EMERGENCE OF NONTRIVIAL MINIMIZERS FOR THE THREE-DIMENSIONAL OHTA–KAWASAKI ENERGY

Hans Knüpfer, Cyrill B. Muratov, Matteo Novaga

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 nontrivial minimizers. We identify the scaling in which a sharp transition from asymptotically trivial to nontrivial 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.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalPure and Applied Analysis
Volume2
Issue number1
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics

Keywords

  • Gamma convergence
  • energy driven pattern formation

Fingerprint

Dive into the research topics of 'EMERGENCE OF NONTRIVIAL MINIMIZERS FOR THE THREE-DIMENSIONAL OHTA–KAWASAKI ENERGY'. Together they form a unique fingerprint.

Cite this