Non-dimensional groups of measured quantities enable comparison between measurements of animals under different conditions and comparison between species. One of the most used such groups is the Reynolds number, which compares inertial and viscous contributions to forces on swimming animals. This group includes two quantities that are chosen by the researcher: a typical length and speed. Choosing these parameters will affect the numerical value of the Reynolds number, defining the state of the fluid flow. For example, by choosing fish body length as opposed to propulsive fin chord, results may vary by an order of magnitude with consequences for analysis and hydrodynamic regimes. Here, we suggest a standardized set of lengths and speeds to be used for aquatic animal locomotion to enable confident utilization of data from different sources. This framework aims to improve comparative studies within the field.

We present a novel method of measuring thrust of aquatic animals using in situ video data of swimming motions. To demonstrate its utility, the method was applied to several large elasmobranch species, which are typically highly challenging to measure. Using motion tracking software, we analyzed video footage of wild and captive sharks to track their instantaneous position and speed. In order to estimate the force output, we used the tail/body motion based on the swimming modes of the fish to calculate the water displaced by this motion during locomotion. Using Newton 3rd law, we have calculated the instantaneous force exerted by the water on the shark. The force output, that is thrust was calculated by averaging the instantaneous force over the tailbeat cycle. The thrust, for each fish was converted into a nondimensional parameter defined as: scaled thrust, allowing comparisons independent of size based on prior knowledge of the fish length and mass. This scaled thrust was analyzed for various swimming modes and caudal fin morphology to correlate to behavioral features through principal component analysis (PCA) we demonstrate the coupling between morphological traits and hydrodynamic forces. For the species studied the ratio of the upper to lower lobe of the caudal fin (CLAR) emerged as a strong predictor of scaled thrust, accounting for more than 80% of the observed variation. Our findings for the species studied indicate that coastal pelagic species exhibited lower scaled thrust values than benthic species, suggesting that benthic species may be less efficient, expending more energy to remain aloft or compensate for drag relative to generating forward motion. We propose that the unique ecological niches of these species drive behavioral changes that result in morphological adaptations to optimize performance.

Open AccessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Weihs Daniel 2023Comment on: 'The swim-and-sink behaviour of copepods: a revisit to mechanical power requirement and a new hypothesis on function' Jiang (2023)R. Soc. Open Sci.10231180231180http://doi.org/10.1098/rsos.231180SectionOpen AccessCommentComment on: 'The swim-and-sink behaviour of copepods: a revisit to mechanical power requirement and a new hypothesis on function' Jiang (2023) Daniel Weihs Daniel Weihs http://orcid.org/0000-0001-8992-6659 Department of Aerospace, Technion, Haifa, Israel [email protected] Contribution: Conceptualization, Writing – review & editing Google Scholar Find this author on PubMed Daniel Weihs Daniel Weihs http://orcid.org/0000-0001-8992-6659 Department of Aerospace, Technion, Haifa, Israel [email protected] Contribution: Conceptualization, Writing – review & editing Google Scholar Find this author on PubMed Published:04 October 2023https://doi.org/10.1098/rsos.231180This article comments on the following:Research ArticleThe swim-and-sink behaviour of copepods: a revisit to mechanical power requirement and a new hypothesis on functionhttps://doi.org/10.1098/rsos.230347 Houshuo Jiang volume 10issue 7Royal Society Open Science12 July 2023 Review history Review history is available via Web of Science at https://www.webofscience.com/api/gateway/wos/peer-review/10.1098/rsos.231180 A recent paper by Jiang [1] reviews the swim-and-sink (better known as hop and sink) behaviour of small invertebrates such as copepods. The main point in the paper above was to show that our 50 year old suggestion [2, p. 802], that, to quote 'alternating periods of active propulsion and passive gliding may be a common behaviour used in many diverse animals to conserve energy while maintaining a position against the force of gravity' is not correct for the copepods studied by Jiang. This conclusion would be acceptable if the analysis provided, which now is based on computational fluid dynamics (CFD), is itself, more accurate. Unfortunately, even CFD solutions can only be as accurate as the assumptions used as inputs, and when those are inaccurate, so is the result. In Jiang [1] constant speeds, and their ratio, are assumed for both the swim, and the sink phases of motion. This is obviously impossible as this requires infinite accelerations and decelerations at the turning points. The drag on animals of this size is highly speed dependent, as they move in a low Reynolds number transitional regime, so that the total force is not represented accurately anyway in a calculation assuming constant speeds, even when using averages. In reality, a sinusoidal variation of speed is probably a better approximation. The constant speed simplifying assumption cannot show the actual forces (and associated energies) accurately enough to shift the final conclusion from swim-and-sink saving energy, to costing extra energy. So, actually, it is still unclear, if hop and sink behaviour saves or wastes energy relative to continuous hovering in copepods. I hope that this can be determined definitively in future work, now that the capabilities of CFD allow this. Data accessibility This article has no additional data. Declaration of AI use I have not used AI-assisted technologies in creating this article. Authors' contributions D.W.: conceptualization, writing—review and editing. Conflict of interest declaration I declare I have no competing interests. Funding I received no funding for this study. Footnotes © 2023 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.References1. Jiang H. 2023 The swim-and-sink behaviour of copepods: a revisit to mechanical power requirement and a new hypothesis on function. R. Soc. Open Sci. 10, 230347. (doi:10.1098/rsos.230347) Link, ISI, Google Scholar2. Haury L, Weihs D. 1976 Energetically efficient swimming behavior of negatively buoyant zooplankton. Limnol. Oceanogr. 21, 797-803. (doi:10.4319/lo.1976.21.6.0797) Crossref, ISI, Google Scholar Comments Please enable JavaScript to view the comments powered by Disqus. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited byJiang H and Strickler J (2024) An Invited Reply to: A Comment on: 'The swim-and-sink behaviour of copepods: a revisit to mechanical power requirement and a new hypothesis on function' (2023), by Jiang, Royal Society Open Science, 11:1, Online publication date: 1-Jan-2024.Related articlesThe swim-and-sink behaviour of copepods: a revisit to mechanical power requirement and a new hypothesis on function12 July 2023Royal Society Open Science This IssueOctober 2023Volume 10Issue 10 Article InformationPublished by:Royal SocietyOnline ISSN:2054-5703History: Manuscript received10/08/2023Manuscript accepted11/09/2023Published online04/10/2023 License:© 2023 The Authors.Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Citations and impact Keywordsswimsinkbehaviourcopepodsmechanical Subjectsbiomathematicsbiomechanics

