Effective Dielectric Constant Research Articles

Surface properties of the seas of Titan as revealed by Cassini mission bistatic radar experiments

Saturn’s moon Titan was explored by the Cassini spacecraft from 2004 to 2017. While Cassini revealed a lot about this Earth-like world, its radar observations could only provide limited information about Titan’s liquid hydrocarbons seas Kraken, Ligeia and Punga Mare. Here, we show the results of the analysis of the Cassini mission bistatic radar experiments data of Titan’s polar seas. The dual-polarized nature of bistatic radar observations allow independent estimates of effective relative dielectric constant and small-scale roughness of sea surface, which were not possible via monostatic radar data. We find statistically significant variations in effective dielectric constant (i.e., liquid composition), consistent with a latitudinal dependence in the methane-ethane mixing-ratio. The results on estuaries suggest lower values than the open seas, compatible with methane-rich rivers entering seas with higher ethane content. We estimate small-scale roughness of a few millimeters from the almost purely coherent scattering from the sea surface, hinting at the presence of capillary waves. This roughness is concentrated near estuaries and inter-basin straits, perhaps indicating active tidal currents.

Electronic Structure of Biexcitons in Metal Halide Perovskite Nanoplatelets.

A theoretical description of biexcitons in metal halide perovskite nanoplatelets is presented. The description is based on a variational effective mass model, including polaronic effects by means of a Haken potential. The strong quantum and dielectric confinements are shown to squeeze the biexciton under the polaronic radius, which greatly enhances Coulomb attractions and (to a lesser extent) repulsions. This explains the need for effective dielectric constants approaching the high-frequency limit in previous simulations, and the binding energies exceeding 40 meV observed in single-monolayer nanoplatelets. Biexcitons are formed by a pair of weakly interacting excitons, with a roughly rectangular geometry. This translates into a constant ratio between biexciton and exciton binding energies (2D Haynes rule) well below the ideal value of ΔBX/ΔX = 0.228 proposed for squared biexcitons. The ratio is independent of the number of monolayers in the platelet, but it does depend on the lateral and dielectric confinement.

Полосковый резонатор СВЧ с объемным кристаллом: экспериментальные характеристики и определение эффективной диэлектрической проницаемости

The paper presents the results of an experimental study and modeling of the frequency characteristics of a resonator in the form of two strip vibrators, separated by a large gap and covered with a bulk lithium niobate crystal. A metal electrode with a floating potential is installed on the upper surface of the crystal. The frequency dependences of the scattering matrix coefficients of a stripline resonator were measured in the frequency range up to 3 GHz. Electrodynamic analysis was carried out in the COMSOL Multiphysics numerical simulation environment. A comparison was made of experimental and numerical results, which showed good qualitative agreement between the transmission coefficients and reflection coefficients. Resonant oscillations were obtained at two or three frequencies depending on the location and orientation of the crystal. It has been established that at the first resonant frequency the electrode acts as a screen. The absence of an electrode leads to the disappearance of resonance. The simulation carried out in COMSOL made it possible to estimate the effective dielectric constant of the resonator corresponding to the values of the resonant frequencies. The calculation of electromagnetic fields made it possible to establish the types of waves corresponding to resonant frequencies. Knowing the type of waves and estimating the relative dielectric constant made it possible to construct an algorithm for a refined iterative procedure for calculating the values of the resonant frequencies and the effective dielectric constant of the resonator. The possibility of using resonators as single-link bandpass filters with a passband of about 1%, insertion loss of –1.1 dB and minimal return loss of –28 dB at the center frequency is shown.

Modeling of electromagnetic wave reflection from wet soil taken into account of dispersion, heterogeneity and surface roughness

Background. Taking into account temperature, soil composition, surface roughness and the dependence of effective dielectric constant on frequency allows a more accurate assessment of soil moisture and other important parameters, which can be used in various fields such as agriculture, geology, ecology and hydrology. Aim. In this work, we calculate the reflection of a linearly polarized electromagnetic wave from wet soil, taking into account such physical factors as heterogeneity of soil structure, surface roughness and dispersion. Methods. Based on a heterogeneous mathematical model of wet soil, taking into account the dispersion of the dielectric constant of water and surface roughness, expressions are derived for the complex reflection coefficients of electromagnetic waves of vertical and horizontal polarization. Results. The model of loose wet soil with the standard deviation of roughness on the surface was chosen as the object of study. An analysis of the frequency and angular characteristics of the modules of the reflection coefficients was carried out at a fixed level of soil moisture. Conclusion. The data obtained as a result of the calculations is a valuable tool for further improving methods of remote sensing of the Earth and contributes to the development of new technologies for monitoring soil parameters using unmanned aerial vehicles, which opens up prospects for more accurate and efficient analysis of the state of land resources and ecosystems.

Hyperuniformity classes of quasiperiodic tilings via diffusion spreadability.

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent α>0, that characterizes the power-law scaling behavior of the structure factor S(k) as a function of wave number k≡|k| in the vicinity of the origin, e.g., S(k)∼|k|^{α} in cases where S(k) varies continuously with k as k→0. In this paper, we show that the spreadability is an effective method for determining α for quasiperiodic systems where S(k) is discontinuous and consists of a dense set of Bragg peaks. It has been shown in [Phys. Rev. E 104, 054102 (2021)10.1103/PhysRevE.104.054102] that, for media with finite α, the long-time behavior of the excess spreadability S(∞)-S(t) can be fit to a power law of the form t^{-(d-α)/2}, where d is the space dimension, to accurately extract α for the continuous case. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density χ[over ̃]_{_{V}}(k) of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract α for the one-dimensional (1D) limit-periodic period-doubling chain (α=1) and the 1D quasicrystalline Fibonacci chain (α=3) to within 0.02% of the analytically known exact results. Moreover, we obtain a value of α=5.97±0.06 for the two-dimensional Penrose tiling and present plausible theoretical arguments strongly suggesting that α is exactly equal to six. We also show that, due to the self-similarity of the structures examined here, one can truncate the small-k region of the scattering information used to compute the spreadability and obtain an accurate value of α, with a small deviation from the untruncated case that decreases as the system size increases. This strongly suggests that one can obtain a good estimate of α for an infinite self-similar quasicrystal from a modestly sized finite sample. The methods described here offer a simple and general procedure to characterize accurately the large-scale translational order present in quasicrystalline and limit-periodic media in any space dimension that are self-similar. Moreover, the scattering information extracted from these two-phase media encoded in χ[over ̃]_{_{V}}(k), can be used to estimate their physical properties, such as their effective dynamic dielectric constants, effective dynamic elastic constants, and fluid permeabilities.

Development of Wearable Textile MIMO Antenna for Sub-6 GHz Band New Radio 5G Applications.

In this paper, an irregular octagonal two-port MIMO patch antenna is designed specifically for New Radio (NR) 5G applications in the mid-band sub-6 GHz. The proposed antenna comprises an irregularly shaped patch antenna equipped with a regular 50-ohm feed line and a parasitic strip line antenna, and is partially grounded. Jeans material serves as a substrate with an effective dielectric constant of 1.6 and a thickness of 1 mm. This material is studied experimentally. The proposed antenna design undergoes analysis and optimization using the ANSYS HFSS tool. Furthermore, the design incorporates the influence of the slot on both the ground plane and the parasitic strip line to optimize performance, enhance isolation, and improve impedance matching among antenna elements. The dimensions of the jeans substrate are 40 mm × 50 mm. The simulated impedance bandwidth ranged from 3.6 GHz to 7 GHz and the measured bandwidth was slightly narrower, from 4.35 GHz to 7 GHz. The simulation results demonstrated an isolation level greater than 12 dB between antenna elements, while the measured results reached 28.5 dB, and the peak gain for this proposed antenna stood at 6.74 dB. These qualities made this proposed antenna suitable for various New Radio mid-band 5G wireless applications within the sub-6 GHz band, such as N79, Wi-Fi-5/6, V2X, and DSRC applications.

