Displacement Length Research Articles

Simultaneous Brightfield, Fluorescence, and Optical Coherence Tomographic Imaging of Contracting Cardiac Trabeculae <em>Ex Vivo</em>

In cardiac muscle, intracellular Ca2+ transients activate contractile myofilaments, causing contraction, macroscopic shortening, and geometric deformation. Our understanding of the internal relationships between these events has been limited because we can neither 'see' inside the muscle nor precisely track the spatio-temporal nature of excitation-contraction dynamics. To resolve these problems, we have constructed a device that combines a suite of imaging modalities. Specifically, it integrates a brightfield microscope to measure local changes of sarcomere length and tissue strain, a fluorescence microscope to visualize the Ca2+ transient, and an optical coherence tomograph to capture the tissue's geometric changes throughout the time-course of a cardiac cycle. We present here the imaging infrastructure and associated data collection framework. Data are collected from isolated rod-like tissue structures known as trabeculae carneae. In our instrument, a pair of position-controlled platinum hooks hold each end of an ex vivo muscle sample while it is continuously superfused with nutrient-rich saline solution. The hooks are under independent control, permitting real-time control of muscle length and force. Lengthwise translation enables the piecewise scanning of the sample, overcoming limitations associated with the relative size of the microscope imaging window (540 µm by 540 µm) and the length of a typical trabecula (>2000 µm). Platinum electrodes at either end of the muscle chamber stimulate the trabecula at a user-defined rate. We exploit the stimulation signal as a trigger for synchronizing the data from each imaging window to reconstruct the entire sample twitching under steady-state conditions. Applying image-processing techniques to these brightfield imaging data provides tissue displacement and sarcomere length maps. Such a collection of data, when incorporated into an experiment-modeling pipeline, will provide a deeper understanding of muscle contractile homogeneity and heterogeneity in physiology and pathophysiology.

Simultaneous Brightfield, Fluorescence, and Optical Coherence Tomographic Imaging of Contracting Cardiac Trabeculae Ex Vivo.

In cardiac muscle, intracellular Ca2+ transients activate contractile myofilaments, causing contraction, macroscopic shortening, and geometricdeformation. Our understanding of the internal relationships between these events has been limited because we can neither 'see' inside the muscle nor precisely track the spatio-temporal nature of excitation-contraction dynamics. To resolve these problems, we have constructed a device that combines a suite of imaging modalities. Specifically, it integrates a brightfield microscope to measure local changes of sarcomere length and tissue strain, a fluorescence microscope to visualize the Ca2+ transient, and an optical coherence tomograph to capture the tissue's geometricchanges throughout the time-course of a cardiac cycle. We present here the imaging infrastructure and associated data collection framework. Data are collected from isolated rod-like tissue structures known as trabeculae carneae. In our instrument, a pair of position-controlled platinum hooks hold each end of an ex vivo muscle sample while it is continuously superfused with nutrient-rich saline solution. The hooks are under independent control, permitting real-time control of muscle length and force. Lengthwise translation enables the piecewise scanning of the sample, overcoming limitations associated with the relative size of the microscope imaging window (540 µm by 540 µm) and the length of a typical trabecula (>2000 µm). Platinum electrodes at either end of the muscle chamber stimulate the trabecula at a user-defined rate. We exploit the stimulation signal as a trigger for synchronizing the data from each imaging window to reconstruct the entire sample twitching under steady-state conditions. Applying image-processing techniques to these brightfield imaging data provides tissue displacement and sarcomere length maps. Such a collection of data, when incorporated into an experiment-modeling pipeline, will provide a deeper understanding of muscle contractile homogeneity and heterogeneity in physiology and pathophysiology.

