Academic Journal
Pattern formation with repulsive soft-core interactions: Discrete particle dynamics and Dean-Kawasaki equation
| Title: | Pattern formation with repulsive soft-core interactions: Discrete particle dynamics and Dean-Kawasaki equation |
|---|---|
| Authors: | Bernd Blasius, Emilio Hernández-García, Jean-Baptiste Delfau, Hélène Ollivier, Cristóbal López |
| Contributors: | Ministerio de Economía y Competitividad (España), European Commission, European Cooperation in Science and Technology, Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72] |
| Source: | Digital.CSIC. Repositorio Institucional del CSIC Consejo Superior de Investigaciones Científicas (CSIC) instname |
| Publication Status: | Preprint |
| Publisher Information: | American Physical Society (APS), 2016. |
| Publication Year: | 2016 |
| Subject Terms: | Statistical Mechanics (cond-mat.stat-mech), 0103 physical sciences, FOS: Physical sciences, Pattern Formation and Solitons (nlin.PS), Nonlinear Sciences - Pattern Formation and Solitons, 01 natural sciences, Condensed Matter - Statistical Mechanics, 3. Good health |
| Description: | Brownian particles interacting via repulsive soft-core potentials can spontaneously aggregate, despite repelling each other, and form periodic crystals of particle clusters. We study this phenomenon in low-dimensional situations (one and two dimensions) at two levels of description: performing numerical simulations of the discrete particle dynamics, and by linear and nonlinear analysis of the corresponding Dean-Kawasaki equation for the macroscopic particle density. Restricting to low dimensions and neglecting fluctuation effects we gain analytical insight into the mechanisms of the instability leading to clustering which turn out to be the interplay between diffusion, the intracluster forces and the forces between neighboring clusters. We show that the deterministic part of the Dean-Kawasaki equation provides a good description of the particle dynamics, including width and shape of the clusters, in a wide range of parameters, and analyze with weakly nonlinear techniques the nature of the pattern-forming bifurcation in one and two dimensions. Finally, we briefly discuss the case of attractive forces. |
| Document Type: | Article |
| Language: | English |
| ISSN: | 2470-0053 2470-0045 |
| DOI: | 10.1103/physreve.94.042120 |
| DOI: | 10.48550/arxiv.1605.09311 |
| DOI: | 10.13039/501100000780 |
| DOI: | 10.13039/501100000921 |
| DOI: | 10.13039/501100003329 |
| Access URL: | https://digital.csic.es/bitstream/10261/157278/1/pattern_formation_Delfau.pdf https://pubmed.ncbi.nlm.nih.gov/27841471 http://arxiv.org/abs/1605.09311 http://hdl.handle.net/10261/157278 https://www.ncbi.nlm.nih.gov/pubmed/27841471 https://link.aps.org/pdf/10.1103/PhysRevE.94.042120 https://arxiv.org/pdf/1605.09311.pdf https://digital.csic.es/bitstream/10261/157278/1/pattern_formation_Delfau.pdf https://www.arxiv.org/abs/1605.09311 http://export.arxiv.org/pdf/1605.09311 |
| Rights: | APS Licenses for Journal Article Re-use arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....d7ee1ce35c212fd566d7e63d5b924ecf |
| Database: | OpenAIRE |
| ISSN: | 24700053 24700045 |
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| DOI: | 10.1103/physreve.94.042120 |