The nondimensional groups which characterize a group of dynamically equivalent single exible link (SFL) manipulators are determined. A scaling law for linear rational controllers is developed for dynamically equivalent SFL systems. As an example of the applicability of this theoretical scaling law to even sophisticated control techniques, it is veriied experimentally for an H 1 control strategy.

The Paris power law, which relates fatigue-crack growth rates to the applied stress-intensity range, is an example of a scaling law with the inherent property of incomplete similarity. Previous considerations of dimensions and self-similarity have suggested that the assumed ‘materials constants’ in this law are also a function of specimen size. In this note, the question of the size-dependence ...

Scaling research has seen remarkable progress in the past several decades. Many scaling relationships were discovered within and across individual and population levels, such as species–abundance relationship, Taylor’s law, and density mass allometry. However none of these established patterns incorporate individual variation in the formulation. Individual body size variation is a key evolution...

For the first time to our knowledge, a detailed theoretical basis is provided for the well-known inverse-square scaling law of holographic diffraction, which states that replay diffraction efficiency eta = gamma/M2, where M is the number of gratings stored and gamma is a constant system parameter. This law is shown to hold for photopolymer recording media governed by the predictions of the nonl...

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad-hoc, tedious, and time consuming. Here we present an algorithm that obtains a scaling law in the form of a power law from experimental data...

The ability to ascertain the extent of product sale fluctuations for each store and locality is indispensable to inventory management. This study analyzed POS data from 158 convenience stores in Kawasaki City, Kanagawa Prefecture, Japan and found a power scaling law between the mean and standard deviation of product sales quantities for several product categories. For the statistical domains of...

We show how the hypothesis that galaxy discs conform to self-similar dynamics leads to the identification of an annular region of the optical disc which is such that, corresponding to the Tully-Fisher scaling law defined on the exterior annular boundary, there is a similar scaling law defined on the interior annular boundary. This result is confirmed at the level of statistical certainty over s...

Urban population scaling of resource use, creativity metrics, and human behaviors has been widely studied. These studies have not looked in detail at the full range of human environments which represent a continuum from the most rural to heavily urban. We examined monthly police crime reports and property transaction values across all 573 Parliamentary Constituencies in England and Wales, findi...

Urban population scaling of resource use, creativity metrics, and human behaviors has been widely studied. These studies have not looked in detail at the full range of human environments which represent a continuum from the most rural to heavily urban. We examined monthly police crime reports and property transaction values across all 573 Parliamentary Constituencies in England and Wales, findi...

Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the...