MATEC Web Conf.
Volume 145, 2018NCTAM 2017 – 13th National Congress on Theoretical and Applied Mechanics
|Number of page(s)||5|
|Published online||09 January 2018|
Order parameter profiles in a system with Neumann – Neumann boundary conditions
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, 1113 Sofia, Bulgaria.
* The authors gratefully acknowledge the financial support via contract DN 02/8 with Bulgarian National Science Fund. e-mail: firstname.lastname@example.org
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In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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