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Tommaso Ruggeri

Publications and source records attributed to Tommaso Ruggeri.

At least 19 recordsLinked to original sources
arXiv2026

Toward a Rational Extended Thermodynamics of dispersive elastic media

We develop a one-dimensional theory of dispersive elasticity within Rational Extended Thermodynamics, taking local first-order balance laws rather than higher spatial gradients as the fundamental description. A supplementary mechanical-energy law and the Ruggeri--Strumia main-field principle determine the admissible stress, internal fluxes and production. A canonical two-field hierarchy is symmetric hyperbolic under explicit convexity conditions and contains nonlinear elasticity and a generalized-stress theory as principal subsystems. For the reversible linear singular two-field class, elimination of the fast stress mode yields the Love--Rosenau equation exactly, together with a necessary and sufficient realizability condition. Nonlinear elastic stresses and non-quadratic higher-field energies are compatible with the same RET architecture; for the exact nonlinear Love--Rosenau reduction we retain quadratic higher-field inertia while allowing nonlinear elastic stress. The reduced equation admits a travelling-wave first integral. For the leading cubic elastic correction we obtain an exact parametric smooth solitary pulse in a supersonic velocity window, while the truncated-cosine compacton is excluded. Direct simulations of the hyperbolic parent system show finite-time pulse persistence in the reversible regime and slow decay under weak dissipation. The local parent energy flux is kept distinct from interstitial working in the reduced theory.

math-ph↗
arXiv2026

Nonisothermal Shock Structure and Universal Flow-Index Thresholds in a Hyperbolic Power-Law Fluid

We investigate whether the two flow-index thresholds previously found for isothermal shock profiles persist when the full nonisothermal dynamics is taken into account in a hyperbolic power-law relaxation model of Rational Extended Thermodynamics. The nonisothermal profile problem is structurally different from its isothermal counterpart: restoring the energy balance determines the temperature along the traveling wave and feeds it back into the pressure, the relaxation production, the temperature-dependent consistency coefficient, and the characteristic structure. Under thermodynamic stability, $p_\theta\ge0$, and strict convexity of the reduced Hugoniot pressure, no nontrivial constant-temperature compressive profile can satisfy the full equations. We derive an exact global characteristic-ordering identity and prove that the positive nonequilibrium characteristic speed has its strict global minimum at the unperturbed upstream state. Consequently, a monotone continuous profile exists for $1 \Mst$ the Boillat--Ruggeri theorem excludes a $C^1$ profile and any admissible piecewise-smooth connection must contain a subshock. Despite the thermomechanical coupling, the shock-thickness classification remains unchanged: $m=2$ is the weak-shock threshold and $m=1$ the near-critical threshold as $M_0\nearrow\Mst$. The corresponding exponents are constitutive-independent within the present class, while finite limiting values and prefactors depend on the equation of state, internal energy, and temperature-dependent consistency coefficient. For the Tait--Murnaghan example, increasing the reference temperature lowers the critical Mach number when the dimensional viscous--relaxation scale is fixed and, for the thermally thinning law considered, reduces the resolved shock thickness.

physics.flu-dyn↗
arXiv2026

Six-Field Rational Extended Thermodynamics of Polyatomic Gases in Curved Spacetime

We formulate a generally covariant six-field Rational Extended Thermodynamics model (RET$_6$) for relativistic polyatomic gases, with the dynamical pressure as the only non-equilibrium variable. The model is based on a polyatomic extension of the Boltzmann-Chernikov kinetic equation, where the one-particle distribution depends also on an internal-energy variable, and on the Maximum Entropy closure of the associated relativistic moment hierarchy. The resulting field equations, closure relations, and production term are therefore fixed by the underlying kinetic structure rather than postulated phenomenologically. We extend the RET$_6$ model from Minkowski spacetime to a general curved spacetime by the minimal coupling prescription and couple it to the Einstein equations. As a first structural result, we prove a kinetic-theory no-go theorem in this polyatomic RET setting stating that any stress-energy tensor induced by a non-negative relativistic one-particle distribution function satisfies the strong energy condition. We then specialize the theory to a homogeneous and isotropic Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) spacetime. In this setting the dynamical pressure modifies the expansion dynamics with respect to the perfect-fluid Euler case, but the no-go theorem excludes acceleration driven by the RET$_6$ gas alone. Finally, we reintroduce a cosmological constant and study the combined $\Lambda$RET$_6$ model. For the diatomic equation of state and a constant positive relaxation time, we prove the existence and local stability of a de Sitter attractor at late times. Numerical integrations show that, for representative post-recombination initial data and constant relaxation times, the expansion history rapidly approaches that of $\Lambda$CDM, with small non-equilibrium corrections controlled by the relaxation time and by the initial value of the dynamical pressure.

