M. Woldenberg

Publications38
h-index15
Citations997
Highly Influential Citations48
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Tree asymmetry--a sensitive and practical measure for binary topological trees.
TLDR
It is shown that the variance in tree-asymmetry values for these observed branching patterns corresponds perfectly with the variance predicted by the used growth model. Expand
Diameters and cross‐sectional areas of branches in the human pulmonary arterial tree
TLDR
The mean value of the exponent z in the equation flow = k (diameterz) was found to be 2.3 ± 0.1, which is equal to the optimal value for minimizing power and metabolic costs for fully developed turbulent flow. Expand
Finding the optimal lengths for three branches at a junction.
TLDR
An exact analytical solution to the problem of locating the junction point between three branches so that the sum of the total costs of the branches is minimized, and the value of x determined whether a junction was best fitted by a surface, volume, drag or power minimization model. Expand
Hydraulic geometry and minimum rate of energy dissipation
The theory of minimum rate of energy dissipation states that a system is in an equilibrium condition when its rate of energy dissipation is at its minimum value. This minimum value depends on the… Expand
Branching and Self‐Organization in Marine Modular Colonial Organisms: A Model
TLDR
A model of branching and colony growth in Caribbean gorgonian corals using parameters and variables related to actual modular structures and a scaling power law suggesting self‐organized criticality is developed. Expand
A generalization of the optimal models of arterial branching
Optimal models of arterial branching angles are usually based on the assumption that the equation relating flow and radius is given byf=kr3, as proposed by Murray in 1926. An exception is the model… Expand
Models for growth, decline and regrowth of the dendrites of rat Purkinje cells induced from magnitude and link-length analysis.
TLDR
Analysis of Purkinje neurons of rats aged 1, 10, 18 and 28 months to investigate growth and decline in the magnitude of the dendritic tree finds that exterior links are longer than interior links (non-terminal or intermediate segments), which indicates that they follow a Fibonacci series of link lengths. Expand
Relation of branching angles to optimality for four cost principles.
TLDR
A comparison of the principles demonstrates that, for most cases, a is smaller for the principle which has the smaller c value, which is to be expected in most but not all cases. Expand
HORTON'S LAWS JUSTIFIED IN TERMS OF ALLOMETRIC GROWTH AND STEADY STATE IN OPEN SYSTEMS
Rivers are open systems and achieve a steady state or grow allometrically, according to the general equation y = ax b . This equation yields a straight line on double logarithmic paper and reflects a… Expand
Energy Flow and Spatial Order Mixed Hexagonal Hierarchies of Central Places
r T HE existence and nature of the central-place hierarchy have been hotly debated, and one criticism has been that methods used to detect the hierarchy are subjective and probably biased. In answer… Expand
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