{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:42:22Z","timestamp":1776811342489,"version":"3.51.2"},"reference-count":15,"publisher":"European Society of Computational Methods in Sciences and Engineering","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"published-print":{"date-parts":[[2021,11,1]]},"abstract":"<jats:p>This work reports numerical explorations in advection of one passive tracer by point vortices living in the unbounded plane. The main objective is to find the energy-optimal displacement of one passive particle (point vortex with zero circulation) surrounded by N point vortices. The direct formulation of the corresponding control problems is presented. The restrictions are due to (i) the ordinary differential equations that govern the displacement of the passive particle around the point vortices, (ii) the available time T to go from the initial position z0 to the final destination zf, and (iii) the maximum absolute value umax that is imposed on the control variables. The latter consist in staircase controls, i.e., the control is written as a finite linear combination of characteristic functions on the real interval. The resulting optimization problems are solved numerically. The numerical results shows the existence nearly\/quasi optimal control for the cases of N=1, N=2, N=3, and N=4 vortices.<\/jats:p>","DOI":"10.3233\/jcm-204710","type":"journal-article","created":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T13:46:12Z","timestamp":1615902372000},"page":"1215-1229","source":"Crossref","is-referenced-by-count":6,"title":["The control of the displacement of a passive particle in a point vortex flow"],"prefix":"10.66113","volume":"21","author":[{"given":"Carlos","family":"Balsa","sequence":"first","affiliation":[{"name":"Research Centre in Digitalization and Intelligent Robotics (CeDRI), Instituto Polit\u00e9cnico de Bragan\u00e7a, Campus de Santa Apol\u00f3nia, 5300-253 Bragan\u00e7a, Portugal"}]},{"given":"S\u00edlvio M.A.","family":"Gama","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica (Faculdade de Ci\u00eancias) da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"}]}],"member":"55691","reference":[{"issue":"4","key":"10.3233\/JCM-204710_ref1","doi-asserted-by":"crossref","first-page":"042901","DOI":"10.1063\/1.4943901","article-title":"Dynamics of restricted three and four vortices problem on the plane","volume":"57","author":"Andrade","year":"2016","journal-title":"Journal of Mathematical Physics"},{"issue":"7","key":"10.3233\/JCM-204710_ref2","doi-asserted-by":"crossref","first-page":"2465","DOI":"10.1063\/1.868194","article-title":"Chaotic advection in point vortex models and two-dimensional turbulence","volume":"6","author":"Babiano","year":"1994","journal-title":"Physics of Fluids"},{"key":"10.3233\/JCM-204710_ref4","doi-asserted-by":"crossref","first-page":"B68","DOI":"10.1115\/1.1483351","article-title":"Practical methods for optimal control using nonlinear programming","volume":"55","author":"Betts","year":"2002","journal-title":"Applied Mechanics Reviews"},{"issue":"2","key":"10.3233\/JCM-204710_ref6","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1140\/epjb\/e2007-00276-2","article-title":"Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations","volume":"59","author":"Chavanis","year":"2007","journal-title":"The European Physical Journal B-Condensed Matter and Complex Systems"},{"key":"10.3233\/JCM-204710_ref7","doi-asserted-by":"crossref","unstructured":"Y. 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