The detection of the electric field vertical distribution underneath thundercloud: Principle and applications

During the Florida 89 experiment at Kennedy Space Center, a new system was used in order to obtain the vertical distribution of the electric field underneath thunderstorms. It consists of a standard shutter field mill at ground level and five other field sensors suspended from a cable fastened to a tethered balloon located at an altitude of about 1000 meters. It also includes a reception station for telemetered information transmitted by sensors, a processing system in order to store data, and real time display on a screen to show the simultaneous field variations at each level along with the instantaneous electric field profile. The first results obtained show the great importance of the electric field vertical distribution. The field detected at a height of 600m reaches 65 kV/m while that at the surface does not exceed 5 kV/m. The field intensity in altitude is a better criterion for determining the right moment to launch a rocket devoted to flash triggering. Using Gauss's law, the simultaneous field variations at several levels are used in order to evaluate charge densities. Average values close to 1nC.m(-3) are calculated in layers up to 600 m. The calculation of different average charge densities leads to the characterization of the layer between cloud and ground just before the leader propagation in the case of cloud to ground flash

Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem

We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law "angle of incidence equals angle of reflection" are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. This is a magnetic analog of Hilbert's fourth problem asking to describe the Finsler metrics whose geodesics are straight lines.Comment: 27 pages, 6 figure

On the Cartan matrix of Mackey algebras

Let k be a field of characteristic p>0, and G be a finite group. The first result of this paper is an explicit formula for the determinant of the Cartan matrix of the Mackey algebra mu_k(G) of G over k. The second one is a formula for the rank of the Cartan matrix of the cohomological Mackey algebra comu_k(G) of G over k, and a characterization of the groups G for which this matrix is non singular. The third result is a generalization of this rank formula and characterization to blocks of comu_k(G) : in particular, if b is a block of kG, the Cartan matrix of the corresponding block comu_k(b) of comu_k(G) is non singular if and only if b is nilpotent with cyclic defect groups

Variational Theory of Balance Systems

In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constitutive relation C of a balance system is realized as a mapping between a (partial) k-jet bundle and the extended dual bundle similar to the Legendre mapping of the Lagrangian Field Theory. Invariant (variational) form of the balance system corresponding to a constitutive relation C is studied. Special cases of balance systems -Lagrangian systems of order 1 with arbitrary sources and RET (Rational Extended Ther- modynamics) systems are characterized in geometrical terms. Action of auto- morphisms of the configurational bundle on the constitutive mappings C is studied and it is shown that the symmetry group Sym(C) of C acts on the sheaf of solutions Sol(C) of he balance system. Suitable version of Noether Theorem for an action of a symmetry group is presented together with the special forms for semi- Lagrangian and RET balance systems and examples of energy momentum and gauge symmetries balance laws

Elaboration of the New Paradigm of Interdisciplinary Investigations

In the article, the problem of construction a meta-theory for approaching the complex phenomena of Reality is discussed. The integrated information system is formulated. Such postulate is a suggested basis for creation of a unified methodology of cognition (investigation) which makes it possible to elaborate a new paradigm of interdisciplinary investigations as a separate scientific discipline which has its own methods and special objects. The article will be of interest to philosophers and methodologists of scienc