Thin presentation of knots and lens spaces

This paper concerns thin presentations of knots K in closed 3-manifolds M^3 which produce S^3 by Dehn surgery, for some slope gamma. If M does not have a lens space as a connected summand, we first prove that all such thin presentations, with respect to any spine of M have only local maxima. If M is a lens space and K has an essential thin presentation with respect to a given standard spine (of lens space M) with only local maxima, then we show that K is a 0-bridge or 1-bridge braid in M; furthermore, we prove the minimal intersection between K and such spines to be at least three, and finally, if the core of the surgery K_gamma yields S^3 by r-Dehn surgery, then we prove the following inequality: |r| <= 2g, where g is the genus of K_gamma.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-23.abs.htm

Resonance modes in a 1D medium with two purely resistive boundaries: calculation methods, orthogonality and completeness

Studying the problem of wave propagation in media with resistive boundaries can be made by searching for "resonance modes" or free oscillations regimes. In the present article, a simple case is investigated, which allows one to enlighten the respective interest of different, classical methods, some of them being rather delicate. This case is the 1D propagation in a homogeneous medium having two purely resistive terminations, the calculation of the Green function being done without any approximation using three methods. The first one is the straightforward use of the closed-form solution in the frequency domain and the residue calculus. Then the method of separation of variables (space and time) leads to a solution depending on the initial conditions. The question of the orthogonality and completeness of the complex-valued resonance modes is investigated, leading to the expression of a particular scalar product. The last method is the expansion in biorthogonal modes in the frequency domain, the modes having eigenfrequencies depending on the frequency. Results of the three methods generalize or/and correct some results already existing in the literature, and exhibit the particular difficulty of the treatment of the constant mode

Distributed Intelligent MEMS: Progresses and Perspectives

International audienceMEMS research has until recently focused mainly on the engineering process, resulting in interesting products and a growing market. To fully realize the promise of MEMS, the next step is to add embedded intelligence. With embedded intelligence, the scalability of manufacturing will enable distributed MEMS systems consisting of thousands or millions of units which can work together to achieve a common goal. However, before such systems can become a reallity, we must come to grips with the challenge of scalability which will require paradigm-shifts both in hardware and software. Furthermore, the need for coordinated actuation, programming, communication and mobility management raises new challenges in both control and programming. The objective of this article is to report the progresses made by taking the example of two research projects and by giving the remaining challenges and the perspectives of distributed intelligent MEMS

About Dissipative and Pseudo Port-Hamiltonian Formulations of Irreversible Newtonian Compressible Flows

In this paper we consider the physical-based modeling of 3D and 2D Newtonian fluids including thermal effects in order to cope with the first and second principles of thermodynamics. To describe the energy fluxes of non-isentropic fluids we propose a pseudo port-Hamiltonian formulation, which includes the rate of irreversible entropy creation by heat flux. For isentropic fluids, the conversion of kinetic energy into heat by viscous friction is considered as an energy dissipation associated with the rotation and compression of the fluid. Then, a dissipative port-Hamiltonian formulation is derived for this class of fluids. In the 2D case we modify the vorticity operators in order to preserve the structure of the proposed models. Moreover, we show that a description for inviscid or irrotational fluids can be derived from the proposed models under the corresponding assumptions leading to a pseudo or dissipative port-Hamiltonian structures

Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

Erratum to: Scaling up strategies of the chronic respiratory disease programme of the European Innovation Partnership on Active and Healthy Ageing (Action Plan B3: Area 5).

[This corrects the article DOI: 10.1186/s13601-016-0116-9.]

Erratum to: Scaling up strategies of the chronic respiratory disease programme of the European Innovation Partnership on Active and Healthy Ageing (Action Plan B3: Area 5).

[This corrects the article DOI: 10.1186/s13601-016-0116-9.]