• Login
    View Item 
    •   Home
    • Research
    • Articles
    • View Item
    •   Home
    • Research
    • Articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguideTheses and Dissertations LibguideSubmit an Item

    Statistics

    Display statistics

    Pattern formation of a nonlocal, anisotropic interaction model

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Type
    Article
    Authors
    Burger, Martin
    Düring, Bertram
    Kreusser, Lisa Maria
    Markowich, Peter A. cc
    Schönlieb, Carola-Bibiane
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Computer Science Program
    Date
    2018-01-16
    Online Publication Date
    2018-01-16
    Print Publication Date
    2018-03
    Permanent link to this record
    http://hdl.handle.net/10754/626979
    
    Metadata
    Show full item record
    Abstract
    We consider a class of interacting particle models with anisotropic, repulsive–attractive interaction forces whose orientations depend on an underlying tensor field. An example of this class of models is the so-called Kücken–Champod model describing the formation of fingerprint patterns. This class of models can be regarded as a generalization of a gradient flow of a nonlocal interaction potential which has a local repulsion and a long-range attraction structure. In contrast to isotropic interaction models the anisotropic forces in our class of models cannot be derived from a potential. The underlying tensor field introduces an anisotropy leading to complex patterns which do not occur in isotropic models. This anisotropy is characterized by one parameter in the model. We study the variation of this parameter, describing the transition between the isotropic and the anisotropic model, analytically and numerically. We analyze the equilibria of the corresponding mean-field partial differential equation and investigate pattern formation numerically in two dimensions by studying the dependence of the parameters in the model on the resulting patterns.
    Citation
    Burger M, Düring B, Kreusser LM, Markowich PA, Schönlieb C-B (2018) Pattern formation of a nonlocal, anisotropic interaction model. Mathematical Models and Methods in Applied Sciences 28: 409–451. Available: http://dx.doi.org/10.1142/S0218202518500112.
    Sponsors
    M.B. acknowledges support by ERC via Grant EU FP 7—ERC Consolidator Grant 615216 LifeInverse and by the German Science Foundation DFG via EXC 1003 Cells in Motion Cluster of Excellence, Munster, Germany. B.D. has been supported by the Leverhulme Trust Research Project Grant “Novel discretizations for higherorder nonlinear PDE” (RPG-2015-69). L.M.K. was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) Grant EP/L016516/1. C.-B.S. acknowledges support from Leverhulme Trust Project on breaking the non-convexity barrier, EPSRC Grant No. EP/M00483X/1, the EPSRC Center No. EP/N014588/1 and the Cantab Capital Institute for the Mathematics of Information. The authors would like to thank Carsten Gottschlich and Stephan Huckemann for introducing them to the Kucken–Champod model and for very useful discussions on the dynamics required for simulating fingerprints. The authors are grateful to the referees for their thorough review and valuable remarks that helped to improve the paper.
    Publisher
    World Scientific Pub Co Pte Lt
    Journal
    Mathematical Models and Methods in Applied Sciences
    DOI
    10.1142/S0218202518500112
    arXiv
    1610.08108
    Additional Links
    http://www.worldscientific.com/doi/abs/10.1142/S0218202518500112
    Relations
    Is Supplemented By:
    • [Dataset]
      Burger, M., Düring, B., Kreusser, L., Markowich, P. A., & Schoenlieb, C.-B. (2017). Research data supporting 'Pattern formation of a nonlocal, anisotropic interaction model' [Data set]. Apollo - University of Cambridge Repository. https://doi.org/10.17863/CAM.9169. DOI: 10.17863/cam.9169 Handle: 10754/663996
    ae974a485f413a2113503eed53cd6c53
    10.1142/S0218202518500112
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2023  DuraSpace
    Quick Guide | Contact Us | KAUST University Library
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.