Loading rate effect on fracture process in Brazilian splitting tests of Beishan granites

In the present study, to reveal the loading rate effect on fracture process in Beishan granite, a series of Brazilian splitting tests under conventionally monotonic loading and stepwise loading conditions were performed to observe the crack propagation process of granites, with the aid of a digital image correlation (DIC) technique. The fracture process zone (FPZ) length and opening displacement ahead of notch tips, and so on were measured, and the loading-rate dependence was acquired correspondingly. The experimental results show that the peak load, axial and lateral deformation of granite gradually increased with the increasing loading rate. With the increase in the loading rate, the stress level for fracture initiation decreased, while the critical opening displacement and FPZ length gradually increased. The granite underwent insignificant deformation during the constant stress loading period when a lower stress was applied. When a larger stress was applied, obvious three-stage creep deformation was observed. The opening displacement ahead of notch tips increased slowly at a constant rate during the primary and secondary creep stages, then exhibited an approximately exponential increase with increasing time during the tertiary creep. Moreover, the FPZ length of granite at the critical state under conventional loading was higher than that under stepwise loading. The inner mechanism is analyzed to explain the rate-dependent fracturing behavior.

Spreading behavior of dodecane-oleic acid collector mixture in low-rank coal flotation

Spreading of water-insoluble collectors on the mineral surface is important in flotation. In this study, the spreading behavior of dodecane (D), oleic acid (OA), and dodecane-oleic acid (D-OA) mixture in low-rank coal flotation was investigated. The viscosity and oil/water interfacial tension was measured to calculate the spreading coefficient and speed. The relaxation of coal-oil–water contact angle and the movement of three- phase contact line during the collector droplet spreading process were interpreted using the molecular kinetic (MK) model. It was found that the order of absolute values of spreading coefficient were D-OA < OA < D, and the spreading speeds were in the order of OA < D-OA < D. D-OA had the smallest coal-oil–water contact angle and the longest contact line length. The addition of OA can enhance the interaction between D and the low-rank coal surface, but at the same time reduce the spreading speed. This was mainly because OA not only increased the spreading force of the droplet but also increased the spreading resistance. MK model fitting results showed that the length of molecular displacement increased in the order of D < D-OA < OA, indicating that the hydrophobic sites were more dense than hydrophilic ones on the coal surface and D-OA interacted with both sites simultaneously. The molecular substitution frequency and the free energy of wetting activation had an opposite order. High molecular substitution frequency meant fast-spreading velocity, and thus the MK model fitting parameters were consistent with the contact angle relaxation results.

Seakeeping and resistance analysis of 1200 GT passenger ship fitted with NACA 4412 stern foil using CFD method

Seakeeping performance is one of the requirements to ensure the convenience and safety of life at sea, especially for passenger ships. In this paper, the result of computational fluid dynamics (CFD) analyses concerning the effect of NACA 4412 stern foil to the improvement of seakeeping quality and resistance of 1200 GT passenger ship are presented. The fitting of stern foil has become a popular method for the improvement of ship design. Stern foil is hydrofoil attached to the transom of the vessel located at the stern part below the waterline. The analysis was developed on the conditions of regular and irregular head waves. The CFD computation on 8 variations of the stern foil position and attack angle has been carried out by using Numeca Fine/Marine. The study confirms that the ship resistance decrease by 3.6 % at the service speed of the ship. The improvement of heaving and pitching amplitudes, as well as heaving acceleration, are significant for the hull vane located at 50% of displacement draft and 1% of displacement length with the attack angle of −4°.

Abstract 3120: MMP-7 increases migration by decreasing intercellular cell junction complexes in prostate cancer microtumors formed by perlecan/HSPG2