Iterative synthesis method for high‐directivity symmetrical stepped‐impedance microstrip parallel‐line coupler

AbstractTraditional quarter‐wavelength parallel‐line couplers (QWPLC) in microstrip form suffer heavily in low directivity because of unbalanced even‐mode and odd‐mode phase velocities. Related schemes to improve directivity lead to complex structures and large dimensions. This study derives and validates an iterative synthesis method to design a high‐directivity microstrip coupler adopting a symmetric stepped‐impedance microstrip coupled line (SSIMCL). Given that the even‐mode and odd‐mode effective dielectric constants (EDCs) vary with the characteristic impedances, the authors take the EDCs of traditional QWPLC as the initial values for an SSIMCL, and the characteristic impedances and EDCs can be computed and converged in several iterations, resulting in good phase delay balance and high coupler directivity. A 20‐dB microstrip coupler working at 1 GHz with high directivity is designed, fabricated, and measured. The obtained maximum directivity is 47 dB and approximately 1 GHz, while the relative bandwidth with a directivity higher than 20 dB and a return loss better than 20 dB is larger than 70%. The novel microstrip coupler also features a compact, simple structure shorter than λg/4.

Development of microfluidically reconfigurable antenna using additive manufacturing

This research presents a microfluidically reconfigurable additively manufactured antenna. The proposed configuration demonstrates the applicability of additive manufacturing (AM) for fabricating intricate and lightweight structures. Additionally, it established the feasibility of microfluidic technology for achieving continuous frequency reconfigurability. The proposed antenna utilizes the dielectric fluid for reconfiguration, facilitated by pumping it in and out of microfluidic structures using a syringe pump. The incorporation of dielectric fluid in the channels alters the effective dielectric constant of the substrate and causes perturbations in the electric field distributions around the metallic patch. To validate the proposed idea, a prototype of the microfluidically reconfigurable 3D-printed antenna is designed, fabricated, and tested. The operating frequency is reconfigured from 2.38 to 3.49 GHz with a tuning range of 1.11 GHz, and the radiation pattern remains stable across considered cases. It is observed that measured results are in good agreement with simulated values. The prototype of the antenna design is fabricated using a single machining process, eliminating the need for traditional machining. The proposed antenna’s configuration is advantageous for various applications such as IEEE802.11b/g/n, IEEE802.15.1, and IEEE802.16.

Real and damped modes for an interacting fermion–antifermion pair: exciton in monolayer medium

In this manuscript, we investigate the interaction between a fermion–antifermion pair in (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-dimensions, governed by a Coulomb-type inter-particle potential. We explore analytical solutions for a fully covariant two-body Dirac equation derived from quantum electrodynamics, focusing on a spinless composite system. We present a non-perturbative second-order wave equation and derive a solution using the generators of the sℓ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s\\ell _{2}$$\\end{document} algebra. Subsequently, we determine the relativistic frequency modes of the system and extend our findings to electron–hole pairs in a monolayer medium in the vicinity of substrate. We analyze the impact of the effective dielectric constant (ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon$$\\end{document}) of the surrounding medium on the real and damped modes of an exciton. Our results indicate that the ground state binding energy of the system can vary from the order of eV to a few meV, depending on changes in ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon$$\\end{document}. Additionally, we observe that the decay time for the ground state of such an exciton is on the order of ∼10-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 10^{-12}$$\\end{document} s. These findings suggest that the evolution of such a pair can be controlled by adjusting the effective dielectric constant of the surrounding medium.

