Big Data Dimensional Analysis

The ability to collect and analyze large amounts of data is a growing problem within the scientific community. The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity and variety. One of the main challenges associated with big data variety is automatically understanding the underlying structures and patterns of the data. Such an understanding is required as a pre-requisite to the application of advanced analytics to the data. Further, big data sets often contain anomalies and errors that are difficult to know a priori. Current approaches to understanding data structure are drawn from the traditional database ontology design. These approaches are effective, but often require too much human involvement to be effective for the volume, velocity and variety of data encountered by big data systems. Dimensional Data Analysis (DDA) is a proposed technique that allows big data analysts to quickly understand the overall structure of a big dataset, determine anomalies. DDA exploits structures that exist in a wide class of data to quickly determine the nature of the data and its statical anomalies. DDA leverages existing schemas that are employed in big data databases today. This paper presents DDA, applies it to a number of data sets, and measures its performance. The overhead of DDA is low and can be applied to existing big data systems without greatly impacting their computing requirements.Comment: From IEEE HPEC 201

Dimensional Analysis and Weak Turbulence

In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave interactions responsible for nonlinear energy transfer is known. Furthermore one can easily derive conditions for the breakdown of the weak turbulence approximation. It is found that for incompletely self-similar systems dominated by three wave interactions, the weak turbulence approximation usually cannot break down at small scales. It follows that such systems cannot exhibit small scale intermittency. For systems dominated by four wave interactions, the incomplete self-similarity property implies that the scaling of the interaction coefficient depends only on the physical dimension of the system. These results are used to build a complete picture of the scaling properties of the surface wave problem where both gravity and surface tension play a role. We argue that, for large values of the energy flux, there should be two weakly turbulent scaling regions matched together via a region of strongly nonlinear turbulence.Comment: revtex4, 10 pages, 1 figur

Dimensional analysis and Rutherford Scattering

Dimensional analysis, and in particular the Buckingham $\Pi$ theorem is widely used in fluid mechanics. In this article we obtain an expression for the impact parameter from Buckingham's theorem and we compare our result with Rutherford's original discovery found in the early twentieth century