printing). Cambridge: Cambridge University Press. Seebacher, F. 2001. A new method to calculate allometric length-mass relationships of dinosaurs. Journal of Vertebrate Paleontology 21, no. 1:5160. DOI: 10.1671/0272-4634(2001)021[0051:ANMTCA]2.0.CO;2. Sereno, P. C., H. C. E. Larsson, C. A Sidor, and B. Gado. 2001. The giant crocodyliform Sarcosuchus from the Cretaceous of Africa. Science 294, no. 5546:1516-1519. DOI: 10.1126/science.1066521. Shimada, K., M. J. Everhart, R. Decker, and P. D. Decker. 2010. A new skeletal remain of the durophagous shark, Ptychodus mortoni, from the Upper Cretaceous of North America: an indication of gigantic body size. Cretaceous Research 31, no. 2:249-254. DOI: 10.1016/j. cretres.2009.11.005. Shimada, K., M. F. Bonnan, M. A. Becker, and M. L. Griffiths. 2021. Ontogenetic growth pattern of the extinct megatooth shark Otodus megalodon – implications for its reproductive biology, development, and life expectancy. Historical Biology 33, no. 12:3254-3259. DOI: 10.1080/08912963.2020.1861608. Shirazi, M. 1972. Theory of Arterial Circulation. Wright-Patterson Air Force Base, OH: United States Aerospace Medical Research Laboratory. Smith, H. B. 2022. Wild West hermeneutics, Part 3: The patriarchal life spans. Bible and Spade 35, no. 3-4:42-52. Spiegel, M. R. 1994. Schaum’s Outline Series: Mathematical Handbook of Formulas and Tables. New York: McGraw-Hill. Stahl, W. R. 1967. Scaling of respiratory variables in mammals. Journal of Applied Physiology 22, no. 3: 453-460. DOI: 10.1152/jappl.1967.22.3.453. Tenney, S. M. and D. Bartlett, Jr. 1967. Comparative quantitative morphology of the mammalian lung: Trachea. Respiratory Physiology 3, no. 2:130-135. DOI: 10.1016.0034-5687(67)90002-3. Thomas, G. B., Jr. and R. L. Finney. 1988. Calculus and Analytic Geometry, 7th edition. Reading, Massachusetts: Addison-Wesley Publishing Company. Thompson, D. W. 1917. On Growth and Form. London: Cambridge University Press. Tomkins, J. P. 2019. Recent humans with archaic features upend evolution. Acts & Facts 48, no. 4 (April): 15. Tredennick, A. T., L. P. Bentley, and N. P. Hanan. 2013. Allometric convergence in savanna trees and implications for the use of plant scaling models in variable ecosystems. PLOS ONE 8, no. 3:1-11. DOI: 10.1371/ journal.pone.0058241. von Bertalanffy, L. 1938. A quantitative theory of organic growth (inquiries on growth laws II). Human Biology 10, no. 2:181-213. DOI: Weibel, E. R. 1972. Morphometric estimation of pulmonary diffusion capacity. V. Comparative morphometry of alveolar lungs. Respiration Physiology 14, no. 1:26-43. DOI: 10.1016/0034-5687(72)90015-1. Weibel, E. R. 1972. Morphometric estimation of pulmonary diffusion capacity. V. Comparative morphometry of alveolar lungs. Respiration Physiology 14, no. 1:26-43. DOI: 10.1016/0034-5687(72)90015-1. West, G. B. and J. H. Brown. 2005. The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. The Journal of Experimental Biology 208, no. 9:1575-1592. DOI: 10.1242/jeb.01589. West, G. B., J. H. Brown, and B. J. Enquist. 1997. A general model for the origin of allometric scaling laws in biology. Science 276, no. 5309:122126. DOI: 10.1126/science.276.5309.122 West, G. B., J. H. Brown, and B. J. Enquist. 2000. The origin of universal scaling laws in biology. In J. H. Brown and G. B. West (editors), Scaling in Biology, pp. 87-112. Oxford: Oxford University Press. West, G. B., J. H. Brown, and B. J. Enquist. 2001. A general model for ontogenetic growth. Nature 413, no. 6856:628-631. DOI: 10.1038/35098076. Whitcomb, J. C. and H. M. Morris. 1991. The Genesis Flood: The Biblical Record and Its Scientific Implications (35th printing). Phillipsburg, New Jersey: Presbyterian & Reformed Publishing Company. White, C. R. and R. S. Seymour. 2003. Mammalian basal metabolic rate is proportional to body mass2/3. Proceedings of the National Academy of Sciences 100, no. 7:4046-4049. DOI: 10.1073/pnas.0436428100. White, C. R. and R. S. Seymour. 2005. Review: Allometric scaling of mammalian metabolism. The Journal of Experimental Biology 208, no. 9:1611-1619. DOI: 10.1242/jeb.01501. Wieland, C. and J. D. Sarfati. 2011. Some bugs do grow bigger with higher oxygen. Journal of Creation 25, no. 1:13-14. Wintner, S P. and G. Cliff. 1999. Age and growth determination of the white shark, Carcharodon carcharias, from the east coast of South Africa. Fishery Bulletin 97, no. 1:153-169. Womersley, J. R. 1955. Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. Journal of Physiology 127, no. 3:553-563. DOI: 10.1113/jphysiol.1955.sp005276. Woodward, H. 2005. Bone histology of the sauropod dinosaur Alamosaurus sanjuanensis from the Javelina Formation, Big Bend National Park, Texas [masters thesis]. Lubbock, Texas: Texas Tech University. APPENDIX A: Optimization for Narrow Blood Vessels These derivations are included as “guideposts” to other researchers, as details of the derivations are not always clearly or succinctly explained in the literature. Appendices A through C primarily follow the methodology of Savage et al. (2008), as they include details omitted in the overview provided by WBE. For a fluid with viscosity μ the Hagen-Poiseuille formula gives the hydrodynamic resistance R to laminar, steady fluid flow in a short pipe of length l and radius r. One may derive the Hagen-Poiseuille expression by solving the Navier-Stokes equation (in cylindrical coordinates r, z, and ϕ) for steady-state (no time dependence, and no z-dependence of velocity upon position) laminar flow of an incompressible fluid in a short, azimuthally symmetric pipe. The fluid undergoes motion in only the z-direction and is subject to the boundary condition that fluid velocity at the pipe wall (r R) is zero. Solving this equation in cylindrical coordinates yields an expression for Δ in terms of current velocity ( ) in the z-direction. Averaging this over the cross-sectional area of the pipe yields an expression for the volume current flow Q ̇ : (A1) Physicists and electrical engineers will note the similarity between Eq. (A1) and the equation ΔV IR. Hence the expression for the hydrodynamic resistance R is (A2) For a hierarchical fluid distribution network with N + 1 levels of HEBERT Allometric and metabolic scaling 2023 ICC 223
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