Biomedical subjects

D H Rothman

Publications and source records attributed to D H Rothman.

8 recordsLinked to original sources

PubMed2001

Coupled length scales in eroding landscapes.

We report results from an empirical study of the anisotropic structure of eroding landscapes. By constructing a novel correlation function, we show quantitatively that small-scale channel-like features of landscapes are coupled to the large-scale structure of drainage basins. We show additionally that this two-scale interaction is scale-dependent. The latter observation suggests that a commonly applied effective equation for erosive transport may itself depend on scale.

Journal Article↗

PubMed2001

Global biodiversity and the ancient carbon cycle.

Paleontological data for the diversity of marine animals and land plants are shown to correlate significantly with a concurrent measure of stable carbon isotope fractionation for approximately the last 400 million years. The correlations can be deduced from the assumption that increasing plant diversity led to increasing chemical weathering of rocks and therefore an increasing flux of carbon from the atmosphere to rocks, and nutrients from the continents to the oceans. The CO(2) concentration dependence of photosynthetic carbon isotope fractionation then indicates that the diversification of land plants led to decreasing CO(2) levels, while the diversification of marine animals derived from increasing nutrient availability. Under the explicit assumption that global biodiversity grows with global biomass, the conservation of carbon shows that the long-term fluctuations of CO(2) levels were dominated by complementary changes in the biological and fluid reservoirs of carbon, while the much larger geological reservoir remained relatively constant in size. As a consequence, the paleontological record of biodiversity provides an indirect estimate of the fluctuations of ancient CO(2) levels.

Animals↗

PubMed2001

Re-examination of the "3/4-law" of metabolism.

We examine the scaling law B is proportional to M(alpha)which connects organismal resting metabolic rate B with organismal mass M, where alpha is commonly held to be 3/4. Since simple dimensional analysis suggests alpha = 2/3, we consider this to be a null hypothesis testable by empirical studies. We re-analyse data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting alpha = 2/3 in favor of alpha = 3/4. For mammals, we find a possible breakdown in scaling for larger masses reflected in a systematic increase in alpha. We also review theoretical justifications of alpha = 3/4 based on dimensional analysis, nutrient-supply networks, and four-dimensional biology. We find that present theories for alpha = 3/4 require assumptions that render them unconvincing for rejecting the null hypothesis that alpha = 2/3.

Animals↗

PubMed2001

Basins of attraction on random topography.

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat slopes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained analytically. The convergence of flow lines correlates positively with drainage area, so that lower slopes are associated with larger basins. As a consequence, we explain the observed relation between the local slope of a landscape and the area of the drainage basin geometrically. To some extent, the slope-area relation comes about not because of fluvial erosion of the landscape, but because of the way rivers choose their path. Our results are supported by numerically generated surfaces as well as by real landscapes.

Journal Article↗

PubMed2000

Geometry of river networks. I. Scaling, fluctuations, and deviations.

This paper is the first in a series of three papers investigating the detailed geometry of river networks. Branching networks are a universal structure employed in the distribution and collection of material. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary, suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, here we report a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of a subbasin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density, and provide observations and explanations of deviations from scaling. We show that fluctuations about scaling are substantial, and grow with system size. We find strong deviations from scaling at small scales which can be explained by the existence of a linear network structure. At intermediate scales, we find slow drifts in exponent values, indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations, and will not be improved by increases in network resolution.

Ecosystem↗

PubMed2000

Geometry of river networks. II. Distributions of component size and number.

The structure of a river network may be seen as a discrete set of nested subnetworks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon, and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power-law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.

Ecosystem↗

PubMed2000

Geometry of river networks. III. Characterization of component connectivity.

Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we explore the presence of randomness in river network structure and the details of its consequences. We first show that an averaged view of network architecture is provided by a proposed self-similarity statement about the scaling of drainage density, a local measure of stream concentration. This scaling of drainage density is shown to imply Tokunaga's law, a description of the scaling of side branch abundance along a given stream, as well as a scaling law for stream lengths. We then consider fluctuations in drainage density and consequently the numbers of side branches. Data are analyzed for the Mississippi River basin and a model of random directed networks. Numbers of side streams are found to follow exponential distributions, as are intertributary distances along streams. Finally, we derive a joint variation of side stream abundance with stream length, affording a full description of fluctuations in network structure. Fluctuations in side stream numbers are shown to be a direct result of fluctuations in stream lengths. This is the last paper in a series of three on the geometry of river networks.

Ecosystem↗

PubMed1999

Unified view of scaling laws for river networks.

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.

Journal Article↗