arXiv subjects

F. Demontis

Publications and source records attributed to F. Demontis.

4 recordsLinked to original sources

arXiv2023

On two possible ways to recover Ordinary Thermodynamics from Extended Thermodynamics of Polyatomic gases

We consider two possible ways, i.e., the Maxwellian Iteration and the Chapman-Enskog Method, to recover Relativistic Ordinary Thermodynamics from Relativistic Extended Thermodynamics of Polyatomic gases with N moments. Both of these methods give the Eckart equations which are the relativistic version of the Navier-Stokes and Fourier laws as a first iteration. However, these methods do not lead to the same expressions of the heat conductivity \chi, the shear viscosity \mu, and the bulk viscosity \nu which appear as coefficients in the Eckart equations. In particular, we prove that the expressions of \chi, \mu, and \nu obtained via the Chapman-Enskog method do not depend on N , while those obtained through the Maxwellian Iteration depend on N . Moreover, we also prove that these two methods lead to the same results in the nonrelativistic limit.

math-ph↗

arXiv2023

Rogue wave formation scenarios for the focusing nonlinear Schr\"odinger equation with parabolic-profile initial data on a compact support

We study the (1+1) focussing nonlinear Schr\"{o}dinger equation for an initial condition with compactly-supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blow-up in finite time, generalising a result by Talanov et al. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semi-classical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularisation of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counter-propagating dispersive dam break flows, as in the box problem recently studied by El, Khamis and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics.

math-ph↗

arXiv2018

Effective Generation of Closed-form Soliton Solutions of the Continuous Classical Heisenberg Ferromagnet Equation

The non-topological, stationary and propagating, soliton solutions of the classical continuous Heisenberg ferromagnet equation are investigated. A general, rigorous formulation of the Inverse Scattering Transform for this equation is presented, under less restrictive conditions than the Schwartz class hypotheses and naturally incorporating the non-topological character of the solutions. Such formulation is based on a new triangular representation for the Jost solutions, which in turn allows an immediate computation of the asymptotic behaviour of the scattering data for large values of the spectral parameter, consistently improving on the existing theory. A new, general, explicit multi-soliton solution formula, amenable to computer algebra, is obtained by means of the matrix triplet method, producing all the soliton solutions (including breather-like and multipoles), and allowing their classification and description.

math-ph↗

arXiv2010

Wave Speed in the Macroscopic Extended Model for Ultrarelativistic Gases

An exact macroscopic extended model for ultrarelativistic gases, with an arbitrary number of moments, is present in the literature. Here we exploit equations determining wave speeds for that model. We find interesting results; for example, the whole system for their determination can be divided into independent subsystems and some, but not all, wave speeds are expressed by rational numbers. Moreover, the extraordinary property that these wave speeds for the macroscopic model are the same of those in the kinetic model, is proved.

math-ph↗