Numerical size estimates of inclusions in Kirchhoff-Love elastic plates

The size estimates approach for Kirchhoff--Love elastic plates allows to determine upper and lower bounds of the area of an unknown elastic inclusion by measuring the work developed by applying a couple field on the boundary of the plate. Although the analytical process by which such bounds are determined is of constructive type, it leads to rather pessimistic evaluations. In this paper we show by numerical simulations how to obtain such bounds for practical applications of the method. The computations are developed for a square plate under various boundary loads and for inclusions of different position, shape and stiffness. The sensitivity of the results with respect to the relevant parameters is also analyzed

Resonator-based detection in nanorods

In this paper the axial vibrational behaviour of nanorods with an attached point-mass is studied, using the modified strain energy theory. The natural frequencies of the nanorod with the concentrated mass are obtained for different boundary conditions. The effects of the concentrated mass intensity, mass location, as well as the value of scale parameters have been analysed. For the case of small intensity of the concentrated mass, the natural frequencies of the nanorod can be estimated using a first order perturbative solution. These approximate results are compared with those corresponding to the exact solution. For this case, from the properties of the eigenvalue perturbative theory, the identification of single point mass in uniform nanorods (mass intensity and position) is addressed. The results obtained encourage the use of axial vibrations of nanorods as a very precise sensing technique

Explicit Determination of Pinned-Pinned Beams with a Finite Number of Given Buckling Loads

We present an analytical procedure for the exact, explicit construction of Euler-Bernoulli beams with given values of the first N buckling loads. The result is valid for pinned-pinned (P-P) end conditions and for beams with regular bending stiffness. The analysis is based on a reduction of the buckling problem to an eigenvalue problem for a vibrating string, and uses recent results on the exact construction of Sturm-Liouville operators with prescribed natural frequencies

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data (i.e. nondestructive boundary displacement and traction measurements) on the accessible outer boundary. This inverse geometric problem in three-dimensional elasticity is approximated using the method of fundamental solutions (MFS). The parameters describing the boundary of the unknown void, its centre, and the contraction and dilation factors employed for selecting the fictitious surfaces where the MFS sources are to be positioned, are taken as unknowns of the problem. In this way, the original inverse geometric problem is reduced to finding the minimum of a nonlinear least-squares functional that measures the difference between the given and computed data, penalized with respect to both the MFS constants and the derivative of the radial coordinates describing the position of the star-shaped void. The interior source points are anchored and move with the void during the iterative reconstruction procedure. The feasibility of this new method is illustrated in several numerical examples

Clinical, Radiographic, Histopathologic, and Serologic Features and their Differentiation from Wegener Granulomatosis

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Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure

Reconfigurable photon localization by coherent drive and dissipation in photonic lattices

7 pags., 4 figs.The engineering of localized modes in photonic structures is one of the main targets of modern photonics. An efficient strategy to design these modes is to use the interplay of constructive and destructive interference in periodic photonic lattices. This mechanism is at the origin of the defect modes in photonic bandgaps, bound states in the continuum, and compact localized states in flat bands. Here, we show that in lattices of lossy resonators, the addition of external optical drives with a controlled phase enlarges the possibilities of manipulating interference effects and allows for the design of novel types of localized modes. Using a honeycomb lattice of coupled micropillars resonantly driven with several laser spots at energies within its photonic bands, we demonstrate the localization of light in at-will geometries down to a single site. These localized modes are fully reconfigurable and have the potentiality of enhancing nonlinear effects and of controlling light-matter interactions with single site resolution.Ministerio de Ciencia, Innovación y Universidades (PGC2018-094792-B-100); Consejo Superior de Investigaciones Científicas (PTI-001); Comunidad de Madrid (CAM 2020 Y2020/TCS-6545); Narodowe Centrum Nauki (DEC-2019/32/T/ST3/00332); Agence Nationale de la Recherche (ANR-11-LABX-0007, ANR-16-CE30-0021, ANR-16-IDEX-0004 ULNE, ANR-QUAN-0003-05); European Research Council (820392, 865151, 949730), Région Hauts-de-France

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl