Seminare über Quantenfeldtheorie

We propose a mesoscopic computational model for studying the mechanics of fibrils or, in general, bundles of optionally cross-linked polymers. The model offers a set of parameters whose values can be tuned to match the properties or ambient conditions of the fibril under consideration, such as the extent of cross-linking, the temperature, and the dimensions of the fibril. Although it is fairly general in its applicability, the model is discussed in the context of collagen fibrils. Monte Carlo simulation of this model is made possible by means of a recently introduced move known as TRACTRIX, and we outline an adaptation of this technique which is specially suited for bundles of many polymers. In particular, this adaptation enables the simultaneous deformation, in one simulation step, of several polymers spanning the entire cross-section of the fibril. By subjecting our model fibril to external forces that cause it to bend, estimates of the axial Young's Modulus of collagen fibrils can be made after comparing the bent profile with a Timoshenko beam in a tip-loaded cantilever setup. The results are in good agreement with those obtained by laboratory experiment.

Kontakt: R. Vink

The construction of an infinite tensor product of the C*-algebra C_0(R) is not obvious, because it has no unit, and it has no nonzero projection. Based on a choice of an approximate identity, we construct here an infinite tensor product of C_0(R), denoted L_V, and use it to find (partial) group algebras for the full continuous representation theory of R^(N). We obtain an interpretation of the Bochner–Minlos theorem in R^(N) as the pure state space decomposition of the partial group algebras which generate L_V. We analyze the representation theory of L_V, and show that there is a bijection between a natural set of representations of L_V and Rep(R^(N),H) , but that there is an extra part which essentially consists of the representation theory of a multiplicative semigroup Q which depends on the initial choice of approximate identity.

Kontakt: K.-H. Rehren

Kontakt: K.-H. Rehren