gr-qc↗
arXiv2026

Acceleration Waves and the K-Condition in Viscoelastic Solids and Non-Newtonian Fluids

The K-condition introduced by Shizuta and Kawashima provides a sufficient criterion for the global existence of smooth solutions to dissipative hyperbolic systems. For genuinely nonlinear characteristic fields, a weaker K-condition becomes necessary, although not sufficient. In this paper, we analyze this weaker K-condition through the study of acceleration waves propagating in an equilibrium state. We investigate two classes of hyperbolic models: one describing viscoelasticity with linear dissipation, and the other non-Newtonian fluids asymptotically converging to a power-law behavior. For viscoelastic models, the weaker K-condition is always satisfied and acceleration waves remain bounded. For non-Newtonian fluids, the validity of the condition depends on the power-law index $m$: it holds for Newtonian fluids ($m=1$), is violated for shear-thinning fluids ($m<1$), and leads to an instantaneous regularization of acceleration waves for shear-thickening fluids ($m>1$).

math-ph↗
arXiv2025

Self-Similar Radially Symmetric Solutions of the Relativistic Euler Equations with Synge Energy

We consider self-similar, radially symmetric solutions of the relativistic Euler equations with constitutive relations from relativistic kinetic theory, based on Synge energies for monatomic and its extension to diatomic gases. For the corresponding initial--boundary value problem, including the spherical piston problem, we prove existence and uniqueness of solutions valid for all values of the relativistic parameter $γ= mc^{2}/(k_{B}T)$, thus covering both the classical limit $(γ\to \infty)$ and the ultra-relativistic regime $(γ\to 0)$. We further establish key structural properties of Synge energies, showing the strict negativity of the second derivative with respect to pressure at constant entropy and the monotone dependence of the characteristic velocity on $γ$. These results extend the classical theory of self-similar flows to the relativistic framework with kinetic-theory-based constitutive equations.

math.AP↗
arXiv2025

Emergent behaviors of relativistic thermodynamic flocks with Synge energy

Collective motion and self-organization of interacting particles, such as flocking and swarming, can be viewed as nonequilibrium analogues of collective dynamics in gases. Motivated by the analogy between gas mixtures and Cucker--Smale models, we introduce a polyatomic classical model and its relativistic counterpart based on the Synge energy, and analyze their large-time behavior. The relativistic formulation provides a physically consistent setting for multi-species systems where inertia and internal energy depend on temperature, as occurs in astrophysical plasmas or relativistic fluids. Using the entropy principle, we derive uniform lower bounds for temperature and establish asymptotic flocking under various communication kernels. For nearly constant interactions, flocking emerges from arbitrary initial data. The results clarify how thermodynamic effects and relativistic corrections modify the emergence of coherent motion in particle systems, bridging kinetic theory, relativistic fluid mixtures, and collective dynamics.

math.AP↗
arXiv2025

Rational Extended Thermodynamics for Non-Newtonian Fluids with Finite Relaxation Time

We introduce a one-dimensional, hyperbolic model for non-Newtonian fluids with finite relaxation time, derived within the framework of Rational Extended Thermodynamics (RET). Unlike classical parabolic models, our formulation preserves finite signal speeds, thermodynamic consistency, and mathematical well-posedness. The model captures viscoelastic phenomena via a nonlinear evolution of stress, converging to power-law rheology in the vanishing relaxation limit. Notably, it mimics the Phan-Thien-Tanner model under steady shear, but derives from first principles, offering a predictive alternative to empirical rheology.

math-ph↗
arXiv2025

The Maximum Entropy Principle in Nonequilibrium Thermodynamics: A Brief History and the Contributions of Wolfgang Dreyer

We present a brief history of how the famous Maximum Entropy Principle was used as closure of moments of the Boltzmann equation. In particular, we want to remark on the important role of two fundamental papers by Wolfgang Dreyer, one in the classical framework and one in a relativistic context, to use this principle and to compare the result with the macroscopic theory of Rational Extended Thermodynamics.

