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The analytical methods proposed should yield the intended results and are the least intrusive analytical means of obtaining those results.
Computer simulations also allow the designers to check or present the results obtained by analytical means.
In some cases problems are chosen for which exact solutions are already obtainable by analytical means.
Analysis of area and particle size and distribution is easily done by conventional analytical means once the images have been digitally captured.
Current frameworks and guidelines in addressing SoSE challenges lack analytical means of objective SoS level decision-making.
The effective mechanical behavior of hexagonal honeycombs was studied by analytical means and correlated with experimental results for aluminum honeycombs.
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The study also provides an analytical mean to capture the critical source location periodicity that has been experimentally observed.
The analytical mean-field estimates are compared with the results of computational homogenization performed using the finite element (FE) method.
We develop an analytical mean-field theory for the brush in the "dry" state which demonstrates the thermodynamic advantage of backfolding for a fraction of the brush chains.
An analytical mean field model of grain coarsening in particle-containing alloys was shown to adequately predict this transition in coarsening behaviour.
The present model predicts a quasi-stationary grain size distribution more symmetrical than that by the analytical mean field theory by Hillert.
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