Factor ordering and large-volume dynamics in quantum cosmology

Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be significant even in certain low-curvature regimes, provided that they add up during long cosmic evolution. The analysis of such terms is therefore an important problem to make sure that the theory shows acceptable semiclassical behavior. This paper presents a general search for terms of this type as corrections in effective equations for a k=0 isotropic quantum cosmological model with a free, massless scalar field. Specifically, the question of whether such models can show a collapse by quantum effects is studied, and it turns out that factor-ordering choices in the Hamiltonian constraint are especially relevant in this regard. A systematic analysis of factor-ordering ambiguities in effective equations is therefore developed.Comment: 27 pages, 3 figure

Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model

Laboratory experiments simulating gravity-driven coastal surface currents produced by estuarine fresh-water discharges into the ocean are discussed. The currents are generated inside a rotating tank filled with salt water by the continuous release of buoyant fresh water from a small source at the fluid surface. The height, the width and the length of the currents are studied as a function of the background rotation rate, the volumetric discharge rate and the density difference at the source. Two complementary experimental data sets are discussed and compared with each other. One set of experiments was carried out in a tank of diameter 1 m on a small-scale rotating turntable. The second set of experiments was conducted at the large-scale Coriolis Facility (LEGI, Grenoble) which has a tank of diameter 13 m. A simple geostrophic model predicting the current height, width and propagation velocity is developed. The experiments and the model are compared with each other in terms of a set of non-dimensional parameters identified in the theoretical analysis of the problem. These parameters enable the corresponding data of the large-scale and the small-scale experiments to be collapsed onto a single line. Good agreement between the model and the experiments is found

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

What is the object of the encapsulation of a process?

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this ''object'' produced by the ''encapsulation'' of a process? Here, we outline the development of some of the theories (including Piaget, Dienes, Davis, Greeno, Dubinsky, Sfard, Gray, and Tall) and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra? Is the same development used in axiomatic mathematics? What is the role played by imagery