Doppler Spectrum Estimation by Ramanujan Fourier Transforms

The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical sequences with several resonances p/q. These sums are almost periodic according to time n of resonances and aperiodic according to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT) for the estimation of the Doppler spectrum for the weather radar signal

Small Perturbations of an Interface for Elastostatic Problems

We consider solutions to the Lam\'e system in two dimensions. By using systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation), we establish a rigorous asymptotic expansion for the perturbations of the displacement field caused by small perturbations of the shape of an elastic inclusion with C2-boundary. We extend these techniques to determine a relationship between traction-displacement measurements and the shape of the object and derive an asymptotic expansion for the perturbation in the elastic moments tensors (EMTs) due to the presence of small changes in the interface of the inclusion.Comment: 42pages,0 figures. arXiv admin note: text overlap with arXiv:1601.0677

Turbulent spots and waves in a model for plane Poiseuille flow

International audienceThe structure of a turbulent spot in plane Poiseuille flow is investigated using a model derived from the Navier-Stokes equations through a Galerkin method. The mean profile of the streamwise velocity inside the turbulent spot has the characteristic flat profile of a turbulent Poiseuille flow. The waves developing at the wing tips of the spot have an asymmetric streamwise velocity with respect to the channel centerline, whereas their associated wall-normal velocity component is symmetric. On the outskirts of the spot, a large-scale flow occupying the full gap between the plates is observed. It is characterized by a streamwise inflow toward the spot and a spanwise outflow from the spot. A detailed comparison with the numerical simulations and the experiments in the literature shows that these results are in fair agreement with the main features of the transitional plane Poiseuille flow. © 2007 American Institute of Physics

Modeling of plane Couette flow. II. On the spreading of a turbulent spot

International audienceIn this paper, we study the spreading mechanism of turbulent spots in plane Couette flow, where fluid is sheared between two parallel plates moving in opposite directions. The analysis of the coherent structures on the border between the laminar and turbulent regions reveals the existence of many vortices with wall-normal axes occupying the full gap between the plates. The streamwise component of the velocity field of these vortices is the streaks. Due to their self-advection, these vortices move parallel to the plates. During their motions, they carry the other perturbation components such as the streamwise and spanwise vortices. © 2007 American Institute of Physics

Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents

We study global existence and asymptotic behavior of the solutions to models for chemotaxis systems with chemo attractants and repellents in three dimensions. Chemo attractants and repellents may be called chemo agents. For Part I, we use the logistic model for the mass. The interactions between chemo agents and the mass are taken into account. For Part II, we consider the case when mass is conserved and we use the Lotka-Volterra type model for chemo agents. To accomplish this, we use the Fourier transform and energy method. We show the existence of global solutions by the energy method. Also, we establish $L^q$ time-decay for the linear homogeneous system by using the Fourier transform and finding Green\u27s matrix. Then, we find $L^q$ time-decay for the nonlinear system using solution representation by Duhamel\u27s principle and time-weighted estimates

Modeling e-Business with eBML

In this paper we demonstrate that modeling e-business strategies is important in a time where the first e-business disillusionment has taken place. The objective of this Paper is twofold. First we propose a theoretical e-business model framework (eBMF) for aligning e-business initiatives and projects. This framework rep-resents an ontology, which will allow firms to develop a sound e-business model, in an environment that is amongst other things characterized by new forms of network organizations. Second we show why the eX-tensible Markup Language (XML) is an adequate technology for describing this theoretical framework in a formal way.xml, e-business models, e-business

Existence of global solutions to chemotaxis fluid system with logistic source

We establish the existence of global solutions and L q time-decay of a three dimensional chemotaxis system with chemoattractant and repellent. We show the existence of global solutions by the energy method. We also study L q time-decay for the linear homogeneous system by using Fourier transform and finding Green’s matrix. Then, we find L q time-decay for the nonlinear system using solution representation by Duhamel’s principle and time-weighted estimate

Multi-Layered Optimal Navigation System For Quadrotors UAV

Purpose This paper aims to propose a new multi-layered optimal navigation system that jointly optimizes the energy consumption, improves the robustness and raises the performance of a quadrotor unmanned aerial vehicle (UAV). Design/methodology/approach The proposed system is designed as a multi-layered system. First, the control architecture layer links the input and the output spaces via quaternion-based differential flatness equations. Then, the trajectory generation layer determines the optimal reference path and avoids obstacles to secure the UAV from collisions. Finally, the control layer allows the quadrotor to track the generated path and guarantees the stability using a double loop non-linear optimal backstepping controller (OBS). Findings All the obtained results are confirmed using several scenarios in different situations to prove the accuracy, energy optimization and the robustness of the designed system. Practical implications The proposed controllers are easily implementable on-board and are computationally efficient. Originality/value The originality of this research is the design of a multi-layered optimal navigation system for quadrotor UAV. The proposed control architecture presents a direct relation between the states and their derivatives, which then simplifies the trajectory generation problem. Furthermore, the derived differentially flat equations allow optimization to occur within the output space as opposed to the control space. This is beneficial because constraints such as obstacle avoidance occur in the output space; hence, the computation time for constraint handling is reduced. For the OBS, the novelty is that all controller parameters are derived using the multi-objective genetic algorithm (MO-GA) that optimizes all the quadrotor state’s cost functions jointly