{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:43:23Z","timestamp":1787341403429,"version":"3.56.0"},"reference-count":27,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","award":["PGC2018-098218-B-100"],"award-info":[{"award-number":["PGC2018-098218-B-100"]}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2019\/14827-0"],"award-info":[{"award-number":["2019\/14827-0"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2019\/24915-4"],"award-info":[{"award-number":["2019\/24915-4"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Spiders perform a task similar to solving an inverse problem when detecting the position of a prey, a mate, or a predator perturbing the orb-web. Recent work has advanced in the study of the orb-web as a sensor when it is subjected to small transverse vibrations, using a continuous membrane model for the orb-web. However, in-plane vibrations have not been investigated yet as data for the prey detection problem. In the present work, we develop the structure of the small in-plane vibratory response of an axially symmetric orb-web supported at the boundary. Additionally, we prove that knowledge of the in-plane dynamic response inside an annulus centered at the origin of the orb-web, where the spider is assumed to stay for a sufficiently large registration time, allows us to determine uniquely the in-plane distributed load simulating the prey's impact. The theoretical outcome is illustrated with a numerical implementation of the reconstruction method.<\/jats:p>","DOI":"10.1137\/20m1372792","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T10:47:37Z","timestamp":1635763657000},"page":"2297-2322","source":"Crossref","is-referenced-by-count":10,"title":["Detecting a Prey in a Spider Orb-Web from In-Plane Vibration"],"prefix":"10.1137","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2248-6422","authenticated-orcid":true,"given":"Alexandre","family":"Kawano","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2186-7688","authenticated-orcid":true,"given":"Antonino","family":"Morassi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ram\u00f3n","family":"Zaera","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,11,1]]},"reference":[{"key":"atypb1","unstructured":"F. G. Barth,\n                      A Spider's World: Senses and Behavior\n                      , translated from the German by M. A. Biedermann-Thorson, Springer-Verlag, 2002."},{"key":"atypb2","unstructured":"H. Bohr,\n                      Almost Periodic Functions\n                      , Chelsea Publishing Company, 1947."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/10\/4\/006"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1081\/PDE-120016136"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"C. Corduneanu,\n                      Almost Periodic Oscillations and Waves\n                      , Springer, 2009.","DOI":"10.1007\/978-0-387-09819-7"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7125"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/19M1262322"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2020.106838"},{"key":"atypb9","unstructured":"A. Kawano, A. Morassi, and R. Zaera,\n                      Asymptotic Estimates for the Spectrum of a Class of In-Plane Orb-Web's Vibration\n                      , Technical report, University of Udine, 2020."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2020.107310"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.201800252"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/090763524"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00619783"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/21\/6\/016"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00192316"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00292977"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/BF00292978"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1126\/science.213.4505.363"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2017.02.018"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s00114-018-1561-1"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2019.0201"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2008.09.013"},{"key":"atypb23","first-page":"143","author":"Otto A.","year":"2018","journal-title":"Springer"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/11\/2\/013"},{"key":"atypb25","unstructured":"R. Young,\n                      An Introduction to Nonharmonic Fourier Series\n                      , rev. 1st ed., Academic Press, 2001."},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"R. Zaera, \u00d3. Serrano, J. Fern\u00e1ndez-S\u00e1ez, and A. Morassi,\n                      Eco-localization of a prey in a spider orb-web\n                      , J. Vib. Control, published online February 16, 2021,https:\/\/doi.org\/10.1177\/1077546321993548.","DOI":"10.1177\/1077546321993548"},{"key":"atypb27","unstructured":"A. Zemanian,\n                      Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications\n                      , unabridged, slightly corrected republication of the work first published by McGraw-Hill Book Co., 1965, Dover Books Adv. Math., Dover Publications, Inc., 1987."}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1372792","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:16:57Z","timestamp":1787339817000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1372792"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1372792"],"URL":"https:\/\/doi.org\/10.1137\/20m1372792","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}