Distributed feather-inspired flow control mitigates stall and expands flight envelope.

Multiple rows of feathers, known as the covert feathers, contour the upper and lower surfaces of bird wings. These feathers have been observed to deploy passively during high angle of attack maneuvers and are suggested to play an aerodynamic role. However, there have been limited attempts to capture their underlying flow physics or assess the function of multiple covert rows. Here, we first identify two flow control mechanisms associated with a single covert-inspired flap and their location sensitivity: a pressure dam mechanism and a previously unidentified shear layer interaction mechanism. We then investigate the additivity of these mechanisms by deploying multiple rows of flaps. We find that aerodynamic benefits conferred by the shear layer interaction are additive, whereas benefits conferred by the pressure dam effect are not. Nevertheless, both mechanisms can be exploited simultaneously to maximize aerodynamic benefits and mitigate stall. In addition to wind tunnel experiments, we implement multiple rows of covert-inspired flaps on a bird-scale remote-controlled aircraft. Flight tests reveal passive deployment trends similar to those observed in bird flight and comparable aerodynamic benefits to wind tunnel experiments. These results indicate that we can enhance aircraft controllability using covert-inspired flaps and form insights into the aerodynamic role of covert feathers in avian flight.

Aerodynamic efficiency explains flapping strategies used by birds.

A faster cruising speed increases drag and thereby the thrust (T) needed to fly, while weight and lift (L) requirement remains constant. Birds can adjust their wingbeat in multiple ways to accommodate this change in aerodynamic force, but the relative costs of different strategies remain largely unknown. To evaluate the efficiency of several kinematic strategies, I used a robotic wing [E. Ajanic, A. Paolini, C. Coster, D. Floreano, C. Johansson, Adv. Intell. Syst. 5, 2200148 (2023)] and quantitative flow measurements. I found that, among the tested strategies, changing the mean wingbeat elevation provides the most efficient solution to changing thrust-to-lift ratio (T/L), offering insight into why birds tend to beat their wings with a greater ventral than dorsal excursion. I also found that although propulsive efficiency (ηp) may peak at a Strouhal number (St, measure of relative flapping speed) near 0.3, the overall efficiency of generating force decreases with St. This challenges the expectance of a specific optimal St for flapping flight and instead suggest the chosen St depends on T/L. This may explain variation in preferred St among birds and why bats prefer flying at higher St than birds [G. K. Taylor, R. L. Nudds, A. L. Thomas, Nature 425, 707-711 (2003)], since their body shape imposes relatively higher thrust requirements [F. T. Muijres, L. C. Johansson, M. S. Bowlin, Y. Winter, A. Hedenström, PLoS One 7, e37335 (2012)]. In addition to explaining flapping strategies used by birds, my results suggest alternative, efficient, flapping motions for drones to explore aiming to extend their flight range.

Flock2: A model for orientation-based social flocking.

The aerial flocking of birds, or murmurations, has fascinated observers while presenting many challenges to behavioral study and simulation. We examine how the periphery of murmurations remain well bounded and cohesive. We also investigate agitation waves, which occur when a flock is disturbed, developing a plausible model for how they might emerge spontaneously. To understand these behaviors a new model is presented for orientation-based social flocking. Previous methods model inter-bird dynamics by considering the neighborhood around each bird, and introducing forces for avoidance, alignment, and cohesion as three dimensional vectors that alter acceleration. Our method introduces orientation-based social flocking that treats social influences from neighbors more realistically as a desire to turn, indirectly controlling the heading in an aerodynamic model. While our model can be applied to any flocking social bird we simulate flocks of starlings, Sturnus vulgaris, and demonstrate the possibility of orientation waves in the absence of predators. Our model exhibits spherical and ovoidal flock shapes matching observation. Comparisons of our model to Reynolds' on energy consumption and frequency analysis demonstrates more realistic motions, significantly less energy use in turning, and a plausible mechanism for emergent orientation waves.

Aerodynamic integration produces a vehicle shape with a negative drag coefficient.