math-ph↗
arXiv2024

Optimal convergence speed in the classical limits of relativistic Cucker-Smale models

We study quantitative estimates for the flocking and uniform-time classical limit to the relativistic Cucker-Smale (in short RCS) model introduced in \cite{Ha-Kim-Ruggeri-ARMA-2020}. Different from previous works, we do not neglect the relativistic effect on the presence of the pressure in momentum equation. For the RCS model, we provide a quantitative estimate on the uniform-time classical limit with an optimal convergence rate which is the same as in finite-time classical limit under a relaxed initial condition. We also allow corresponding initial data for the RCS and Cucker-Smale (CS) model to be different in the classical limit. This removes earlier constraints employed in the previous classical limit. As a direct application of this optimal convergence rate in the classical limit of the RCS model, we derive an optimal convergence rate for the corresponding uniform-time classical limit for the kinetic RCS model.

math.AP↗
arXiv2024

A Novel ES-BGK Model for Non-Polytropic Gases with Internal State Density Independent of the Temperature

A novel ES-BGK-based model of non-polytropic rarefied gases in the framework of kinetic theory is presented. Key features of this model are: an internal state density function depending only on the microscopic energy of internal modes (avoiding the dependence on temperature seen in previous reference studies); full compliance with the H-theorem; feasibility of the closure of the system of moment equations based on the maximum entropy principle, following the well-established procedure of Rational Extended Thermodynamics. The structure of planar shock waves in carbon dioxide (CO$_2$) obtained with the present model is in general good agreement with that of previous results, except for the computed internal temperature profile, which is qualitatively different with respect to the results obtained in previous studies, showing here a consistently monotonous behavior across the shock structure, rather than the non monotonous behavior previously found.

cond-mat.stat-mech↗
arXiv2024

On the comparison between phenomenological and kinetic theories of gas mixtures with applications to flocking

We study the compression between the phenomenological and kinetic models for a mixture of gases from the viewpoint of collective dynamics. In the case in which constituents are Eulerian gases, balance equations for mass, momentum, and energy are the same in the main differential part, but production terms due to the interchanges between constituents are different. They coincide only when the thermal and mechanical diffusion are sufficiently small. In this paper, we first verify that both models satisfy the universal requirements of conservation laws of total mass, momentum, and energy, Galilean invariance and entropy principle. Following the work of Ha and Ruggeri (ARMA 2017), we consider spatially homogeneous models which correspond to the generalizations of the Cucker Smale model with the thermal effect. In these circumstances, we provide analytical results for the comparison between two resulting models and also present several numerical simulations to complement analytical results.

math.DS↗
arXiv2024

Energy of a non-linear viscoelastic model compatible with fractional relaxation

Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the non-linear realm, provided that the viscous energy function is given. This work aims at establishing a possible constitutive law for the viscous energy such that the relaxation modulus of the fractional Maxwell model of order $α\in (1/2, 1]$ is contained within the solutions of the (non-linear) relaxation experiment. Necessary and sufficient conditions for the existence of this coincident solution are discussed, together with a numerical evaluation of the viscous energy associated with the non-linear model.

math-ph↗
arXiv2024

A Nonlinear approach to Viscoelasticity via Rational Extended Thermodynamics

In the one-dimensional isothermal case, we introduce a simple model of nonlinear viscoelasticity within the Rational Extended Thermodynamics (RET) framework. The differential system is determined by the universal principles of RET, exhibiting symmetric hyperbolic form and ensuring the existence of smooth solutions for appropriately small initial data. In the linear case, the equation for viscous stress reduces to the well-known Maxwell model, thereby representing a plausible nonlinear extension of the Maxwell-type model. The total stress instead satisfies a non-linear Zener model.

cond-mat.soft↗
arXiv2023

Dispersion Relations of Longitudinal and Transverse Waves in a Rarefied Polyatomic Gas based on Rational Extended Thermodynamics

We present a complete analysis of the dispersion relations for longitudinal and transverse waves in a rarefied polyatomic gas based on Rational Extended Thermodynamics (RET), which describes the evolution of a non-polytropic gas in nonequilibrium. Observability of the second mode of the longitudinal wave and the transverse wave is discussed although these waves are usually not payed much attention. The cases of CO$_2$ gas and para-H$_2$ gas are specifically analyzed as typical examples.

physics.flu-dyn↗
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↗