Virtual modelling of the impact of torsional loading on osteoporotic vertebrae buckling.

Purpose: This study aimed to evaluate the biomechanical response or load transfer on the osteoporotic L1 vertebra under torsional loading. Methods: To achieve this goal, a numerical model of osteoporotic vertebra in various trabecular bone degenerations was developed and tested. The mechanical behavior of the model was represented taking into account the anisotropic properties of the cancellous bone, which provided a more realistic mechanical picture of the biological subsystem. To ensure the reliability of osteoporotic degradation, the thinning of cortical bone and the appearance of gaps between trabecular bone and cortical bone were also taken into account when creating the models. Results: Finite element (FE) analysis showed that the deformations of cortical bone thinning and detachment of the cortical bone from the trabecular tissue lead to local instability of the vertebra. As a result, the cortical bone of a vertebra loses its load-bearing capacity, even if the strength limit is not reached. Conclusions: The results obtained allow us to state that taking into account the thinning of the trabeculae, which creates voids, is extremely important for load-bearing capacity of osteoporotic vertebrae. However, a limitation of this study is the lack of experimental data to ensure consistency with the computer simulation results.

CutFEM-based MEG forward modeling improves source separability and sensitivity to quasi-radial sources: A somatosensory group study.

Source analysis of magnetoencephalography (MEG) data requires the computation of the magnetic fields induced by current sources in the brain. This so-called MEG forward problem includes an accurate estimation of the volume conduction effects in the human head. Here, we introduce the Cut finite element method (CutFEM) for the MEG forward problem. CutFEM's meshing process imposes fewer restrictions on tissue anatomy than tetrahedral meshes while being able to mesh curved geometries contrary to hexahedral meshing. To evaluate the new approach, we compare CutFEM with a boundary element method (BEM) that distinguishes three tissue compartments and a 6-compartment hexahedral FEM in an n = 19 group study of somatosensory evoked fields (SEF). The neural generators of the 20 ms post-stimulus SEF components (M20) are reconstructed using both an unregularized and a regularized inversion approach. Changing the forward model resulted in reconstruction differences of about 1 centimeter in location and considerable differences in orientation. The tested 6-compartment FEM approaches significantly increase the goodness of fit to the measured data compared with the 3-compartment BEM. They also demonstrate higher quasi-radial contributions for sources below the gyral crowns. Furthermore, CutFEM improves source separability compared with both other approaches. We conclude that head models with 6 compartments rather than 3 and the new CutFEM approach are valuable additions to MEG source reconstruction, in particular for sources that are predominantly radial.

Feasibility of magnetomyography with optically pumped magnetometers in a mobile magnetic shield.

While magnetomyography (MMG) using optically pumped magnetometers (OPMs) is a promising method for non-invasive investigation of the neuromuscular system, it has almost exclusively been performed in magnetically shielded rooms (MSRs) to date. MSRs provide extraordinary conditions for biomagnetic measurements but limit the widespread adoption of measurement methods due to high costs and extensive infrastructure. In this work, we address this issue by exploring the feasibility of mobile OPM-MMG in a setup of commercially available components. From field mapping and simulations, we find that the employed zero-field OPM can operate within a large region of the mobile shield, beyond which residual magnetic fields and perturbations become increasingly intolerable. Moreover, with digital filtering and moderate averaging a signal quality comparable to that in a heavily shielded MSR is attained. These findings facilitate practical and cost-effective implementations of OPM-MMG systems in clinical practice and research.

Numerical Study of Tangential Traction Mechanism between Pattern Blocks of Agricultural Radial Tires and Soft Soil.

With the increasing requirements of agricultural machinery, the study of the contact relationship between the tire-soil interface and the improvement of traction efficiency has gradually become a main concern. In this study, the pattern on the agricultural tire was simplified into single-pitch pattern blocks. The pattern blocks were made of rubber material that was highly resistant to abrasion and bending. The experiment was carried out by pressing the three types of patterned block construction into the soil and the pure sliding under the soil. The simulation used the Coupled Eulerian-Lagrangian Method (CEL) to verify the experimental results. We found that the herringbone pattern block was subjected to the highest stress for the same depth of downward pressure. The horizontal force generated by the pure sliding was also the highest. The results showed that the numerically simulated and experimentally measured data exhibited similar trends and average values. In addition, the increase in the contact area between the tire and the soil reduced the compaction and sinking of the soil. The herringbone pattern structure not only had a large contact area but also produced the most significant shear force on the soil. Thus, it may generate greater traction in actual operations.

