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Pattern formation with repulsive soft-core interactions: Discrete particle dynamics and Dean-Kawasaki equation

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Τίτλος: Pattern formation with repulsive soft-core interactions: Discrete particle dynamics and Dean-Kawasaki equation
Συγγραφείς: Bernd Blasius, Emilio Hernández-García, Jean-Baptiste Delfau, Hélène Ollivier, Cristóbal López
Συνεισφορές: Ministerio de Economía y Competitividad (España), European Commission, European Cooperation in Science and Technology, Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
Πηγή: Digital.CSIC. Repositorio Institucional del CSIC
Consejo Superior de Investigaciones Científicas (CSIC)
instname
Publication Status: Preprint
Στοιχεία εκδότη: American Physical Society (APS), 2016.
Έτος έκδοσης: 2016
Θεματικοί όροι: 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
Περιγραφή: 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.
Τύπος εγγράφου: Article
Γλώσσα: 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
Σύνδεσμος πρόσβασης: 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
Αριθμός Καταχώρησης: edsair.doi.dedup.....d7ee1ce35c212fd566d7e63d5b924ecf
Βάση Δεδομένων: OpenAIRE
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  Data: Pattern formation with repulsive soft-core interactions: Discrete particle dynamics and Dean-Kawasaki equation
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  Data: 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.
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