Negative drag coefficients are normally associated with a vessel outfitted with a sail to extract energy from the wind and propel the vehicle forward. Therefore, the notion of a heavy vehicle, that is, a semi truck, that generates negative aerodynamic drag without a sail or any external appendages may seem implausible, especially given the fact that these vehicles have some of the largest drag coefficients on the road today. However, using both wind tunnel measurements and computational fluid dynamics simulations, we demonstrate aerodynamically integrated vehicle shapes that generate negative body-axis drag in a crosswind as a result of large negative frontal pressures that effectively "pull" the vehicle forward against the wind, much like a sailboat. While negative body-axis drag exists only for wind yaw angles above a certain analytical threshold, the negative frontal pressures exist at smaller yaw angles and subsequently produce body-axis drag coefficients that are significantly less than those of modern heavy vehicles. The application of this aerodynamic phenomenon to the heavy vehicle industry would produce sizable reductions in petroleum use throughout the United States.

Pterosaurs evolved a muscular wing-body junction providing multifaceted flight performance benefits: Advanced aerodynamic smoothing, sophisticated wing root control, and wing force generation.

Pterosaurs were the first vertebrate flyers and lived for over 160 million years. However, aspects of their flight anatomy and flight performance remain unclear. Using laser-stimulated fluorescence, we observed direct soft tissue evidence of a wing root fairing in a pterosaur, a feature that smooths out the wing-body junction, reducing associated drag, as in modern aircraft and flying animals. Unlike bats and birds, the pterosaur wing root fairing was unique in being primarily made of muscle rather than fur or feathers. As a muscular feature, pterosaurs appear to have used their fairing to access further flight performance benefits through sophisticated control of their wing root and contributions to wing elevation and/or anterior wing motion during the flight stroke. This study underscores the value of using new instrumentation to fill knowledge gaps in pterosaur flight anatomy and evolution.

Perceptual, aerodynamic and acoustic outcomes of surgical technique for sulcus vocalis patients: A systematic review and meta analysis.

BACKGROUND: Sulcus Vocalis (SV) is a voice disorder characterized by the parallel invagination of the vocal fold epithelium that adheres to the vocal ligament. This condition disrupts the vibratory function, leading to glottal incompetence, hoarseness, and vocal impairment. Despite various proposed surgical techniques, a standardized treatment approach remains elusive. METHODS: We conducted a comprehensive search across PubMed/Medline, Embase, Web of Science, Scholar, and the Cochrane Library for studies on SV treatment. The inclusion criteria comprised original studies comparing pre- and post-treatment vocal outcomes in SV patients, published in English. We excluded case reports, reviews, studies without continuous data, and patients with vocal scar/atrophy. RESULTS: Fifteen observational studies were included (361 patients, 53.73 % male, average age 41.64 years). 80 % of these studies employed self-reported outcomes, while 81.25 % analyzed acoustic/aerodynamic data. The follow-up period varied from 4 to 44 months. All techniques significantly improved Voice Handicap Index (VHI) scores (p < 0.001). Dissective and combined techniques exhibited greater reductions in VHI-30/10 (p < 0.001). Maximum Phonation Time (MPT) improved significantly across all techniques (p < 0.001), with dissective techniques demonstrating superior MPT outcomes (p < 0.001). Jitter improved significantly for dissective and injective techniques (p < 0.001), as did Shimmer for all techniques (p < 0.001). Notably, combined techniques displayed the most significant reductions (p < 0.001). CONCLUSIONS: Surgical treatments significantly improve subjective, aerodynamic, and acoustic outcomes in SV patients. Dissective and combined dissective/injective techniques appear to yield better perceptual and phonatory outcomes compared to injective techniques alone. Further research is necessary to establish the optimal treatment approach for SV.

Prediction of Drivers' Subjective Evaluation of Vehicle Reaction Under Aerodynamic Excitations.

OBJECTIVE: The objectives are to determine which quantities are important to measure to determine how drivers perceive vehicle stability, and to develop a regression model to predict which induced external disturbances drivers are able to feel. BACKGROUND: Driver experience of a vehicle's dynamic performance is important to auto manufacturers. Test engineers and test drivers perform several on-road assessments to evaluate the vehicle's dynamic performance before sign-off for production. The presence of external disturbances such as aerodynamic forces and moments play a significant role in the overall vehicle assessment. As a result, it is important to understand the relation between the subjective experience of the drivers and these external disturbances acting on the vehicle. METHOD: A sequence of external yaw and roll moment disturbances of varying amplitudes and frequencies is added to a straight-line high-speed stability simulation test in a driving simulator. The tests are performed with both common and professional test drivers, and their evaluations to these external disturbances are recorded. The sampled data from these tests are used to generate the needed regression model. RESULTS: A model is derived for predicting which disturbances drivers can feel. It quantifies difference in sensitivity between driver types and between yaw and roll disturbances. CONCLUSION: The model shows a relationship between steering input and driver sensitivity to external disturbances in a straight-line drive. Drivers are more sensitive to yaw disturbance than roll disturbance and increased steering input lowers sensitivity. APPLICATION: Identify the threshold above which unexpected disturbances such as aerodynamic excitations can potentially create unstable vehicle behaviour.