Spatio-temporal electric field distributions in an atmospheric plasma jet impinging on a microchannel array surface

The electric field distribution in the ionization waves (IWs) propagating over a microchannel array dielectric surface, with the channels either empty or filled with distilled water, is measured by ps electric field induced second harmonic generation. The surface IW is initiated by the atmospheric pressure N2–Ar plasma jet impinging on the surface vertically and powered by ns pulse discharge bursts. The results show that the electric field inside the microchannels, specifically its horizontal component, is enhanced by up to a factor of 2. The field enhancement region is localized within the channels. The vertical electric field inside the channels lags in time compared to the field measured at the ridges, indicating the transient reversal of the IW propagation direction across the channels (toward the jet). This is consistent with the phase-locked plasma emission images and confirmed by the kinetic modeling predictions, which show that the IW ‘jumps’ over the empty channels and propagates into the channels only after the jump between the adjacent ridges. When the channels are filled with water, the wave speed increases by up to 50%, due to the higher effective dielectric constant of the surface. No evidence of a significant electric field enhancement near the dielectric surface (ceramic or water) has been detected, within the spatial resolution of the present diagnostic, ∼100 μm.

Research and design of metasurface antennas based on composite dielectric materials

The metasurface has the ability to regulate electromagnetic waves, which is widely used for polarization state control, impedance bandwidth expansion, vortex beam generation, and high-directional antennas. Research shows that the substrate of the metasurface has a significant impact on the performance of the antenna. The equivalent dielectric constant of composite dielectric materials is investigated by using the characteristic mode analysis (CMA). A novel metasurface with composite dielectric substrate is proposed. The composite dielectric material consists of a substrate with a dielectric constant of 3.55 and an air gap. The calculation results of the effective dielectric constant of composite dielectric materials are basically consistent with the simulation results. Based on this composite dielectric material, a metasurface antenna is designed. S11 is less than-10 dB in the frequency range of 5.22–7.87 GHz. The peak boresight gain is 10.44 dBi at 6.5 GHz.

A novel methodology for designing Mono/Bi-slab X-band microwave absorbers of Carbon-Powder composites

This work introduces a methodology for the design of X-band microwave absorbers using carbon-graphite powder composites. The reflection loss (RL) is adjusted through variations in sample thickness, mono/bi-slab geometries, and effective dielectric constant. The impact of the particle size of the powders and the volume fraction (v.f.) of the composites on the effective dielectric permittivity has been systematically investigated. The Nicolson-Ross-Weir (NRW) conversion and the Birchak dielectric mixing model were employed. Optimal absorption conditions predicted by RL simulations were validated through experimental waveguide measurements for mono/bi-slab systems of paraffin-carbon composite samples. The mono-slabs with a particle size of 3.5 μm showed the best versatility for tailoring the RL in the X-band through v.f. variations while maintaining a fixed thickness of 2 mm. In addition, a bi-slab system (powder-paraffin/paraffin) for such powder size, at 18.0 % of v.f., showed an enhanced RL with a bandwidth of 2.6 GHz and a minimum of − 40 dB (at 11 GHz). Other dielectrics based on resin:paint mixtures were tested to replace the paraffin-matrix, revealing a strong powder-matrix interaction capable of modulating the effective dielectric permittivity. Finally, experimental antenna RL measurements conducted in free space were corroborated by theoretical simulations based on the waveguide characterizations.

Characterization of synthetic opals filled with copper

Photonic crystals based on synthetic opals filled with copper were produced by using the electrochemical deposition technique. Copper nanocrystal formation together with some quantity of their oxides inside opal pores was proved by the X-ray diffraction pattern. An angular behavior of reflectance maximum for opals with different copper content was satisfactorily described in the framework of theBragg light diffraction model. Effective dielectric constant of the opal-copper structures was determined.