A Revised Abaqus® Procedure for Fracture Path Simulation Based on the Material Effort Criterion.

This paper presents the results of computer simulations of fracture in three laboratory tests: the three-point bending of a notched beam cut from sandstone, the pull-out test of a self-undercutting anchor fixed in sandstone, and the pull-out test of a bar embedded in concrete. Five material failure criteria were used: Rankine, Coulomb-Mohr, Drucker-Prager, Ottosen-Podgórski, and Hoek-Brown. These criteria were implemented in the Abaqus® FEA system to work with the crack propagation modeling method-extended finite element method (X-FEM). All criteria yielded similar force-displacement relationships and similar crack path shapes. The improved procedure gives significantly better, close-to-real crack propagation paths than can be obtained using the standard subroutines built into the Abaqus® system.

Strength and Fracture Toughness of TIG- and Laser-Welded Joints of Low Carbon Ferritic Steels.

This paper presents the results of experimental testing of joints welded using conventional TIG and laser methods. The welded components were sheets of the low-carbon steels 13CrMo4-5 and 16Mo3. Welded joints were made using different levels of linear welding energy. In the case of laser welding, a bifocal beam with longitudinal positioning of the focal lengths in relation to the welding direction was used. Experimental tests on welded joints included a bending test and determination of hardness distribution, mechanical properties, and fracture toughness, as well as microstructural research in the material of the various joint zones. Based on the determined strength characteristics, the true stress-strain relationships were defined, and a numerical model of the laser joints was developed in Abaqus 6.12-3. The modelled joint was subjected to loading to determine the most stressed areas of the joints. The numerical results were compared with those obtained using GOM's Aramis 3D 5M digital image correlation system. The system used made it possible to record displacements on the surface of the analysed joints in real time. Good agreement was obtained between the strain fields calculated numerically and those recorded using the Aramis 3D 5M video system. The numerical calculations provided information on the strains and stresses occurring inside the analysed joint during loading. It was found that the welded joints were characterised by increased hardness and high strength properties in relation to the base material. The bending test of the laser-welded joints gave a positive result-no cracks were observed on the face or root of the weld. The fracture toughness of the joint zones is slightly lower in relation to that of the base material, but no brittle fracture was observed.

Correlations between the Aging Behavior and Finite Element Method Simulation of Three Silicone Elastomers.

The material parameters required to describe material behavior can change with the age of the components due to chemical and physical aging processes. The finite element method (FEM) is a tool for designing components for later use. The aim of this study is to correlate the change in the mechanical properties of silicone elastomers from standard tests over a longer period of time with the parameters of the Mooney-Rivlin model. To date, there are no publications on the development of the Mooney-Rivlin parameters of silicone elastomers over a storage period. For this purpose, the Shore A hardness, rebound elasticity, compression set and tensile properties were investigated over an aging period of approx. 200 days on two liquid silicone rubbers (LSRs) and one room-temperature-vulcanizing (RTV) silicone rubber. Depending on the silicone elastomer used, different trends in the characteristic values can be observed over the storage period. In general, increases in the Shore A hardness, rebound resilience and stress at a 100% strain with a decrease in the compression set can be determined. In addition to standard tensile tests, the material's multiaxial behavior under tension was probed, and it was found that the similarly stress at a 100% strain increased. Finite element simulations verified the standard tensile test and corresponding Mooney-Rivlin model parameters. These parameters from the uniaxial tensile were validated in the multiaxial behavior, and the model's accuracy in representing material properties and the influence of aging on the FEM simulation were affirmed.

The Galvanic Corrosion of AM60B Coupled with DC01 in Simulated Environments with Varying Water Salinity.

The galvanic corrosion performance of AM60B coupled to DC01 was characterized in simulated environments with varying water salinity. The results showed that the coupled DC01 effectively accelerated the corrosion rate of AM60B, and the increased salt concentration had a significant effect on the deterioration process. The corrosion of AM60B mainly exhibits metal dissolution, and the formed Mg(OH)2 has weak a protective effect on the alloy substrate. Furthermore, the distributions of the corrosion potential and the corrosion current density of the AM60B/DC01 couple were simulated and intensively discussed.

