Aurelio H. Heredia Jiménez

Using a theory of homogenization that consists in the discretization of the inclusion of a binary phononic crystal in small volumes, in which the material parameters can be expanded in Fourier series, we have determined the dependence of the effective elastic parameters as a function of the frequency. In particular, the frequency dependence of all the elements that constitute the effective tensors of stiffness (moduli of elasticity) and density was analyzed for a 1D phononic crystal conformed of materials whose main characteristic is the high contrast between their elastic properties. In this dynamic case of homogenization, it was found that the effective parameters can reproduce the exact dispersion relations for the acoustic modes that propagate along the periodicity direction of the crystal. Particularly, in the second pass band (high-frequency branch) corresponding to the transverse vibrational modes, the homogenized elastic phononic crystal exhibits a metamaterial behavior because the effective C₄₄-component (shear modulus) and dynamic mass density were found to be both negative. It is noteworthy that the study derived from this homogenization technique can lead to design of double negative metamaterial systems for potential applications.

In this research work, we present the synthesis and characterization of four different TiO₂ structures, such as nanotubes, nanocavities, nanosheets assembled on nanocavities and nanobowls assembled on nanocavities, prepared by electrochemical anodization using organic electrolytes. After synthesis, the structures were thermally annealed to pass from the amorphous phase to the anatase phase, which is one of the most important crystalline structures of TiO₂ due to its high photocatalytic activity and stability. The unique morphology and topography were studied using scanning electron microscopy (SEM) and atomic force microscopy (AFM). The elemental composition was determined by energy-dispersive X-ray spectroscopy (EDS). The anatase phase was verified by Raman microscopy and X-ray diffraction (XRD), the band gap energy was calculated by the Kubelka–Munk function, and the main defect states that generate the emission, as well as their lifetime, were determined by photoluminescence spectroscopy and time response photoluminescence (TRPL), respectively. The TiO₂ nanomaterials were tested as catalysts in the photodegradation of a solution of methylene blue using a UV lamp at room temperature. The results showed complex morphologies and different surface roughness areas of these nanomaterials. Furthermore, a relationship between defect states, band gap energy, and photocatalytic activity was established. We found that the catalytic activity was improved as an effect of geometric parameters and oxygen vacancies.

With the application of a homogenization theory, based on the Fourier formalism (which provides efficient and exact formulas by which to determine all the components of the effective stiffness and mass density tensors, valid in the regime of large wavelengths), a new approach to calculate the effective quasi-static response in three-dimensional solid-solid phononic crystals is reported. The formulas derived in this work for calculating the effective elastic parameters show a dependence, in terms of summations over the vectors, of the reciprocal lattice by the discretization of the volume of the inclusion in small parts (e.g., small cubes), to obtain a system of equations from which we define the effective response. In particular, we present the numerical results calculated for several cubic lattices with solid constituents and different shapes of inclusions in the unit cell versus the filling fraction, as well as for fixed values of it. By this means, we analyzed the effect of the type of Bravais lattice of the materials, and the geometry of the inclusions that constitute the three-dimensional phononic array, on the resulting effective anisotropy. Finally, our theory confirms other well-known results with previous homogenization theories as a particular case study. In this regard, the examples and results shown here can be useful for the design of metamaterials with predetermined elastic properties.

In this paper, a n-i-p planar heterojunction simulation of Sn-based iodide perovskite solar cell (PSC) is proposed. The solar cell structure consists of a Fluorine-doped tin oxide (FTO) substrate on which titanium oxide (TiO₂) is placed; this material will act as an electron transporting layer (ETL); then, we have the tin perovskite CH₃NH₃SnI₃ (MASnI₃) which is the absorber layer and next a copper zinc and tin sulfide (CZTS) that will have the function of a hole transporting layer (HTL). This material is used due to its simple synthesis process and band tuning, in addition to presenting good electrical properties and stability; it is also a low-cost and non-toxic inorganic material. Finally, gold (Au) is placed as a back contact. The lead-free perovskite solar cell was simulated using a Solar Cell Capacitance Simulator (SCAPS-1D). The simulations were performed under AM 1.5G light illumination and focused on getting the best efficiency of the solar cell proposed. The thickness of MASnI₃ and CZTS, band gap of CZTS, operating temperature in the range between 250 K and 350 K, acceptor concentration and defect density of absorber layer were the parameters optimized in the solar cell device. The simulation results indicate that absorber thicknesses of 500 nm and 300 nm for CZTS are appropriate for the solar cell. Further, when optimum values of the acceptor density (N_A) and defect density (N_t), 10¹⁶ cm⁻³ and 10¹⁴ cm⁻³, respectively, were used, the best electrical values were obtained: J_sc of 31.66 mA/cm², V_oc of 0.96 V, FF of 67% and PCE of 20.28%. Due to the enhanced performance parameters, the structure of the device could be used in applications for a solar energy harvesting system.

The ability to plan a multiple-target path that goes through places considered important is desirable for autonomous mobile robots that perform tasks in industrial environments. This characteristic is necessary for inspection robots that monitor the critical conditions of sectors in thermal, nuclear, and hydropower plants. This ability is also useful for applications such as service at home, victim rescue, museum guidance, land mine detection, and so forth. Multiple-target collision-free path planning is a topic that has not been very studied because of the complexity that it implies. Usually, this issue is left in second place because, commonly, it is solved by segmentation using the point-to-point strategy. Nevertheless, this approach exhibits a poor performance, in terms of path length, due to unnecessary turnings and redundant segments present in the found path. In this paper, a multiple-target method based on homotopy continuation capable to calculate a collision-free path in a single execution for complex environments is presented. This method exhibits a better performance, both in speed and efficiency, and robustness compared to the original Homotopic Path Planning Method (HPPM). Among the new schemes that improve their performance are the Double Spherical Tracking (DST), the dummy obstacle scheme, and a systematic criterion to a selection of repulsion parameter. The case studies show its effectiveness to find a solution path for office-like environments in just a few milliseconds, even if they have narrow corridors and hundreds of obstacles. Additionally, a comparison between the proposed method and sampling-based planning algorithms (SBP) with the best performance is presented. Furthermore, the results of case studies show that the proposed method exhibits a better performance than SBP algorithms for execution time, memory, and in some cases path length metrics. Finally, to validate the feasibility of the paths calculated by the proposed planner; two simulations using the pure-pursuit controlled and differential drive robot model contained in the Robotics System Toolbox of MATLAB are presented.