The use of multiple scales that result in the collection of redundant information may lead to increased study burden (e.g., multiple scales, multiple items per scale, and a 30- to 45-minute time requirement to administer each scale).
Finally, the governing equation is solved analytically by conducting the method of multiple scales (MMS) which results in frequency-response curves of FG porous cylindrical shells in the presence of damping effect.
As a result, a multiple scale UGKS-AS is developed and used for the flow simulation from the free molecular transport to the Navier Stokes solutions.
Furthermore the data indicated that 14 or more soil observations are needed per homogeneous area to achieve acceptable results and that multiple scale covariates were useful to map different parts of the landscape.
We evaluated Canada Warbler (Cardellina canadensis) responses to changes in habitat characteristics (landscape metrics, landcover, and microhabitat features) at multiple spatial scales resulting from timber harvests (clear-cut, heavy partial, and light partial) between 1996 and 2009.
In the first, we discretize the equations of motion using the Galerkin procedure and then apply the method of multiple scales to the resulting system of non-linear ordinary-differential equations to obtain approximate solutions (discretization approach).
In this section, numerical results can be achieved using the multiple scale method explained in Section 3.
Our result concerns more peculiarly multisummability and multiple scale analysis in the complex parameter ϵ.
The theoretical results are obtained to second order approximations applying the multiple scale perturbation technique (MSPT).
Reducing dimensions down to the micrometer scale results in numerous advantages including small sample volumes, high throughput detection, and the ability to combine multiple processes.