The Reynolds number, which describes the relative importance of viscous and inertial contributions is commonly used to analyze forces on fish and other aquatic animals. However, this number is based on steady, time-independent conditions, while all swimming motions have a periodic component. Here we apply periodic flow conditions to define a new non-dimensional group, which we name the “Periodic Swimming Number, P ”, which rectifies this lacuna. This new non-dimensional number embodies the periodic motion and eliminates the arbitrariness of choosing a length scale in the Reynolds number for Body –Caudal-Fin (BCF) swimming. We show that the new number has the advantage of compressing known data on fish swimming to two orders of magnitude, vs. over six required when using the existing Reynolds number and can point to a new comparison of swimming effectiveness for swimming modes.

The collision of two objects simultaneously moving at hypervelocity (> 5 km/s) speeds can result in terminal failure of both, a scenario that threatens functional space facilities. Performing a ballistic experiment when both are moving at such speeds is almost impossible under controlled conditions, necessitating prediction by numerical modeling. The models and experimental data appearing in the literature are limited to stationary targets. However, when both are moving at similar speeds, these are not sufficient. This paper investigates the hypervelocity glancing collision between a sphere and a tube moving in orthogonal paths at relative speeds of up to 20 km/s. The target damage is correlated with geometrical parameters of the model, including the projectile diameter and the target's wall thickness and curvature. The differences are most dominant when the projectile exceeds the wave velocity of the material for targets that are thicker than one-quarter of the projectile diameter. The results of this study indicate that, whereas the target's curvature of a stationary impact does influence the perforation damage patterns for a projectile velocity of the order of the wave velocity, the opposite occurs in glancing collisions, in which case the tubular target can be modeled by a planar one.

The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429–1450, 2018), Vermolen and Gefen (BMM 12:301–323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340–348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.

Damage to cylindrical shells, such as pipes and structural elements, that results from collision with supersonically moving particles is studied. Unlike existing work, we examine the effects of off-center impact, where the impactor hits at an angle to the cylinder diameter at the point of contact. A numerical assessment of damage and perforation patterns is calculated. New types of damage patterns, including cases of breakup and ricocheting impactors are shown and discussed.

