scholarly journals A sticky situation

2017 ◽  
Vol 820 ◽  
pp. 1-4
Author(s):  
P.-T. Brun

The whirling helical structure obtained when pouring honey onto toast may seem like an easy enough problem to solve at breakfast. Specifically, one would hope that a quick back-of-the-envelope scaling argument would help rationalize the observed behaviour and predict the coiling frequency. Not quite: multiple forces come into play, both in the part of the flow stretched by gravity and in the coil itself, which buckles and bends like a rope. In fact, the resulting abundance of regimes requires the careful numerical continuation method reported by Ribe (J. Fluid Mech., vol. 812, 2017, R2) to build a complete phase diagram of the problem and untangle this sticky situation.

1989 ◽  
Vol 62 (13) ◽  
pp. 1524-1527 ◽  
Author(s):  
E. B. Sirota ◽  
H. D. Ou-Yang ◽  
S. K. Sinha ◽  
P. M. Chaikin ◽  
J. D. Axe ◽  
...  

Author(s):  
Chintien Huang ◽  
Chenning Hung ◽  
Kuenming Tien

This paper investigates the numerical solutions of equations for the eight-position rigid-body guidance of the cylindrical-spherical (C-S) dyad. We seek to determine the number of finite solutions by using the numerical continuation method. We derive the design equations using the geometric constraints of the C-S dyad and obtain seven quartic polynomial equations and one quadratic equation. We then solve the system of equations by using the software package Bertini. After examining various specifications, including those with random complex numbers, we conclude that there are 804 finite solutions of the C-S dyad for guiding a body through eight prescribed positions. When designing spatial dyads for rigid-body guidance, the C-S dyad is one of the four dyads that result in systems of equal numbers of equations and unknowns if the maximum number of allowable positions is specified. The numbers of finite solutions in the syntheses of the other three dyads have been obtained previously, and this paper provides the computational kinematic result of the last unsolved problem, the eight-position synthesis of the C-S dyad.


2004 ◽  
Vol 93 (24) ◽  
Author(s):  
Rajeev Kapri ◽  
Somendra M. Bhattacharjee ◽  
Flavio Seno

2007 ◽  
Vol 75 (3) ◽  
Author(s):  
Jose A. R. Cembranos ◽  
Jonathan L. Feng ◽  
Louis E. Strigari

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