Game information dynamic models based on fluid mechanics

Abstract This paper is concerned with the proposal of two different kinds of novel information dynamic models based on fluid mechanics. These models are a series of approximate solutions for the flow past a flat plate at zero incidence. The five Base Ball games in the World Series 2010 have been analyzed using the models. It is found that the first model represents one game group where information of game outcome increases very rapidly with increasing the game length near the end and takes the full value at the end. The second model represents another game group where information gradually approaches to the full value at the end. Three game-progress patterns are identified according to information pattern in the five games, viz., balanced, seesaw and one-sided games. In a balanced game, both of the teams have no score during the game. In a seesaw game, one team leads score(s), then the other team leads score(s) and this may be repeated alternately. In a one-sided game, only one team gets score(s), but the other no score. It is suggested that the present models make it possible to discuss the information dynamics in games and/or practical problems such as projects starting from zero information and ending with full information.

[1]  Takeo Nakagawa,et al.  Stream meanders on a smooth hydrophobic surface , 1984, Journal of Fluid Mechanics.

[2]  H. Schlichting Boundary Layer Theory , 1955 .

[3]  Pradeep Sen,et al.  A versatile HDR video production system , 2011, SIGGRAPH 2011.

[4]  Yaser Sheikh,et al.  Motion capture from body-mounted cameras , 2011, SIGGRAPH 2011.

[5]  G. Parker On the cause and characteristic scales of meandering and braiding in rivers , 1976, Journal of Fluid Mechanics.

[6]  W. Tollmien,et al.  Über Flüssigkeitsbewegung bei sehr kleiner Reibung , 1961 .

[7]  Richard H. Rand,et al.  Fluid Mechanics of Green Plants , 1983 .

[8]  Leonidas J. Guibas,et al.  Probabilistic reasoning for assembly-based 3D modeling , 2011, SIGGRAPH 2011.

[9]  R. L. Solso Cognition and the visual arts , 1994 .

[10]  Doug L. James,et al.  Animating fire with sound , 2011, SIGGRAPH 2011.

[11]  Hiroyuki Iida,et al.  An Application of Game-Refinement Theory to Mah Jong , 2004, ICEC.

[12]  T. Nagatani,et al.  Chaotic jam and phase transition in traffic flow with passing. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  H. Takayasu,et al.  Dynamic phase transition observed in the Internet traffic flow , 2000 .

[14]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[15]  R. Wyatt,et al.  Quantum wave packet dynamics with trajectories: Implementation with adaptive Lagrangian grids , 2000 .

[16]  S. S. Stevens On the psychophysical law. , 1957, Psychological review.

[17]  H. Blasius Grenzschichten in Flüssigkeiten mit kleiner Reibung , 1907 .