A universal formula for avian egg shape

Narushin, Valeriy G.; Romanov, Michael N; Griffin, Darren K.

doi:10.1101/2020.08.15.252148

Cited by 4 publications

(5 citation statements)

References 18 publications

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“…The research, described the bird eggs by indexes derived from photographic egg profiles was continuing (Mattas, 2001;Tlapák, 2008;Duman et al, 2016;Biggins et al, 2018). The new works dealing with egg description by equations and formulas began to appear (Möller, 2009;Narushin et al, 2020), this geometric morphometry has gained particular popularity in the oology (Deeming & Ruta, 2014;Attard et al, 2019). Recently, some articles, dedicated to the connection between the egg shapes and their biological significance, were published (Stoddard et al, 2017;Birkhead et al, 2018).…”

Section: Discussionmentioning

confidence: 99%

<span>Mathematical interpretation of avian egg shapes</span>

et al. 2020

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The general principles of ovoid shapes and their mathematical interpretation were considered concerning previous data and experience. Previously, bird egg description was carried out using the composite ovoid model. According to this model, an ovoid is considered as a set of arcs with a smooth transition between them. The studied group of eggs was named true ovoid. They differ from other forms in size of their infundibular zone radius (thick end) that is almost equal to half of the diameter (0.5D ± 0.01 ˂ ri = 0.5D).We suggested that this commonality, a priori, implies the presence of an abstract geometric model, which is a satisfactory solution and logical approach for analyzing the diversity of natural ovoids. Such a model is a system of circles passing into each other. This allows, within a single system, to assign a vendor code to each form, which involves the name, geometric shape, and quantitative parameters that can be implemented in bird taxonomy.Early, 0.01 D was chosen as the model difference value and the ratio of symmetrical eggs in the analyzed database was 1.1%. In this research, we extended the difference value to 0.05 D and this covered 6.0% of the egg shapes. This is the maximum interval at which the curvature of the polar zones does not visually differ. We revealed that the variability in the egg shapes depends on the radii of curvature of the lateral and polar arcs. The larger the radius of the lateral arches, the greater the degree of freedom for variation of the lateral arches. We supposed that our data could associate any form of bird egg with its biological content. In turn, many ovoid features relevant to other natural objects can be used in bird taxonomical study.

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Section: Discussionmentioning

confidence: 99%

<span>Mathematical interpretation of avian egg shapes</span>

et al. 2020

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“…For determining the limits for w/L, we used the theoretical background of Obradović et al (2013) who studied modifications of the geometric contours of Hügelschäffer's model as well as our own results (Narushin et al, 2020c). Accordingly, the minimal value of w is 0 (in this case the Hügelschäffer's ovoid is transformed in the ellipsoid) and the maximum one is not more than wmax = (L -B)/2, wherefrom the maximum possible value of w/L for any avian egg does not exceed 0.25.…”

Section: Methodsmentioning

confidence: 99%

Non-destructive measurement of chicken egg characteristics: Improved formulae for calculating egg volume and surface area

Narushin¹,

Romanov

Griffin

2021

Biosystems Engineering

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“…The surface energy may be estimated as E 1 = C 1 h γ, with C 1 representing the circumference of an asymmetric ellipse that has the same semimajor and semiminor axis lengths as the droplet, but “egg” shaped, formally known as Hügelschäffer's ovoid. The following equation was employed for this purpose, [ 43,47 ]

{((), \frac{x}{a})}^{2} + {((), \frac{y}{b}, {normale}^{c x})}^{2} = 1,

with c = 0.35 to match the asymmetric shape of the observed droplet in this state. The circumference of this shape is given by

C_{1} = 2 \int_{- a}^{a} \sqrt{{(() 1 - \frac{x^{2}}{a^{2}})}^{- 1} b^{2} {normale}^{- 2 c x} {(() \frac{c x^{2}}{a^{2}} - \frac{x}{a^{2}} - c)}^{2} + 1} d x,

and there is no known approximate solution to this equation.…”

Section: Methodsmentioning

confidence: 99%

“…The surface energy may be estimated as E 1 = C 1 h𝛾, with C 1 representing the circumference of an asymmetric ellipse that has the same semimajor and semiminor axis lengths as the droplet, but "egg" shaped, formally known as Hügelschäffer's ovoid. The following equation was employed for this purpose, [43,47] ( x a…”

Section: (A1))mentioning

confidence: 99%

Manipulation and Mixing of 200 Femtoliter Droplets in Nanofluidic Channels Using MHz‐Order Surface Acoustic Waves

2021

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Controllable manipulation and effective mixing of fluids and colloids at the nanoscale is made exceptionally difficult by the dominance of surface and viscous forces. The use of megahertz (MHz)-order vibration has dramatically expanded in microfluidics, enabling fluid manipulation, atomization, and microscale particle and cell separation. Even more powerful results are found at the nanoscale, with the key discovery of new regimes of acoustic wave interaction with 200 fL droplets of deionized water. It is shown that 40 MHz-order surface acoustic waves can manipulate such droplets within fully transparent, high-aspect ratio, 100 nm tall, 20-130 micron wide, 5-mm long nanoslit channels. By forming traps as locally widened regions along such a channel, individual fluid droplets may be propelled from one trap to the next, split between them, mixed, and merged. A simple theory is provided to describe the mechanisms of droplet transport and splitting.

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A universal formula for avian egg shape

Cited by 4 publications

References 18 publications

<span>Mathematical interpretation of avian egg shapes</span>

<span>Mathematical interpretation of avian egg shapes</span>

Non-destructive measurement of chicken egg characteristics: Improved formulae for calculating egg volume and surface area

Manipulation and Mixing of 200 Femtoliter Droplets in Nanofluidic Channels Using MHz‐Order Surface Acoustic Waves

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