Sentence examples for outer expansion from inspiring English sources

The first corrective term of the outer expansion can be straightforwardly expressed as a function of the crack length.

In this method we compare the inner expansion of the outer solutions with the outer expansion of the inner solutions to obtain the unknown constants (K_{1} - K_{5}).

Our computational approach accounts intercalation induced electrode expansion, stress generation caused by mechanical boundaries, compression of the electrodes and the separator, outer expansion of the cell and finally the influence of the ionic transport within the electrolyte.

First, all fields are expanded in terms of the small parameter, ε, appearing in the free energy expression, which is proportional to the interface width, both in the bulk domains (outer expansion) and in the close vicinity of the interface (inner expansion).

The outer expansions are the same as in Eq. (18), with t replaced by t1.

Inner and outer expansions are developed in terms of both a small parameter Ca1/3 and a small parameter DeCa/1/3.

The different orders of the outer problem can now be obtained by plugging in the outer expansions in the balance equations.

Therefore, the next order in the outer expansions (ε2) must be considered to determine ( {c}_{alpha}^1 ) and ( {mu}_{alpha}^1 ) in the void phase.

Next, a matched asymptotic expansion is worked out by constructing "inner" and "outer" expansions for frequencies near and not near resonance frequencies, respectively.

Never say that outer-borough chain expansion is without some, uh, local character.

Now matching conditions to connect the outer and inner expansions at the interface must be found.