Aggregation in nondiffusion limited colloidal particle suspensions follows a temporal power-law dependence that is consistent with classical diffusion limited cluster aggregation models; however, the dynamic scaling exponents observed in these systems are not adequately described by diffusion limited cluster aggregation models, which expect these scaling exponents to be constant over all experi...

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We construct, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by "stat...

Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of 'universal' scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relatio...

Developmental constraints and selective pressures interact to determine the strength of allometric scaling relationships between body size and the size of morphological traits among related species. Different traits are expected to relate to body size with different scaling exponents, depending on how their function changes disproportionately with increasing body size. For trematodes parasitic ...

We study the statistics of single-particle Lagrangian velocity in a shell model of turbulence. We show that the small-scale velocity fluctuations are intermittent, with scaling exponents connected to the Eulerian structure function scaling exponents. The observed reduced scaling range is interpreted as a manifestation of the intermediate dissipative range, as it disappears in a Gaussian model o...

We introduce a set of scaling exponents for characterizing global 3D morphologic properties of mass distribution, branching and taper in neuronal dendritic arbors, capable of distinguishing functionally relevant changes in dendritic complexity that standard Sholl analysis and fractal analysis cannot. We demonstrate that the scaling exponent for mass distribution, d(M), comprises a sum of indepe...