Theoretical prediction of the effective dynamic dielectric constant of disordered hyperuniform anisotropic composites beyond the long-wavelength regime [Invited

Torquato and Kim [Phys. Rev. X 11, 296 021002 (2021)10.1103/PhysRevX.11.021002] derived exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor ε e (k q ,ω) that treat general statistically anisoropic three-dimensional (3D) two-phase composite microstructures, which are valid well beyond the long-wavelength regime. Here, we demonstrate that truncating this general rapidly converging expansion at the two- and three-point levels is a powerful theoretical tool from which one can extract accurate approximations suited for various microstructural symmetries. Among other results, we show that such truncations yield closed-form formulas applicable to transverse polarization in layered media and transverse magnetic polarization in transversely isotropic media, respectively. We apply these formulas to estimate ε e (k q ,ω) for models of 3D disordered hyperuniform layered and transversely isotropic media: nonstealthy hyperuniform media and stealthy hyperuniform media. In particular, we show that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (trivially implying no Anderson localization, in principle) within finite wave number intervals through the third-order terms. For all models considered here, we validate that the second-order formulas, which depend on the spectral density, are already very accurate well beyond the long-wavelength regime by showing very good agreement with the finite-difference time-domain (FDTD) simulations. The high predictive power of the second-order formula is due to the fact that higher-order contributions are negligibly small, implying that it very accurately approximates multiple scattering through all orders. This implies that there can be no Anderson localization within the predicted perfect transparency interval in stealthy hyperuniform layered and transversely isotropic media in practice because the localization length (associated with only possibly negligibly small higher-order contributions) should be very large compared to any practically large sample size. Our predictive theory provides the foundation for the inverse design of novel effective wave characteristics of disordered and statistically anisotropic structures by engineering their spectral densities.

Design and performance analysis of 3-D braided piezoelectric composite vibration energy harvester

In this article, an innovative three-dimensional (3-D) braided piezoelectric composite vibration energy harvester (BPCVEH) is designed. The geometry and representative volume unit (RVU) models of the 3-D braided piezoelectric composites (BPCs) are established based on the braided process. The effective elastic, piezoelectric, and dielectric constants of the 3-D BPCs are also predicted. The electro-mechanical coupling vibration equation of the 3-D BPCVEH under forced vibration is derived, and its output response and vibration mode are analyzed. The effects of environment frequency, load resistance, and external excitation acceleration on the voltage and power response of 3-D BPCVEH with different volume fractions are studied.

Annealing modulated microstructural and electrical properties of plasma-enhanced atomic layer deposition-derived HfO2/SiO2 nanolaminates on AlGaN/GaN

In current work, HfO2/SiO2 nanolaminates and HfO2 films were grown on AlGaN/GaN substrates via plasma-enhanced atomic layer deposition. A comparative study of how rapid thermal annealing modulates the microstructural and electrical properties of both films has been presented. It is found that the HfO2/SiO2 nanolaminate keeps an amorphous structure when thermally treated below 600 °C, whereas crystal grains appear within the 800 °C annealed sample. High-temperature annealing facilitates the transformation from Hf–O and Si–O to Hf–O–Si in the HfO2/SiO2 nanolaminates, forming an HfSiO4 composite structure simultaneously. The 800 °C annealed HfO2/SiO2 shows a low k value and large leakage current density. While the 600 °C annealed HfO2/SiO2 possesses an effective dielectric constant of 18.3, a turn-on potential of 9.0 V, as well as a leakage density of 10−2 μA/cm2 at gate biases of both −10 and 2 V, revealing good potential in fabricating high electron mobility transistors.

Оптические свойства сверхтонких пленок Pd и Pt на кварцевой подложке и на пленках триоксида вольфрама

Based on ellipsometry and transmission spectra, optical parameters of palladium and platinum films were determined. The Pd and Pt films had a thickness of 5 – 7 nm and were studied both on a SiO2 and WO3 substrates. Despite the extremely small thicknesses, the parameters of most films were well described by isotropic dielectric constant. An interesting feature was that films deposited directly on a SiO2 substrate had a positive (rather than negative, characteristic of a metal) real part of the effective dielectric constant, while the films deposited on WO3 exhibited metallic properties for unannealed films and properties characteristic of metal-dielectric composites for films that have been annealed (some of the films annealed at 300°C in argon retained their metallic properties).

