Strong convergence of the solutions of the linear elasticity and uniformity of asymptotic expansions in the presence of small inclusions

Ammari, H.,Kang, H.,Kim, K.,Lee, H. Academic Press 2013 Journal of differential equations Vol.254 No.12

We consider the Lame system of linear elasticity when the inclusion has the extreme elastic constants. We show that the solutions to the Lame system converge in appropriate H<SUP>1</SUP>-norms when the shear modulus tends to infinity (the other modulus, the compressional modulus is fixed), and when the bulk modulus and the shear modulus tend to zero. Using this result, we show that the asymptotic expansion of the displacement vector in the presence of small inclusion is uniform with respect to Lame parameters.

OPTIMIZATION ALGORITHM FOR RECONSTRUCTING INTERFACE CHANGES OF A CONDUCTIVITY INCLUSION FROM MODAL MEASUREMENTS

H. Ammari,E. Beretta,E. Francini,H. Kang,Mikyoung Lim 한국산업응용수학회 2009 한국산업응용수학회 학술대회 논문집 Vol.2009 No.5

We propose an original optimization approach for reconstructing interface changes of a conductivity inclusion from measurements of eigenvalues and eigenvectors associated with the transmission problem for the Laplacian. Let Ω be a smooth domain and D be an inclusion contained in Ω whose boundary is also assumed to be smooth. Shape deformation of D causes a perturbation of modal parameters. The aim of this work is to show how this information can be used to reconstruct the unknown deformation. For doing so, we rigorously derive an asymptotic formula for the perturbations in the eigenvalues of the transmission problem for the Laplacian that are due to small deformations of the interface of an inclusion. Based on this formula, we design an efficient reconstruction algorithm from modal measurements. Our algorithm consists on minimizing a functional whose minimizer yields certain geometric properties of the unknown inclusion. It naturally follows from a key identity that is in some sense dual to the asymptotic formula. Numerical experiments showing the viability of our algorithm are presented. Our results in this paper extend those established in the context of small volume inclusions as well as those for the conductivity interface problem. In fact, on one hand, in a series of recent papers [5,3,1,2] we have derived high-order asymptotic expansions of the eigenvalue perturbations due to the presence of small inclusions and used them for locating the inclusions and identifying some of their geometric features. On the other hand, in [4], we have derived highorder terms in the asymptotic expansions of the boundary perturbations of steady-state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion. Based on these derivations, we have designed an effective algorithm to determine some geometric features of the shape perturbation of the inclusion based on boundary measurements.

Reconstruction of inhomogeneous conductivities via the concept of generalized polarization tensors

Ammari, H.,Deng, Y.,Kang, H.,Lee, H. Gauthier-Villars 2014 Annales de l'Institut Henri Poincaré. Analyse non Vol.31 No.5

This paper extends the concept of generalized polarization tensors (GPTs), which was previously defined for inclusions with homogeneous conductivities, to inhomogeneous conductivity inclusions. We begin by giving two slightly different but equivalent definitions of the GPTs for inhomogeneous inclusions. We then show that, as in the homogeneous case, the GPTs are the basic building blocks for the far-field expansion of the voltage in the presence of the conductivity inclusion. Relating the GPTs to the Neumann-to-Dirichlet (NtD) map, it follows that the full knowledge of the GPTs allows unique determination of the conductivity distribution. Furthermore, we show important properties of the the GPTs, such as symmetry and positivity, and derive bounds satisfied by their harmonic sums. We also compute the sensitivity of the GPTs with respect to changes in the conductivity distribution and propose an algorithm for reconstructing conductivity distributions from their GPTs. This provides a new strategy for solving the highly nonlinear and ill-posed inverse conductivity problem. We demonstrate the viability of the proposed algorithm by preforming a sensitivity analysis and giving some numerical examples.

Decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions

Ammari, H.,Kang, H.,Lee, H.,Lim, M.,Zribi, H. Academic Press 2009 Journal of differential equations Vol.247 No.11

When two inclusions get closer and their conductivities degenerate to zero or infinity, the gradient of the solution to the conductivity equation blows up in general. In this paper, we show that the solution to the conductivity equation can be decomposed into two parts in an explicit form: one of them has a bounded gradient and the gradient of the other part blows up. Using the decomposition, we derive the best possible estimates for the blow-up of the gradient. We then consider the case when the inclusions have positive permittivities. We show quantitatively that in this case the size of the blow-up is reduced.

