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Simulating the motion of the leech: A biomechanical application of DAEs (1998)

Alscher, Christian ; Beyn, Wolf-Jürgen

Springer

Numerical algorithms 19 (1998), S. 1-12

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ISSN: 1572-9265

Keywords: Lagrange's equations of motion ; viscoelasticity ; semi-explicit methods ; 92C10

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract In this paper a mathematical model is developed for the dynamical behaviour of a hydrostatic skeleton. The basic configuration is taken from the worm-like shape of the medicinal leech. It consists of a sequence of hexahedra with damped elastic springs as edges to model the various parts of the musculature. The system is stabilized by the constraint of constant volume either in the whole body or in prescribed compartments. We set up Lagrange's equations of motion with the Lagrange multipliers being the pressure values in the compartments. The equations of motion lead to a large differential-algebraic system which is solved by an application of semi-explicit numerical methods. Though the model has not yet been adapted to experimental data, first simulations with a simplified set of parameters show that it is capable of generating basic movements of the leech such as crawling and swimming.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1019146221279

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Ozonolyse von Dihydrolinalool (1975)

Richter, Wolf Jürgen

Weinheim : Wiley-Blackwell

Liebigs Annalen 1975 (1975), S. 401-405

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ISSN: 0075-4617

Keywords: Chemistry ; Organic Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Description / Table of Contents: Ozonolysis of Dihydrolinalool(+)-(R)-3,7-Dimethyl-6-octen-3-ol (dihydrolinalool, 2) is prepared from (+)-(S)-3,7-dimethyl-1.6-octadien-3-ol (linalool, 1) by partial hydrogenation. The compound is ozonized in ethyl acetate and hydrogenated, and the resulting hemi-acetal 3b reduced to (+)-(R)-3-methyl-3-hexanol (4) by the Wolff-Kishner method. The analogous procedure in methanol or ethanol yields (i-)-(2R,5S)-2-ethyl-5-methoxy-2-methyloxolane (5a) and its (-)-(2R,5R)-isomer 5b, or the corresponding 5-ethoxy compounds. The mechanism and synthetic utility of this reaction are discussed.

Notes: Aus ( +)-(S)-3,7-Dimethyl-1,6-octadien-3-ol (Linalool, 1) erhält man durch partielle Hydrierung (+)-(R)-3,7-Dimethyl-6-octen-3-ol (Dihydrolinalool, 2). Dieses liefert nach Ozonolyse in Essigester und anschließender Hydrierung ein Halbacetal 3b, das nach Wolff-Kishner-Reduktion zu (+)-(R)-3-Methyl-3-hexanol (4) f¨hrt. Bei Verwendung von Methanol oder Äthanol sind die Reaktionsprodukte (+)-(2R,5S)-2-Äthyl-5-methoxy-2-methyloxolan (5a) sowie das (-)-(2R,SR)-Isomer 5b bzw. die anlogen 5-Äthoxyverbindungen. Bildungsweise und Anwendbarkeit dieser Reaktion werden erörtert.

Additional Material: 1 Tab.