scholarly journals Mathematical interpretation of artificial ovoids and avian egg shapes (part I)

2019 ◽  
Vol 10 (1) ◽  
pp. 92-102
Author(s):  
I. S. Mytiai ◽  
A. V. Matsyura
Keyword(s):  
Computer Software ◽  
Vertical Axis ◽  
Small Radius ◽  
Radius Of Curvature ◽  
Lateral Side ◽  
Horizontal Line ◽  
Large Radius ◽  
Geometrical Figure ◽  
The Real ◽  
Bird Eggs

We performed comparative analysis of curvature characteristics of bird eggs and used ovoid profiles from various authors, our own geometric profiles, and archive bird egg profiles from our database. We suggested that the possible ovoids arise by changing the curvature radii of the polar and lateral zones. We compared the constructed curves and curves presented in oological literature with the pictures of the real bird egg profiles. The volume of actual material includes 16,490 eggs from 800 species of 20 bird orders. Specially designed computer software had calculated the radius of curvature of real bird eggs from photos and drew out the half-profiles presented in our article. We supposed that the asymmetrical ovoid is the most widespread geometric egg-shaped figure, which can easily be obtained by combination of circles. We also calculated that if the ovoid diameter were taken as a unit, then the radius obtuse (infundibular) pole would be equal to its half-length, lateral (side arcs) is equal two lengths, and the cloacal arch is 1–√2/2. From this suggestion, we concluded that the length of the ovoid is 2–√2/2 and its cloacal radius is equal to the difference between the length of ovoid and its diameter (rc = L–D). We analyzed the geometry of this asymmetrical oval and came to the conclusion that this is the basic form able to generate the derivative forms. We discovered that the centres of the arcs which form it lie on one basic/supporting circle, the diameter of which is equal to the ovoid diameter. All other ovoids, which have radius equal to radius of the infundibular zone we called the real ovoids. The changes in the radii of the lateral arcs are caused by the movement of their centres along a horizontal line passing through the centre of the base circle. This causes the prolongation or shortening of the ovoids. Sizes of cloacal arcs depended on the lateral, and their centres are placed along the vertical axis. Variability of the sizes of the abovementioned arcs caused the variability of form of the bird eggs. For their classification, we have proposed to divide them into five groups: sphere-like, circle, obtuse, droplet, and cone-shaped. Further, we separated some more groups: short, shortened, normal, lengthened, and long; according to the sizes of cloacal arcs – large radius, middle radius, and small radius ovoids. As a result, we have 80 forms of real ovoids – standards which describe the varieties of bird eggs. Each of them has its own number, name, geometrical figure, polynomic equation, and correlations of ovoid parameters. This set of ovoids is sufficient to describe the specifics of any form of bird eggs.

scholarly journals COMPARATIVE ANALYSIS OF MAMMALIAN SPERM MOTILITY

1972 ◽  
Vol 53 (2) ◽  
pp. 561-573 ◽  
Author(s):  
David M. Phillips
Keyword(s):  
High Speed ◽  
Mammalian Species ◽  
Chinese Hamster ◽  
Small Radius ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Cross Sectional ◽  
Mammalian Sperm ◽  
High Speed Cinematography ◽  
Pass Through

Spermatozoa of several mammalian species were studied by means of high-speed cinematography and electron microscopy. Three types of motile patterns were observed in mouse spermatozoa. The first type involved an asymmetrical beat which seemed to propel the sperm in circular paths. The second type involved rotation of the sperm and appeared to allow them to maintain straight paths. In the third type of pattern, the sperm appeared to move by crawling on surfaces in a snakelike manner. Spermatozoa of rabbit and Chinese hamster also had an asymmetrical beat which sometimes caused them to swim in circles. In spite of the asymmetry of the beat, these spermatozoa were also able to swim in straight paths by rotating around a central axis as they swam. Spermatozoa of some species appeared very flexible; their flagella formed arcs with a very small radius of curvature as they beat. Spermatozoa of other species appeared very stiff, and their flagella formed arcs with a very large radius of curvature. The stiffness of the spermatozoan appeared to correlate positively with the cross-sectional area of the dense fibers. This suggests that the dense fibers may be stiff elastic elements. Opossum sperm become paired as they pass through the epididymis. Pairs of opossum spermatozoa beat in a coordinated, alternating manner.

