Simple Force Research Articles

Blind prediction and post-experimental analysis of RC core wall’s cyclic flexural response using MVLEM-FD

AbstractBlind prediction and post-experimental studies of the flexural cyclic response of a U-shaped core wall, tested at UCLouvain, Belgium, are presented. The tested specimen (referred to as UW1) was modelled using a relatively simple 3D force–displacement-based version of the beam–column multiple-vertical-line-element (MVLEM-FD), developed at the University of Ljubljana (UL), using standard element parameters. The blind prediction accurately identified critical failure points within the specimen. However, the predicted type of failure, attributed to the rupture of longitudinal bars in the boundary region of flanges was somewhat different from that observed in the experiment. These bars were indeed ruptured, but their rupture was preceded by their buckling and the spalling of the surrounding concrete core. Moreover, the predicted force–displacement hysteretic loop exhibited a slight shift compared to experimental observations. Post-experimental studies revealed that this discrepancy was primarily due to the modelling of the loading at the top of the wall rather than the modelling of the wall itself. Specifically, an additional bending moment induced by the eccentricity of the vertical load applied using three actuators, which was overlooked in the blind prediction. Upon correcting the loading, the agreement between the numerical studies and experiment was considerably improved in terms of both the global and local response quantities. Additionally, minor improvements in modelling the boundary regions of the wall’s flanges, considering the relatively large unconfined concrete cover, were introduced, leading to enhanced estimations of near-collapse response.

Numerical simulation of open channel basaltic lava flow through topographical bends

In this study, we utilised computational fluid dynamics to investigate the behaviour of open-channel basaltic lava flows navigating bends on shield volcanoes. Our focus was on understanding the relationship between flow velocity, rheology, and bend geometry. Employing a simple Force Balance Model (FBM), which considers the equilibrium between hydrostatic pressure and centrifugal force, we accurately approximated the changes in the height of the lava’s free surface through various bend geometries. Our analysis includes examining the influence of channel depth, width, and bend radius on the flow, revealing that variations in these parameters significantly affect the flow’s vertical displacement. Additionally, the bend sector angle emerged as a critical factor, indicating a minimum angle necessary for the flow to fully develop before exiting the bend.Further, we assessed the applicability of the Shallow Water Equations (SWE) for modelling the inertial displacement of the lava flow in bends, finding a good fit. The study extended to comparing the FBM’s predictions of the tilt angle of the flow’s free surface with the SWE results, showing notable agreement under specific conditions, particularly at a bend angle of 90 degrees. The impact of fluid density was also considered, revealing that density is a contributing factor to the development of the wetted line in the bend, a factor that is not captured by the simple FBM model. Finally, we explored different rheologies akin to natural lava flows, such as viscoplastic flow, and determined that factors like yield stress, consistency index, and power law index have a small impact on the flow behaviour in a steady-state condition within a bend.

An accurate and locking-free geometric exact beam formulation on the special orthogonal group SO(3)

An accurate and locking-free geometric exact beam formulation (GEBF) on the special orthogonal group SO(3) is developed for slender beams with large deformations and large rotations. Due to the nonlinear nature of the spatial rotations, the classical GEBFs usually have a non-constant mass matrix and complex expressions of inertia forces; meanwhile, the singularity and locking issues are also key matters of concern. Aiming at resolving these drawbacks, two main contributions are achieved in the present work. First, the angular velocity is independently interpolated, resulting in a constant mass matrix and explicitly representable inertial forces, which can offer significant advantages for efficient dynamic simulations. Second, inspired by the assumed natural strain method in shell theory, the stretch-shear strain is interpolated to obtain simplified and locking-free elastic forces, which is a new attempt to alleviate the locking problems for the GEBFs. In addition, the special orthogonal group SO(3) is utilized for updating incremental rotation vectors to eliminate singularities, and objective strain measurement is achieved by employing relative rotation vector interpolation. The effectiveness and superiority of the developed low-order and high-order elements are demonstrated through numerical simulations of standard benchmark examples. The present work contributes to the advancement of accurate and reliable formulation for slender beams; the constant mass matrix, the locking-free characteristics, and the elegant form of the formulation make it particularly suitable for multibody dynamic analysis.

