Qualitative physics using dimensional analysis

Flow Characteristics of Rectangular Broad-Crested Weirs with Sloped Upstream Face

“…(1) and (2) which emphasize the correct determination of the weir discharge coefficient (Bhaskar and Nigam, 1990).…”

Improving neural network models of physical systems through dimensional analysis

“…Dimensional analysis provides three constraints that the neural network models must satisfy, and these arise from the principle of dimensional homogeneity, product theorem and Buckingham's Pi theorem [10,11,14]. The Buckingham's Pi theorem provides the basis for generating a set of dimensionless products that satisfy these constraints, which in one form can be stated as follows: If a physical situation is characterised by n variables and r basic dimensions occur in the dimensional representations of these variables, then there are n − r independent dimensionless products that are sufficient to describe the situation.…”

“…It is possible to transform one set to another using simple operations. The basis variables are selected through a search process, and the search space is limited by using the basis selection heuristics suggested by Bhaskar and Nigam [14]. Performance of networks on the reduced π term sets is used to determine the final set of dimensionless variables to use.…”

Internal dose, uncertainty analysis, and complexity of risk models

“…Such causal knowledge must come from biological or other considerations . Bhaskar and Nigam (1990) discuss in detail for simple physical models the interplay between the mathematical constraints implied by dimensional analysis and the qualitative knowledge of system dynamics and of the interdependencies among variables needed to deduce specific formulas describing input-output behaviors.…”