Quantaloids Describing Causation and Propagation of Physical Properties

A general principle of causal duality for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of quantaloids and quantaloidal morphisms appear naturally within this setting; as in the case of causal duality, they originate from primitive physical reasonings on the lattices of properties of physical systems. Furthermore, an essentially dynamical operational foundation for studying physical systems is outlined; complementary as it is to the existing static operational foundation, it leads to the natural axiomatization of causal duality in operational quantum logic.     

Zur Theorie der Substitutionsgruppen

Ohne Zusammenfassung     

Following the cat: A preface for the next three papers

The three papers to follow, by Chris Rasmussen and three of his students, build from a task design the authors of this note developed in the 1990s. To introduce these papers, which extend our prior work in new directions, we sketch some background here.     

Modeling the Behavior of Heat-Shrinkable Thin Films

We describe an asymptotic model for the behavior of PET-like heat-shrinkable thin films that includes both membrane and bending energies when the thickness of the film is positive. We compare the model to Koiter’s shell model and to models in which a membrane energy or a bending energy are obtained by Γ-convergence techniques. We also provide computational results for various temperature distributions applied to the films.