{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T14:06:19Z","timestamp":1773410779126,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2011,5,3]],"date-time":"2011-05-03T00:00:00Z","timestamp":1304380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As wireless sensor networks (WSNs) are increasingly being deployed in some important applications, it becomes imperative that we consider application requirements in in-network processes. We intend to use a WSN to aid information querying and navigation within a dynamic and real-time environment. We propose a novel method that relies on the heat diffusion equation to finish the navigation process conveniently and easily. From the perspective of theoretical analysis, our proposed work holds the lower constraint condition. We use multiple scales to reach the goal of accurate navigation. We present a multi-scale gradient descent method to satisfy users\u2019 requirements in WSNs. Formula derivations and simulations show that the method is accurately and efficiently able to solve typical sensor network configuration information navigation problems. Simultaneously, the structure of heat diffusion equation allows more flexibility and adaptability in searching algorithm designs.<\/jats:p>","DOI":"10.3390\/s110504794","type":"journal-article","created":{"date-parts":[[2011,5,4]],"date-time":"2011-05-04T09:03:57Z","timestamp":1304499837000},"page":"4794-4807","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":127,"title":["Information Potential Fields Navigation in Wireless Ad-Hoc Sensor Networks"],"prefix":"10.3390","volume":"11","author":[{"given":"Wei","family":"Wei","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]},{"given":"Yong","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}]}],"member":"1968","published-online":{"date-parts":[[2011,5,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Awerbuch, B, and Peleg, D (1991, January 3\u20136). Concurrent Online Tracking of Mobile Users. Zurich, Switzerland.","DOI":"10.1145\/115992.116013"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Buragohain, C, Agrawal, D, and Suri, S (2006, January 23\u201329). Distributed Navigation Algorithms for Sensor Networks. Barcelona, Spain.","DOI":"10.1109\/INFOCOM.2006.191"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cot\u00e9, A, Meyerson, A, and Poplawski, L (2008, January 25\u201327). Randomized K-Server on Hierarchical Binary Trees. Cambridge, MA, USA.","DOI":"10.1145\/1374376.1374411"},{"key":"ref_4","unstructured":"Einstein, A (1956). Investigations on the Theory of the Brownian Movement, Dover Publications."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gao, J, Guibas, LJ, Milosavljevic, N, and Hershberger, J (2007, January 25\u201327). Sparse Data Aggregation in Sensor Networks. 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San Diego, CA, USA."},{"key":"ref_10","unstructured":"Madden, S, Franklin, MJ, Hellerstein, JM, and Hong, W (2002, January 9\u201311). TAG: A Tiny Aggregation Service for Ad-Hoc Sensor Networks. Boston, MA, USA."},{"key":"ref_11","unstructured":"McOwen, RC (2004). Partial Differential Equation: Methods and Applications, Tsinghua University Press."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ni, S-Y, Tseng, Y-C, Chen, Y-S, and Sheu, J-P (1999, January 15\u201319). The Broadcast Storm Problem in a Mobile Ad Hoc Network. Seattle, WA, USA.","DOI":"10.1145\/313451.313525"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lin, HJ, Lu, MH, and Gao, J (2008, January 13\u20136). Composable Information Gradients in Wireless Sensor Networks. St Louis, MO, USA.","DOI":"10.1109\/IPSN.2008.21"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Polastre, J, Hui, J, Levis, P, Zhao, J, Culler, D, Shenker, S, and Stoica, I (2005, January 2\u20134). A Unifying Link Abstraction for Wireless Sensor Networks. San Diego, CA, USA.","DOI":"10.1145\/1098918.1098928"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sarkar, R, Zhu, XJ, and Gao, J (2007, January 24\u201327). Hierarchical Spatial Gossip for Multi-Resolution Representations in Sensor Networks. Cambridge, MA, USA.","DOI":"10.1109\/IPSN.2007.4379702"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/5\/4794\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:55:59Z","timestamp":1760219759000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/11\/5\/4794"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,3]]},"references-count":15,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2011,5]]}},"alternative-id":["s110504794"],"URL":"https:\/\/doi.org\/10.3390\/s110504794","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,5,3]]}}}