbed state. Namely, the regions with no sub-shocks, a sub-shock for only one constituent, or sub-shocks for both constituents are comprehensively classified. The most interesting case is that the lighter molecule has more degrees of freedom than that of the heavy one. In this situation, the topology of the various regions becomes different. We also solve the system of the field equations numerically using the parameters in the various regions and confirm whether the sub-shocks emerge or not. Finally, the relationship between an acceleration wave in a constituent and the sub-shock in the other constituent is explicitly derived.

physics.flu-dyn↗

arXiv2022

Relativistic Kinetic Theory of Polyatomic Gases: Classical Limit of a New Hierarchy of Moments and Qualitative Analysis

A relativistic version of the Kinetic Theory for polyatomic gas is considered and a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal modes is presented. In the first part, we prove via classical limit that the truncated system of moments dictates a precise hierarchy of moments in the classical framework. In the second part, we consider the particular physical case of fifteen moments closed via Maximum Entropy Principle in a neighborhood of equilibrium state. We prove that this symmetric hyperbolic system satisfies all the general assumption of some theorems that guarantee the global existence of smooth solutions for initial data sufficiently small.

cond-mat.stat-mech↗

arXiv2021

Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments

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 bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.

cond-mat.stat-mech↗

arXiv2021

Which moments are appropriate to describe gases with internal structure in Rational Extended Thermodynamics?

Motivated by a recent paper of Pennisi (2021) in the relativistic framework, we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differential system of the previous approach is proved to be a \emph{principal subsystem} of the present one. The main idea is that at the molecular level, the total energy is the kinetic energy plus the energy of internal mode due to the rotation and vibration, and the increasing moments contain this total energy as power in which the power index increases with the number of tensorial indexes. In particular, we consider the case of $15$ moments, and we close the system using the variational method of the Maximum Entropy Principle. We prove the convexity of entropy and the possibility to put the system in symmetric form. This more rich kinetic framework may be interesting also as possible applications to biomathematics or other fields in which kinetic models were applied recently with success.

cond-mat.stat-mech↗

arXiv2021

On a relativistic BGK model for polyatomic gases near equilibrium

Recently, a novel relativistic polyatomic BGK model was suggested by Pennisi and Ruggeri [J. of Phys. Conf. Series, 1035, (2018)] to overcome drawbacks of the Anderson-Witting model and Marle model.In this paper, we prove the unique existence and asymptotic behavior of classical solutions to the relativistic polyatomic BGK model when the initial data is sufficiently close to a global equilibrium.

math.AP↗

arXiv2020

Molecular Extended Thermodynamics of Rarefied Polyatomic Gases with a new Hierarchy of Moments

Recently, Pennisi and Ruggeri [J Stat Phys 179, 231-246 (2020)] consider the classical limit of the relativistic theory of moments associated with the Boltzmann-Chernikov equation truncated at a tensorial index $N+1$ and they proved that there exists a unique possible choice of the moments in the classical case for a given $N$ both for monatomic and polyatomic gases. In particular, in polyatomic gases, there exists a new hierarchy of moments that is more general than the one considered in the recent literature. As consequence, when $N=2$, in the classical limit, there is a theory with $15$ fields. In this paper, we consider this system of moments, and we close the system using the maximum entropy principle. It is shown that the theory contains as a principal subsystem the previously polyatomic $14$ fields theory, and in the monatomic limit, in which the dynamical pressure vanishes, the differential system converges instead to Grad 13-moments system to the 14 moments theory proposed by Kremer [Annales de l'I.H.P. Physique théorique, 45, 419-440 (1986)].

cond-mat.stat-mech↗

arXiv2020

Emergent behaviors of Thermodynamic Kuramoto ensemble on a regular ring lattice

The temporal evolution of Kuramoto oscillators influenced by the temperature field often appears in biological oscillator ensembles. In this paper, we propose a generalized Kuramoto type lattice model on a regular ring lattice with the equal spacing assuming that each oscillator has an internal energy (temperature). Our lattice model is derived from the thermodynamical Cucker-Smale model for flocking on the 2D free space under the assumption that the ratio between velocity field and temperature field at each lattice point has a uniform magnitude over lattice points. The proposed model satisfies an entropy principle and exhibits emergent dynamics under some sufficient frameworks formulated in terms of initial data and system parameters. Moreover, the phase-field tends to the Kuramoto phase-field asymptotically.

math.DS↗

arXiv2020

The Riemann problem of relativistic Euler system with Synge energy

In this paper, we study the Riemann problem of relativistic Euler system for rarefied monatomic and diatomic gases when the constitutive equation for the energy is the Synge equation that is the only one compatible with the relativistic kinetic theory. The Synge equation is involved with modified Bessel functions of the second kind and this makes the relativistic Euler system quite complex. Based on delicate estimates of the modified Bessel functions of the second kind, we provide a detailed investigation of basic hyperbolic properties and the structure of elementary waves, especially for the structure of shock waves and in this way, the mathematical theory of the Riemann problem for these relativistic Euler system, which is analogous to the corresponding theory of the classical ones, is rigorously provided.

math-ph↗

arXiv2018

Fluid mixtures in nanotubes

The aim of the paper is the study of fluid mixtures in nanotubes by the methods of continuum mechanics. The model starts from a statistical distribution in mean-field molecular theory and uses a density expansion of Taylor series. We get a continuous expression of the volume free energy with density's spatial-derivatives limited at the second order. The nanotubes can be filled with liquid or vapor according to the chemical characteristics of the walls and of liquid or vapor mixture-bulks. An example of two-fluid mixture constituted of water and ethanol inside carbon nanotubes at 20{\textdegree} C is considered. When diameters are small enough, nanotubes are filled with liquid-mixture whatever are the liquid or vapor mixture-bulks. The carbon wall influences the ratio of the fluid components in favor of ethanol. The fluid-mixture flows across nanotubes can be much more important than classical ones and if the external bulk is vapor, the flow can be several hundred thousand times larger than Poiseuille flow.

