{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T08:25:52Z","timestamp":1772439952189,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2010,7,27]],"date-time":"2010-07-27T00:00:00Z","timestamp":1280188800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Stat Phys"],"published-print":{"date-parts":[[2010,9]]},"DOI":"10.1007\/s10955-010-0023-8","type":"journal-article","created":{"date-parts":[[2010,7,26]],"date-time":"2010-07-26T13:38:48Z","timestamp":1280151528000},"page":"948-984","source":"Crossref","is-referenced-by-count":17,"title":["Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties"],"prefix":"10.1007","volume":"140","author":[{"given":"Francis","family":"Comets","sequence":"first","affiliation":[]},{"given":"Serguei","family":"Popov","sequence":"additional","affiliation":[]},{"given":"Gunter M.","family":"Sch\u00fctz","sequence":"additional","affiliation":[]},{"given":"Marina","family":"Vachkovskaia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,7,27]]},"reference":[{"key":"23_CR1","unstructured":"Aldous, D., Fill, J.: Reversible Markov chains and random walks on graphs. http:\/\/www.stat.berkeley.edu\/~aldous\/RWG\/Chap3.pdf"},{"issue":"3\/4","key":"23_CR2","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s10955-005-7578-9","volume":"121","author":"C. Bernardin","year":"2005","unstructured":"Bernardin, C., Olla, S.: Fourier law and fluctuations for a microscopic model of heat conduction. J.\u00a0Stat. Phys. 121(3\/4), 271\u2013289 (2005)","journal-title":"J.\u00a0Stat. Phys."},{"key":"23_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8163-0","volume-title":"Handbook of Brownian Motion\u2014Facts and Formulae","author":"A.N. Borodin","year":"2002","unstructured":"Borodin, A.N., Salminen, P.: Handbook of Brownian Motion\u2014Facts and Formulae, 2nd edn. Birkh\u00e4user, Basel-Boston-Berlin (2002)","edition":"2"},{"key":"23_CR4","volume-title":"Linear Transport Theory","author":"K.M. Case","year":"1967","unstructured":"Case, K.M., Zweifel, P.F.: Linear Transport Theory. Addison-Wesley, Reading (1967)"},{"key":"23_CR5","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.1090\/S0002-9939-09-09945-6","volume":"137","author":"Z.-Q. Chen","year":"2009","unstructured":"Chen, Z.-Q.: On notions of harmonicity. Proc. Am. Math. Soc. 137, 3497\u20133510 (2009)","journal-title":"Proc. Am. Math. Soc."},{"issue":"3","key":"23_CR6","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/s00205-008-0120-x","volume":"191","author":"F. Comets","year":"2009","unstructured":"Comets, F., Popov, S., Sch\u00fctz, G.M., Vachkovskaia, M.: Billiards in a general domain with random reflections. Arch. Ration. Mech. Anal. 191(3), 497\u2013537 (2009)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"23_CR7","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1007\/s00205-009-0236-7","volume":"193","author":"F. Comets","year":"2009","unstructured":"Comets, F., Popov, S., Sch\u00fctz, G.M., Vachkovskaia, M.: Erratum. Arch. Ration. Mech. Anal. 193, 737\u2013738 (2009)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"3","key":"23_CR8","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1214\/09-AOP504","volume":"38","author":"F. Comets","year":"2010","unstructured":"Comets, F., Popov, S., Sch\u00fctz, G.M., Vachkovskaia, M.: Quenched invariance principle for Knudsen stochastic billiard in random tube. Ann. Probab. 38(3), 1019\u20131061 (2010)","journal-title":"Ann. Probab."},{"key":"23_CR9","volume-title":"Introduction to Queueing Theory","author":"R.B. Cooper","year":"1981","unstructured":"Cooper, R.B.: Introduction to Queueing Theory, 2nd edn. North Holland, Amsterdam (1981)","edition":"2"},{"key":"23_CR10","series-title":"Elementary Theory and Methods","volume-title":"An Introduction to the Theory of Point Processes","author":"D.J. Daley","year":"2003","unstructured":"Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes. Elementary Theory and Methods, vol.\u00a0I, 2nd edn. Springer, New York (2003)","edition":"2"},{"key":"23_CR11","volume-title":"Stochastic Processes","author":"J.L. Doob","year":"1953","unstructured":"Doob, J.L.: Stochastic Processes. Wiley, New York (1953)"},{"key":"23_CR12","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1007\/BF01041608","volume":"55","author":"A. Masi De","year":"1989","unstructured":"De Masi, A., Ferrari, P., Goldstein, S., Wick, W.: An invariance principle for reversible Markov processes. Applications to random motions in random environments. J.