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Abstract. In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.Mathematics Subject Classification. 35Q60.

In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic field-displacement relations inherent to lead zirconate titanate (PZT) devices employed in atomic force microscope stage mechanisms. We focus specifically on PZT rods utilizing d 33 motion and PZT shells driven in d 31 regimes, but the modeling framework is sufficiently general to accommodate a variety of drive geometries. In the first step of the model development, lattice-level energy relations are combined with stochastic homogenization techniques to construct nonlinear constitutive relations which accommodate the hysteresis inherent to ferroelectric compounds. Secondly, these constitutive relations are employed in classical rod and shell relations to construct system models appropriate for presently employed nanopositioner designs. The capability of the models to quantify the frequency-dependent hysteresis inherent to the PZT stages is illustrated through comparison with experimental data. i Report Documentation Page Form Approved OMB No. 0704-0188Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

This paper summarizes the development of a homogenized free energy model which characterizes the temperature-dependent hysteresis and constitutive nonlinearities inherent to relaxor ferroelectric materials. A kernel for the model is developed through mesoscopic energy analysis and extended to provide macroscopic constitutive relations through stochastic homogenization techniques based on the assumption that certain underlying parameters are manifestations of underlying densities rather than constants. Mechanisms characterizing the decrease in hysteresis and saturation polarization polarization as temperatures are increased are constructed using asymptotic properties of the kernel which is derived from statistical mechanics tenets. Attributes of the model are illustrated through comparison with PMN-PT-BT data.

Electromagnetic interrogation techniques have numerous useful applications, including locating mines or bunkers beneath the ground, and detecting abnormal tissue noninvasively within the body. Several recent successful such techniques involve using some type of interface, such as a superconductive metal backing or a standing acoustic wave grating, to reflect an oncoming electromagnetic wave. These electromagnetic wave reflections are then used to identify dielectric properties (conductivity and polarization) of the target materials. Many useful polarization models (for example, Debye, Lorentz, and higher order models) result in a hysteretic term in Maxwell’s equations. Thus, a wide class of electromagnetic interrogation problems involve identification of hysteresis mechanisms. We wish to examine a technique in which an acoustic wave traveling toward the oncoming electromagnetic wave acts as a virtual interface. As a first step in assessing this interrogation technique, we consider the equations describing an acoustic pressure wave produced by a windowed sine wave pulse traveling through a layered medium and develop computational methods for solving these equations. After considering several other approaches, we suggest that an adequate way to solve this system with the finite element method is to use a fully Galerkin scheme in a nonstandard weak formulation. Our approximation methods, resulting in large algebraic systems, are explained and computational findings are presented which support the efficacy of the approach.