Modeling solvation dynamics of transition metal redox ion through on-the-fly multi-objective Bayesian-optimized force field.

Modeling solvation dynamics and properties is crucial for developing electrolytes for electrochemical energy storage and conversion devices. This work reports an on-the-fly multi-objective Bayesian optimization (OTF-MOBO) method to parameterize force fields for modeling ionic solvation structures, thermodynamics, and transport properties using molecular dynamics simulations. By leveraging solvation-free energy and solvation radii as training data, we employ the data-driven OTF-MOBO algorithm to actively optimize the force field parameters. The modeling accuracy was evaluated in molecular dynamics simulations until the Pareto front in the parameter space was reached through minimized prediction errors in both solvation-free energy and solvation radii. Using transition metal redox ions (Fe3+/Fe2+, Cr3+/Cr2+, and Cu2+/Cu+) in aqueous solution as examples, we demonstrate that simple force fields combining the Lenard-Jones potential and Coulombic potential can achieve relative error below 2% in both solvation free energy and solvation radii. The optimized force fields can be further extrapolated to predict solvation entropy and diffusivities with relative error below 10% compared with experiments.

The simplification and analytical verification of the static liquid bridge force model for particle adhesion in inferior seedling substrates

This study examines the adhesion mechanism in varying water contents of inferior seedling substrate blocks, focusing on the adhesion between particles‒particles and particles‒wall of the seedling tray. A simplified static liquid bridge force model based on the Young–Laplace equation is proposed. The correlation between the liquid bridge force and volume is derived and validated against existing experimental. The results indicate that the static liquid bridge force between particles decreases as the distance increases. A critical distance region is identified, where below this distance, a smaller liquid bridge volume results in a greater static liquid bridge force, and beyond this, the trend reverses, except when the solid–liquid contact angle is 50°. Additionally, the solid‒liquid contact angle has a minimal influence on the liquid bridge force between the particles and the inner sidewall of the seedling tray. This study also analyses the change in critical rupture distance during the transition of liquid bridges from pendulum to ring rope type, and this change increases with the liquid bridge volume.

Experimental Study on a Damage-Control and Repairable Fully Precast Beam-Column Joint

ABSTRACT A novel joint with a splice lap was proposed, which was damage-control and repairable fully precast beam-column joint (DRBJ) connected by energy-dissipating connecting steel plates to remarkably diminish the residual displacement of an RC frame under strong earthquakes and ensure the rapid rehabilitation of the structure. Four one-half scale beam-column-joint specimens were designed and fabricated in different connection forms and lap lengths, and one of the specimens was loaded again under the same conditions after repair. Low cyclic loading tests on DRBJ were conducted to investigate their hysteresis curves and energy-dissipation capacities. The test results revealed that the plastic deformation of DRBJ was concentrated on connecting steel plates, while the residual displacement was small. The deformation and bearing capacities of the short-lap joint were higher than those of the long-lap junction, and the bearing, energy consumption, and deformation capacities of the DRBJ connected by strip plates were still superior to those of the DRBJ connected by the rectangular plates. The DRBJ showed satisfactory repairability and energy-dissipation capacity with the help of the strip plates. A simplified force–displacement model was established based on the analysis of the functioning mechanism of DRBJ. The calculated results of the rotational stiffness and the test results agree well, which can provide a reference for the design of this type of splice joint.

Mechanistically Different Mechanochromophores Enable Calibration and Validation of Molecular Forces in Glassy Polymers and Elastomeric Networks.

