Generalized Arago-Fresnel laws: The EME-flow-line description

We study experimentally and theoretically the influence of light polarization on the interference patterns behind a diffracting grating. Different states of polarization and configurations are been considered. The experiments are analyzed in terms of electromagnetic energy (EME) flow lines, which can be eventually identified with the paths followed by photons. This gives rise to a novel trajectory interpretation of the Arago-Fresnel laws for polarized light, which we compare with interpretations based on the concept of "which-way" (or "which-slit") information.Comment: 14 pages, 6 figure

HYSTERESIS MODELLING

A generalization of the Preisach representation including both irreversible and reversible components of magnetization is presented. The Mayergoyz's theorem is extended to the generalized Preisach representation, and the effect of the shape-demagnetizing-field-transformation on the relative weight of reversible and irreversible components of magnetization is considered

Some consequences of the analytical theory of the ferromagnetic hysteresis

Some properties of the transformations in the (J, H) plane of a ferromagnetic material are described. They are consequences of the Preisach model which considers the material as composed of independent elements of volume whose magnetic behaviour is wholly described by a rectangular loop, and assumes that the distribution of elemental loops, statistically independent of J and H, is a property of the material. The most interesting property concerns the determination of the region of the plane (J, H) where the magnetization curve can be found, once the loop is known, and the region where the loop can be found, once the magnetization curve is given. The coercive force of a symmetrical loop cannot be larger than the field strength corresponding to Jv/2 on the magnetization curve, Jv being the intensity of magnetization at the vertex of the loop.On donne une description de quelques propriétés des transformations dans le plan (J, H) d'un matériau ferromagnétique. En adoptant le modèle de Preisach, on considère que le matériau est composé d'éléments de volume indépendant dont le comportement magnétique est complètement représenté par un cycle rectangulaire et on suppose que la distribution des cycles élémentaires est statistiquement indépendante de J et de H, distribution qui est une propriété du matériau. La propriété la plus intéressante se rapporte à la détermination de la région du plan (J,H) dans laquelle la courbe d'aimantation peut être placée, une fois que le cycle d'hystérésis est donné, et de la région où le cycle d'hystérésis peut être trouvée lorsqu'on connaît la courbe d'aimantation. Le champ coercitif d'un cycle symétrique ne peut pas être plus grand que le champ magnétique correspondant à J v/2 sur la courbe d'aimantation ; Jv est l'intensité d'aimantation correspondant au sommet du cycle

A New Look at the Automatic Synthesis of Linear Ranking Functions ✩

The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many terminating loops admit one and algorithms exist to automatically synthesize it. In this paper we present two such algorithms: one based on work dated 1991 by Sohn and Van Gelder; the other, due to Podelski and Rybalchenko, dated 2004. Remarkably, while the two algorithms will synthesize a linear ranking function under exactly the same set of conditions, the former is mostly unknown to the community of termination analysis and its general applicability has never been put forward before the present paper. In this paper we thoroughly justify both algorithms, we prove their correctness, we compare their worst-case complexity and experimentally evaluate their efficiency, and we present an open-source implementation of them that will make it very easy to include termination-analysis capabilities in automatic program verifiers. Keywords: Static analysis, computer-aided verification, termination analysis