{"data":{"id":"10.6084/m9.figshare.c.3734389","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.3734389","prefix":"10.6084","suffix":"m9.figshare.c.3734389","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Cohen, Yossi","nameType":"Personal","givenName":"Yossi","familyName":"Cohen","affiliation":[],"nameIdentifiers":[]},{"name":"Rothman, Daniel H.","nameType":"Personal","givenName":"Daniel H.","familyName":"Rothman","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Supplementary material from \"Exact solution for the Poisson field in a semi-infinite strip\""}],"publisher":"Figshare","container":{},"publicationYear":2017,"subjects":[{"subject":"91504 Fluidisation and Fluid Mechanics","subjectScheme":"FOR"},{"subject":"FOS: Other engineering and technologies","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"10599 Mathematical Physics not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"20304 Thermodynamics and Statistical Physics","subjectScheme":"FOR"},{"subject":"FOS: Mechanical engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2017-04-05","dateType":"Created"},{"date":"2017-04-17","dateType":"Updated"},{"date":"2017","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1098/rspa.20160908","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC BY","rightsUri":"https://creativecommons.org/licenses/by/4.0"}],"descriptions":[{"description":"The Poisson equation is associated with many physical processes. Yet exact analytic solutions for the two-dimensional Poisson field are scarce. Here we derive an analytic solution for the Poisson equation with constant forcing in a semi-infinite strip. We provide a method that can be used to solve the field in other intricate geometries. We show that the Poisson flux reveals an inverse square-root singularity at a tip of a slit, and identify a characteristic length scale in which a small perturbation, in a form of a new slit, is screened by the field. We suggest that this length scale expresses itself as a characteristic spacing between tips in real Poisson networks that grow in response to fluxes at tips.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://figshare.com/collections/Supplementary_material_from_Exact_solution_for_the_Poisson_field_in_a_semi-infinite_strip_/3734389","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":1,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2017-04-05T10:09:18.000Z","registered":"2017-04-05T10:09:19.000Z","published":"2017","updated":"2024-12-19T13:02:01.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.c.373438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