A hyperbolic reaction–diffusion model of chronic wasting disease

Barbera, Elvira; Pollino, Annamaria

doi:10.1007/s11587-023-00831-8

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…The constitutive relations are obtained by the use of physical universal principles like the Galilean invariance and the entropy principles. The propagation of acceleration waves in Rational Extended Thermodynamics is well-developed, providing interesting results; see, for example, [3,[24][25][26][28][29][30][31] and the references therein.…”

Section: Field Equationsmentioning

confidence: 99%

“…Another application field is human health research, such as blood flow [14,32]. Acceleration waves have been applied to different real phenomena, such as the application of fluids in a gravitational atmosphere [24], fluid bubbles [25], fluid mixtures [27], biological applications in chemo-taxis [28], and in chronic wasting diseases [29].…”

Section: Possible Applications In Real Fieldsmentioning

confidence: 99%

“…The objective is to establish a critical value of the amplitude of the wave below which the acceleration wave does not degenerate into a shock. This analysis has also been recently investigated in different materials, such as fluids [24], bubbles [25,26], fluid mixtures [27], and biological models [28,29].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Investigation of 1D Discontinuity Waves in Dilute Granular Gases

Barbera,

Pollino

2023

Mathematics

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The propagation of acceleration waves in dilute granular gases was investigated. Acceleration waves propagating in elastic gases, mixtures, and other materials are widely studied in the literature, but not in granular gases. A thirteen-moment theory for granular gas was considered in the framework of Grad’s theory. The spatially homogeneous solutions were determined, and the hyperbolicity of the model is discussed. The propagation of acceleration waves in a non-constant state was investigated; the amplitude of the fastest mode was derived, and the critical time was evaluated. The acceleration wave propagation velocity in inelastic gases was shown to be lower than in elastic gases.

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Section: Field Equationsmentioning

confidence: 99%

Section: Possible Applications In Real Fieldsmentioning

confidence: 99%

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Mathematical Investigation of 1D Discontinuity Waves in Dilute Granular Gases

Barbera,

Pollino

2023

Mathematics

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“…ET has been applied, with many interesting results, to monoatomic gases [1] and mixtures [2][3][4], showing in particular the possibility of describing the thermal-diffusion effect. Recently, ET has been generalized to dense and rarefied polyatomic gases both in the classical [2,3,5] and in the relativistic framework [6][7][8], with respect to metal electrons [9], quantum systems [10], graphene [11], biological models [12][13][14], blood flow [15,16], heat transfer in different symmetries [17] and gas bubbles [18,19], providing in all cases relevant results. In the last 40 years, there were different attempts to describe viscoelastic fluids using the methods of Extended Thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

An Extended Thermodynamics Study for Second-Grade Adiabatic Fluids

Barbera,

Fazio

2024

Axioms

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A 10-field theory for second-grade viscoelastic fluids is developed in the framework of Rational Extended Thermodynamics. The field variables are the density, the velocity, the temperature and the stress tensor. The particular case of an adiabatic fluid is considered. The field equations are determined by use of physical universal principles such as the Galileian and the Entropy Principles. As already proved, Rational Extended Thermodynamics is able to eliminate some inconsistencies with experiments that arise in Classical Thermodynamics. Moreover, the paper shows that, if the quadratic terms are taken into account, the classical constitutive relations for a second-grade fluid can be obtained as a limit case of the field equations of the present theory.

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A Rational Extended Thermodynamic Model for Nanofluids

Barbera,

Pollino

2024

Fluids

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A model of quasilinear differential equations is derived in the context of Rational Extended Thermodynamics to investigate some non-equilibrium phenomena in nanofluids. Following the classical Buongiorno approach, the model assumes nanofluids to be suspensions of two phases: nanoparticles and the base fluid. The field variables are the classical ones and, in addition, the stress tensors and the heat fluxes of both constituents. Balance laws for all field variables are assumed. The obtained system is not closed; therefore, universal physical principles, such as Galilean Invariance and the Entropy Principles, are invoked to close the set of field equations. The obtained model is also written in terms of the whole nanofluid and compared with the classical Buongiorno model. This allowed also the identifications of some parameters in terms of experimental data. The obtained set of field equations has the advantage to recover the Buongiorno model when the phenomena are near equilibrium. At the same time it consists of a hyperbolic set of field equations. Hyperbolicity guarantees finite speeds of propagation and more suitable descriptions of transient regimes. The present model can be used in order to investigate waves, shocks and other phenomena that can be easily described in hyperbolic systems. Furthermore, as a first application and in order to show the potential of the model, stationary 1D solutions are determined and some thermal properties of nanofluids are studied. The solution exhibits, already in the simplest case herein considered, a more accurate evaluation of some fields like the stress tensor components.

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A hyperbolic reaction–diffusion model of chronic wasting disease

Cited by 3 publications

References 18 publications

Mathematical Investigation of 1D Discontinuity Waves in Dilute Granular Gases

Mathematical Investigation of 1D Discontinuity Waves in Dilute Granular Gases

An Extended Thermodynamics Study for Second-Grade Adiabatic Fluids

A Rational Extended Thermodynamic Model for Nanofluids

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