Sterically distorted donor-acceptor π-systems, termed DA springs, can be progressively planarized under mechanical load causing a bathochromic shift of the photoluminescence (PL) spectrum. By combining theory and experiment, we here use a simple linear force calibration for two different conformational mechanochromophores to determine molecular forces in polymers from the mechanochromic shift in PL wavelength during multiple uniaxial tensile tests. Two systems are used, i) a highly entangled linear glassy polyphenylene and ii) a covalent elastomeric polydimethylsiloxane network. The mean forces estimated by this method are validated using known threshold forces for the mechanochemical ring-opening reactions of two different spiropyran force probes. The agreement between both approaches underlines that these DA springs provide the unique opportunity for the online monitoring of local molecular forces present in diverse polymer matrices.

Assessing the predictive validity of expectancy theory for academic performance

BackgroundDespite expectancy theory’s widespread appeal and influence as a framework for motivation in organizational and educational settings, studies that have examined the theory’s validity for performance-based outcomes, particularly with academic performance as the criterion, have been characterized by inconsistent results. Given numerous methodological concerns associated with past studies (e.g., prevalence of between-person rather than within-person design), we examined the predictive validity of expectancy theory for academic performance using methods that were consistent with the theory’s original conceptualization. Additionally, we assessed the validity of the theory for students’ study effort.MethodsThe final sample included 123 undergraduate students who reported their final grades in four courses. Study effort and other variables were measured with self-report surveys. Because course grades were nested within each person, multilevel modeling was used to test study hypotheses.ResultsBoth the valence model and the force model predicted a student’s current study effort, but contrary to expectations, neither model predicted a student’s final course grades. In contrast, both valence for academic success and the simplified force model (based only on valence and expectancy) predicted current study effort, final course grades, and explained incremental variance beyond cognitive ability. Furthermore, the predictive validity of this force model was relatively stable across the 11 weeks of the study.ConclusionsBased on methods congruent with expectancy theory’s original framework, we find that the force model does not predict academic performance. An alternative version of the model, however, predicts course grades and has incremental validity over cognitive ability. Our results have several significant theoretical and practical implications.

Getting the intermolecular forces correct: introducing the ASTA strategy for a water model.

Having a force field for water providing good bulk properties is paramount for modern studies of most biological systems. Some of the most common three-site force fields are TIP3, SPC/ε or OPC3, providing a decent range of bulk properties. That does not mean though, that they have realistic inter-atomic forces. These force fields have been parameterized with a top-down approach, meaning, by fitting the force field parameters to the experimental bulk properties. This approach has been the governing strategy also for many variants of four- and more-site models. We test a bottom-up approach, in which the force field is parameterized by optimizing the non-bonded inter-atomic forces. Our philosophy is that correct inter-atomic forces lead to correct geometrical and dynamical properties. The first system we try to optimize with the accurately system tailored atomic (ASTA) approach is water, but we aim to eventually probe other systems in the future as well. We applied our ASTA strategy to find a good set of parameters providing accurate bulk properties for the simple three-site force field forms, and also for AMOEBA, a more detailed and polarizable force field. Even though our bottom-up approach did not provide satisfactory results for the simple three-site force fields (with fixed charges), for the case of the AMOEBA force field it led to a modification of the original strategy, giving very good intra- and inter-molecular forces, as compared to accurate quantum chemically calculated reference forces. At the same time, important bulk properties, in this study restricted to the density and diffusion, were accurately reproduced with respect to the experimental values.

Evolution of Light Absorption Enhancement of Black Carbon Aerosols From Biomass Burning in Atmospheric Photochemical Aging

AbstractThe light absorption enhancement (Eabs) of black carbon (BC) coated with non‐BC materials is crucial in the assessment of radiative forcing, yet its evolution during photochemical aging of plumes from biomass burning, the globe's largest source of BC, remains poorly understood. In this study, plumes from open burning of corn straw were introduced into a smog chamber to explore the evolution of Eabs during photochemical aging. The light absorption of BC was measured with and without coating materials by using a thermodenuder, while the size distributions of aerosols and composition of BC coating materials were also monitored. Eabs was found to increase initially, and then decrease with an overall downward trend. The lensing effect dominated in Eabs at 520 nm, with an estimated contribution percentages of 47.5%–94.5%, which is far greater than light absorption of coated brown carbon (BrC). The effects of thickening and chemical composition changes of the coating materials on Eabs were evaluated through comparing measured Eabs with that calculated by the Mie theory. After OH exposure of 1 × 1010 molecules cm−3 s, the thickening of coating materials led to an Eabs increase by 3.2% ± 1.6%, while the chemical composition changes or photobleaching induced an Eabs decrease by 4.7% ± 0.6%. Simple forcing estimates indicate that coated BC aerosols exhibit warming effects that were reduced after aging. The oxidation of light‐absorbing CxHy compounds, such as polycyclic aromatic hydrocarbons (PAHs), to CxHyO and CxHyO>1 compounds in coating materials may be responsible for the photobleaching of coated BrC.

PyFMLab: Open-source software for atomic force microscopy microrheology data analysis

Background Atomic force microscopy (AFM) is one of the main techniques used to characterize the mechanical properties of soft biological samples and biomaterials at the nanoscale. Despite efforts made by the AFM community to promote open-source data analysis tools, standardization continues to be a significant concern in a field that requires common analysis procedures. AFM-based mechanical measurements involve applying a controlled force to the sample and measure the resulting deformation in the so-called force-distance curves. These may include simple approach and retract or oscillatory cycles at various frequencies (microrheology). To extract quantitative parameters, such as the elastic modulus, from these measurements, AFM measurements are processed using data analysis software. Although open tools exist and allow obtaining the mechanical properties of the sample, most of them only include standard elastic models and do not allow the processing of microrheology data. In this work, we have developed an open-source software package (called PyFMLab, as of python force microscopy laboratory) capable of determining the viscoelastic properties of samples from both conventional force-distance curves and microrheology measurements. Methods PyFMLab has been written in Python, which provides an accessible syntax and sufficient computational efficiency. The software features were divided into separate, self-contained libraries to enhance code organization and modularity and to improve readability, maintainability, testability, and reusability. To validate PyFMLab, two AFM datasets, one composed of simple force curves and another including oscillatory measurements, were collected on HeLa cells. Results The viscoelastic parameters obtained on the two datasets analysed using PyFMLab were validated against data processing proprietary software and against validated MATLAB routines developed before obtaining equivalent results. Conclusions Its open-source nature and versatility makes PyFMLab an open-source solution that paves the way for standardized viscoelastic characterization of biological samples from both force-distance curves and microrheology measurements.

Shear-induced depinning of thin droplets on rough substrates

Depinning of liquid droplets on substrates by flow of a surrounding immiscible fluid is central to applications such as cross-flow microemulsification, oil recovery and waste cleanup. Surface roughness, either natural or engineered, can cause droplet pinning, so it is of both fundamental and practical interest to determine the flow strength of the surrounding fluid required for droplet depinning on rough substrates. Here, we develop a lubrication-theory-based model for droplet depinning on a substrate with topographical defects by flow of a surrounding immiscible fluid. The droplet and surrounding fluid are in a rectangular channel, a pressure gradient is imposed to drive flow and the defects are modelled as Gaussian-shaped bumps. Using a precursor-film/disjoining-pressure approach to capture contact-line motion, a nonlinear evolution equation is derived describing the droplet thickness as a function of distance along the channel and time. Numerical solutions of the evolution equation are used to investigate how the critical pressure gradient for droplet depinning depends on the viscosity ratio, surface wettability and droplet volume. Simple analytical models are able to account for many of the features observed in the numerical simulations. The influence of defect height is also investigated, and it is found that, when the maximum defect slope is larger than the receding contact angle of the droplet, smaller residual droplets are left behind at the defect after the original droplet depins and slides away. The model presented here yields considerably more information than commonly used models based on simple force balances, and provides a framework that can readily be extended to study more complicated situations involving chemical heterogeneity and three-dimensional effects.

Simplified Formula for Nominal Force at Critical Welds in the Lower Chord Node of a Novel Bracket-Crane Truss Structure

In the realm of practical engineering, engineers commonly employ rod system models for modeling and analysis, which consequently precludes them from calculating the nominal forces exerted on welds at intricate nodes. This paper addresses the design challenges of the innovative bracket-crane truss structure by proposing a simplified nominal force calculation formula for critical welds of the integrated node. This study commences with the establishment of the frame model and ABAQUS multiscale models, utilizing engineering project drawings and data, followed by a verification of the similarities between the two simulation methods. This similarity of outcomes provides a foundation for directly using the computational results from the frame model in future calculations of the forces at the weld locations. From a mechanical standpoint, this paper derives nominal force calculation formulas for horizontal and vertical welds at critical locations for three node types. Additionally, a formula for calculating nominal shear forces in vertical welds at the end plate of support nodes is introduced. The applicability of these derived formulas is subsequently validated, ensuring their efficacy in accurately capturing relevant forces at critical locations. The presented nominal force calculation formula serves as a valuable tool for optimizing the design and guaranteeing the structural integrity of the integrated node within this distinctive engineering context.

Phase synchronization between culture and climate forcing.

Over the history of humankind, cultural innovations have helped improve survival and adaptation to environmental stress. This has led to an overall increase in human population size, which in turn further contributed to cumulative cultural learning. During the Anthropocene, or arguably even earlier, this positive sociodemographic feedback has caused a strong decline in important resources that, coupled with projected future transgression of planetary boundaries, may potentially reverse the long-term trend in population growth. Here, we present a simple consumer/resource model that captures the coupled dynamics of stochastic cultural learning and transmission, population growth and resource depletion in a changing environment. The idealized stochastic mathematical model simulates boom/bust cycles between low-population subsistence, high-density resource exploitation and subsequent population decline. For slow resource recovery time scales and in the absence of climate forcing, the model predicts a long-term global population collapse. Including a simplified periodic climate forcing, we find that cultural innovation and population growth can couple with climatic forcing via nonlinear phase synchronization. We discuss the relevance of this finding in the context of cultural innovation, the anthropological record and long-term future resilience of our own predatory species.

Impact of surface current and temperature feedback on kinetic energy over the North-East Atlantic from a coupled ocean / atmospheric boundary layer model

A one-dimensional Atmospheric Boundary Layer (ABL1D) model is coupled with the NEMO ocean model and implemented over the Iberian–Biscay–Ireland (IBI) area at 1/36° resolution to investigate the damping effect of the current and the thermal feedback on the kinetic energy (KE) at the mesoscale. This type of coupling between an ocean model and an ABL1D is a newly proposed approach as an alternative of intermediate complexity between bulk forcing and full coupling with an atmosphere model. In ABL1D, the prognostic tracers are nudged toward large-scale variables and the wind is guided by a low-frequency geostrophic wind provided from the ERA-Interim reanalyses. First, the ABL1D is successfully validated against satellite observations regarding the wind, and the dynamic coupling coefficient (linking the near surface wind and wind-stress to the of the surface currents) are consistent with the literature, over the period 2016–2017. Our results show that the thermal feedback has a negligible impact on kinetic energy (KE) and does not influence the strength of the current feedback in the region. Given the ABL1D physics, this further indicates that the changes in the vertical wind structure caused by CFB are primarily governed by local mechanical mechanisms associated with surface wind-stress condition, rather than by thermodynamic or non-local processes within the planetary boundary layer. The induced KE reduction by the current feedback amounts to 14% at the surface and propagates down to 2000 m, indicating that it can modify the vertical distribution of KE throughout the water column. KE reductions in the surface boundary layer (0 – 300 m) and in the interior (300 – 2000 m) are attributed to a reduction of the surface wind work by 4%, and of the pressure work by 7%, respectively. The Ekman pumping anomalies induced by the current feedback tend to attenuate eddy activity and horizontal pressure gradients at depth, illustrating the potential of the current feedback to induce a geostrophic adjustment on the water column. These results illustrate the relevance of the proposed ABL1D coupling approach for reproducing the wind-current coupling (a.k.a. current feedback effect) which cannot be taken into account straightforwardly with simple bulk forcing.

Sea Ice‐Driven Iceberg Drift in Baffin Bay

AbstractBaffin Bay is the travel destination of most icebergs calving from west Greenland. They commonly follow the bay's cyclonic circulation and might end up far south along the coast of Newfoundland and Labrador, where many shipping routes converge. Given the hazard that icebergs pose to marine transportation, understanding their distribution is fundamental. One of the forces driving iceberg drift arises from the presence of sea ice. Observations in the Southern Ocean indicate that icebergs get locked in thick and concentrated sea ice. We present observations that support the occurrence of this sea ice locking mechanism (SIL) in Baffin Bay as well. Most iceberg models, however, represent the sea ice force over an iceberg as a simple drag force. Here, we implement a new parameterization in the iceberg module of the Nucleus for European Modeling of the Ocean (NEMO‐ICB) to represent SIL. We show that, by using this new parameterization, icebergs are more likely to travel outside of the Baffin Island Current during winter, which is supported by satellite observations. There is a slight improvement in the representation of iceberg severity along the coast of Newfoundland and Labrador and a slight shift of iceberg melt toward this region and Lancaster Sound/Hudson Strait. Although the impacts of icebergs on sea ice are still not represented, and targeted observations are needed for model calibration regarding sea ice concentration thresholds from which icebergs get locked, we are confident that this model improvement takes iceberg modeling one step forward toward reality.

Towards engineering a portable platform for laparoscopic pre-training in virtual reality with haptic feedback

BackgroundLaparoscopic surgery is a surgical technique in which special instruments are inserted through small incision holes inside the body. For some time, efforts have been made to improve surgical pretraining through practical exercises on abstracted and reduced models. MethodsThe authors strive for a portable, easy to use and cost-effective Virtual Reality-based (VR) laparoscopic pre-training platform and therefore address the question of how such a system has to be designed to achieve the quality of today's gold standard using real tissue specimens. Current VR controllers are limited regarding haptic feedback. Since haptic feedback is necessary or at least beneficial for laparoscopic surgery training, the platform to be developed consists of a newly designed prototype laparoscopic VR controller with haptic feedback, a commercially available head-mounted display, a VR environment for simulating a laparoscopic surgery, and a training concept. ResultsTo take full advantage of benefits such as repeatability and cost-effectiveness of VR-based training, the system shall not require a tissue sample for haptic feedback. It is currently calculated and visually displayed to the user in the VR environment. On the prototype controller, a first axis was provided with perceptible feedback for test purposes. Two of the prototype VR controllers can be combined to simulate a typical both-handed use case, e.g., laparoscopic suturing. A Unitybased VR prototype allows the execution of simple standard pre-trainings. ConclusionsThe first prototype enables full operation of a virtual laparoscopic instrument in VR. In addition, the simulation can compute simple interaction forces. Major challenges lie in a realistic real-time tissue simulation and calculation of forces for the haptic feedback. Mechanical weaknesses were identified in the first hardware prototype, which will be improved in subsequent versions. All degrees of freedom of the controller are to be provided with haptic feedback. To make forces tangible in the simulation, characteristic values need to be determined using real tissue samples. The system has yet to be validated by cross-comparing real and VR haptics with surgeons.

Чисельне дослідження впливу довжини стрижня на його критичні сили

The effect of changing the length of a longitudinally compressed rod on its critical forces is numerically investigated. The research is carried out on the example of a two-span rectilinear rod of bending stiffness constant along length, which is compressed by a constant lengthwise longitudinal force and hinged on one of the ends on an absolutely rigid support, and inside - on a support of finite stiffness. The change in the length of the rod occurs due to the movement of the end hinge support with the corresponding increase or decrease of the adjacent section of the rod without changing the position and characteristics of the remaining constraints. The dependence of the critical forces of the rod on the position of this support and, accordingly, on the length of the adjacent compressed section of the rod is investigated. Calculations are performed on the basis of the use of known exact analytical expressions of the influence functions of a rod of constant cross-section compressed by a longitudinal force constant by length. In the considered examples, qualitative signs of increase, decrease, and extremum of simple critical forces when changing the length of the rod, related to the qualitative features of the corresponding buckling forms, established earlier theoretically, were fully confirmed. In particular, exact calculations have shown that the increase or decrease of the simple critical force when the length of the fragment of the rod adjacent to the movable support is changed is determined by the type of the corresponding buckling form in the neighborhood of this support. Different possible configurations of buckling forms are considered, and the behavior of critical forces when changing the length of the rod are considered for each of the configurations. In order to verify the previously established theoretical results, which relate to the study of the behavior of not only the main critical forces, but also higher simple critical forces, which have an arbitrary number in the spectrum, the calculations are carried out in the article for the second critical forces of the rods considered in the given examples. The results of the calculations are shown in the form of graphs, which represent configurations of buckling forms of various possible types in connection with the corresponding changes in critical forces. Graphs of the dependence of the second critical force of the studied rods on their length are also given. It has been demonstrated that under certain conditions, reducing the length of the rod can lead to a reduction in its critical force.

Joint Resonance Analysis in Multiple Modes of Soft Ferromagnetic Rectangular Thin Plate

In this article, the nonlinear principal and internal resonance properties of a soft ferromagnetic rectangular thin plate are investigated in a magnetic field environment. The nonlinear partial differential equation of motion of a soft ferromagnetic rectangular thin plate is derived under the effect of homogeneous simple harmonic excitation. The system of nonlinear differential equations with multiple degrees of freedom is established by the assumed one-sided fixed trilateral simply support condition using the Galerkin’s method. The system of nonlinear differential equations is solved by the multiscale method to obtain the response of two modes under the simple harmonic force at the principal and internal resonance. The numerical results of the system response show that when the frequency of the simple harmonic force is close to one of the modes (first-order or second-order mode) causing it to resonate, the other mode will also resonate internally. The magnetic field can have an inhibiting effect on the resonant response of the system and also affect the kinematic state of the system. The internal resonance provides a mechanism for transferring energy from a high mode to a lower mode.

Prepared for landing: A simple activation strategy scales muscle force to landing height

Before landing from a jump or fall, animals preactivate muscles to stiffen their limb joints but it is unclear how muscles tune limb stiffness and how collision forcefulness is anticipated. We measured electromyography and force from the lateral gastrocnemius muscle during landings in turkeys, an animal model that allows for direct measurements of muscle force. Many studies of landings in humans and other animals have found the duration of muscle preactivation to be constant, starting approximately 100 ms before impact, irrespective of fall duration. Therefore, we hypothesized a lack of relationship between fall duration (as dictated by drop height), muscle activity onset-time, and force at toe-down. Contrary to our expectations, both muscle activity and force rose from briefly after fall initiation until toe-down. Preactivation duration was proportional to fall height, while the rate of force rise was consistent across drop heights, resulting in force at landing and leg stiffness being proportional to fall height. Onset of muscle activity lagged 22 ± 7 ms (mean ± S.E.M.) from fall initiation, consistent with a reflex response initiation of the force ramp-up. Together, our results suggest that a constant (clock-like) rate of motor unit recruitment, initiated at fall initiation provides a preactivation that is proportional to drop height. The result is a tuning of pre-landing muscle force, providing a limb stiffening that is proportional to impact intensity, possibly without using information about fall distance.