Abstract Background: Polarized epithelium is stabilized by lateral cell-cell interactions via cell adhesion molecules (CAMs) and by cell-matrix interactions with basement membrane including with perlecan/HSPG2 (pln). Prostate cancer (PCa) patients with bone metastases have circulating pln fragments, with inverse correlation between MMP-7 staining and loss of pln in cancer tissue. Cleavage of pln by MMP-7 increases cell-matrix interactions and dysregulates cell signaling, permitting migration. We earlier showed pln domain IV-3 (DmIV-3) drives cell-cell cohesion and, when digested with MMP-7, drives cell dyscohesion. Methods: To evaluate the impact of MMP-7 and pln fragments on microtumor dyscohesion and cell migration, uniformly sized PCa microtumors were pre-formed in a microwell system. Pre-formed microtumors were transferred to Dm IV-3 or full length perlecan (FL pln) coated wells for 16-24 hrs. Microtumors were treated with MMP-7 alone or MMP-7 plus predigested Dm IV-3 fragments or MMP-7 plus FL pln fragments. For live cell imaging, tracking of migratory cells leaving microtumors was performed with Imaris software. Co-location of cell adhesion complex components was assessed with Imaris Spots. Results: Pre-formed microtumors cultured with DmIV-3 cleaved by MMP-7 showed lower Pearson's correlation values at cell boundaries compared to microtumors treated with intact Dm IV-3. Line scan analysis revealed E-cadherin and F-actin fluorescent signals were enriched and co-aligned in microtumors treated with Dm IV-3; enrichment and co-alignment were reduced when DmIV-3 fragments and MMP-7 were present. Track number detected per cell cluster was highest in the presence of FL pln fragments plus MMP-7 along with a measurable change in distribution of track displacement lengths of cells toward high values. Conclusion: Boundary reorganization promotes a migratory cell phenotype in microtumors treated with MMP-7 and DmIV-3 fragments. DmIV-3 fragments generated by MMP-7 cleavage can enhance cell dyscohesion by disrupting interactions between CAMs. Ongoing work will identify DmIV-3 fragment(s) positively associated with tumor dyscohesion that play key roles in secondary metastasis formation. Following patterns of dyscohesion of pre-formed microtumors provides a good model to study dynamic changes in intercellular junction components and quantitate cell migration patterns that foster circulating tumor cell formation and metastasis. Citation Format: Lissette A. Cruz, Tristen V. Tellman, Oleg Igoshin, Daniel Carson, Mary (Cindy) Farach-Carson. MMP-7 increases migration by decreasing intercellular cell junction complexes in prostate cancer microtumors formed by perlecan/HSPG2 [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 3120.

Displacement between anterior chamber width obtained by swept-source anterior segment optical coherence tomography and white-to-white distance.

PurposeTo determine the relationship between the external limbal location, represented by white-to-white (WTW) distance, and the actual angle location, represented by spur-to-spur (STS) and angle-to-angle (ATA) distances.Methods166 eyes from 166 participants were imaged using CASIA2 anterior chamber optical coherence tomography (AS-OCT) and LenStar LS 900 optical biometer. The horizontal ATA and STS were measured using the swept-source Fourier-domain AS-OCT (CASIA2). The horizontal WTW was automatically measured using LenStar. The displacement lengths (DL) between WTW-STS and WTW-ATA were calculated. Bland-Altman plots and intraclass correlation were performed.ResultsThe study showed that WTW has a positive correlation with STS (ICC = 0.82, p<0.001) and ATA (ICC = 0.82, p<0.001). The Bland-Altman analysis demonstrated that the mean difference of WTW-STS is 0.10 mm (95% CI 0.06 to 0.14 mm) with limits of agreement of -0.42 to 0.63 mm between WTW and STS, and the mean difference of WTW-ATA is 0.10 mm (95% CI 0.06 to 0.15 mm) with limits of agreement of -0.48 to 0.64 mm between WTW and ATA. Linear regression with adjustment showed that a WTW value greater than 12.07 mm is associated with a greater DL (WTW-STS DL ß 0.18, p = 0.003; WTW-ATA DL ß 0.14, p = 0.03).ConclusionsGreater WTW was significantly associated with higher displacement of WTW from the two distances representing anterior chamber width. External limbal location may not accurately represent the actual angle location in eyes with larger WTW.

Dynamic characteristics of droplet impingement on microscale hole-patterned surfaces with anodization

This study aims to experimentally examine the dynamic characteristics of a liquid droplet impinging on the microscale hole-patterned surfaces with the anodization method to make the hydrophilic hole-patterned surface. We studied static and dynamic wetting behavior and compared the hydrophobic characteristics of a drilled hole-patterned surface. The equilibrium contact angle, the dynamic contact diameter, and the dynamic contact angle are measured over time by using image analysis. By modeling the force balance between capillary and hydrostatic forces, the liquid displacement length and equilibrium contact angle of the anodized bare surfaces is estimated and compared with experimental data. It is found that the dynamic contact angle decreased with an increase in the hole area fraction for the anodized hole-patterned surface. In contrast, the equilibrium contact angle and the dynamic contact angle in the hole-patterned surface without the anodization increased with the hole area fraction, showing different tendencies. It is also shown that the dynamic contact diameter increased more on the area fraction and Weber number on the hole-patterned surfaces with the anodization.