scholarly journals Identification of Apical and Cervical Curvature Radius of Human Molars

2015 ◽  
Vol 26 (4) ◽  
pp. 351-356 ◽  
Author(s):  
Carlos Estrela ◽  
Mike R. Bueno ◽  
Fernando B. Barletta ◽  
Orlando A. Guedes ◽  
Olavo C. Porto ◽  
...  
Keyword(s):  
Sagittal Plane ◽  
Small Radius ◽  
Radius Of Curvature ◽  
Curvature Radius ◽  
Large Radius ◽  
Chi Square ◽  
Root Canals ◽  
Plane Analysis ◽  
Chi Square Test ◽  
Curved Root Canals

<p>To determine the frequency of apical and cervical curvatures in human molars using the radius method and cone-beam computed tomography (CBCT) images. Four hundred images of mandibular and maxillary first and second molars were selected from a database of CBCT exams. The radius of curvature of curved root canals was measured using a circumcenter based on three mathematical points. Radii were classified according to the following scores: 0 - straight line; 1 - large radius (r>8 mm, mild curvature); 2 - intermediate radius (r>4 and r<8 mm, moderate curvature); and 3 - small radius (r≤4 mm, severe curvature). The frequency of curved root canals was analyzed according to root canal, root thirds, and coronal and sagittal planes, and assessed using the chi-square test (significance at α=0.05). Of the 1,200 evaluated root canals, 92.75% presented curved root canals in the apical third and 73.25% in the cervical third on coronal plane images; sagittal plane analysis yielded 89.75% of curved canals in the apical third and 77% in the cervical third. Root canals with a large radius were significantly more frequent when compared with the other categories, regardless of root third or plane. Most root canals of maxillary and mandibular first and second molars showed some degree of curvature in the apical and cervical thirds, regardless of the analyzed plane (coronal or sagittal).</p>

Study of Insertion Force and Deformation for Suturing With Precurved NiTi Guidewire

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Yancheng Wang ◽  
Roland K. Chen ◽  
Bruce L. Tai ◽  
Kai Xu ◽  
Albert J. Shih
Keyword(s):  
Experimental Study ◽  
Minimally Invasive ◽  
Ex Vivo ◽  
Nickel Titanium ◽  
Small Radius ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Position Measurement ◽  
Insertion Force ◽  
Before And After

This research presents an experimental study evaluating stomach suturing using a precurved nickel–titanium (NiTi) guidewire for an endoscopic minimally invasive obesity treatment. Precise path planning is critical for accurate and effective suturing. A position measurement system utilizing a hand-held magnetic sensor was used to measure the shape of a precurved guidewire and to determine the radius of curvature before and after suturing. Ex vivo stomach suturing experiments using four different guidewire tip designs varying the radius of curvature and bevel angles were conducted. The changes in radius of curvature and suturing force during suturing were measured. A model was developed to predict the guidewire radius of curvature based on the measured suturing force. Results show that a small bevel angle and a large radius of curvature reduce the suturing force and the combination of small bevel angle and small radius of curvature can maintain the shape of guidewire for accurate suturing.

