Transport in branched systems I : steady-state response

Abstract Branched or fractal-like extended surfaces are commonly found in natural systems and in engineered systems such as heterogeneous catalysts to enhance the rates of heat or mass transfer, or chemical reaction. Simple models can be derived to simulate the effectiveness and efficiency of these structures and provide some speculation concerning transport limitations affecting the evolutionary design of natural branching structures. Though the surface area of branching structures increases with each successive generation, their efficiency and effectiveness quickly approach asymptotic values. The transport limitations inherent in the structures render subsequent branching ineffective. Such limitations, characterized by environmentally driven, external transport resistances, may affect branching patterns found in plant root systems, mammalian motoneurons, and animal circulatory systems

[1]  Davis H. Hartman,et al.  Digital High Speed Interconnects: A Study Of The Optical Alternative , 1986 .

[2]  M. G. Taylor,et al.  The input impedance of an assembly of randomly branching elastic tubes. , 1966, Biophysical journal.

[3]  I Segev,et al.  Propagation of action potentials along complex axonal trees. Model and implementation. , 1991, Biophysical journal.

[4]  A synergic approach to plant pattern generation. , 1990, Mathematical biosciences.

[5]  D. Bray BRANCHING PATTERNS OF INDIVIDUAL SYMPATHETIC NEURONS IN CULTURE , 1973, The Journal of cell biology.

[6]  P. Kramer,et al.  Physiology of trees. , 1961 .

[7]  D. P. Sekulic,et al.  Extended surface heat transfer , 1972 .

[8]  Stuart W. Churchill,et al.  Correlating equations for laminar and turbulent free convection from a horizontal cylinder , 1975 .

[9]  T. McMahon,et al.  Tree structures: deducing the principle of mechanical design. , 1976, Journal of theoretical biology.

[10]  M. Sernetz,et al.  The organism as bioreactor. Interpretation of the reduction law of metabolism in terms of heterogeneous catalysis and fractal structure. , 1985, Journal of theoretical biology.

[11]  W. Rall Branching dendritic trees and motoneuron membrane resistivity. , 1959, Experimental neurology.

[12]  H P Clamann,et al.  Relation between structure and function in information transfer in spinal monosynaptic reflex. , 1992, Physiological Reviews.

[13]  J. Passioura,et al.  Water Transport in and to Roots , 1988 .

[14]  W. Rall Membrane potential transients and membrane time constant of motoneurons. , 1960, Experimental neurology.

[15]  W. R. Gardner,et al.  Water Uptake by Plants: I. Divided Root Experiments , 1977 .

[16]  W. R. Gardner DYNAMIC ASPECTS OF WATER AVAILABILITY TO PLANTS , 1960 .

[17]  Thomas R. Nelson,et al.  Pulse propagation on a fractal network. I.: structural and temporal scaling characteristics , 1992 .

[18]  L. D. Hutcheson,et al.  Optical Interconnects For High Speed Computing , 1986 .

[19]  Pulse propagation on a fractal network , 1992 .

[20]  G. Froment,et al.  Chemical Reactor Analysis and Design , 1979 .

[21]  D Winne,et al.  Effect of villosity and distension on the absorptive and secretory flux in the small intestine. , 1989, Journal of theoretical biology.

[22]  Transport function of branching structures and the surface law for basic metabolic rate , 1992 .

[23]  R Suzuki,et al.  Simulation analysis of excitation conduction in the heart: propagation of excitation in different tissues. , 1986, Journal of theoretical biology.

[24]  David T. Clarkson,et al.  Factors Affecting Mineral Nutrient Acquisition by Plants , 1985 .

[25]  P. J. Schneider,et al.  Conduction heat transfer , 1974 .

[26]  W. R. Gardner,et al.  Water Uptake By Plants: II. The Root Contact Model , 1977 .

[27]  J. Piiper,et al.  4 Model Analysis of Gas Transfer in Fish Gills , 1984 .

[28]  W. Cameron,et al.  Quantitative analysis of the dendrites of cat phrenic motoneurons stained intracellularly with horseradish peroxidase , 1985, The Journal of comparative neurology.

[29]  G. Froment,et al.  Deactivation of catalysts by coke formation in the presence of internal diffusional limitation , 1982 .

[30]  R. Burke,et al.  Membrane area and dendritic structure in type‐identified triceps surae alpha motoneurons , 1987, The Journal of comparative neurology.

[31]  W. H. PREECE The Magnetic Storm of May 14, 1878 , 1878, Nature.

[32]  G. Mitchison Neuronal branching patterns and the economy of cortical wiring , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[33]  G Cumming,et al.  Angles of branching and diameters of branches in the human bronchial tree. , 1967, The Bulletin of mathematical biophysics.

[34]  F.J. Leonberger,et al.  Optical interconnections for VLSI systems , 1984, Proceedings of the IEEE.

[35]  C. Daxboeck,et al.  5 Oxygen and Carbon Dioxide Transfer Across Fish Gills , 1984 .

[36]  B. West Physiology in Fractal Dimensions , 1990 .

[37]  C. Koch,et al.  Effect of geometrical irregularities on propagation delay in axonal trees. , 1991, Biophysical journal.

[38]  T. A. Wilson,et al.  Design of the Bronchial Tree , 1967, Nature.