Experimental and Theoretical Analysis of Rayleigh and Leaky-Sezawa Waves Propagating in ZnO/Fused Silica Substrates.

Piezoelectric c-axis oriented zinc oxide (ZnO) thin films, from 1.8 up to 6.6 µm thick, have been grown by the radio frequency magnetron sputtering technique onto fused silica substrates. A delay line consisting of two interdigital transducers (IDTs) with wavelength λ = 80 µm was photolithographically implemented onto the surface of the ZnO layers. Due to the IDTs' split-finger configuration and metallization ratio (0.5), the propagation of the fundamental, third, and ninth harmonic Rayleigh waves is excited; also, three leaky surface acoustic waves (SAWs) were detected travelling at a velocity close to that of the longitudinal bulk wave in SiO2. The acoustic waves' propagation in ZnO/fused silica was simulated by using the 2D finite-element method (FEM) technique to identify the nature of the experimentally detected waves. It turned out that, in addition to the fundamental and harmonic Rayleigh waves, high-frequency leaky surface waves are also excited by the harmonic wavelengths; such modes are identified as Sezawa waves under the cut-off, hereafter named leaky Sezawa (LS). The velocities of all the modes was found to be in good agreement with the theoretically calculated values. The existence of a low-loss region in the attenuation vs. layer thickness curve for the Sezawa wave below the cut-off was theoretically predicted and experimentally assessed.

Highly Sensitive Plasmon Refractive Index Sensor Based on MIM Waveguide.

This paper introduces a novel plasmon refractive index nanosensor structure based on Fano resonance. The structure comprises a metal-insulator-metal (MIM) waveguide with an inverted rectangular cavity and a circle minus a small internal circle plus a rectangular cavity (CMSICPRC). This study employs the finite element method (FEM) to analyze the sensing characteristics of the structure. The results demonstrate that the geometrical parameters of specific structures exert a considerable influence on the sensing characteristics. Simulated experimental data show that the maximum sensitivity of this structure is 3240 nm/RIU, with a figure of merit (FOM) of 52.25. Additionally, the sensor can be used in biology, for example, to detect the concentration of hemoglobin in blood. The sensitivity of the sensor in this application, according to our calculations, can be 0.82 nm∙g/L.

Design and Fabrication of High-Performance Piezoelectric Micromachined Ultrasonic Transducers Based on Aluminum Nitride Thin Films.

Ultrasound is widely applied in diverse domains, such as medical imaging, non-destructive evaluation, and acoustic communication. Piezoelectric micromachined ultrasonic transducers (PMUTs) capable of generating and receiving ultrasonic signals at the micrometer level have become a prominent technology in the field of ultrasound. It is important to enrich the models of the PMUTs to meet the varied applications. In this study, a series of PMUT devices featured with various top electrode configurations, square, circular, and doughnut, were designed to assess the influence of shape on the emission efficacy. It was demonstrated that the PMUTs with a circular top electrode were outperformed, which was calculated from the external acoustic pressure produced by the PMUTs operating in the fundamental resonant mode at a specified distance. Furthermore, the superior performance of PMUT arrays were exhibited through computational simulations for the circular top electrode geometries. Conventional microelectromechanical systems (MEMS) techniques were used to fabricate an array of PMUTs based on aluminum nitride (AlN) films. These findings make great contributions for enhancing the signal transmission sensitivity and bandwidth of PMUTs, which have significant potential in non-destructive testing and medical imaging applications.

Distribution and propagation of stress and strain in cube honeycombs as trabecular bone substitutes: Finite element model analysis.