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

Coexistence of large-radius and small-radius polaron states in a quantum wire

1995 ◽  
Vol 17 (11-12) ◽  
pp. 1723-1728
Author(s):  
Y. Shinozuka ◽  
N. Ishida
Keyword(s):  
Quantum Wire ◽  
Small Radius ◽  
Large Radius

Résonateur ouvert en géométrie sphérique

1980 ◽  
Vol 58 (1) ◽  
pp. 80-86 ◽  
Author(s):  
Gilles Duret ◽  
Gérard Zepp ◽  
Alain Wick
Keyword(s):  
Radius Of Curvature ◽  
Large Radius ◽  
Open Resonators

Most of the approximate theories of the spherical open resonators are insufficient, except for the very large radius of curvature. It is often necessary to consider other cases. The theory we have developed is applicable for any curvature and aperture of the mirrors. This theory also allows study of multi-dielectric cavities. This method is accurately studied in detail in this paper.

scholarly journals Triple Oxygen Isotope Measurements by Multi-Collector Secondary Ion Mass Spectrometry

2021 ◽  
Vol 8 ◽  
Author(s):  
Nordine Bouden ◽  
Johan Villeneuve ◽  
Yves Marrocchi ◽  
Etienne Deloule ◽  
Evelyn Füri ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Oxygen Isotope ◽  
Spatial Resolution ◽  
Secondary Ion Mass Spectrometry ◽  
Small Radius ◽  
Large Radius ◽  
Ion Mass Spectrometry ◽  
Secondary Ion ◽  
Isotope Measurements

Secondary ion mass spectrometry (SIMS) is a powerful technique for in situ triple oxygen isotope measurements that has been used for more than 30 years. Since pioneering works performed on small-radius ion microprobes in the mid-80s, tremendous progress has been made in terms of analytical precision, spatial resolution and analysis duration. In this respect, the emergence in the mid-90s of the large-radius ion microprobe equipped with a multi-collector system (MC-SIMS) was a game changer. Further developments achieved on CAMECA MC-SIMS since then (e.g., stability of the electronics, enhanced transmission of secondary ions, automatic centering of the secondary ion beam, enhanced control of the magnetic field, 1012Ω resistor for the Faraday cup amplifiers) allow nowadays to routinely measure oxygen isotopic ratios (18O/16O and 17O/16O) in various matrices with a precision (internal error and reproducibility) better than 0.5‰ (2σ), a spatial resolution smaller than 10 µm and in a few minutes per analysis. This paper focuses on the application of the MC-SIMS technique to the in situ monitoring of mass-independent triple oxygen isotope variations.

Experimental and Computational Investigation of Shaped Film Cooling Holes Designed to Minimize Inlet Separation

2020 ◽  
Author(s):  
Fraser B. Jones ◽  
Dale W. Fox ◽  
David G. Bogard
Keyword(s):  
Film Cooling ◽  
Velocity Ratio ◽  
Tangential Velocity ◽  
Velocity Fields ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Combustion Gases ◽  
Shaped Hole ◽  
Manufacturing Technologies ◽  
Film Cooling Holes

Abstract Film cooling is used to protect turbine components from the extreme temperatures by ejecting coolant through arrays of holes to create an air buffer from the hot combustion gases. Limitations in traditional machining meant film cooling holes universally have sharp inlets which create separation regions at the hole entrance. The present study uses experimental and computational data to show that these inlet separation are a major cause of performance variation in crossflow fed film cooling holes. Three hole designs were experimentally tested by independently varying the coolant velocity ratio (VR) and the coolant channel velocitty ratio (VRc) to isolate the effects of crossflow on hole performance. Leveraging additive manufacturing technologies, the addition of a 0.25D radius fillet to the inlet of a 7-7-7 shaped hole is shown to significantly improve diffuser usage and significantly reduce variation in performance with VRc. A second AM design used a very large radius of curvature inlet to reduce biasing caused by the inlet crossflow. Experiments showed that this “swept” hole design did minimize biasing of coolant flow to one side of the shaped hole and it significantly reduced variations due to varying VRc. RANS simulations at six VR and three VRc conditions were made for each geometry to better understand how the new geometries changed the velocity field within the hole. The sharp and rounded inlets were seen to have very similar tangential velocity fields and jet biasing. Both AM inlets created more uniform, slower velocity fields entering the diffuser. The results of this paper indicate large improvements in film cooling performance can be found by leveraging AM technology.

