Mathematical Models of Viscous Friction

Buttà, Paolo; Cavallaro, Guido; Marchioro, Carlo

doi:10.1007/978-3-319-14759-8

Cited by 9 publications

(14 citation statements)

References 51 publications

(17 reference statements)

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“…Beyond existence and locality, much less is known about the long-time behavior of the infinite dynamics. In the case of classical particle systems, we just mention some nontrivial results obtained in recent years, aimed at a microscopic justification of viscous friction [4][5][6]9,10]. In the present context, we are not able to give an example of flocking for the individuals contained in the tunnel.…”

Section: Introductionmentioning

confidence: 88%

“…The existence of the time evolution for systems composed by infinitely many particles moving according to Newton's laws of motion is a classical issue in non-equilibrium statistical mechanics, and several studies have been devoted to this subject, see, e.g., [3,7,8,11,12,14,20,21,24,25,27]. For a summary, see for instance Appendix 1 of [9]. The difficulty of the problem is related to the dimension of the space and the kind of mutual interaction among the particles.…”

Section: Introductionmentioning

confidence: 99%

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Cucker–Smale Type Dynamics of Infinitely Many Individuals with Repulsive Forces

Buttà

Marchioro

2020

J Stat Phys

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Cucker–Smale Type Dynamics of Infinitely Many Individuals with Repulsive Forces

Buttà

Marchioro

2020

J Stat Phys

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“…The Arzelà-Ascoli theorem implies that K is a compact subset of C b ([0, ∞)). 3 We prove next that the map K W → V W ∈ K is continuous in the topology of C b ([0, ∞)).…”

Section: 7mentioning

confidence: 96%

Wall effect on the motion of a rigid body immersed in a free molecular flow

Koike¹

2018

Kinetic &Amp; Related Models

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Motion of a rigid body immersed in a semi-infinite expanse of gas in a d-dimensional region bounded by an infinite plane wall is studied for free molecular flow on the basis of the free Vlasov equation under the specular boundary condition. We show that the velocity V (t) of the body approaches its terminal velocity V∞ according to a power law V∞ − V (t) ≈ Ct −(d−1) by carefully analyzing the pre-collisions due to the presence of the wall. The exponent d − 1 is smaller than d + 2 for the case without the wall found in the classical work by Caprino, Marchioro and Pulvirenti [Comm. Math. Phys., 264 (2006), pp. 167-189] and thus slower convergence rate results from the presence of the wall.

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“…3 Set x = x1 and ignore the condition |x ⊥ | ≤ 1 when d = 1. 4 In this paper, the length scale √ 2R * T * 0/ω * in [29] is replaced by the size of the rigid body, which is the radius of the cylinder when d = 3; the width of the for x ∈ Ω(t), ξ ∈ R 3 and t > 0. Here, κ > 0 is the Knudsen number for the collisions between the molecules and the obstacles.…”

Section: Motion Of a Rigid Body In A Lorentz Gasmentioning

confidence: 99%

Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect

Koike

2018

J Stat Phys

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Linear motion of a rigid body in a special kind of Lorentz gas is mathematically analyzed. The rigid body moves against gas drag according to Newton's equation. The gas model is a special Lorentz gas consisting of gas molecules and background obstacles, which was introduced in (Tsuji and Aoki: J. Stat. Phys. 146, 620-645, 2012). The specular boundary condition is imposed on the resulting kinetic equation. This study complements the numerical study by Tsuji and Aoki cited above -although the setting in this paper is slightly different from theirs, qualitatively the same asymptotic behavior is proved: The velocity V (t) of the rigid body decays exponentially if the obstacles undergo thermal motion; if the obstacles are motionless, then the velocity V (t) decays algebraically with a rate t −5 independent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroy the memory effect due to recollision.Keywords Lorentz gas · Rigid body motion · Moving boundary problem · Recollision · Memory effect · Long time behavior IntroductionFluid force acting on a moving body in a fluid is not solely determined by the instantaneous velocity of the body; it also depends on the past history of motion. This is because the disturbance made in the fluid is not immediately wiped away and affects the future motion of the body. The important of this

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Mathematical Models of Viscous Friction

Cited by 9 publications

References 51 publications

Cucker–Smale Type Dynamics of Infinitely Many Individuals with Repulsive Forces

Cucker–Smale Type Dynamics of Infinitely Many Individuals with Repulsive Forces

Wall effect on the motion of a rigid body immersed in a free molecular flow

Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect

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