{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T08:29:11Z","timestamp":1759825751538,"version":"3.40.3"},"publisher-location":"New York, NY","reference-count":14,"publisher":"Springer New York","isbn-type":[{"type":"electronic","value":"9781461473206"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-1-4614-7320-6_233-1","type":"book-chapter","created":{"date-parts":[[2014,5,27]],"date-time":"2014-05-27T19:27:03Z","timestamp":1401218823000},"page":"1-7","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Nernst-Planck Equation"],"prefix":"10.1007","author":[{"given":"Reinoud","family":"Maex","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,4,20]]},"reference":[{"key":"233-1_CR1","volume-title":"Simple membrane electrodiffusion theory","author":"RA Arndt","year":"1972","unstructured":"Arndt RA, Roper LD (1972) Simple membrane electrodiffusion theory. Physical Biological Sciences Misc, Blacksburg"},{"key":"233-1_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1228-7","volume-title":"Physics with illustrative examples from medicine and biology","author":"GB Benedek","year":"2000","unstructured":"Benedek GB, Villars FMH (2000) Physics with illustrative examples from medicine and biology, 2nd edn. Springer, New York. Originally published by Addison-Wesley (1979)","edition":"2"},{"key":"233-1_CR3","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/S0006-3495(65)86707-8","volume":"5","author":"H Cohen","year":"1965","unstructured":"Cohen H, Cooley JW (1965) The numerical solution of the time-dependent Nernst-Planck equations. Biophys J 5:145\u2013162","journal-title":"Biophys J"},{"key":"233-1_CR4","doi-asserted-by":"crossref","DOI":"10.1525\/9780520326514","volume-title":"Membranes, ions and impulses","author":"KS Cole","year":"1968","unstructured":"Cole KS (1968) Membranes, ions and impulses. University of California Press, Berkeley"},{"key":"233-1_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s002329900026","volume":"150","author":"RS Eisenberg","year":"1996","unstructured":"Eisenberg RS (1996) Computing the field in proteins and channels. J Membr Biol 150:1\u201325. [PDF] Posted on arXiv.org with Paper ID arXiv:1009.2857, September 15, 2010","journal-title":"J Membr Biol"},{"key":"233-1_CR6","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1085\/jgp.27.1.37","volume":"27","author":"DE Goldman","year":"1943","unstructured":"Goldman DE (1943) Potential, impedance, and rectification in membranes. J Gen Physiol 27:37\u201360","journal-title":"J Gen Physiol"},{"key":"233-1_CR7","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1098\/rspa.1939.0051","volume":"171","author":"NF Mott","year":"1939","unstructured":"Mott NF (1939) The theory of crystal rectifiers. Proc R Soc Lond A 171:27\u201338","journal-title":"Proc R Soc Lond A"},{"key":"233-1_CR8","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1515\/zpch-1888-0274","volume":"2","author":"W Nernst","year":"1888","unstructured":"Nernst W (1888) Zur Kinetik der in L\u00f6sung befindlichen K\u00f6rper. Zeitschr f Phys Chem 2:613\u2013637","journal-title":"Zeitschr f Phys Chem"},{"key":"233-1_CR9","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1515\/zpch-1889-0412","volume":"4","author":"W Nernst","year":"1889","unstructured":"Nernst W (1889) Die elektromotorische Wirksamkeit der Ionen. Zeitschr f Phys Chem 4:129\u2013181","journal-title":"Zeitschr f Phys Chem"},{"key":"233-1_CR10","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1002\/andp.18902750202","volume":"39","author":"M Planck","year":"1890","unstructured":"Planck M (1890a) \u00dcber die Erregung von Elektricit\u00e4t und W\u00e4rme in Elektrolyten. Wied Ann Phys 39:161\u2013186","journal-title":"Wied Ann Phys"},{"key":"233-1_CR11","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1002\/andp.18902760802","volume":"40","author":"M Planck","year":"1890","unstructured":"Planck M (1890b) \u00dcber die Potentialdifferenz zwischen zwei verd\u00fcnnten L\u00f6sungen bin\u00e4rer Electrolyte. Wied Ann Phys 40:561\u2013576. Reprinted in: Ostwalds Klassiker der exacten Wissenschaften, vol 299 Harri Deutsch, Frankfurt am Main, pp 139\u2013154","journal-title":"Wied Ann Phys"},{"key":"233-1_CR12","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1007\/BF01330612","volume":"94","author":"M Planck","year":"1935","unstructured":"Planck M (1935) Zur Theorie der Elektrizit\u00e4tserregung in Electrolyten. Zeitschr f Phys 94:469\u2013472. Reprinted in: Ostwalds Klassiker der exacten Wissenschaften, vol 299 Harri Deutsch, Frankfurt am Main, pp 229\u2013232","journal-title":"Zeitschr f Phys"},{"key":"233-1_CR13","doi-asserted-by":"publisher","first-page":"e21204","DOI":"10.1371\/journal.pone.0021204","volume":"6","author":"C Song","year":"2011","unstructured":"Song C, Corry B (2011) Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations. PLoS One 6:e21204","journal-title":"PLoS One"},{"key":"233-1_CR14","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1515\/zpch-1887-0151","volume":"1","author":"JH van\u2019t Hoff","year":"1887","unstructured":"van\u2019t Hoff JH (1887) Die Rolle des osmotischen Druckes in der Analogie zwischen L\u00f6sungen und Gasen. Zeitschr f Phys Chem 1:481\u2013508","journal-title":"Zeitschr f Phys Chem"}],"container-title":["Encyclopedia of Computational Neuroscience"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4614-7320-6_233-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,16]],"date-time":"2023-02-16T22:38:34Z","timestamp":1676587114000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-1-4614-7320-6_233-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9781461473206"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-1-4614-7320-6_233-1","relation":{},"subject":[],"published":{"date-parts":[[2014]]},"assertion":[{"value":"12 February 2014, 15:21:19","order":1,"name":"received","label":"Received","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"12 February 2014, 15:21:19","order":2,"name":"accepted","label":"Accepted","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"20 April 2014","order":3,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}