Viscoelastic modulus reconstruction using time harmonic vibrations

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the Fr\'echet derivatives of the least-squares discrepancy functional with respect to the shear modulus and shear viscosity. The proposed iterative reconstruction method using this Fr\'echet derivative does not require any differentiation of the displacement data for the full isotropic linearly viscoelastic model, whereas the standard reconstruction methods require at least double differentiation. Because the minimization problem is ill-posed and highly nonlinear, this adjoint-based optimization method needs a very well-matched initial guess. We find a good initial guess. For a well-matched initial guess, numerical experiments show that the proposed method considerably improves the quality of the reconstructed viscoelastic images.Comment: 15 page

Identification and control of acoustic radiation modes

A formulation is given of reduced-order acoustic radiation sensors and\ud reduced-order actuators for broadband sound fields. Methods are presented\ud to determine these descriptions from measured data, and their\ud application in systems for broadband active noise control is discussed.\ud One application area is the reduction of sound radiated from plates with\ud structural actuators and structural sensors, using measured or modeled\ud versions of the most efficiently radiating patterns of a vibrating body,\ud the so-called radiation modes. The second application of the radiation\ud mode theory is in active noise barriers for the reduction of traffic noise.\ud Without special precautions most of these systems suffer from spillover;\ud a technique is given to arrive at good reductions at the error sensors with\ud reduced spillover

Quantitative photoacoustic imaging in radiative transport regime

The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and thermodynamic properties of heterogeneous media from data of absorbed energy distribution inside the media. There have been extensive theoretical and computational studies on the inverse problem in QPAT, however, mostly in the diffusive regime. We present in this work some numerical reconstruction algorithms for multi-source QPAT in the radiative transport regime with energy data collected at either single or multiple wavelengths. We show that when the medium to be probed is non-scattering, explicit reconstruction schemes can be derived to reconstruct the absorption and the Gruneisen coefficients. When data at multiple wavelengths are utilized, we can reconstruct simultaneously the absorption, scattering and Gruneisen coefficients. We show by numerical simulations that the reconstructions are stable.Comment: 40 pages, 13 figure

Feedback control of the acoustic pressure in ultrasonic wave propagation

Classical models for the propagation of ultrasound waves are the Westervelt equation, the Kuznetsov and the Khokhlov-Zabolotskaya-Kuznetsov equations. The Jordan-Moore-Gibson-Thompson equation is a prominent example of a Partial Differential Equation (PDE) model which describes the acoustic velocity potential in ultrasound wave propagation, where the paradox of infinite speed of propagation of thermal signals is eliminated; the use of the constitutive Cattaneo law for the heat flux, in place of the Fourier law, accounts for its being of third order in time. Aiming at the understanding of the fully quasilinear PDE, a great deal of attention has been recently devoted to its linearization -- referred to in the literature as the Moore-Gibson-Thompson equation -- whose mathematical analysis is also of independent interest, posing already several questions and challenges. In this work we consider and solve a quadratic control problem associated with the linear equation, formulated consistently with the goal of keeping the acoustic pressure close to a reference pressure during ultrasound excitation, as required in medical and industrial applications. While optimal control problems with smooth controls have been considered in the recent literature, we aim at relying on controls which are just $L^2$ in time; this leads to a singular control problem and to non-standard Riccati equations. In spite of the unfavourable combination of the semigroup describing the free dynamics that is not analytic, with the challenging pattern displayed by the dynamics subject to boundary control, a feedback synthesis of the optimal control as well as well-posedness of operator Riccati equations are established.Comment: 39 pages; submitte

Stellar model fits and inversions

The recent asteroseismic data from the CoRoT and Kepler missions have provided an entirely new basis for investigating stellar properties. This has led to a rapid development in techniques for analysing such data, although it is probably fair to say that we are still far from having the tools required for the full use of the potential of the observations. Here I provide a brief overview of some of the issues related to the interpretation of asteroseismic data.Comment: Proc. ESF Conference : "The Modern Era of Helio- and Asteroseismology", Obergurgl, 20 - 25 May, 2012. To appear in Astron. Nach. Guest editor: Markus Rot