Rational Unfoldings of
±Xk
and Their Relation with Geometric
Equilibrium Theory
Authors
W. Kuyk (in real life, Willem Kuijk - here are a few other
of his many works) and
Lieven Smits
Bibliographical Reference
Acta
Applicandae Mathematicae, volume 19 (1990), pages 87-95.
Abstract
In this paper, two theorems determine the locus B ('buoyancy locus') of the
centre of gravity of the displaced water of a ship with any number of 2n
sides, as a function of the arbitrary continuous curves that make
up those sides, and that generalize the classical wall-sided case
(n = 1).
Although the theorems may have interest from the pure geometrical point
of view, they have been obtained with a view to simulate
processes in biology that, in analogy to the self-righting of ships,
are self-regulating, such as the neural control of the body heat and
the servo-control of the heart rate.
AMS Subject Classifications (1985)
28A75, 52A10, 26B15.
Availability
There are a few reprints left. If your library does not have this
particular journal issue, ask for a reprint by emailing me your postal address.
Remove "unwanted" from the address below.
lieven@sterunwanted.be
References
- Janssens, J. and Kuyk, W., A Set of Integral-differential Equations
for the Ventricular Cardiac Suction Pump, in B. Schmidt (ed.), "Proc. 3rd
European Simulation Congress," Erlangen 1990, pp. 567-572.
- Kuyk, Willem, The Human Thermostat, in G.C. Vansteenkiste (ed.),
"Proc. 2nd European Simulation Congress," Antwerp 1986, pp. 713-719.
- Kuyk, Willem, Servocontrol of the Heart Rate in Homeothermic Animals,
Bull. Math. Biol. 48 (1986), 107-124.
- Kuyk, Willem and Smits, Lieven,
On the Geometries of the Rational Unfoldings of
±Xk, Acta Applic. Math. 19
(1990), 77-86.
- Poston, T. and Stewart, I., "Catastrophe Theory and its Applications,"
Pitman, London 1978.
- Thom, R., "Méthodes mathématiques de la
morphogénèse," Edition 10-18, UGE, Paris 1974.
-
Zeeman, E.C.,
"Catastrophe Theory: Selected Papers 1972-1977,"
Addison-Wesley, Reading, Mass. 1977.
History of this page
- Sep-Oct 2002: move to new site and update contact information
- 25 May 1998: add list of references
- 7 May 1998: include other information about the paper
- 1 Apr 1998: creation of the abstract