Altered wing phenotypes of captive-bred migratory birds lower post-release fitness.

Captive breeding and release to the wild is a globally important conservation tool. However, captivity can result in phenotypic changes that incur post-release fitness costs, especially if they affect strenuous or risky behaviours. Bird wing shape is critical for migration success and suboptimal phenotypes are strongly selected against. In this study, I demonstrate surprising plasticity of bird wing phenotypes in captivity for 4/16 studied species. In a model species, captive-born juveniles with wild wing phenotypes (a 1-mm longer distal primary flight feather) survived post-release at 2.7 times the rate of those with captive phenotypes (i.e. a shorter distal feather). Subtle phenotypic changes and their fitness impacts are more common than widely realised because they are easily overlooked. To improve captive breeding for conservation, practitioners must surveil phenotypic changes and find ways to mitigate them.

Flow development and leading edge vorticity in bristled insect wings.

Small flying insects such as the tiny thrip Gynaikothrips ficorum have wings with bristles attached to a solid shaft instead of solid membranes. Air passing through the bristle fringe, however, makes bristled insect wings less effective for aerodynamic force production. In this study, we quantified the ability of bristled wings to generate a leading edge vortex (LEV) for lift support during wing flapping, scored its circulation during wing translation, and investigated its behaviour at the stroke reversals. The data were measured in robotic model wings flapping with a generic kinematic pattern at Reynolds number of ~ 3.4, while applying two-dimensional particle image velocimetry. We found that aerodynamic performance due to LEV circulation linearly decreases with increasing bristle spacing. The wings of Gynaikothrips ficorum might thus produce approximately 9% less aerodynamic force for flight than a solid membranous wing. At the stroke reversals, leading and trailing edge vortices dissipate quickly within no more than ~ 2% of the stroke cycle duration. This elevated dissipation makes vortex shedding obsolete during the reversals and allows a quick build-up of counter-vorticity when the wing reverses flapping direction. In sum, our findings highlight the flow conditions associated with bristled wing design in insects and are thus significant for assessing biological fitness and dispersal of insects flying in a viscosity-dominated fluid regime.

Lessons from natural flight for aviation: then, now and tomorrow.

Powered flight was once a capability limited only to animals, but by identifying useful attributes of animal flight and building on these with technological advances, engineers have pushed the frontiers of flight beyond our predecessors' wildest imaginations. Yet, there remain many key characteristics of biological flight that elude current aircraft design, motivating a careful re-analysis of what we have learned from animals already, and how this has been revealed experimentally, as well as a specific focus on identifying what remains unknown. Here, we review the literature to identify key contributions that began in biology and have since been translated into aeronautical devices or capabilities. We identify central areas for future research and highlight the importance of maintaining an open line of two-way communication between biologists and engineers. Such interdisciplinary, bio-informed analyses continue to push forward the frontiers of aeronautics and experimental biology alike.

Effects of wing damage and moult gaps on vertebrate flight performance.

Vertebrates capable of powered flight rely on wings, muscles that drive their flapping and sensory inputs to the brain allowing for control of the motor output. In birds, the wings are formed of arrangements of adjacent flight feathers (remiges), whereas the wings of bats consist of double-layered skin membrane stretched out between the forelimb skeleton, body and legs. Bird feathers become worn from use and brittle from UV exposure, which leads to loss of function; to compensate, they are renewed (moulted) at regular intervals. Bird feathers and the wings of bats can be damaged by accident. Wing damage and loss of wing surface due to moult almost invariably cause reduced flight performance in measures such as take-off angle and speed. During moult in birds, this is partially counteracted by concurrent mass loss and enlarged flight muscles. Bats have sensory hairs covering their wing surface that provide feedback information about flow; thus, wing damage affects flight speed and turning ability. Bats also have thin, thread-like muscles, distributed within the wing membrane and, if these are damaged, the control of wing camber is lost. Here, I review the effects of wing damage and moult on flight performance in birds, and the consequences of wing damage in bats. I also discuss studies of life-history trade-offs that make use of experimental trimming of flight feathers as a way to handicap parent birds feeding their young.

