Potentiality and Contradiction in Quantum Mechanics

Following J.-Y.B\'eziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in \cite{are14}. Our conclusion was that such states are \ita{contraries} (\ita{i.e.} both can be false, but both cannot be true), contradicting previous analyzes that have led to different results, such as those claiming that those states represent \ita{contradictory} properties (\ita{i. e.} they must have opposite truth values). In this chapter we bring the issue once again into the center of the stage, but now discussing the metaphysical presuppositions which underlie each kind of analysis and which lead to each kind of result, discussing in particular the idea that superpositions represent potential contradictions. We shall argue that the analysis according to which states in superposition are contrary rather than contradictory is still more plausible

Applications of remote sensing to stream discharge predictions

A feasibility study has been initiated on the use of remote earth observations for augmenting stream discharge prediction for the design and/or operation of major reservoir systems, pumping systems and irrigation systems. The near-term objectives are the interpolation of sparsely instrumented precipitation surveillance networks and the direct measurement of water loss by evaporation. The first steps of the study covered a survey of existing reservoir systems, stream discharge prediction methods, gage networks and the development of a self-adaptive variation of the Kentucky Watershed model, SNOPSET, that includes snowmelt. As a result of these studies, a special three channel scanner is being built for a small aircraft, which should provide snow, temperature and water vapor maps for the spatial and temporal interpolation of stream gages

Noise elimination by piecewise cross correlation of photometer outputs

A piecewise cross correlation technique has been developed to analyze the outputs of remote detection devices. The purpose of this technique is to eliminate the noise from optical background fluctuations, from transmission fluctuations and from detectors by calculating the instantaneous product of the detector output and a reference signal. Each noise component causes positive and negative oscillations of the instantaneous product and may thus be cancelled by an integration of the instantaneous product. The resultant product mean values will then contain the desired information on the spatial and temporal variation of emission, absorption and scattering processes in the atmosphere

Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scien- tific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science

M82 - A radio continuum and polarisation study II. Polarisation and rotation measures

The composition and morphology of the interstellar medium in starburst galaxies has been well investigated, but the magnetic field properties are still uncertain. The nearby starburst galaxy M82 provides a unique opportunity to investigate the mechanisms leading to the amplification and reduction of turbulent and regular magnetic fields. Possible scenarios of the contribution of the magnetic field to the star-formation rate are evaluated. Archival data from the VLA and WSRT were combined and re-reduced to cover the wavelength regime between 3cm and 22cm. All observations revealed polarised emission in the inner part of the galaxy, while extended polarised emission up to a distance of 2kpc from the disk was only detected at 18cm and 22cm. The observations hint at a magnetised bar in the inner part of the galaxy. We calculate the mass inflow rate due to magnetic stress of the bar to 7.1 solar masses per year, which can be a significant contribution to the star-formation rate of M82 of approximately 13 solar masses per year. The halo shows polarised emission, which might be the remnant of a regular disk field. Indications for a helical field in the inner part of the outflow cone are provided. The coherence length of the magnetic field in the centre is similar to the size of giant molecular clouds. Using polarisation spectra more evidence for a close coupling of the ionised gas and the magnetic field as well as a two-phase magnetic field topology were found. Electron densities in the halo are similar to the ones found in the Milky Way. The magnetic field morphology is similar to the one in other nearby starburst galaxies with possible large-scale magnetic loops in the halo and a helical magnetic field inside the outflow cones. The special combination of a magnetic bar and a circumnuclear ring are able to significantly raise the star-formation rate in this galaxy by magnetic braking

Nonconforming decomposition methods: Techniques for linear elasticity

Mortar finite element methods provide a powerful tool for the numerical approximation of partial differential equations. Many domain decomposition techniques based on the coupling of different discretization schemes or of nonmatching triangulations along interior interfaces can be analyzed within this framework. Here, we present a mortar formulation based on dual basis functions and a special multigrid method. The starting point for our multigrid method is a symmetric positive definite system on the unconstrained product space. In addition, we introduce a new algorithm for the numerical solution of a nonlinear contact problem between two linear elastic bodies It will be shown that our method can be interpreted as an inexact Dirichlet-Neumann algorithm for the nonlinear problem. The boundary data transfer at the contact zone is essential for the algorithm. It is realized by a scaled mass matrix which results from a mortar discretization on non-matching triangulations with dual basis Lagrange multipliers. Numerical results illustrate the performance of our approach in 2D and 3D

Domain decomposition methods on nonmatching grids and some applications to linear elasticity problems

Domain decomposition techniques provide a powerful tool for the coupling of different discretization methods or nonmatching triangulations across subregion boundaries. Here, we consider mortar finite elements methods for linear elasticity and diffusion problems. These domain decomposition techniques provide a more flesible approach than standard conforming formulations. The mortar solution is weakly continuous at subregion boundaries, and its jump is orthogonal to a suitable Lagrange multiplier space. Our approach is based on dual bases for the Lagrange true for the standard mortar method [2]. The biorthogonality relation guarantees that the Lagrange multiplier can be locally eliminated, and that we obtain a symmetric positive semidefinite system on the unconstrained product space. This system will be solved by multigrid techniques. Numerical results illustrate the performance of the multigrid method in 2D and 3D

Monotone methods on non-matching grids for non-linear contact problems

Nonconforming domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We use a generalized mortar method based on dual Lagrange multipliers for the discretization of a nonlinear contact problem between linear elastic bodies. In the case of unilateral contact problems, pointwise constraints occur and monotone multigrid methods yield efficient iterative solvers. Here, we generalize these techniques to nonmatching triangulations, where the constraints are realized in terms of weak integral conditions. The basic new idea is the construction of a nested sequence of nonconforming constrained spaces. We use suitable basis transformations and a multiplicative correction. In contrast to other approaches, no outer iteration scheme is required. The resulting monotone method is of optimal complexity and can be implemented as a multigrid method. Numerical results illustrate the performance of our approach in two and three dimensions

Kinetic energy cascades in quasi-geostrophic convection in a spherical shell

We consider triadic nonlinear interaction in the Navier-Stokes equation for quasi-geostrophic convection in a spherical shell. This approach helps understanding the origin of kinetic energy transport in the system and the particular scheme of mode interaction, as well as the locality of the energy transfer. The peculiarity of convection in the sphere, concerned with excitation of Rossby waves, is considered. The obtained results are compared with our previous study in Cartesian geometry