Kinetics of bubble interaction with low rank coal surface in the presence of adsorbed dodecane-oleic acid collector mixture

ABSTRACT Bubble–particle interactions are crucial in the flotation process, and the influence of adsorbed chemicals on bubble-surface collisions/attachment is important to fully understand the role of mixed collector in low-rank coal (LRC) flotation. In this paper, the process of rising bubble attachment to LRC surface in the presence of adsorbed dodecane (D)-oleic acid (OA) collector mixture was studied using high-speed video camera and molecular-kinetic (MK) model. The results showed that collector adsorbed on LRC surface reduced the collision times, the time for stopping collision and reaching standstill. Mixed collector showed more obvious advantages than single collectors in accelerating bubble-surface collisions/attachment and increasing contact line length. Only when OA and OA-D were adsorbed, the wetting film between bubble and LRC surface broke and a stable three-phase contact was formed. The molecular displacement length of D-OA was smaller than that of single collectors, indicating the adsorption sites of bubbles on LRC surface treated with D-OA were more dense, and the higher displacement frequency of D-OA meant that the molecular displacement rate and TPCL expansion velocity was faster. D-OA enhanced the hydrophobicity of LRC surface through the synergistic effect between OA and D, which promoted the kinetics of bubble interaction with LRC surface.

Analysis of surface changes from undermining and building site categorization: The case study in mining location Louky near Karvina

Repeated geodetic observations were applied in mining location Louky near Karviná to detect surface changes from undermining in complex geo-mechanical conditions. Analyses of the subsidence magnitude and the length and direction of horizontal displacements showed that the subsidence trough was formed unevenly not only due to the position of the exploited local longwall panels and their different size but also showed a notable effect of the dominant tectonic fault. The significantly uneven development of the subsidence trough negatively affects line constructions. Terrain deformations of the road and stream pipeline were computed and classified into the building site categories according to the Czech standard ČSN 73 0039. The course of individual deformations in the monitored locality is influenced by a complex geo-mechanical situation. While the course of the subsidence curves is continuous at the observed pipeline and the classification of individual sections into building site categories corresponds with that, the road profile points out a more complex development of surface deformations. At the end of the observed period, 5 % of the profiles’ sections fell into category III (medium intensity), 49 % into category IV (moderate intensity) and 32 % stayed in category V (very moderate intensity of mining effects).

Demonstration of Interference Patterns by the Random Walk of Particles

Visualization of interference phenomena by Chladni patterns is treated. The formation of the pattern in the Young's double-slit experiment is described by a new model of driven random walk exhibited by particles bouncing on a vibrating surface. In the model the mean length of horizontal displacement is described deterministically by the wave amplitude. The presented example indicates that such formation of interference patterns can take place without any pilot-waves associated to particles. In spite od this, the pheomenon remeinds to formation of interference patterns observed at scattering of particles in quantum mechanics.

Late Holocene Deformation near the Southern Limits of the Wabash Valley Seismic Zone of Kentucky and Indiana, Central United States, with Seismic Implications

ABSTRACTThe Wabash Valley seismic zone (WVSZ) is a region of diffuse, modern intraplate seismicity in the central United States with a history of strong, late Quaternary and Holocene seismicity as determined through paleoliquefaction studies. Yet, there are no specific faults linked to these strong WVSZ paleoearthquakes, some of which were as large as Mw 7.2–7.5. A multidisciplinary investigation of a linear, 5-kilometer-long and ∼3-meter-high scarp on the Ohio River floodplain in the southernmost WVSZ in western Kentucky evaluated whether the scarp is a fluvial landform or a tectonic feature. Geomorphic mapping and optically stimulated luminescence geochronology show that the age and orientation of the scarp are inconsistent with surrounding fluvial landforms. Trenching, core drilling, seismic reflection, electrical resistivity profiling, and cross sections of petroleum well logs all indicate a blind fault directly underlies the scarp. The scarp is interpreted to be the fold axis of a down-to-the-west monocline formed in alluvium by slip on the underlying blind fault, herein named the Uniontown fault. The Uniontown fault connects the Hovey Lake fault, striking N20°E and having ∼0.5 km of documented strike-slip offset, with an unnamed fault complex to the south that strikes N40°E, suggesting the Uniontown fault is part of a larger, Paleozoic structure that has been reactivated with strike-slip deformation. Geomorphic mapping utilizing luminescence and radiocarbon geochronology indicates that folding and faulting occurred ∼3.5 ka. Paleoliquefaction was suppressed by a thick clay cap in the main Ohio Valley, but paleoliquefaction features are widespread on Ohio River tributaries. Gravel dikes at one site had a maximum age of 3.4±0.4 ka, confirming the region has experienced strong, late Holocene shaking. Estimates using vertical displacement and rupture length indicate that slip on the Uniontown scarp could produce an Mw 6.2–7.7 earthquake, which is comparable to other large paleoearthquakes in the WVSZ paleoseismic record.

Using Motion Tracking to Analyze Forceps Paths During Simulated Forceps-Assisted Vaginal Deliveries.

The purpose of this study was to evaluate the ability of motion tracking to discern variation in forceps paths during standardized simulated forceps-assisted vaginal deliveries among experienced and inexperienced obstetric providers. This is a pilot study involving 24 obstetrics and gynecology residents and 6 faculty at a single institution. Each participant was filmed performing standardized simulated forceps-assisted vaginal deliveries on a high-fidelity model. Motion tracking software (Kinovea, Medoc, France) was used to track the path of the forceps shank. Data were analyzed for total path length, total x-plane displacement, total y-plane displacement, and final forceps angle. One-way analysis of variance was used to evaluate for statistically significant differences between groups based on education year, with Turkey HSD post hoc test to identify interactions. Statistically significant differences were noted between groups in the total path length (F = 7.57, P < 0.001) and total y-plane displacement (F = 5.79, P < 0.001). On pairwise comparison, significant differences were noted between faculty and postgraduate year 1 as well as faculty and postgraduate year 2 for total y-plane displacement and total path length. Significant differences were not observed between groups for total x-plane displacement (F = 0.89, P = 0.475) and final forceps angle (F = 2.45, P = 0.052). Motion tracking of standardized simulated forceps-assisted vaginal deliveries identifies statistically significant differences between experienced and inexperienced obstetric providers. Our findings suggest that motion tracking can be used to design an educational intervention to improve forceps technique among obstetrics and gynecology residents.

Do intraplate and plate boundary fault systems evolve in a similar way with repeated slip events?

As repeated slip events occur on a fault, energy is partly dissipated through rock fracturing and frictional processes in the fault zone and partly radiated to the surface as seismic energy. Numerous field studies have shown that the core of intraplate faults is wider on average with increasing total displacement (and hence slip events). In this study we compile data on the fault core thickness, total displacement and internal structure (e.g., fault core composition, host rock juxtaposition, slip direction, fault type, and/or the number of fault core strands) of plate boundary faults to compare to intraplate faults (within the interior of tectonic plates). Fault core thickness data show that plate boundary faults are anomalously narrow by comparison to intraplate faults and that they remain narrow regardless of how much total displacement they have experienced or the local structure of the fault. By examining the scaling relations between seismic moment, average displacement and surface rupture length for plate boundary and intraplate fault ruptures, we find that for a given value of displacement in an individual earthquake, plate boundary fault earthquakes typically have a greater seismic moment (and hence earthquake magnitude) than intraplate events. We infer that narrow plate boundary faults do not process intact rock as much during seismic events as intraplate faults. Thus, plate boundary faults dissipate less energy than intraplate faults during earthquakes meaning that for a given value of average displacement, more energy is radiated to the surface manifested as higher magnitude earthquakes. By contrast, intraplate faults dissipate more energy and get wider as fault slip increases, generating complex zones of damage in the surrounding rock and propagating through linkage with neighbouring structures. The more complex the fault geometry, the more energy has to be consumed at depth during an earthquake and the less energy reaches the surface.

