Conformal Villarceau Rotors

We consider Villarceau circles as the orbits of specific composite rotors in 3D conformal geometric algebra that generate knots on nested tori. We compute the conformal parametrization of these circular orbits by giving an equivalent, position-dependent simple rotor that generates the same parametric track for a given point. This allows compact derivation of the quantitative symmetry properties of the Villarceau circles. We briefly derive their role in the Hopf fibration and as stereographic images of isoclinic rotations on a 3-sphere of the 4D Clifford torus. We use the CGA description to generate 3D images of our results, by means of GAviewer. This paper was motivated by the hope that the compact coordinate-free CGA representations can aid in the analysis of Villarceau circles (and torus knots) as occurring in the Maxwell and Dirac equations

Survey Plan Improvement by Detecting Sea Floor Dynamics in Archived Echo Sounder Surveys

La publication de cartes a jour de mers peu profondes necessite l'execution de nouveaux leves periodiques. Les informations sur le comportement du fond de la mer permettent d'ameliorer la planification des frequences d'execution des nouveaux leves , laquelle pourrait etre assuree par l'analyse d'une serie de leves du fond archivee. Nous presentons une methode qui permet d'extraire ces dynamiques en utilisant l'analyse des deformations. Il s'agit de la modelisation d'un plan incline pour une zone limitee du fond. La methode permet de juger si les differences entre les leves sont statistiquement importantes du point de vue de la precision du leve. C'est ainsi que differentes sortes de comportement du fond de la mer peuvent etre detectees et que les dimensions des deformations detectees et que les deformations detectees sont estimees. Cette procedure est illustree a l'aide d'un exemple concernant la mer du Nord.La publicacion de cartas actualizadas requiere nuevas levantamientos periodicos. La informacion sabre el comportamiento del fonda marino mejora Ia planificacion de las frecuencias de los nuevas levantamientos, lo que puede lograrse mediante el analisis de una serie de levantamientos de archivo del fonda submarino. Presentamos aqui un metoda para obtener esa dinamica, utilizando analisis de deformacion, que modelan una superficie en pendiente para un area limitada del fondo submarino. Este metoda determina si las diferencias entre levantamientos tienen importancia estadTstica con respecto a la precision del levantamiento. De esta manera se podran detectar diferentes tipos de comportamiento del fondo submarino y asr calcular las deformaciones detectadas. El procedimiento se ilustra con un ejemp/o en el Mar del Norte

Neoclassical Theory of Elementary Charges with Spin of 1/2

We advance here our neoclassical theory of elementary charges by integrating into it the concept of spin of 1/2. The developed spinorial version of our theory has many important features identical to those of the Dirac theory such as the gyromagnetic ratio, expressions for currents including the spin current, and antimatter states. In our theory the concepts of charge and anticharge relate naturally to their "spin" in its rest frame in two opposite directions. An important difference with the Dirac theory is that both the charge and anticharge energies are positive whereas their frequencies have opposite signs