Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

H. Knüpfer - C. Muratov - M. Novaga

Emergence of non-trivial minimizers for the three-dimensional Ohta-Kawasaki energy

created by novaga on 07 Nov 2018
modified on 09 Nov 2018

[BibTeX]

Submitted Paper

Inserted: 7 nov 2018
Last Updated: 9 nov 2018

Year: 2018

ArXiv: 1811.03499 PDF

Abstract:

This paper is concerned with the diffuse interface Ohta-Kawasaki energy in three space dimensions, in a periodic setting, in the parameter regime corresponding to the onset of non-trivial minimizers. We identify the scaling in which a sharp transition from asymptotically trivial to non-trivial minimizers takes place as the small parameter characterizing the width of the interfaces between the two phases goes to zero, while the volume fraction of the minority phases vanishes at an appropriate rate. The value of the threshold is shown to be related to the optimal binding energy solution of Gamow's liquid drop model of the atomic nucleus. Beyond the threshold the average volume fraction of the minority phase is demonstrated to grow linearly with the distance to the threshold. In addition to these results, we establish a number of properties of the minimizers of the sharp interface screened Ohta-Kawasaki energy in the considered parameter regime. We also establish rather tight upper and lower bounds on the value of the transition threshold.


Download:

Credits | Cookie policy | HTML 5 | CSS 2.1