On the rigid-lid approximation for two shallow layers of immiscible fluids with small density contrast

The rigid-lid approximation is a commonly used simplification in the study of density-stratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the surface are negligible compared with interface displacements. In this paper, we offer a rigorous justification of this approximation in the case of two shallow layers of immiscible fluids with constant and quasi-equal mass density. More precisely, we control the difference between the solutions of the Cauchy problem predicted by the shallow-water (Saint-Venant) system in the rigid-lid and free-surface configuration. We show that in the limit of small density contrast, the flow may be accurately described as the superposition of a baroclinic (or slow) mode, which is well predicted by the rigid-lid approximation; and a barotropic (or fast) mode, whose initial smallness persists for large time. We also describe explicitly the first-order behavior of the deformation of the surface, and discuss the case of non-small initial barotropic mode.Comment: Compared to version 2, typos have been corrected and additional remarks/discussion added. To appear in Journal of Nonlinear Scienc

Spectral asymptotics of a broken delta interaction

This paper is concerned with the spectral analysis of a Hamiltonian with a $\delta$-interaction supported along a broken line with angle $\theta$. The bound states with energy slightly below the threshold of the essential spectrum are estimated in the semiclassical regime $\theta\to 0$.Comment: 20 page

Mining Heterogeneous Multivariate Time-Series for Learning Meaningful Patterns: Application to Home Health Telecare

For the last years, time-series mining has become a challenging issue for researchers. An important application lies in most monitoring purposes, which require analyzing large sets of time-series for learning usual patterns. Any deviation from this learned profile is then considered as an unexpected situation. Moreover, complex applications may involve the temporal study of several heterogeneous parameters. In that paper, we propose a method for mining heterogeneous multivariate time-series for learning meaningful patterns. The proposed approach allows for mixed time-series -- containing both pattern and non-pattern data -- such as for imprecise matches, outliers, stretching and global translating of patterns instances in time. We present the early results of our approach in the context of monitoring the health status of a person at home. The purpose is to build a behavioral profile of a person by analyzing the time variations of several quantitative or qualitative parameters recorded through a provision of sensors installed in the home

Patent Office in innovation policy: Nobody's perfect

The number of patent applications and "bad" patents issued has been rising rapidly in recent years. Based on this trend, we study the overload problem within the Patent Office and its consequences on the firms' R&D incentives. We assume that the examination process of patent applications is imperfect, and that its quality is poorer under congestion. Depend- ing on policy instruments such as submission fees and the toughness of the non-obviousness requirement, the system may result in a high-R&D equilibrium, in which firms self-select in their patent applications, or in an equilibrium with low R&D, opportunistic patent applications and the issuance of bad patents. Multiple equilibria often coexist, which deeply undermines the effectiveness of policy instruments. We investigate the robustness of our conclusions as to how the value of patent protection is formalized, taking into consideration the introduction of a penalty system for rejected patent applications, as well as the role of commitment to a given IP protection policy.patent office ; patent quality ; congestion ; innovation

A payload for investigating the influence of convection on GaAs crystal growth

A comparative study of the influence of buoyancy driven fluid flow on gallium arsenide (GaAs) crystal growth was undertaken. Crystals will be grown from melts with different degrees of convective flow including growth in the microgravity environment of space. The space growth of GaAs will be performed in a Get Away Special payload. A well insulated growth furnace was designed for both Earth-based and space-based experiments. The self contained payload will carry two such furnaces in addition to a large battery power source and a microprocessor-based control and data acquisition system for regulating the growth process with high precision. The microcomputer will also monitor the growth conditions and measure and record the acceleration in 3 axes