Enabling a leading-edge vortex (LEV) is a possible mechanism to significantly increase the lift on wings. This is well known for slender delta wings, for which various analytical models were developed and show accurate predictions of the lift enhancement. This paper shows that, when suitably designing the wing planform, LEVs can also exist on high-aspect-ratio (high-AR) wings. In this study, a quasi-three-dimensional flow model is presented for solving the stationary LEV phenomenon over a high-AR swept back wing, with sweep increasing toward the wingtip. Our model captures the three-dimensional phenomenon by satisfying conservation of mass and vorticity within the LEV, and using a combination of strip theory and the lifting-line theory. Our model predictions are compared with flow visualization data on a parabolic swept back wing. Results confirm that suitable sweep wing geometry can fix an LEV steadily over the upper wing surface, resulting in significant lift enhancement of up to 70%.

The collisions of space debris, whether human-origin or natural, and spacecraft are essentially hypervelocity impacts. Such collisions pose a serious threat to satellites and spacecraft. While multiple studies, both theoretical and experimental, have dealt with such collisions, none has thoroughly considered the effect of the target's motion during penetration. This results in a different type of collision, beyond normal or oblique penetration, referred to as glancing collision in this work. This paper studies numerically the effects of such glancing collisions, in which the speeds of both participants are of the same order of magnitude, and not collinear. As an example a simulation of a collision between a projectile moving at 2-10 km/s and a finite target plate moving at 10 km/s laterally, both made of 6061-T6 alloy, also compared to experimental data. The resulting damage is compared to that caused by normal, including comparison with existing experimental data, as well as oblique impact by projectiles at the same velocities where the target is stationary. Two types of projectiles were considered: a sphere and a short cylinder having a hemispherical head. The investigation reveals that glancing collisions result in vastly different craters' shapes and damage patterns with respect to normal collisions. The craters become shallower and more elongated and the damage is not axisymmetric. While the glancing collision is similar to oblique collision for spherical projectiles, it becomes vastly different for elongated non-spherical projectiles.

We provide an innovative, bioengineering, mechanobiology-based approach to rapidly (2-h) establish the in vivo metastatic likelihood of patient tumor-samples, where results are in direct agreement with clinical histopathology and patient outcomes. Cancer-related mortality is mostly due to local recurrence or to metastatic disease, thus early prediction of tumor-cell-fate may critically affect treatment protocols and survival rates. Metastasis and recurrence risks are currently predicted by lymph-node status, tumor size, histopathology and genetic testing, however, these are not infallible and results may require days/weeks. We have previously observed that subpopulations of invasive cancer-cells will rapidly (1–2 h) push into the surface of physiological-stiffness, synthetic polyacrylamide gels, reaching to cell-scale depths, while normal or noninvasive cells do not considerably indent gels. Here, we evaluate the mechanical invasiveness of established breast and pancreatic cell lines and of tumor-cells from fresh, suspected pancreatic cancer tumors. The mechanical invasiveness matches the in vitro metastatic potential in cell lines as determined with Boyden chamber assays. Moreover, the mechanical invasiveness directly agrees with the clinical histopathology in primary-site, pancreatic-tumors. Thus, the rapid, patient-specific, early prediction of metastatic likelihood, on the time-scale of initial resection/biopsy, can directly affect disease management and treatment protocols.

The main cause (90%) of cancer-related deaths is due to metastasis, spreading of cancer to distant sites in the body. Metastasis requires cells to dynamically adapt to the changing environments tha...

No AccessSurvey PapersNovel Propulsion Systems for Micro Aerial VehiclesA. Lidor, D. Weihs and E. SherA. LidorTechnion—Israel Institute of Technology, Haifa 3200003, Israel, D. WeihsTechnion—Israel Institute of Technology, Haifa 3200003, Israel and E. SherTechnion—Israel Institute of Technology, Haifa 3200003, IsraelPublished Online:28 Oct 2018https://doi.org/10.2514/1.B36930SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail About References [1] McMichael J. and Francis M., "Micro Air Vehicles—Toward a New Dimension in Flight," Defense Advanced Research Projects Agency, TTO Document, 1997, pp. 1–9, https://fas.org/irp/program/collect/mav.htm [retrieved 2 Feb. 2013]. Google Scholar[2] Francis M. 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All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the ISSN 0748-4658 (print) or 1533-3876 (online) to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsElectric GeneratorsElectrochemical CellsEnergyEnergy ConversionEnergy FormsEnergy Forms, Production and ConversionEnergy ProductionEnergy StorageEnergy Storage and BatteriesFuel CellsHeat EnginesInternal Combustion EnginesPower StationThermoelectric Generators KeywordsPropulsion SystemEnergy DensityPhase Change MaterialsStatistical ThermodynamicsAerospace EngineeringGerman Aerospace CenterDamage AssessmentProton Exchange Membrane Fuel CellsLatent Heat Thermal Energy StorageBrake Specific Fuel ConsumptionPDF Received26 September 2017Accepted5 August 2018Published online28 October 2018

