January & February  2008, 22(1&2): 101-109. doi: 10.3934/dcds.2008.22.101

A billiard model for a gas of particles with rotation

1. 

26 Egerton Road, Arlington, MA 02474, United States

Received  July 2007 Revised  September 2007 Published  June 2008

The hard sphere gas is a mathematical model in which several spherical particles collide elastically with each other in a compact Euclidean domain. Using the fact that this system can be modeled as point billiard, its dynamical properties have been investigated extensively, with a great deal of progress towards establishing a central hypothesis, viz., that the system is ergodic. Here we consider the implications of extending the model to include non-spherical particles which have rotational as well as translational components of motion. We show that the point billiard model which forms the basis of the hard sphere gas investigations can be extended to the non-spherical case.
Citation: David Cowan. A billiard model for a gas of particles with rotation. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 101-109. doi: 10.3934/dcds.2008.22.101
[1]

Viktor I. Gerasimenko, Igor V. Gapyak. Hard sphere dynamics and the Enskog equation. Kinetic & Related Models, 2012, 5 (3) : 459-484. doi: 10.3934/krm.2012.5.459

[2]

Yusheng Jia, Weishi Liu, Mingji Zhang. Qualitative properties of ionic flows via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential: Ion size effects. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1775-1802. doi: 10.3934/dcdsb.2016022

[3]

Hong Lu, Ji Li, Joseph Shackelford, Jeremy Vorenberg, Mingji Zhang. Ion size effects on individual fluxes via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential: Analysis without electroneutrality boundary conditions. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1623-1643. doi: 10.3934/dcdsb.2018064

[4]

Soumya Kundu, Soumitro Banerjee, Damian Giaouris. Vanishing singularity in hard impacting systems. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 319-332. doi: 10.3934/dcdsb.2011.16.319

[5]

Frédéric Lebon, Raffaella Rizzoni. Modeling a hard, thin curvilinear interface. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1569-1586. doi: 10.3934/dcdss.2013.6.1569

[6]

W. Patrick Hooper, Richard Evan Schwartz. Billiards in nearly isosceles triangles. Journal of Modern Dynamics, 2009, 3 (2) : 159-231. doi: 10.3934/jmd.2009.3.159

[7]

Serge Tabachnikov. Birkhoff billiards are insecure. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 1035-1040. doi: 10.3934/dcds.2009.23.1035

[8]

Simon Castle, Norbert Peyerimhoff, Karl Friedrich Siburg. Billiards in ideal hyperbolic polygons. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 893-908. doi: 10.3934/dcds.2011.29.893

[9]

Richard Evan Schwartz. Outer billiards and the pinwheel map. Journal of Modern Dynamics, 2011, 5 (2) : 255-283. doi: 10.3934/jmd.2011.5.255

[10]

Mickaël Kourganoff. Uniform hyperbolicity in nonflat billiards. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1145-1160. doi: 10.3934/dcds.2018048

[11]

Domokos Szász. Algebro-geometric methods for hard ball systems. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 427-443. doi: 10.3934/dcds.2008.22.427

[12]

Hong-Kun Zhang. Free path of billiards with flat points. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4445-4466. doi: 10.3934/dcds.2012.32.4445

[13]

W. Patrick Hooper, Richard Evan Schwartz. Erratum: Billiards in nearly isosceles triangles. Journal of Modern Dynamics, 2014, 8 (1) : 133-137. doi: 10.3934/jmd.2014.8.133

[14]

Richard Evan Schwartz. Unbounded orbits for outer billiards I. Journal of Modern Dynamics, 2007, 1 (3) : 371-424. doi: 10.3934/jmd.2007.1.371

[15]

Jean Dolbeault, Maria J. Esteban, Michał Kowalczyk, Michael Loss. Improved interpolation inequalities on the sphere. Discrete & Continuous Dynamical Systems - S, 2014, 7 (4) : 695-724. doi: 10.3934/dcdss.2014.7.695

[16]

Jorge Rebaza. Uniformly distributed points on the sphere. Communications on Pure & Applied Analysis, 2005, 4 (2) : 389-403. doi: 10.3934/cpaa.2005.4.389

[17]

Charles Pugh, Michael Shub. Periodic points on the $2$-sphere. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1171-1182. doi: 10.3934/dcds.2014.34.1171

[18]

Mapundi K. Banda, Michael Herty, Axel Klar. Gas flow in pipeline networks. Networks & Heterogeneous Media, 2006, 1 (1) : 41-56. doi: 10.3934/nhm.2006.1.41

[19]

Martin Gugat, Falk M. Hante, Markus Hirsch-Dick, Günter Leugering. Stationary states in gas networks. Networks & Heterogeneous Media, 2015, 10 (2) : 295-320. doi: 10.3934/nhm.2015.10.295

[20]

Marco Caponigro, Anna Chiara Lai, Benedetto Piccoli. A nonlinear model of opinion formation on the sphere. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4241-4268. doi: 10.3934/dcds.2015.35.4241

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]