Subwavelength phononic bandgap opening in bubbly media

Ammari, H.,Fitzpatrick, B.,Lee, H.,Yu, S.,Zhang, H. Academic Press 2017 Journal of differential equations Vol.263 No.9

<P>The aim of this paper is to show both analytically and numerically the existence of a subwavelength phononic bandgap in bubble phononic crystals. The key result is an original formula for the quasi-periodic Minnaert resonance frequencies of an arbitrarily shaped bubble. The main findings in this paper are illustrated with a variety of numerical experiments. (c) 2017 Elsevier Inc. All rights reserved.</P>

Transient anomaly imaging by the acoustic radiation force

Ammari, H.,Garapon, P.,Guadarrama Bustos, L.,Kang, H. Academic Press 2010 Journal of differential equations Vol.249 No.7

This paper is devoted to provide a solid mathematical foundation for a promising imaging technique based on the acoustic radiation force, which acts as a dipolar source. From the rigorously established asymptotic expansions of near- and far-field measurements of the transient wave induced by the anomaly, we design asymptotic imaging methods leading to a quantitative estimation of physical and geometrical parameters of the anomaly.

Performance Study of Small Capacity Solar Autonomous Absorption Air-Conditioning System Coupled with a Low-Energy Residential Building Under Batna (Algeria) Climate

Et-tahir Ammari,Mounir Aksas,Abdelmoumene H. Benmachiche 대한설비공학회 2018 International Journal Of Air-Conditioning and Refr Vol.26 No.1

Solar absorption cooling technology has enormous potential for air-conditioning applications as the need for cooling coincides mostly with the availability of solar radiation. Due to the geographical nature and vast territory of Algeria and the presence of many isolated rural areas, there is a great need for autonomous systems that use only solar energy without auxiliary boiler to meet the cooling demand in summer. In this study, we propose a dynamic simulation model for solar autonomous absorption air-conditioning systems developed using the TRNSYS-EES software. The model used to study the feasibility and evaluate the functioning of the system under Batna, Algeria weather conditions. The proposed system uses solar thermal flat plate collectors to drive a small capacity single-effect LiBr/water absorption chiller to meet the cooling demand of a typical low-energy residential building covering a total floor area of 120 m2. A model of 4.5 kW commercial absorption chiller has been modeled with EES software. The validation results showed excellent agreement between the prediction and the experimental data (R 2 >0.988 R2>0.988) and proved the model ability to predict the performance of the chiller. The analysis of dynamic results indicates that the proposed system and selected size enable the chiller to work for a duration of up to 10 h a day. This allowed ensuring a sufficient and continuous cold water supply (between 8 ∘ ∘C and 18 ∘ ∘C) and maintaining the comfort temperature between 26 ∘ ∘C and 28 ∘ ∘C.

A Multi-Drone System for Oil Spill Detection: A Simulation and Emulation Platform

A. Al Maashri,J. Ghommam,A. Saleem,N. Nasiri,O. Eldirdiry,H. Bourdoucen,G. Al Rawas,A. Al-Kamzari,A. Ammari 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11

This paper presents a model for a multi-drone system used for detecting oil spills in seawater. The system is designed to provide an early warning for oil-derivative contamination that may threaten maritime life forms. The system hosts a lightweight machine vision algorithm for detecting oil spills and generating a path for the drones to follow. Also, the system incorporates robust communication; allowing the drones to collaborate as they track the generated path. To achieve autonomous tracking for drones, a robust control scheme is proposed. Specifically, the drone’s dynamics model is decomposed into two subsystems in terms of time scale transformation; leading to inner and outer loop dynamics. A combination of nonlinear integral sliding surface and backstepping procedure is employed to produce appropriate thrust and torque forces, which guarantees robust tracking performances of the drones. The proposed system was verified both in simulation as well as in an indoor multi-drone verification environment. The results attest to the efficacy of the developed model.