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This study presents a computational framework to investigate and predict the complicated multiphase properties of eco-friendly lead-free piezoelectric materials, which are crucial for sustainable technological progress. Although their electromechanical properties vary by phase, lead-free piezoelectric materials show a considerable thermo-electromechanical response. Lead-free materials such as Bi$_{0.5}$Na$_{0,5}$TiO$_{3}$ (BNT) and other BNT-type piezoelectric materials transition to rhombohedral (R3c), orthorhombic (Pnma), tetragonal (P4bm), and cubic (Cc) phases with temperature variation. These phases are determined by the symmetry and alignment of the ferroelectric domains. Multiple phases can occur simultaneously under specific thermal, electrical, and mechanical conditions, leading in complex multiphase behaviour. These materials' performance must be assessed by studying such behaviour. This study uses Landau-Ginzburg-Devonshire theory to simulate material micro-domain phase transitions. The computational model for BNT-type piezoelectric material covers temperature-induced ferroelectric domain switching and phase transitions. Therefore, the developed computational approach will assist us in better understanding the influence of these materials' complex multiphase behaviour on creating sustainable solutions with green technologies.

In recent times, there have been notable advancements in haptic technology, particularly in screens found on mobile phones, laptops, LED screens, and control panels. However, it is essential to note that the progress in high-temperature haptic applications is still in the developmental phase. Due to its complex phase and domain structures, lead-free piezoelectric materials such as BNT-based haptic technology behave differently at high temperatures than ambient conditions. Therefore, it is essential to investigate the aspects of thermal management and thermal stability, as temperature plays a vital role in the phase and domain transition of BNT material. A two-dimensional thermo-electromechanical model has been proposed in this study to analyze the thermal stability of BNT material by analyzing the impact of temperature on effective electromechanical properties and mechanical and electric field parameters. However, the thermo-electromechanical modelling of BNT ceramics examines the macroscopic effects of the applied thermal field on mechanical and electric field parameters as phase change and microdomain dynamics are not considered in this model. This study analyzes the impact of thermo-electromechanical coupling on the performance of BNT-type piezoelectric materials compared to conventional electromechanical coupling. The results predicted a significant improvement in piezoelectric response compared to electromechanical coupling due to increased thermoelectric effect in absence of phase change and microdomain switching for temperature boundary conditions below depolarization temperature ($T_{d}$~200$^{\circ}$C for pure BNT material)., Comment: 37 pages, 13 figures

This paper presents an innovative hierarchical meta-modelling approach for predicting the effective elastic properties of stone injected with composite cement grouts containing Carbon NanoTubes (CNTs) for structural rehabilitation purposes. The study first addresses the homogenization of the nano- and micro-scales through numerical representative volume elements. The first numerical model focuses on the cement matrix doped with randomly oriented CNTs, while the second model represents the porous stone with CNT/cement grout filling the pores. However, the computational burden associated with these models poses a significant limitation when analysing large-scale macrostructural elements. To overcome this challenge, a hierarchical meta-modelling approach based on two nested Kriging surrogate models is proposed. This approach offers a fast and accurate alternative to bypass the time-consuming numerical homogenization process. The first surrogate model establishes a connection between the microstructural characteristics of the CNTs and cement and the effective elastic properties of the composite grout. Subsequently, a second meta-model expands over the first one by introducing two additional variables: the elastic modulus of the stone and the porosity, allowing for estimation of the overall elastic properties of CNT/cement/stone composites. The accuracy and efficiency of the proposed hierarchical meta-model is demonstrated through detailed parametric analyses. To showcase its potential for optimizing rehabilitation interventions, the paper is closed with its application to a benchmark case study of a stone column injected with CNT/cement grout.

This paper reviews the application of coherent acoustic phonons in the form of piezoelectrically-generated surface acoustic waves to control the response of integrated photonic acousto-optic waveguide structures. We first address the fundamental properties of the acoustic fields in piezoelectric materials as well as the piezoelectric generation of surface acoustic waves using interdigital transducers. The mechanism responsible for the interaction between light and the acoustic modes in the photonic waveguide structures and the modulation of the response of the devices is carefully reviewed. Next, we discuss the most important developments in the field of integrated acousto-optical device applications, with focus on devices built upon three-dimensional optical waveguides. Finally, prospects for acousto-optic device applications by use of surface acoustic waves are summarized.

We find a new lower bound for the maximal number of zeros to harmonic polynomials, $p(z)+\overline{q(z)}$, when ${\rm deg}\, p = n$ and ${\rm deg}\, q = n-2$., Comment: 8 pages, 3 figures, 2 tables

In this paper we sharpen significantly several known estimates on the maximal number of zeros of complex harmonic polynomials. We also study the relation between the curvature of critical lemniscates and its impact on geometry of caustics and the number of zeros of harmonic polynomials., Comment: 18 pages, 7 figures, Theorem 1 corrected and a remark added