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1

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The limits of hamiltonian structures in three-dimensional elasticity, shells, and rods (1996)

Ge, Z. ; Kruse, H. P. ; Marsden, J. E.

Springer

Journal of nonlinear science 6 (1996), S. 19-57

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ISSN: 1432-1467

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Summary This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material andderive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02433809

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2

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On the Bifurcation and Stability of Rigidly Rotating Inviscid Liquid Bridges (1998)

Kruse, H.-P. ; Scheurle, J.

Springer

Journal of nonlinear science 8 (1998), S. 215-232

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ISSN: 1432-1467

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Summary. We consider a mathematical model that describes the motion of an ideal fluid of finite volume that forms a bridge between two fixed parallel plates. Most importantly, this model includes capillarity effects at the plates and surface tension at the free surface of the liquid bridge. We point out that the liquid can stick to the plates due to the inner pressure even in the absence of adhesion forces. We use both the Hamiltonian structure and the symmetry group of this model to perform a bifurcation and stability analysis for relative equilibrium solutions. Starting from rigidly rotating, circularly cylindrical fluid bridges, which exist for arbitrary values of the angular velocity and vanishing adhesion forces, we find various symmetry-breaking bifurcations and prove corresponding stability results. Either the angular velocity or the angular momentum can be used as a bifurcation parameter. This analysis reduces to find critical points and corresponding definiteness properties of a potential function involving the respective bifurcation parameter.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s003329900049

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Liquidchromatographische Reindarstellung (HPLC) der cis/trans-Isomeren und massenspektrometrische Charakterisierung von 3,5-Di-n-alkyl-1,2,4-trithiolanen (1981)

Kruse, H.-P. ; Anger, H.

New York, NY : Wiley-Blackwell

Journal für Praktische Chemie/Chemiker-Zeitung 323 (1981), S. 169-173

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ISSN: 0021-8383

Keywords: Chemistry ; Organic Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Notes: Liquid Chromatographic Preparation of cis/trans-Isomers and Mass Spectrometric Characterization of 3,5-Di-n-alkyl-1,2,4-trithiolanes

Additional Material: 3 Ill.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/prac.19813230124

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4

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Folgeprodukte halogenierter Aldehyde. XIV [1]. Synthesen mit 1,2,2,2-Tetrachlorethylisocyanat (1978)

Zinner, H. ; Rosenthal, U. ; Kruse, H.-P. ; [et al.]

New York, NY : Wiley-Blackwell

Journal für Praktische Chemie/Chemiker-Zeitung 320 (1978), S. 625-633

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ISSN: 0021-8383

Keywords: Chemistry ; Organic Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Notes: Derivatives of Halogenated Aldehydes. XIV. Reactions of 1,2,2,2-Tetrachloroethyl Isocyanate1,2,2,2-Tetrachloroethyl isocyanate 2 reacts with alcohols or phenols to form the N-tetrachloroethyl-O-alkyl(aryl) urethanes 3-6. With thioalcohols and thiophenols the corresponding thiourethanes 11-12 are obtained. In these compounds the chlorine in position 1 can be substituted by treatment with a nucleophilic compound in the presence of a base by way of an elimination addition mechanism. In these reactions the compounds 7-10 and 13-14 are formed. Amines attack 2 at both active centres to give the substituted ureas 15-18. Diphenyl amine, some carboxylic acid amides and benzazoles, however, react only with the isocyanate group to form the compounds 19-25. Reactions of 2-amino-benzazoles, 2-amino-pyridine and amidines with 2 yield the heterocyclic compounds 26-31.

Additional Material: 1 Tab.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/prac.19783200416

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