Models for Predicting Velopharyngeal Competence Based on Speech and Resonance Errors and Velopharyngeal Area Estimation.

OBJECTIVE: To develop tools for predicting velopharyngeal competence (VPC) based on auditory-perceptual assessment and its correlation with objective measures of velopharyngeal orifice area. DESIGN: Methodological study. PARTICIPANTS AND METHODS: Sixty-two patients with repaired cleft palate, aged 6 to 45 years, underwent aerodynamic evaluation by means of the pressure-flow technique and audiovisual recording of speech samples. Three experienced speech-language pathologists analysed the speech samples by rating the following resonance, visual, and speech variables: hypernasality, audible nasal air emission, nasal turbulence, weak pressure consonants, facial grimacing, active nonoral errors, and overall velopharyngeal competence. The correlation between the perceptual speech variables and velopharyngeal orifice area estimates was analysed with Spearman's correlation coefficient. Two statistical models (discriminant and exploratory) were used to predict VPC based on the orifice area estimates. Sensitivity and specificity analyses were performed to verify the clinical applicability of the models. RESULTS: There was a strong correlation between VPC (based on the orifice area estimates) and each speech variable. Both models showed 88.7% accuracy in predicting VPC. The sensitivity and specificity for the discriminant model were 92.3% and 97.2%, respectively, and 96.2% and 94.4% for the exploratory model. CONCLUSION: Two predictor models based on ratings of resonance, visual, and speech variables and a simple calculation of a composite variable, SOMA (Eng. "sum"), were developed and found to be efficient in predicting VPC defined by orifice estimates categories based on aerodynamic measurements. Both tools may contribute to the diagnosis of velopharyngeal dysfunction in clinical practice.

Wavelet-Based Identification for Spinning Projectile with Gasodynamic Control Aerodynamic Coefficients Determination.

Identification of a spinning projectile controlled with gasodynamic engines is shown in this paper. A missile model with a measurement inertial unit was developed from Newton's law of motion and its aerodynamic coefficients were identified. This was achieved by applying the maximum likelihood principle in the wavelet domain. To assess the results, this was also performed in the time domain. The outcomes were obtained for two cases: when noise was not present and when it was included in the data. In all cases, the identification was performed in the passive mode, i.e., no special system identification experiments were designed. In the noise-free case, aerodynamic coefficients were estimated with high accuracy. When noise was included in the data, the wavelet-based estimates had a drop in their accuracy, but were still very accurate, whereas for the time domain approach the estimates were considered inaccurate.

Performance Improvement of a Vehicle Equipped with Active Aerodynamic Surfaces Using Anti-Jerk Preview Control Strategy.

This paper presents a formulation of a preview optimal control strategy for a half-car model equipped with active aerodynamic surfaces. The designed control strategy consists of two parts: a feed-forward controller to deal with the future road disturbances and a feedback controller to deal with tracking error. An anti-jerk functionality is employed in the design of preview control strategy that can reliably reduce the jerk of control inputs to improve the performance of active aerodynamic surfaces and reduce vehicle body jerk to enhance the ride comfort without degrading road holding capability. The proposed control scheme determines proactive control action against oncoming potential road disturbances to mitigate the effect of deterministically known road disturbances. The performance of proposed anti-jerk optimal control strategy is compared with that of optimal control without considering jerk. Simulation results considering frequency and time domain characteristics are carried out using MATLAB to demonstrate the effectiveness of the proposed scheme. The frequency domain characteristics are discussed only for the roll inputs, while time domain characteristics are discussed for the corresponding ground velocity inputs of bump and asphalt road, respectively. The results show that using anti-jerk optimal preview control strategy improves the performance of vehicle dynamics by reducing jerk of aerodynamic surfaces and vehicle body jerk simultaneously.

Covering Nasometer Microphones with Plastic Wrap for Infection Control Increases Retest Variability of Nasalance Scores.