For designing trabecular (Tb) bone substitutes suffering from osteoporosis, finite element model (FEM) simulations were conducted on honeycombs (HCs) of 8 × 8 × 1 (2D) and 8 × 8 × 8 (3D) assemblies of cube cellular units consisting of 0.9 mm long Nylon® 66 (PA, Young's modulus E: 2.83 GPa) and polyethylene (PE, E: 1.1 GPa) right square prisms. Osteoporotic damage to the Tb bone was simulated by removing the inner vertical struts (pillars; the number of removed pillars: Δn ≤ 300) and by thinning the strut (thickness, d: 0.4-0.1 mm), while the six facade lattices were kept flawless. Uniform and uniaxial compressive loads on the HCs induced elastic deformation of the struts. The pillars held almost all the load, while the horizontal struts (beams) shared little. E for PA 3D HCs of all d smoothly decreased with Δn. PA 3D HCs of 0.2 mm struts deserved to be the substitutes for Tb bone, while PE 3D HCs of 0.05 mm struts were only for the Tb bone of the poorest bone quality. For the PA 3D HCs, the maximum von Mises stress (σM) first rapidly increased with Δn and showed a break at Δñ50, then gradually approached the yield stress of PA (50 MPa). Moreover, small portions of the stress were transferred from the façade pillars to the adjacent inner beams, especially those near the lost-pillar sites, denoted as X defects. The floor beams of thinner struts associated with the X-defects were lifted, and similar lifting effects in smaller amounts were propagated to the other floors. The 3DHCs of the thicker struts showed no such flexural deformations. The concept of force percolation through the remaining struts was proposed to interpret those mechanical behaviors of the HCs.

Numerical simulation study on opening blood-brain barrier by ultrasonic cavitation.

Experimental studies have shown that ultrasonic cavitation can reversibly open the blood-brain barrier (BBB) to assist drug delivery. Nevertheless, the majority of the present study focused on experimental aspects of BBB opening. In this study, we developed a three-bubble-liquid-solid model to investigate the dynamic behavior of multiple bubbles within the blood vessels, and elucidate the physical mechanism of drug molecules through endothelial cells under ultrasonic cavitation excitation. The results showed that the large bubbles have a significant inhibitory effect on the movement of small bubbles, and the vibration morphology of intravascular microbubbles was affected by the acoustic parameters, microbubble size, and the distance between the microbubbles. The ultrasonic cavitation can significantly enhance the unidirectional flux of drug molecules, and the unidirectional flux growth rate of the wall can reach more than 5 %. Microjets and shock waves emitted from microbubbles generate different stress distribution patterns on the vascular wall, which in turn affects the pore size of the vessel wall and the permeability of drug molecules. The vibration morphology of microbubbles is related to the concentration, arrangement and scale of microbubbles, and the drug permeation impact can be enhanced by optimizing bubble size and acoustic parameters. The results offer an extensive depiction of the factors influencing the blood-brain barrier opening through ultrasonic cavitation, and the model may provide a potential technique to actively regulate the penetration capacity of drugs through endothelial layer of the neurovascular system by regulating BBB opening.

Mechanical modeling of the petiole-lamina transition zone of peltate leaves.

Plant leaves have to deal with various environmental influences. While the mechanical properties of petiole and lamina are generally well studied, only few studies focused on the properties of the transition zone joining petiole and lamina. Especially in peltate leaves, characterised by the attachment of the petiole to the abaxial side of the lamina, the 3D leaf architecture imposes specific mechanical stresses on the petiole and petiole-lamina transition zone. Several principles of internal anatomical organisation have been identified. Since the mechanical characterisation of the transition zone by direct measurements is difficult, we explored the mechanical properties and load-bearing mechanisms by finite-element simulations. We simulate the petiole-lamina transition zone with five different fibre models that were abstracted from CT data. For comparison, three different load cases were defined and tested in the simulation. In the proposed model, the fibres are represented in a smeared sense, where we considered transverse isotropic behavior in elements containing fibres. In a pre-processing step, we determined the fibre content, direction, and dispersion and fed them into our model. The simulations show that initially, matrix and fibres carry the load together. After relaxation of the stresses in the matrix, the fibres carry most of the load. Load dissipation and stiffness differ according to fibre arrangement and depend, among other things, on orientation and cross-linking of the fibres and fibre amount. Even though the presented method is a simplified approach, it is able to show the different load-bearing capacities of the presented fibre arrangements. STATEMENT OF SIGNIFICANCE: In plant leaves, the petiole-lamina transition zone is an important structural element facilitating water and nutrient transport, as well as load dissipation from the lamina into the petiole. Especially in peltate leaves, the 3D leaf architecture imposes specific mechanical stresses on the petiole-lamina transition zone. This study aims at investigating its mechanical behavior using finite-element simulations. The proposed continuum mechanical anisotropic viscoelastic material model is able to simulate the transition zone under different loads while also considering different fibre arrangements. The simulations highlight the load-bearing mechanisms of different fibre organisations, show the mechanical significance of the petiole-lamina transition zone and can be used in the design of a future biomimetic junction in construction.

