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|Title: ||An Example of Microstructure with Multiple Scales|
|Authors: ||Winter, M|
|Keywords: ||Calculus of variations, Singular perturbation|
Young measure, martensitic phase transformation
|Publication Date: ||1997|
|Publisher: ||Cambridge University Press|
|Citation: ||European J Appl Math 8 (1997), 185-207|
|Abstract: ||This paper studies a vectorial problem in the calculus of variations
arising in the theory of martensitic microstructure.
The functional has an integral representation where the integrand
is a nonconvex function of the gradient with exactly four minima.
We prove that the Young measure corresponding
to a minimising sequence is homogeneous and unique for certain linear
We also consider the singular perturbation of the problem
by higher-order gradients.
We study an example of microstructure involving infinite sequential
calculate its energy and length scales
in the zero limit of the perturbation.|
|Appears in Collections:||Mathematical Science|
Dept of Mathematics Research Papers
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