The Nasometer is a popular instrument for the acoustic assessment of nasality. In light of the currently ongoing COVID-19 global pandemic, clinicians may have wondered about the infection control procedures for the Nasometer. The current research investigated whether nasalance scores are affected if the Nasometer 6450 microphone casings are covered with a material such as rolled polyvinyl chloride household wrap. For the experiment, pre-recorded sound files from two speakers were played back through a set of small loudspeakers. Nasalance scores from two baselines and three wrap cover conditions were compared. While there was no statistically significant condition effect in a repeated-measures analysis of variance, the within-condition cumulative differences in nasalance scores were 2 for the initial baseline, 42 for wrap cover 1, 24 for wrap cover 2, 78 for wrap cover 3, and 8 for the final baseline. Mean differences between the wrap cover and the baseline conditions were 8.2 to 15.3 times larger, and cumulative differences were 8.3 to 16.6 times larger than between the two baselines. Based on the higher cumulative and mean differences observed, clinicians should not cover Nasometer microphones with household wrap as this increases variability of nasalance scores. Since there is evidence that the COVID-19 virus can survive for some time on metal surfaces, clinicians should be mindful of the fact that the Nasometer microphone housings can only be cleaned superficially and should be handled with gloves to minimize any possible risk of touch transfer of pathogens to the next speaker or the clinician.

Optimisation and Efficiency Improvement of Electric Vehicles Using Computational Fluid Dynamics Modelling.

Due to the rise in awareness of global warming, many attempts to increase efficiency in the automotive industry are becoming prevalent. Design optimization can be used to increase the efficiency of electric vehicles by reducing aerodynamic drag and lift. The main focus of this paper is to analyse and optimise the aerodynamic characteristics of an electric vehicle to improve efficiency of using computational fluid dynamics modelling. Multiple part modifications were used to improve the drag and lift of the electric hatchback, testing various designs and dimensions. The numerical model of the study was validated using previous experimental results obtained from the literature. Simulation results are analysed in detail, including velocity magnitude, drag coefficient, drag force and lift coefficient. The modifications achieved in this research succeeded in reducing drag and were validated through some appropriate sources. The final model has been assembled with all modifications and is represented in this research. The results show that the base model attained an aerodynamic drag coefficient of 0.464, while the final design achieved a reasonably better overall performance by recording a 10% reduction in the drag coefficient. Moreover, within individual comparison with the final model, the second model with front spitter had an insignificant improvement, limited to 1.17%, compared with 11.18% when the rear diffuser was involved separately. In addition, the lift coefficient was significantly reduced to 73%, providing better stabilities and accounting for the safety measurements, especially at high velocity. The prediction of the airflow improvement was visualised, including the pathline contours consistent with the solutions. These research results provide a considerable transformation in the transportation field and help reduce fuel expenses and global emissions.

IMPACT OF THE NASAL VALVE SHAPE ON THE OLFACTORY FUNCTION AND SUBJECTIVE PERCEPTION OF THE NASAL BREATHING.

OBJECTIVE: The aim: To study the impact of the internal nasal valve shape on respiratory and olfactory nose function as well as on quality of life. PATIENTS AND METHODS: Materials and methods: The study involved 17 volunteers who noted satisfaction of nasal breathing in the absence of changes during endorhinoscopy. The study was con¬ducted in two stages: stage 1 involved assessing initial indicators of quality of life by the SNOT-22 questionnaire, performing active anterior rhinomanometry, and estimating the olfactory function (Sniffin' Sticks); stage 2 consisted in re-assessing the mentioned indicators after changing the shape and lumen of the internal nasal valve. The sodium alginate self-hardening gel was used for simulating the narrowing of the nasal valve. It was applied to the mucous in the upper part of the nasal valve area, obturating the diffuser above the level of attachment of the middle nasal turbinate to a depth of 3-4 mm from nasal vestibule. RESULTS: Results: Air resistance did not change significantly after partial blockage of the internal nasal valve, although, 16 out of 17 patients showed signs of hyposmia with an average Sniffin' Sticks test score 8.68 ± 0.15. CONCLUSION: Conclusions: The simulated partial blockage of the internal nasal valve lumen in its upper part in the area of the diffuser does not significantly affect the resistance of the air passing through the nasal passages, but the olfactory function is impaired, which is reflected the quality of life.