Dimensionless numerical analysis method for flexible body with large deformation, displacement and time-varying length

A tethered system, which is a multibody system in which multiple rigid bodies are connected via a flexible tether, is currently used for space and deep-sea exploration. In order to perform accurate work with such tethered systems, the ability to comprehend tether dynamics behavior with large deformation/displacement and time-varying length is crucial. Numerical analyses are beneficial in that it is difficult to carry out experiments in such environment. In this paper, an efficient numerical approach is proposed for a flexible body motion with time-varying length using a dimensionless equation of motion. Generally Absolute Nodal Coordinate Formulation (ANCF), which is a nonlinear finite element method is effective for dynamic simulation of a flexible body motion. VFE-ANCF, which applies variable-domain finite element (VFE) as a method of expressing time-varying length to ANCF, was proposed to represent the motion of a flexible body with large deformation, displacement and time-varying length. However, conventional approach using VFE-ANCF has a problem that the accuracy changes depending on the length change. So in this paper, to avoid this problem, dimensionless variables are introduced using representative value that changes with time-varying length. In addition, the usefulness of this method is shown by comparing the numerical results using this method and the conventional method.

Postural stability at different heights as well as in natural standing position and during tandem stance in female athletes who practice artistic gymnastics

The aim of this work was the assessment of postural stability at different heights as well as in natural standing position and during tandem stance in female athletes who practice artistic gymnastics. The study comprised 34 athletes aged 8-12, practicing artistic gymnastics at a sports club "Korona Kraków". The research tool was CQ-Stab 2P two-platform posturograph. The elevation was achieved using the Light SPL platform. The data were analyzed based on Wilcoxon signed-rank test and Spearman's rank correlation. The height at which the posturograph was set differentiated the path length of the statokinesiogram, both in the natural stance ( p = 0.035) and tandem stance ( p = 0.012). When the posturograph was placed on the floor, statistically significantly higher sway area delimited by the COP point ( p < 0.001), statokinesiogram path length ( p < 0.001), mean amplitude of COP displacement ( p < 0.001) and mean frequency of COP displacement ( p = 0.048) values were recorded in the tandem stance position. On the other hand, when the posturograph was placed on a landing, statistically significantly higher sway area delimited by the COP point ( p < 0.001), statokinesiogram path length ( p < 0.001) and mean frequency of COP displacement ( p < 0.001) values were recorded in the tandem stance position. Increasing height was accompanied by deterioration of stability indices. Postural stability improves with training experience.

Improving Paleoseismic Earthquake Magnitude Estimates with Rupture Length Information: Application to the Puget Lowland, Washington State, U.S.A.

ABSTRACTBoth earthquake displacement and rupture length correlate with magnitude, and, therefore, observations of each from past earthquakes can be used to estimate the magnitude of those earthquakes in the absence of instrumental records. We extend the Bayesian inversion method of Biasi and Weldon (2006), which estimates paleoearthquake magnitude from displacement observations, to incorporate both rupture length and surface displacement measurements into the magnitude inversion. We then use this method on 27 late-Pleistocene to Holocene paleoearthquakes in the Puget Lowland region of Washington. Observations of (typically vertical) fault separation per event range from 0.6 to 7 m, implying net displacement per event of up to 10±4 m for the largest event. Rupture lengths are estimated to vary between the smallest contiguous mapped scarps to the full extent of the faults mapped from geology and geophysical observations. Although, a few of the ruptures may be longer than 150 km, the ruptures have a median of 53 km, indicating that earthquakes in the Puget Lowland have relatively high displacement-to-length ratios. By considering both datasets, we find that all events were between M 6.3 and 7.5, generally consistent with the expected seismicity from the U.S. Geological Survey National Seismic Hazard Map for the region. The simultaneous use of both length and displacement data in the magnitude inversion decreases both the estimated earthquake magnitudes and the uncertainty. The magnitude reduction, in particular, is due to the relatively short rupture lengths possible for Puget Lowland faults. This implies a decrease in the seismic hazard (relative to a displacement-only assessment) to a highly populated and rapidly urbanizing region.