Towards Design Optimization of Compliant Mechanisms: A Hybrid Pseudo-Rigid-Body Model-Finite Element Method Approach and an Accurate Empirical Compliance Equation for Circular Flexure Hinges.

Innovative designs such as morphing wings and terrain adaptive landing systems are examples of biomimicry and innovations inspired by nature, which are actively being investigated by aerospace designers. Morphing wing designs based on Variable Geometry Truss Manipulators (VGTMs) and articulated helicopter robotic landing gear (RLG) have drawn a great deal of attention from industry. Compliant mechanisms have become increasingly popular due to their advantages over conventional rigid-body systems, and the research team led by the second author at Toronto Metropolitan University (TMU) has set their long-term goal to be exploiting these systems in the above aerospace applications. To gain a deeper insight into the design and optimization of compliant mechanisms and their potential application as alternatives to VGTM and RLG systems, this study conducted a thorough analysis of the design of flexible hinges, and single-, four-, and multi-bar configurations as a part of more complex, flexible mechanisms. The investigation highlighted the flexibility and compliance of mechanisms incorporating circular flexure hinges (CFHs), showcasing their capacity to withstand forces and moments. Despite a discrepancy between the results obtained from previously published Pseudo-Rigid-Body Model (PRBM) equations and FEM-based analyses, the mechanisms exhibited predictable linear behavior and acceptable fatigue testing results, affirming their suitability for diverse applications. While including additional linkages perpendicular to the applied force direction in a compliant mechanism with N vertical linkages led to improved factors of safety, the associated increase in system weight necessitates careful consideration. It is shown herein that, in this case, adding one vertical bar increased the safety factor by 100N percent. The present study also addressed solutions for the precise modeling of CFHs through the derivation of an empirical polynomial torsional stiffness/compliance equation related to geometric dimensions and material properties. The effectiveness of the presented empirical polynomial compliance equation was validated against FEA results, revealing a generally accurate prediction with an average error of 1.74%. It is expected that the present investigation will open new avenues to higher precision in the design of CFHs, ensuring reliability and efficiency in various practical applications, and enhancing the optimization design of compliant mechanisms comprised of such hinges. A specific focus was put on ABS plastic and aluminum alloy 7075, as they are the materials of choice for non-load-bearing and load-bearing structural components, respectively.

Hominini-specific regulation of the cell cycle by stop codon readthrough of FEM1B.

FEM1B is a substrate-recognition component of the CRL2 E3 ubiquitin-protein ligase. This multi-protein complex targets specific proteins for ubiquitylation, which leads to their degradation. Here, we demonstrate the regulation of FEM1B expression by stop codon readthrough (SCR). In this process, translating ribosomes readthrough the stop codon of FEM1B to generate a C-terminally extended isoform that is highly unstable. A total of 81 nucleotides in the proximal 3'UTR of FEM1B constitute the necessary and sufficient cis-signal for SCR. Also, they encode the amino acid sequence responsible for the degradation of the SCR product. CRISPR-edited cells lacking this region, and therefore SCR of FEM1B, showed increased FEM1B expression. This in turn resulted in reduced expression of SLBP (a target of FEM1B-mediated degradation) and replication-dependent histones (target of SLBP for mRNA stability), causing cell cycle delay. Evolutionary analysis revealed that this phenomenon is specific to the genus Pan and Homo (Hominini). Overall, we show a relatively recently evolved SCR process that relieves the cell cycle from the negative regulation by FEM1B.

Monitoring Surface Deformations in a Fossil Landslide Zone and Identifying Potential Failure Mechanisms: A Case Study of Gümüshane State Hospital.

