scholarly journals The Hairy Ball problem is PPAD-complete

Author(s):  
Paul W. Goldberg ◽  
Alexandros Hollender
Keyword(s):  
Author(s):  
Gaurang Ruhela ◽  
Anirvan DasGupta

We consider the problem of a hopping ball excited by a travelling harmonic wave on an elastic surface. The ball, considered as a particle, is assumed to interact with the surface through inelastic collisions. The surface motion due to the wave induces a horizontal drift in the ball. The problem is treated analytically under certain approximations. The phase space of the hopping motion is captured by constructing a phase-velocity return map. The fixed points of the return map and its compositions represent periodic hopping solutions. The linear stability of the obtained periodic solution is studied in detail. The minimum frequency for the onset of periodic hops, and the subsequent loss of stability at the bifurcation frequency, have been determined analytically. Interestingly, for small values of wave amplitude, the analytical solutions reveal striking similarities with the results of the classical bouncing ball problem.


2021 ◽  
pp. 174702182110693
Author(s):  
Cyril Thomas ◽  
Marion Botella ◽  
André Didierjean

To facilitate our interactions with the surroundings, the human brain sometimes reshapes the situations that it faces in order to simplify them. This phenomenon has been widely studied in the context of reasoning, especially through the attribute substitution error. It has however been given much less attention in the field of perception. Recent research on the bat-and-ball problem suggests that reasoners are able to intuitively detect attribute substitution errors. Using a perceptual illusion drawn from the field of magic, we investigate the extent to which a perceptual form of attribute substitution depends on executive resources and can be detected. We also investigate the relationship between susceptibility to attribute substitution error in the flushtration count illusion and in a French adaptation of the bat-and ball problem. Finally, we investigate the link between the intuitive cognitive style (assessed by the Cognitive Reflection Test) and the susceptibility to the flushtration count illusion. Our results suggest that participants do not detect perceptual attribute substitution error, that this phenomenon could be independent of the executive resources allocated to the task, and could rest on mechanisms distinct from those that produce errors in reasoning. We discuss differences between these two phenomena, and factors that may explain them.


2000 ◽  
Vol 67 (4) ◽  
pp. 720-726
Author(s):  
S. Djerassi

It has been observed that balls pressed between elastic bodies spin when subjected to linear, cyclic motion. This paper proposes an explanation to this phenomenon, based upon the stick-slip theory. To this end, a modified, vectorial formulation of the stick-slip theory is presented. The formulation is applied to a model comprising a ball pressed between pairs of springs and dampers. A computer program based on this formulation is used to predict the resulting motion. Predictions are shown to agree with experimental results. [S0021-8936(01)00701-2]


2019 ◽  
Vol 193 ◽  
pp. 214-228 ◽  
Author(s):  
Bence Bago ◽  
Matthieu Raoelison ◽  
Wim De Neys
Keyword(s):  

1964 ◽  
Vol 9 (3) ◽  
pp. 513-514
Author(s):  
B. A. Sevast’yanov ◽  
V. P. Chistyakov

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