Abstrakt: Current literature on fluid configurations under capillary attractions generally is based on postulates introduced in 1830 by Gauss. By neglecting bulk energy variations within the fluid, these postulates lead to an essentially geometrical problem. I will present an example indicating that bulk energy terms can indeed be significant, and I will derive and examine the equations obtained by taking account of energy changes imposed by fluid compressibility. The formal character of the mathematical problem then changes, but remains geometrical. Solutions of the new equations share some striking features that occur with the classical equations, but also new exotic behavior appears that was previously not encountered. Experimental tests of the predictions may be feasible.
Abstrakt: The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. The talk presents a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a more precise description of contact phenomena than before.
|Organizátoři:||Prof. RNDr. M. Feistauer, DrSc.,|
|Prof. RNDr. J. Haslinger, DrSc., Doc. RNDr. J. Málek, CSc.,|
|RNDr. Š. Nečasová, CSc., Mgr. M. Pokorný, Ph.D.,|
|Doc. RNDr. M Rokyta, CSc., Doc. Ing. T. Roubíček, DrSc.|