Sentence examples for dimensional analysis where from inspiring English sources

For the damping coefficient α in our simulation, it is found there may exist an approximating relation to the dimensionless damping parameter, used in Day et al. (2005) and Dalguer and Day (2007), as, based on dimensional analysis, where Δt is the time step.

This is equivalent to mapping a variable from p-dimensional space to m-dimensional space for analysis, where m < p. After dimensionality reduction, according to the definition given in Section 2.3.1, the MD d x,G j ) between x and G j can be achieved by calculating the distance between y = (y 1, y 2, …, y m )′ and G j ∗(j = 1, 2, …, k).

The boiler tube temperatures obtained from the one dimensional model are transferred and used as boundary conditions in a full three dimensional finite element analysis where deformations are solved for and stress results obtained due to thermal expansion within the boiler tube walls and the adjacent support structure.

Due to the structure of the analysis problems in computational settings, the complexity of the problem space manifests itself as a high-dimensional analysis problem, where dimensionality is most often associated with the number of measurements being considered simultaneously.

Iterative learning control is an application for two-dimensional control systems analysis where it is possible to simultaneously address error convergence and transient response specifications but there is a requirement to enforce frequency attenuation of the error between the output and reference over the complete spectrum.

The purpose of the previous section was to illustrate how our conclusions based on the one dimensional analysis are directly relevant to a two-dimensional situation where locations, shapes, and properties of the inclusions were known.

This chapter addresses certain points raised in Chapter 2, where the principles and methods for carrying out a dimensional analysis were discussed.

Since FWER controlling procedures are often too conservative in high dimensional screening studies [ 7], they are rather weak if applied to exon-level analysis where the number of tests increases more than 10 times with respect to gene-level.

where the inertial range depends on the wavenumber and the turbulent energy dissipation from dimensional analysis.

The method of dimensional analysis is used in every field of engineering, especially in such fields as fluid dynamics and thermodynamics where problems with many variables are handled.

Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis.