On the Boltzmann gas mixture equation: Linking the kinetic and fluid regimes

Bianca, Carlo; Dogbe, Christian

doi:10.1016/j.cnsns.2015.05.015

Cited by 11 publications

(8 citation statements)

References 33 publications

(37 reference statements)

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“…Specifically the paper shows that, depending on the magnitude of the parameters which define the scaling, the macroscopic quantities (number density, mean velocity and local temperature) of the two subsystems are solution of the acoustic equation, the linear incompressible Euler equation and the incompressible Navier-Stokes equation. The derivation is formally tackled by the recent moment method proposed by Bardos et al [3] and the results generalize the analysis performed in [4].…”

Section: Derivation Of the Macroscopic Equationsmentioning

confidence: 67%

“…The present paper has been devoted to generalize the asymptotic analysis proposed in [4]. According we summarized our results in the table 1.…”

Section: Research Perspectivesmentioning

confidence: 91%

“…It is worth stressing that we did not try to get all possible scalings. In particular, one can easily derive simplified models to those we have here [4]. It is worth stressing that for the derivation of the rescaled equations system we can think the solutions of (3.1a)-(3.1b) as scaled solutions of (1.1a)-(1.1b), that is, if F α (t, x, v) solves the Boltzmann mixture equations (1.1a)-(1.1b) then the parabolic scaling…”

Section: Derivation Of the Macroscopic Equationsmentioning

confidence: 99%

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Recovering Navier–Stokes Equations from Asymptotic Limits of the Boltzmann Gas Mixture Equation

Bianca

Dogbe

2016

Commun. Theor. Phys.

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This paper is devoted to the derivation of macroscopic fluid dynamics from the Boltzmann mesoscopic dynamics of a binary mixture of hard-sphere gas particles. Specifically the hydrodynamics limit is performed by employing different time and space scalings. The paper shows that, depending on the magnitude of the parameters which define the scaling, the macroscopic quantities (number density, mean velocity and local temperature) are solution of the acoustic equation, the linear incompressible Euler equation and the incompressible Navier-Stokes equation. The derivation is formally tackled by the recent moment method proposed by Bardos et al. [3] and the results generalize the analysis performed in [4].

show abstract

Section: Derivation Of the Macroscopic Equationsmentioning

confidence: 67%

“…The present paper has been devoted to generalize the asymptotic analysis proposed in [4]. According we summarized our results in the table 1.…”

Section: Research Perspectivesmentioning

confidence: 91%

Section: Derivation Of the Macroscopic Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Recovering Navier–Stokes Equations from Asymptotic Limits of the Boltzmann Gas Mixture Equation

Bianca

Dogbe

2016

Commun. Theor. Phys.

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“…The KTAP has been actively used for modeling phenomena not only in physics (see e.g., Reference [39,40]) but also in many other areas of applied and life sciences, for example in the political [41], economic and social [42][43][44][45][46][47] systems, psychological interactions [48], the dynamics of crowds [49][50][51][52][53][54] and swarms [55][56][57][58][59][60][61], traffic flow [62][63][64][65][66][67][68] and so forth.…”

Section: Examplesmentioning

confidence: 99%

Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

Kolev

2019

Mathematics

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A new mathematical model of a general autoimmune disease is presented. Basic information about autoimmune diseases is given and illustrated with examples. The model is developed by using ideas from the kinetic theory describing individuals expressing certain functions. The modeled problem is formulated by ordinary and partial equations involving a variable for a functional state. Numerical results are presented and discussed from a medical view point.

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“…Classically different kinds of scalings lead to different kinds of equations: parabolic and hyperbolic [172][173][174][175][176][177][178][179][180][181]. Specifically by defining a rescaling of time and space variables (low-field or high-field scaling), and under suitable technical assumptions, macroscopic equations typically of the mechanics continuum approach are derived.…”

Section: The Thermostatted Kinetic Theorymentioning

confidence: 99%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis is a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades.

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On the Boltzmann gas mixture equation: Linking the kinetic and fluid regimes

Cited by 11 publications

References 33 publications

Recovering Navier–Stokes Equations from Asymptotic Limits of the Boltzmann Gas Mixture Equation

Recovering Navier–Stokes Equations from Asymptotic Limits of the Boltzmann Gas Mixture Equation

Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

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