physics.flu-dyn↗

arXiv2017

Ultrarelativistic limit of a Rarefied Gas with Internal Structure

The aim of this letter is to check the ultra-relativistic limit of a recent model proposed by Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] for a relativistic gas with internal structure. Considering an Eulerian fluid 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 for monatomic gases, while for larger degrees of freedom the energy increases with the degree of freedom itself. The limiting equations are accompanied with the explicit expression of the characteristic velocities of the hyperbolic system.

cond-mat.stat-mech↗

arXiv2017

On the sub-shock formation in extended thermodynamics

In hyperbolic dissipative systems, the solution of the shock structure is not always continuous and a discontinuous part (sub-shock) appears when the velocity of the shock wave is greater than a critical value. In principle, the sub-shock may occur when the shock velocity $s$ reaches one of the characteristic eigenvalues of the hyperbolic system. Nevertheless, Rational Extended Thermodynamics (ET) for a rarefied monatomic gas predicts the sub-shock formation only when $s$ exceeds the maximum characteristic velocity of the system evaluated in the unperturbed state $λ^{\max}_0$. This fact agrees with a general theorem asserting that continuous shock structure cannot exist for $s >λ^{\max}_0 $. In the present paper, first, the shock structure is numerically analyzed on the basis of ET for a rarefied polyatomic gas with $14$ independent fields. It is shown that, also in this case, the shock structure is still continuous when $s$ meets characteristic velocities except for the maximum one and therefore the sub-shock appears only when $s >λ^{\max}_0 $. This example reinforces the conjecture that, the differential systems of ET theories have the special characteristics such that the sub-shock appears only for $s$ greater than the unperturbed maximum characteristic velocity. However, in the second part of the paper, we construct a counterexample of this conjecture by using a simple $2 \times 2$ hyperbolic dissipative system which satisfies all requirements of ET. In contrast to previous results, we show the clear sub-shock formation with a slower shock velocity than the maximum unperturbed characteristic velocity.

physics.flu-dyn↗

arXiv2017

Rational Extended Thermodynamics of a Rarefied Polyatomic Gas with Molecular Relaxation Processes

We present a more refined version of rational extended thermodynamics of rarefied polyatomic gases in which molecular rotational and vibrational relaxation processes are treated individually. In this case we need a triple hierarchy of the moment system and the system of balance equations is closed via the maximum entropy principle. Three different types of the production terms in the system, which are suggested by a generalized BGK-type collision term in the Boltzmann equation, are adopted. In particular, the rational extended thermodynamic theory with seven independent fields (ET7) is analyzed in detail. Finally, the dispersion relation of ultrasonic wave derived from the ET7 theory is confirmed by the experimental data for CO2, Cl2, and Br2 gases.

cond-mat.stat-mech↗

arXiv2015

Dynamical pressure for fluid mixtures with several temperatures

We consider binary mixtures of fluids with components having different temperatures. A new dynamical pressure term is associated with the difference of temperatures between components even if fluid viscosities are null. The non-equilibrium dynamical pressure can be measured and may be convenient in several physical situations as for example in cosmological circumstances where a dynamical pressure played a major role in the evolution of the early universe.

physics.class-ph↗

arXiv2015

Non-Linear Maximum Entropy Principle for a Polyatomic Gas subject to the Dynamic Pressure

We establish Extended Thermodynamics (ET) of rarefied polyatomic gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. The closure is accomplished by the Maximum Entropy Principle (MEP) adopting a distribution function that takes into account the internal degrees of freedom of a molecule. The distribution function is not necessarily near equilibrium. The result is in perfect agreement with the phenomenological ET theory. To my knowledge, this is the first example of molecular extended thermodynamics with a non-linear closure. The integrability condition of the moments requires that the dynamical pressure should be bounded from below and from above. In this domain the system is symmetric hyperbolic. Finally we verify the K-condition for this model and show the existence of global smooth solutions.

math-ph↗

arXiv2012

On the Müller paradox for thermal-incompressible media

In his monograph Thermodynamics, I. Müller proves that for incompressible media the volume does not change with the temperature. This Müller paradox yields an incompatibility between experimental evidence and the entropy principle. This result has generated much debate within the mathematical and thermodynamical communities as to the basis of Boussinesq approximation in fluid dynamics. The aim of this paper is to prove that for an appropriate definition of incompressibility, as a limiting case of quasi thermal-incompressible body, the entropy principle holds for pressures smaller than a critical pressure value. The main consequence of our result is the physically obvious one, that for very large pressures, no body can be perfectly incompressible. The result is first established in the fluid case. In the case of hyperelastic media subject to large deformations the approach is similar, but with a suitable definition of the pressure associated with convenient stress tensor decomposition.

physics.class-ph↗

arXiv2012

A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials

In this paper we consider the conditions on quasi-thermal-incompressible so that they satisfy all the principles of thermodynamics, including the stability condition associated with the concavity of the chemical potential. We analyze the approximations under which a quasi-thermal-incompressible medium can be considered as incompressible. We find that the pressure cannot exceed a very large critical value and that the compressibility factor must be greater than a lower limit that is very small. The analysis is first done for the case of fluids and then extended to the case of thermoelastic solids.

physics.class-ph↗