The flowfield resulting from a starting source type singularity is presented. This is a generalization of the classical source in potential flow to time dependent situations, including sources in oncoming flow. This model is applicable to initial spreading of oil on the surface of the sea resulting from an underwater leak

Pied kingfishers ( Ceryle rudis ) capture fish by plunge diving from hovering that may last several minutes. Hovering is the most energy-consuming mode of flight and depends on active wing flapping and facing headwind. The power for hovering is mass dependent increasing as the cube of the size, while aerodynamic forces increase only quadratically with size. Consequently, birds above a certain body mass can hover only with headwind and for very short durations. Hummingbirds are referred to as the only birds capable of hovering without wind (sustained hovering) due to their small size (ca. 2-20 gr), high wing-beat frequency and unique anatomy. We studied the hovering characteristics of pied kingfishers in relation to wind and sun orientation, in 139 hovers. Furthermore, plunge diving necessitates the coping with the visual effects of light at the air/water interface. The kingfishers oriented their body axis towards the wind more than towards the sun. Hovering in little or no wind was common. With increased wind speed (a) orientation precision increased, (b) wing beat amplitude did not change, (c) wing beat frequency decreased and (d) body tilt became more horizontal. The head was highly stabilized and with orientations that indicated monocular viewing of prey. We conclude that pied kingfishers achieve sustained hovering. This is despite their being significantly heavier than the theoretical maximum and showing ordinary kinematics and morphology. Head stabilization is a means of aiding viewing of submerged prey across the interface.

We present here a novel explanation for the explosion limits phenomenon, based on the concept of thermodynamic stability analysis of the fuel-oxidizer mixture. This concept is demonstrated by a detailed statistical thermodynamic analysis of the explosion limits of the H-2-O-2 system. It is shown that while the magnitude of the relative fluctuations in the number of molecules is very small, the reactants approach their thermodynamic stability limit at the explosion limit, thus contributing to the onset of self-ignition. It is also found out that the products (H2O) behave in an opposite manner, being on the verge of stability in the non-explosive region, and becoming stable above the explosion limit. The different chain-carriers are on the verge of thermodynamic stability over the complete range (both explosive and non-explosive regions), a fact that sits well with their short residence time as known from chemical kinetics and experiments. We conclude that the unique nature of the branching limits phenomenon can be considered as a thermodynamic stability problem, promoting the idea that a universal self-ignition criterion can be developed. (C) 2018 Elsevier Ltd. All rights reserved.

We propose a mathematical formalism and method for simulating the effects of the mechanochemical environment on the differentiation path and fate of stem cells. We provide a numerical methodology used for the numerical approximation of solutions of partial differential equations, based on a finite element approach, to describe the time evolution and spatial distribution of chemical and mechanical signals. Further, all cells are considered as independent entities, which may migrate through the domain of computation and which are subject to differentiation, division, and evolution of geometry. The model is applied to the development of adipose and muscle tissue. The developed framework is generic and can be applied to other similar biological processes and medical applications.

We propose a unified model for the three branches of the explosion limits of an H2–O2 mixture. By using different expressions for the ignition delay time at each limit, and by utilizing the Le-Chatelier rule, we obtain an analytical expression for the ignition delay time of the mixture. We show that by solving the time delay equation for a selected typical ignition delay time we obtain a single expression for the Z-shape explosion limits.

Salps are marine invertebrates comprising multiple jet-propelled swimming units during a colonial life-cycle stage. Using theory, we show that asynchronous swimming with multiple pulsed jets yields substantial hydrodynamic benefit due to the production of steady swimming velocities, which limit drag. Laboratory comparisons of swimming kinematics of aggregate salps ( Salpa fusiformis and Weelia cylindrica ) using high-speed video supported that asynchronous swimming by aggregates results in a smoother velocity profile and showed that this smoother velocity profile is the result of uncoordinated, asynchronous swimming by individual zooids. In situ flow visualizations of W. cylindrica swimming wakes revealed that another consequence of asynchronous swimming is that fluid interactions between jet wakes are minimized. Although the advantages of multi-jet propulsion have been mentioned elsewhere, this is the first time that the theory has been quantified and the role of asynchronous swimming verified using experimental data from the laboratory and the field.