Frequency self-compensating technique for mitigating detuning effects due to bending for wearable patch antennas

This paper presents the design analysis and measurement of a linearly polarized microstrip patch antenna resonating in the X-band regime with a self-compensating mechanism to mitigate the detuning effects due to bending. The antenna is studied for its variation in the resonant frequency for bending radii up to 20 mm and a compensation of ≈50% is achieved as compared to its counterpart. The compensation technique is realized by altering the effective dielectric constant of the substrate by injecting dielectric fluids into the grooves incorporated in the substrate, supplemented by a shape variation of the grooves due to bending. The antennas demonstrated in the current work exhibits a gain of more than 7 dBi throughout along with a consistent −10 dB impedance bandwidth.

Exciton–Polaritons in CsPbBr3 Crystals Revealed by Optical Reflectivity in High Magnetic Fields and Two‐Photon Spectroscopy

Cesium lead bromide (CsPbBr3) is a representative material of the emerging class of lead halide perovskite semiconductors that possess remarkable optoelectronic properties. Its optical properties in the vicinity of the bandgap energy are greatly contributed by excitons, which form exciton polaritons due to strong light–matter interactions. Exciton–polaritons in solution‐grown CsPbBr3 crystals are examined by means of circularly polarized reflection spectroscopy measured in high magnetic fields up to 60 T. The excited 2P exciton state is measured by two‐photon absorption. Comprehensive modeling and analysis provides detailed quantitative information about the exciton–polariton parameters: exciton binding energy of 32.5 meV, oscillator strength characterized by longitudinal–transverse splitting of 5.3 meV, damping of 6.7 meV, reduced exciton mass of 0.18m0, exciton diamagnetic shift of 1.6 μeV T−2, and exciton Landé factor . It is shown that the exciton states can be described within a hydrogen‐like model with an effective dielectric constant of 8.7. From the measured exciton longitudinal–transverse splitting, Kane energy of Ep = 15 eV is evaluated, which is in reasonable agreement with values of 11.8–12.5 eV derived from the carrier effective masses.

Multiband terahertz metamaterial perfect absorber for microorganisms detection

We report a multi-resonant terahertz (THz) metamaterial perfect absorber (MPA)-based biosensor in the working frequency range of 0 - 3.8 THz for sensing of microorganisms (such as fungi, yeast) and wheat pesticides. Nearly 100% absorption is realized at f_1= 1.7THz, f_2= 2.8THz, f_3=3.2THz, and f_4=3.5THz. We designed our THz MPA sensor making resonators’ gap area compatible with the microorganisms’ size. To obtain optimum performance of the MPA, a mapping of amplitudes and shifts in the absorption resonance peaks with different structural parameters of the resonators is carried out. A very high-frequency shift is obtained for microorganisms such as Penicillium chrysogenum (fungi), yeast, and pesticides (Imidacloprid, N, N-Diethyldithiocarbamate sodium salt trihydrate, Daminozide, N, N-Diethyldithiocarbamate sodium salt hydrate, and Dicofol). An equivalent circuit model using Advance Design System (ADS) software is developed. The calculated results through the model show similar trends as obtained in the simulations using CST. Investigations of the effect of incidence angle of THz wave on the absorption spectra of the MPA are also carried out. It is found that incidence angle does not impact the stability of the lower resonance absorption peak (1.79THz). Due to the wide working frequency range, the proposed sensor is extremely suitable for the detection of all range of pesticides because their specific absorption fingerprint lies in the frequency range of 0–3.8THz. We believe that our sensor could be a potential detection tool for detecting pesticide residues in agriculture and food products. The THz MPA-based biosensor is capable of detecting a very small change in the effective dielectric constant of the MPA environment. Therefore, it can also offer huge opportunities in label-free biosensing for future biomedical applications.