arXiv subjects

Andrea Mentrelli

Publications and source records attributed to Andrea Mentrelli.

12 recordsLinked to original sources

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

Delta-pulse solution in Zener viscoelastic model

We derive the integral representation of the solution for the propagation of a delta-pulse (impulsive wave) in a semi-infinite, homogeneous, linear viscoelastic medium governed by the Zener model. Starting from the Bromwich integral representation of the response function, we obtain a closed-form integral representation by analytically inverting the relevant Laplace transforms. The result is expressed in terms of modified Bessel functions of the first kind and Macdonald functions of half-integer order, and is shown to reduce to the known Maxwell model solution in the appropriate limit. As an independent computational approach, we derive the steepest descent path (SDP) associated with the phase function of the Bromwich integral, characterizing its saddle points and showing that the SDP can be expressed explicitly as the zero locus of a sixth-degree polynomial in the imaginary part of the complex variable. The two methods are compared numerically for several values of the model parameters, confirming their agreement. While the integral representation provides analytical insight into the structure of the solution, the steepest descent method requires no explicit inversion of the Laplace transform and may therefore prove especially valuable in more general viscoelastic settings where a closed-form integral representation is not available.

math-ph↗

arXiv2026

Pulse waves in the viscoelastic Kelvin-Voigt model: a revisited approach

We calculate the mechanical response $r(x,t$) of an initially quiescent semi-infinite homogeneous medium to a pulse applied at the origin, and this is achieved within the framework of the Kelvin-Voigt model. Although this problem has been extensively studied in the literature because of its wide range of applications -- particularly in seismology -- here, we present a solution in a novel integral form. This integral solution avoids the numerical computation of the solution in terms of the inverse Laplace transform; that is, numerical integration in the complex plane. In particular, we derive integral form expressions for both delta-pulse and step-pulse excitations which are simpler and more computationally efficient than those previously reported in the literature. Furthermore, the obtained expressions allow us to obtain simple asymptotic formulas for $r(x,t$ as $x,t \to 0,\infty$ for both step- and delta-type pulses.

math.GM↗

arXiv2025

Transient waves in linear dispersive media with dissipation: an approach based on the steepest descent path

In the study of linear dispersive media it is of primary interest to gain knowledge of the impulse response of the material. The standard approach to compute the response involves a Laplace transform inversion, i.e., the solution of a Bromwich integral, which can be a notoriously troublesome problem. In this paper we propose a novel approach to the calculation of the impulse response, based on the well assessed method of the steepest descent path, which results in the replacement of the Bromwich integral with a real line integral along the steepest descent path. In this exploratory investigation, the method is explained and applied to the case study of the Klein- Gordon equation with dissipation, for which analytical solutions of the Bromwich integral are available, as to compare the numerical solutions obtained by the newly proposed method to exact ones. Since the newly proposed method, at its core, consists in replacing a Laplace transform inverse with a potentially much less demanding real line integral, the method presented here could be of general interest in the study of linear dispersive waves in presence of dissipation, as well as in other fields in which Laplace transform inversion come into play.

math.GM↗

arXiv2025

Quantum dust cores of black holes and their quasi-normal modes

The quantum description of a gravitationally collapsed ball of dust proposed in Ref.~\cite{Casadio:2023ymt} is characterised by a linear effective Misner-Sharp-Hernandez mass function describing a matter core hidden by the event horizon. After reviewing the original model and some of its refinements, we investigate the quasi-normal mode spectrum of the resulting spacetime and compare it with the Schwarzschild case. Computations are performed within the WKB approximation, based on the Pad\'e approximants up to thirteenth order. Our analysis shows that deviations from the Schwarzschild spectrum are sensitive to the quantum nature of the core surface.