scholarly journals Disk Structure in U Geminorum

1977 ◽  
Vol 42 ◽  
pp. 313-321
Author(s):  
J. Madej ◽  
B. Paczyński
Keyword(s):  
Angular Momentum ◽  
Hot Spot ◽  
Outer Part ◽  
Tangential Velocity ◽  
Radial Component ◽  
Small Radius ◽  
Large Radius ◽  
Disk Structure ◽  
Orbital Periods ◽  
The Difference

AbstractA hot spot at the outer rim of the accretion disk dominates the light of U Geminorum at minimum light. We take this as evidence that there is no accretion from the disk onto the white dwarf between the eruptions, and we assume there is no viscosity in the disk at that time. The hot spot is produced by dissipation of the radial component of velocity of stream falling from the inner Lagrangian point. Angular momentum per unit massis smaller in the stream than it is in the outer parts of the disk. This leads to angular momentum redistribution in the outer part of the disk. The difference of tangential velocity between the stream and the disk is dissipated in few orbital periods. These processes make the outer parts of the disk look like a torus. We calculated the structure of the torus in U Geminorum between the eruptions and we obtained the following oarameters: mass of the torus: 10-9 - 10-8 M⊙ (assumed), its optical thickness: 106, the large radius (i.e. the radius of the disk): 0.5 R⊙ (assumed), the small radius (i.e. the half thickness of the outer parts of the disk): 0.05 R⊙. Conditions at the surface of the torus are similar as on the solar surface.

Intershield geochemical differences among Hawaiian volcanoes: implications for source compositions, melting process and magma ascent paths

1993 ◽  
Vol 342 (1663) ◽  
pp. 121-136 ◽  
Keyword(s):  
Melting Process ◽  
Isotope Ratios ◽  
Magma Ascent ◽  
Small Radius ◽  
Element Abundance ◽  
Isotopic Ratios ◽  
Large Radius ◽  
Major Element Composition ◽  
Mauna Loa ◽  
Melt Segregation

As Hawaiian volcanoes develop, their lavas systematically change in composition and isotopic ratios of Sr, Nd and Pb. These trends provide important constraints for understanding plume-related volcanism as a volcano migrates away from the hotspot. There are also geochemical differences between Hawaiian shields. In particular, lavas from adjacent shields such as Kilauea and Mauna Loa on Hawaii and Koolau and Waianae on Oahu have significant differences in abundances of some major and incompatible elements and isotopic ratios of Sr, Nd and Pb. Some incompatible element abundance ratios, such as Zr/Nb and Sr/Nb, are correlated with intershield differences in Sr and Nd isotope ratios, but these isotopic ratios are not correlated with intershield differences in major element composition, or even parent/daughter abundance ratios such as Rb/Sr and Sm/Nd. Moreover, at Kilauea and Mauna Loa the intershield differences have apparently persisted for a relatively long time, perhaps 100 ka. These intershield geochemical differences provide important constraints on plume volcanism. Specifically, (i) each volcano must have distinct magma ascent paths from the region of melt segregation; (ii) the 25-50 km distance between adjacent, but geochemically distinct, shields requires that the sources vary on a similar scale, and that the melt production region is similarly restricted. The absence of correlations between lava compositions and radiogenic isotope ratios provides evidence for significant differences in melting process such as each shield forming by a different mean extent of melting with melt segregation at different mean pressures. Two types of models are consistent with the intershield geochemical differences: (i) a relatively large radius, ca . 40 km, plume conduit with a systematic spatial distribution of geochemical heterogeneities; or (ii) a small radius, less than 20 km, plume conduit composed of geochemically distinct diapirs. Because relatively small radius diapirs of limited vertical extent are too small to create the large Hawaiian shields, a possible alternative is a continuous conduit containing solitary waves which transport geochemically distinct packets of material.

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