Using the gradients of temperature and internal parameters in Continuum ThermodynamicsIntroduction des gradients de température et de paramètres internes en Thermodynamique des Milieux Continus

In this paper, the possibility of using the gradients of the temperature and of the internal parameters as additional state variables in Continuum Thermodynamics is considered. The expressions of the two principles are discussed and Clausius–Duhem inequality is derived under an appropriate statement of the internal entropy production. Several formulations are proposed and compared to existing results in the literature. To cite this article: P. Ireman, Q.S. Nguyen, C. R. Mecanique 332 (2004).     

Curvature Conditions for Immersions of Submanifolds and Applications

Some curvature conditions about the geodesics emanating from a submanifold are obtained. These conditions are used to to study the topological and geometric properties of the ambient spaces which admit some minimal submanifolds.     

Development of a parallel storm surge model

A new parallel storm surge model, the Parallel Environmental Model (PEM), is developed and tested by comparisons with analytic solutions. The PEM is a 2‐D vertically averaged, wetting and drying numerical model and can be operated in explicit, semi‐implicit and fully implicit modes. In the implicit mode, the propagation, Coriolis and bottom friction terms can all be treated implicitly. The advection and diffusion terms are solved with a parallel Eulerian–Lagrangian scheme developed for this study. The model is developed specifically for use on parallel computer systems and will function accordingly in either explicit of implicit modes. Storm boundary conditions are based on a simple exponential decay of pressure from the centre of a storm. The simulated flooding caused by a major Category 5 hurricane making landfall in the Indian River Lagoon, Florida is then presented as an example application of the PEM. Copyright © 2003 John Wiley & Sons, Ltd.     

Cube factorizations of complete graphs

A cube factorization of the complete graph on n vertices, K_n, is a 3‐factorization of K_n in which the components of each factor are cubes. We show that there exists a cube factorization of K_n if and only if n ≡ 16 (mod 24), thus providing a new family of uniform 3‐factorizations as well as a partial solution to an open problem posed by Kotzig in 1979. © 2004 Wiley Periodicals, Inc.     

Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.