Measurement of internal stresses via the polarization in epitaxial ferroelectric films

The relations between electrical and mechanical properties of constrained ferroelectric films are analyzed. It is shown that the internal stresses and the elastic constants can be determined through the measurement of the electrical response. The change in the polarization is proportional to internal stresses due to film-substrate misfit, whereas the linear electrical and electromechanical responses to external field do not depend on the misfit and are determined by the film constraint. The theoretical results are successfully applied to PbZr 0.2Ti 0.8O (3) films on (001) LaAlO (3) substrate which exhibit a considerable increase in the saturation polarization due to epitaxial stresses. Significant recovery in the piezoelectric constant and susceptibility is theoretically predicted and experimentally verified for specific film configurations which reduce the degree of constraint. The concept presented in this Letter can be expanded to constrained ferromagnetic and superconductor films.     

Dynamics of Thermally-Insulated Nonequilibrium Stefan Problem

We study a two-phase Stefan problem with kinetics. Here we prove existence of a finite-dimensional attractor for the problem without heat losses. Fot the most part we use a more elegant technique of energetic type estimates in appropriately defined weighted Sobolev spaces as opposite to the parabolic potentials of [9]. We demonstrate existence of compact attractors in the Sobolev spaces and prove that the attractor consists of sufficiently regular functions. This allows us to show that the Hausdorff dimension of the attractor is finite.     

Electrical domain morphologies in compositionally graded ferroelectric films

We present a nonlinear thermodynamic formalism coupled with an electrostatic analysis of uniaxial n-layered compositionally graded heteroepitaxial ferroelectric films and extend this formalism to continuously graded ferroelectric films. We show that the domain morphology and its subsequent evolution in the presence of an electric field are determined by the spontaneous polarisation of the film induced through the compositional grading. The results for compositionally graded epitaxial (001) (Ba,Sr)TiO(3) and (001) Pb(Zr,Ti)O(3) films on (001)SrTiO(3) demonstrate that, while the domain morphologies in these two films are different in appearance, the dielectric displacement and the dielectric permittivity of such graded ferroelectric films exhibit a strong nonlinear behaviour which results in a high dielectric tunability. These findings indicate that it is possible to design specific domain structures that will yield desirable dielectric properties by controlling the strength of the compositional grading in the films.     

Spectrum Determination of Terahertz Sources Using Fabry-Perot Interferometer and Bolometer Detector

We describe a method to determine the radiation spectrum of terahertz sources using a transmitted Fabry-Perot interferometer and a bolometer detector. Our novel Fabry-Perot spectrometer can measure the spectrum of an unknown broadband sub-terahertz and terahertz source. The spectrometer does not need to be pre-tuned. We develop a new algorithm to support the measurements using this spectrometer. Our technique allows us to measure the spectrum over more than an octave, and our numerical algorithm is very stable and robust, providing for an accurate spectrum determination. Two Gunn oscillation sources with the main frequencies at 200 GHz and 600 GHz are used to test the proposed method. The spectrum extracted from the measured data shows that this method is accurate and reliable.     

A Hopf bifurcation for a reaction-diffusion equation with concentrated chemical kinetics

A reaction-diffusion equation related to some mathematical models of gasless combustion of solid fuel is studied. A formal bifurcation analysis by B. J. Matkowsky and G. I. Sivashinsky (SIAM J. Appl. Math.35 (1978), 465–478) shows that solutions demonstrate behavior typical for the Hopf bifurcation. A rigorous treatment of this phenomenon is developed. The problem is considered as an evolution equation in a Banach space. To circumvent difficulties involving a possible resonance with the continuous spectrum, appropriate weighted norms are introduced. A suitable version of the Hopf bifurcation theorem is developed and the existence of time periodic solutions is proved for values of the parameter near some critical value.     

Low-Frequency Multidimensional Instabilities for Reacting Shock Waves

This paper presents a weakly nonlinear analysis for one scenario for the development of transversal instabilities in detonation waves in two space dimensions. The theory proposed and developed here is most appropriate for understanding the behavior of regular and chaotically irregular pulsation instabilities that occur in detonation fronts in condensed phases and occasionally in gases. The theory involves low-frequency instabilities and through suitable asymptotics yields a complex Ginzburg-Landau equation that describes simultaneously the evolution of the detonation front and the nonlinear interactions behind this front. The asymptotic theory mimics the familiar theory of nonlinear hydrodynamic instability in outline; however, there are several novel technical aspects in the derivation because the phenomena studied here involve a complex free boundary problem for a system of nonlinear hyperbolic equations with source terms.     

A free boundary problem modeling thermal instabilities: Stability and bifurcation

In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this one-phase model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.     

Positively invariant regions for a problem in phase transitions

Positively invariant regions for the system v _t + p(W) _x = V _xx , W _t –V _x = W _xx are constructed where p < 0, w < , w > , p(w) = 0, w , > 0. Such a choice of p is motivated by the Maxwell construction for a van der Waals fluid. The method of an analysis is a modification of earlier ideas of Chueh, Conley, & Smoller [1]. The results given here provide independent L bounds on the solution (w, v).Dedicated to Professor James Serrin on the occasion of his sixtieth birthday     

Finite Dimensional Attractor for a One-Phase Stefan Problem with Kinetics

For a one-phase free-boundary problem with kinetics, which is known to generate a rich dynamics, we study evolution of the infinitesimal volume along the trajectories in the attractor. We demonstrate that for sufficiently large m that is defined solely by the properties of the kinetics function the m-dimensional volume decays exponentially. This property combined with the uniform differentiability of the semigroup leads to the conclusion that the Hausdorff dimension of the attractor is finite.     

Theoretical investigation of the intrinsic piezoelectric properties for tetragonal BaTiO3 epitaxial films

The orientation dependences of the converse longitudinal piezoelectric constant d_33,f, and the in-plane converse piezoelectric constant e_31,f, are calculated for tetragonal barium titanate epitaxial films. The calculations demonstrate that both e_31,f and d_33,f have their maximum values along an axis close to the (1 1 1) direction of the pseudo-cubic system, which are similar to the orientation dependence results for a tetragonal BaTiO₃ single crystal. The calculated piezoelectric constants for a (1 1 1) oriented BaTiO₃ epitaxial film (e_31,f = −23 C/m², d_33,f = 124 pm/V) suggest that it is a good candidate material for lead-free MEMS applications.