The escalating occurrence of landslides has drawn increasing attention from the scientific community, primarily driven by a combination of natural phenomena such as unpredictable seismic events, intensified precipitation, and rapid snowmelt attributable to climate fluctuations, compounded by inadequacies in engineering practices during site selection. Within the scope of this investigation, contemporary geodetic techniques using the GNSS were employed to monitor structural and surface deformations in and around a hospital edifice situated within an ancient fossil landslide region. Additionally, inclinometer measurements facilitated the determination of slip circle parameters. A subsequent analysis integrated these datasets to scrutinize both the hospital structure and its surrounding slopes. In addition to the finite element method, four different limit equilibrium methods (Bishop, GLE-Morgenstern-Price, Spencer, and Janbu) were used in the evaluation of stability. Since the safety number determined in all analyses was <1, it was determined that the slope containing the hospital building was unstable. The movement has occurred again due to the additional load created by the hospital building built on the currently stable slope, the effect of surface and groundwater, and the improperly designed road route. As a result of geodetic monitoring, it was determined that the sliding speed on the surface was in the N-E direction and was approximately 3 cm, and this situation almost coincided with inclinometer measurements.

Iron Loss and Temperature Rise Analysis of a Transformer Core Considering Vector Magnetic Hysteresis Characteristics under Direct Current Bias.

Direct current (DC) bias induced by the DC transmission and geomagnetically induced current is a critical factor in the abnormal operation of electrical equipment and is widely used in the field of power transmission and distribution system state evaluation. As the main affected component, the vector magnetization state of a transformer core under DC bias has rarely been studied, resulting in inaccurate transformer operation state estimations. In this paper, a dynamic vector hysteresis model that considers the impact of rotating and DC-biased fields is introduced into the numerical analysis to simulate the distribution of magnetic properties, iron loss and temperature of the transformer core model and a physical 110 kV single-phase autotransformer core. The maximum values of B, H and iron loss exist at the corners and T-joint of the core under rotating and DC-biased fields. The corresponding maximum value of the temperature increase is found in the main core limb area. The temperature rise of the 110 kV transformer core under various DC-biased conditions is measured and compared with the FEM (Finite Element Method) results of the proposed model and the model solely based on the magnetization curve B||H. The calculation error of the temperature rise obtained by the improved model is approximately 3.76-15.73% and is much less than the model solely based on magnetization curve B||H (approximately 50.71-66.92%).

Melting and heat management of phase change material using smart ternary-hybrid coolant.

This research investigates the effectiveness of using a smart ternary-hybrid nanofluid to enhance the melting rate and convective behavior of electrically conducting tin (Sn) in a rectangular enclosure under the influence of a uniform magnetic field. The enclosure has adiabatic vertical walls with hot and cold temperatures on the bottom and top walls. The finite element method (FEM) is used to solve the governing equations with appropriate boundary conditions using Galerkin's weighted residual approach. The study focuses on applying tin as the phase change material (PCM), with the highest temperature of 508 K, the lowest temperature of 503 K, and the melting interface temperature of 505 K. To enhance the heat transfer performance, tin-based ternary (graphene (G), silicon carbide (SiC), and nickel (Ni)) hybrid smart coolant is applied into the system. To investigate the mechanism of the melting and convective thermal transfer process, the results of the present study are reported with time for various values of the magnetic field (Ha) and solid concentration of ternary hybrid nanoparticle ( ϕ ). This study represents the streamlines, isothermal lines, melting interface, melting fraction, and heat transfer for the above-mentioned parameters. The results show that increasing the magnetic field reduces the rate of thermal transport by 38.96 % at t = 4000s. However, at a particular time of 2500s, increasing the solid volume fraction of nanoparticles enhances the melting fraction by approximately 8.34 %. Two regression equations are derived for the Nusselt number and melting fraction, with multiple response variables. This article improves understanding of natural convective heat transport during phase change processes for various coolants in different engineering applications.

Enhanced compression performance of an improved rectangular helical spring incorporated support feature.

The spring system functions as a pivotal element of the check valve, with its compression performance significantly influencing the valve's time, flow stability, and other characteristics. Taking cues from conventional springs, a refined rectangular helical spring with integrated support features was thoroughly evaluated for its compression performance. The design approach for this spring was elucidated, encompassing the utilization of the Finite Element Method (FEM) to model its compression behavior. Additionally, a laboratory configuration was implemented to authenticate the findings derived from the FEM simulation. Subsequently, a comparative investigation was carried out between an engineered spring and a conventional spring subjected to analogous processing. The comparative analysis unveiled that the support-featured spring exhibited a diminished lateral offset of 2.84 mm (equivalent to a reduction of 10.1 %) and a force-displacement curve with narrower vibration intervals and smaller amplitudes. Moreover, it exhibited an enhanced force feedback of 17.5 % under identical compression displacement conditions.