Hovering flight in hummingbird hawkmoths: kinematics, wake dynamics and aerodynamic power.

Hovering insects are divided into two categories: 'normal' hoverers that move the wing symmetrically in a horizontal stroke plane, and those with an inclined stroke plane. Normal hoverers have been suggested to support their weight during both downstroke and upstroke, shedding vortex rings each half-stroke. Insects with an inclined stroke plane should, according to theory, produce flight forces only during downstroke, and only generate one set of vortices. The type of hovering is thus linked to the power required to hover. Previous efforts to characterize the wake of hovering insects have used low-resolution experimental techniques or simulated the flow using computational fluid dynamics, and so it remains to be determined whether insect wakes can be represented by any of the suggested models. Here, we used tomographic particle image velocimetry, with a horizontal measurement volume placed below the animals, to show that the wake shed by hovering hawkmoths is best described as a series of bilateral, stacked vortex 'rings'. While the upstroke is aerodynamically active, despite an inclined stroke plane, it produces weaker vortices than the downstroke. In addition, compared with the near wake, the far wake lacks structure and is less concentrated. Both near and far wakes are clearly affected by vortex interactions, suggesting caution is required when interpreting wake topologies. We also estimated induced power (Pind) from downwash velocities in the wake. Standard models predicted a Pind more than double that from our wake measurements. Our results thus question some model assumptions and we propose a reevaluation of the model parameters.

An Introduction to Biomedical Computational Fluid Dynamics.

Computational fluid dynamics (CFD) is a tool that has been used by engineers for over 50 years to analyse heat transfer and fluid flow phenomena. In recent years, there have been rapid developments in biomedical and health research applications of CFD. It has been used to evaluate drug delivery systems, analyse physiological flows (e.g. laryngeal jet flow), facilitate surgical planning (e.g. management of intracranial aneurysms), and develop medical devices (e.g. vascular stents and valve prostheses). Due to the complexity of these fluid flows, it demands an interdisciplinary approach consisting of engineers, computer scientists, and mathematicians to develop the computer programs and software used to solve the mathematical equations. Advances in technology and decreases in computational cost are allowing CFD to be more widely accessible and therefore used in more varied contexts. Cardiovascular medicine is the most common area of biomedical research in which CFD is currently being used, followed closely by upper and lower respiratory tract medicine. CFD is also being used in research investigating cerebrospinal fluid, synovial joints, and intracellular fluid. Although CFD can provide meaningful and aesthetically pleasing outputs, interpretation of the data can be challenging for those without a strong understanding of mathematical and engineering principles. Future development and evolution of computational medicine will therefore require close collaboration between experts in engineering, computer science, and biomedical research. This chapter aims to introduce computational fluid dynamics and present the reader with the basics of biological fluid properties, the CFD method, and its applications within biomedical research through published examples, in hope of bridging knowledge gaps in this rapidly emerging method of biomedical analysis.

Data-driven CFD Scaling of Bioinspired Mars Flight Vehicles for Hover.

One way to improve our model of Mars is through aerial sampling and surveillance, which could provide information to augment the observations made by ground-based exploration and satellite imagery. Flight in the challenging ultra-low-density Martian environment can be achieved with properly scaled bioinspired flapping wing vehicle configurations that utilize the same high lift producing mechanisms that are employed by insects on Earth. Through dynamic scaling of wings and kinematics, we investigate the ability to generate solutions for a broad range of flapping wing flight vehicles masses ranging from insects O(10-3) kg to the Mars helicopter Ingenuity O(100) kg. A scaling method based on a neural-network trained on 3D Navier-Stokes solutions is proposed to determine approximate wing size and kinematic values that generate bioinspired hover solutions. We demonstrate that a family of solutions exists for designs that range from 1 to 1000 grams, which are verified and examined using a 3D Navier-Stokes solver. Our results reveal that unsteady lift enhancement mechanisms, such as delayed stall and rotational lift, are present in the bioinspired solutions for the scaled vehicles hovering in Martian conditions. These hovering vehicles exhibit payloads of up to 1 kg and flight times on the order of 100 minutes when considering the respective limiting cases of the vehicle mass being comprised entirely of payload or entirely of a battery and neglecting any transmission inefficiencies. This method can help to develop a range of Martian flying vehicle designs with mission viable payloads, range, and endurance.