gr-qc↗

arXiv2024

Alternative formulations of the thermodynamics of scalar-tensor theories

We explore alternative formulations of the analogy between viable Horndeski gravity and Eckart's first-order thermodynamics. We single out a class of identifications for the effective stress-energy tensor of the scalar field fluid that, upon performing the imperfect fluid decomposition, yields constitutive relations that can be mapped onto Eckart's theory. We then investigate how different couplings to Einstein's gravity, at the level of the field equations, can affect the thermodynamic formalism overall. Last, we specialize the discussion to the case of ``traditional'' scalar-tensor theories and identify a specific choice of the coupling function that leads to a significant simplification of the formalism.

gr-qc↗

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

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↗

arXiv2022

Energy dissipation in viscoelastic Bessel media

We investigate the specific attenuation factor for the Bessel models of viscoelasticity. We find that the quality factor for this class can be expressed in terms of Kelvin functions and that its asymptotic behaviours confirm the analytical results found in previous studies for the rheological properties of these models.

math-ph↗

arXiv2021

A new approach to the thermodynamics of scalar-tensor gravity

We discuss and expand a new approach to the thermodynamics of scalar-tensor gravity and its diffusion toward general relativity (seen as an equilibrium state) proposed in a previous Letter [Phys. Rev. D 103, L121501 (2021)], upon which we build. We describe scalar-tensor gravity as an effective dissipative fluid and apply Eckart's first order thermodynamics to it, obtaining explicitly effective quantities such as heat flux, "temperature of gravity", viscosities, entropy density, plus an equation describing the "diffusion" to Einstein gravity. These quantities, still missing in the usual thermodynamics of spacetime, are obtained with minimal assumptions. Furthermore, we examine certain exact solutions of scalar-tensor gravity to test the proposed formalism and gain some physical insight on the "approach to equilibrium" for this class of theories.

gr-qc↗

arXiv2017

Asymptotic-Preserving scheme for a strongly anisotropic vorticity equation arising in fusion plasma modelling

The electric potential is an essential quantity for the confinement process of tokamak plasmas, with important impact on the performances of fusion reactors. Understanding its evolution in the peripheral region - the part of the plasma interacting with the wall of the device - is of crucial importance, since it governs the boundary conditions for the burning core plasma. The aim of the present paper is to study numerically the evolution of the electric potential in this peripheral plasma region. In particular, we are interested in introducing an efficient Asymptotic-Preserving numerical scheme capable to cope with the strong anisotropy of the problem as well as the non-linear boundary conditions, and this with no huge computational costs. This work constitutes the numerical follow-up of the more mathematical paper by C. Negulescu, A. Nouri, Ph. Ghendrih, Y. Sarazin, "Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics".

physics.plasm-ph↗

arXiv2016

Turbulence and fire-spotting effects into wild-land fire simulators

This paper presents a mathematical approach to model the effects of phenomena with random nature such as turbulence and fire-spotting into the existing wildfire simulators. The formulation proposes that the propagation of the fire-front is the sum of a drifting component (obtained from an existing wildfire simulator without turbulence and fire-spotting) and a random fluctuating component. The modelling of the random effects is embodied in a probability density function accounting for the fluctuations around the fire perimeter which is given by the drifting component. In past, this formulation has been applied to include these random effects into a wildfire simulator based on an Eulerian moving interface method, namely the Level Set Method (LSM), but in this paper the same formulation is adapted for a wildfire simulator based on a Lagrangian front tracking technique, namely the Discrete Event System Specification (DEVS). The main highlight of the present study is the comparison of the performance of a Lagrangian and an Eulerian moving interface method when applied to wild-land fire propagation. Simple idealised numerical experiments are used to investigate the potential applicability of the proposed formulation to DEVS and to compare its behaviour with respect to the LSM. The results show that DEVS based wildfire propagation model qualitatively improves its performance (e.g., reproducing flank and back fire, increase in fire spread due to pre-heating of the fuel by hot air and firebrands, fire propagation across no fuel zones, secondary fire generation, \dots). Though the results presented here are devoid of any validation exercise and provide only a proof of concept, they show a strong inclination towards an intended operational use. The existing LSM or DEVS based operational simulators like WRF-SFIRE and ForeFire respectively can serve as an ideal basis for the same.

physics.ao-ph↗