Fluid flow in a porous tree-shaped network: Optimal design and extension of Hess–Murray’s law

Miguel, António F.

doi:10.1016/j.physa.2014.12.025

Cited by 33 publications

(32 citation statements)

References 29 publications

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“…This dichotomous branching follows the relationship known in physiology as the Hess-Murray law [29,30] . The idea behind this law is that the diameters of parent and two equal daughter tubes are related as 2 1/3 [31] .…”

Section: Tree Network Of Airwaysmentioning

confidence: 80%

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Penetration of inhaled aerosols in the bronchial tree

Miguel

2017

Medical Engineering & Physics

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Section: Tree Network Of Airwaysmentioning

confidence: 80%

“…The respiratory tree consists of a network of tubes in which each tube splits into two daughter tubes [8,29,30] . This dichotomous branching follows the relationship known in physiology as the Hess-Murray law [29,30] .…”

Section: Tree Network Of Airwaysmentioning

confidence: 99%

Penetration of inhaled aerosols in the bronchial tree

Miguel

2017

Medical Engineering & Physics

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“…The total number of daughter tubes within level i is 2 i (Miguel 2015(Miguel , 2016, and the relationship between the size of the first tube (level 0) and the size of the tube at level i is given by…”

Section: Binary Asymmetric Tree Modelmentioning

confidence: 99%

“…Most branching flow studies available in the literature assume a symmetric or quasi-symmetric branching (Schreiner et al, 1996;Schreiner et al, 1997;Kaimovitz et al, 2008;Bejan and Lorente, 2008;Miguel, 2013bMiguel, , 2015Kasimova et al, 2014). Asymmetry means daughter branches with different sizes.…”

Section: Introductionmentioning

confidence: 99%

Toward an optimal design principle in symmetric and asymmetric tree flow networks

Miguel

2016

Journal of Theoretical Biology

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“…To the animate and inanimate examples (animal locomotion, river basins, turbulence) that were unified as a phenomenon of free-morphing flow design for greater access over time, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] we are now adding examples that belonged traditionally to solid mechanics. For example, the natural occurrence of hexagonal basalt columns is attributed to a principle of maximum energy release.…”

Section: Introductionmentioning

confidence: 99%

The physics origin of the hierarchy of bodies in space

Bejan

Wagstaff

2016

Journal of Applied Physics

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The physical origin of torque and of the rotational second law Am. J. Phys. 83, 121 (2015); 10.1119/1.4896574Rotating frame analysis of rigid body dynamics in space phasor variables Am. J. Phys. 81, 518 (2013) Here we show that bodies of the same size suspended uniformly in space constitute a system (a "suspension") in a state of uniform volumetric tension because of mass-to-mass forces of attraction. The system "snaps" hierarchically, and evolves faster to a state of reduced tension when the bodies coalesce spontaneously nonuniformly, i.e., hierarchically, into few large and many small bodies suspended in the same space. Hierarchy, not uniformity, is the design that emerges, and it is in accord with the constructal law. The implications of this principle of physics in natural organization and evolution are discussed. V C 2016 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4941986] INTRODUCTIONRecent progress on the physics basis of evolutionary organization in nature 1,2 continues to bring together phenomena that were previously considered unrelated. To the animate and inanimate examples (animal locomotion, river basins, turbulence) that were unified as a phenomenon of free-morphing flow design for greater access over time, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] we are now adding examples that belonged traditionally to solid mechanics. For example, the natural occurrence of hexagonal basalt columns is attributed to a principle of maximum energy release. 19 The occurrence of cracks in solids is based on the same principle. [20][21][22] Soil cracking under the drying wind was explained as a phenomenon of evolutionary design that enhances mass flow and accelerates drying. 23 The aggregation of dust particles into clusters and dendrites was shown to be the result of the same tendency, to relieve electrostatic forces of attraction faster, through the evolutionary design of configuration. 24 Here we add to this growing list of evolutionary phenomena the natural occurrence of multi-size hierarchy of bodies suspended in space. The hierarchy of sizes is researched intensely and described regularly in planetary science and astrophysics. [25][26][27][28][29][30][31] Hierarchy emerges in two ways, through accretion (coalescence) and fragmentation resulting from collisions. Viewed from thermodynamics, 32 the system of bodies in space is in a state of internal tension because of gravitational attraction between neighboring bodies. This system "snaps" freely by flowing internally and changing its configuration. Bodies coalesce into larger bodies, and their collision (with fragmentation) dissipates the tension and resulting kinetic energy, en route to reduced body-body attraction throughout the system. This phenomenon has been studied in celestial mechanics under several scenarios, [25][26][27] and is recognized as the basis for the formation process of planets and the asteroid belt.Sizes increase over all scales through accretion. 31 Yet, the natural phenomenon is not only the growth of the body size...

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Fluid flow in a porous tree-shaped network: Optimal design and extension of Hess–Murray’s law

Cited by 33 publications

References 29 publications

Penetration of inhaled aerosols in the bronchial tree

Penetration of inhaled aerosols in the bronchial tree

Toward an optimal design principle in symmetric and asymmetric tree flow networks

The physics origin of the hierarchy of bodies in space

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