Improving accuracy of volume penalised fluid-solid interactions

We analyse and improve the volume-penalty method, a simple and versatile way to model objects in fluid flows. The volume-penalty method is a kind of fictitious-domain method that approximates no-slip boundary conditions with rapid linear damping inside the object. The method can then simulate complex, moving objects in general numerical solvers without specialised algorithms or boundary-conforming grids. Volume penalisation pays for this simplicity by introducing an equation-level error, the model error, that is related to the damping time η≪1. While the model error has been proven to vanish as the damping time tends to zero, previous work suggests convergence at a slow rate of O(η1/2). The stiffness of the damping implies conventional volume penalisation only achieves first order numerical accuracy. We analyse the volume-penalty method using multiple-scales matched-asymptotics with a signed-distance coordinate system valid for arbitrary smooth geometries. We show the dominant model error stems from a displacement length that is proportional to a Reynolds number Re dependent boundary layer of size O(η1/2Re−1/2). The relative size of the displacement length and damping time leads to multiple error regimes. Our key finding derives a simple smoothing prescription for the damping that eliminates the displacement length and reduces the model error to O(η) in all regimes. This translates to second order numerical accuracy. We validate our findings in several comprehensive benchmark problems and finally combine Richardson extrapolation of the model error with our correction to further improve convergence to O(η2).

Nondestructive Determination of Fruit Surface Area Using Archimedean Buoyancy

Estimates of fruit surface area are often required in physiological and technological studies. The objective was to establish a procedure to accurately quantify the fruit surface area based on Archimedean buoyancy measurements. The setup comprised a fixed, linear stepper motor mounted with its spindle vertical and aligned directly above the pan of an electronic balance. A fruit was clamped to the motor spindle and a beaker of water rested on the balance pan. When the motor was activated, the fruit was progressively immersed, stepwise, in the water. Each vertical displacement step increased the buoyant upthrust on the fruit, which was opposed by a corresponding increase in the downthrust on the balance. Pairs of the step displacement length (mm) and corresponding buoyancy increment (g) values were recorded in an MS Excel (Microsoft, Redmond, WA) spreadsheet using Arduino components. Each displacement step immersed another “virtual slice” of the fruit in the water. From each pair of known displacement–buoyancy measurements, the volume (mL) of that slice could be calculated with high precision based on the known density of the liquid (g·mL−1). With the fruit orientated so that its morphological “long” axis was vertical, for most fruitcrop species, the slice can be assumed to have a circular cross-section. Hence, the slice can be analyzed geometrically as a truncated cone of known height (mm) and known volume (mL). Therefore, the surface area of its outer face is calculable. The surface area of the whole fruit was calculated as the cumulative total of the surface areas of all steps (virtual slices). The procedure was evaluated and calibrated using stainless-steel spheres in place of the fruit. However, the measured surface area was slightly greater than that calculated for a sphere. The calculated and measured areas did not differ by more than 1.7%. The surface area determinations were highly reproducible (cv = 0.95%). The magnitude of the displacement steps affected the variability of the surface area measurements. Increasing the step displacements decreased the measurement variability, but there were no significant effects on the surface area measurements of the surface tension of the liquid or of the wettability of the surface of the fruit or the stainless-steel subject. Using stainless-steel spheres (diameter, 5–60 mm) or rubber truncated cones (mean diameter, 8–45 mm) revealed an excellent agreement between the measured and calculated surface areas. Using tomatoes, grapes, blueberries, and strawberries, the measured surface areas were in excellent agreement with those calculated from the fruit dimensions and appropriate geometrical assumptions. The results demonstrate that the surface areas of fruit with approximately circular cross-sections normal to their morphological axes can be determined with high accuracy and reproducibility using Archimedean buoyancy.

Effects of bending stiffness and support excitation of the cable on cable rain-wind induced inclined vibration

The main objective of this paper is to investigate the responses of the inclined cable due to rain-wind induced vibration (RWIV) considering the bending stiffness and support excitation of the cable. The single-degree-of-freedom (SDOF) model is employed to determine the aerodynamic forces. The 3D model of a cable subjected to RWIV is developed using the linear theory of the cable oscillation and the central difference algorithm in which the influences of wind speed change according to the height above the ground, bending stiffness, and support excitation of the cable are considered. The numerical results showed that the cable displacement calculated by considering cable bending stiffness in RWIV is slightly smaller than in the case of neglecting it. And, the cable diameter had a nonlinear relationship with cable displacement, where when both diameter and mass per unit length of cable increase cable displacement will decrease. In addition, the periodic oscillation of cable supports extremely increases the amplitude of RWIV if its frequency is nearby that of the cable.&#x0D; Keywords:&#x0D; 3D model; inclined cable; rain-wind induced vibration; rivulet; analytical model; vibration.