\u00a0Stat. Phys. 55, 787\u2013855 (1989)","journal-title":"J.\u00a0Stat. Phys."},{"key":"23_CR13","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s00220-005-1492-5","volume":"263","author":"A. Faggionato","year":"2006","unstructured":"Faggionato, A., Schulz-Baldes, H., Spehner, D.: Mott law as lower bound for a random walk in a random environment. Commun. Math. Phys. 263, 21\u201364 (2006)","journal-title":"Commun. Math. Phys."},{"key":"23_CR14","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/10\/10\/103004","volume":"10","author":"P. Gaspard","year":"2008","unstructured":"Gaspard, P., Gilbert, T.: Heat conduction and Fourier\u2019s law in a class of many particle dispersing billiards. New J. Phys. 10, 103004 (2008)","journal-title":"New J. Phys."},{"key":"23_CR15","volume-title":"Diffusion in Condensed Matter\u2014Methods, Materials, Models","year":"2005","unstructured":"Heitjans, P., K\u00e4rger, J. (eds.): Diffusion in Condensed Matter\u2014Methods, Materials, Models. Springer, Berlin-Heidelberg (2005)"},{"key":"23_CR16","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00537539","volume":"45","author":"T.M. Liggett","year":"1978","unstructured":"Liggett, T.M.: Random invariant measures for Markov chains, and independent particle systems. Z.\u00a0Wahrscheinlichkeitstheor. verw. Geb 45, 297\u2013313 (1978)","journal-title":"Z.\u00a0Wahrscheinlichkeitstheor. verw. Geb"},{"issue":"12","key":"23_CR17","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.87.125505","volume":"87","author":"K. Malek","year":"2001","unstructured":"Malek, K., Coppens, M.-O.: Effects of surface roughness on self- and transport diffusion in porous media in the Knudsen regime. Phys. Rev. Lett. 87(12), 125505 (2001)","journal-title":"Phys. Rev. Lett."},{"key":"23_CR18","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/S0927-7757(02)00050-X","volume":"206","author":"K. Malek","year":"2003","unstructured":"Malek, K., Coppens, M.-O.: Pore roughness effects on self- and transport diffusion in nanoporous materials. Colloids Surf. A 206, 335\u2013348 (2003)","journal-title":"Colloids Surf. A"},{"issue":"5","key":"23_CR19","doi-asserted-by":"crossref","first-page":"2801","DOI":"10.1063\/1.1584652","volume":"119","author":"K. Malek","year":"2003","unstructured":"Malek, K., Coppens, M.-O.: Knudsen self- and Fickian diffusion in rough nanoporous media. J.\u00a0Chem. Phys. 119(5), 2801\u20132811 (2003)","journal-title":"J.\u00a0Chem. Phys."},{"issue":"5","key":"23_CR20","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1007\/s10955-007-9465-z","volume":"130","author":"P. Mathieu","year":"2008","unstructured":"Mathieu, P.: Quenched invariance principles for random walks with random conductances. J.\u00a0Stat. Phys. 130(5), 1025\u20131046 (2008)","journal-title":"J.\u00a0Stat. Phys."},{"issue":"6","key":"23_CR21","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1007\/s10955-008-9578-z","volume":"132","author":"M.V. Menshikov","year":"2008","unstructured":"Menshikov, M.V., Vachkovskaia, M., Wade, A.R.: Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains. J.\u00a0Stat. Phys. 132(6), 1097\u20131133 (2008)","journal-title":"J.\u00a0Stat. Phys."},{"key":"23_CR22","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.72.030101","volume":"72","author":"S. Russ","year":"2005","unstructured":"Russ, S., Zschiegner, S., Bunde, A., K\u00e4rger, J.: Lambert diffusion in porous media in the Knudsen regime: equivalence of self- and transport diffusion. Phys. Rev. E 72, 030101(R) (2005)","journal-title":"Phys. Rev. E"},{"key":"23_CR23","volume":"127","author":"V.J. Hijkoop van","year":"2007","unstructured":"van Hijkoop, V.J., Dammers, A.J., Malek, K., Coppens, M.-O.: Water diffusion through a membrane protein channel: a\u00a0first passage time approach. J.\u00a0Chem. Phys. 127, 085101 (2007)","journal-title":"J.\u00a0Chem. Phys."},{"issue":"2","key":"23_CR24","doi-asserted-by":"crossref","DOI":"10.1209\/0295-5075\/78\/20001","volume":"78","author":"S. Zschiegner","year":"2007","unstructured":"Zschiegner, S., Russ, S., Bunde, A., K\u00e4rger, J.: Pore opening effects and transport diffusion in the Knudsen regime in comparison to self- (or tracer-) diffusion. Europhys. Lett. 78(2), 200001 (2007)","journal-title":"Europhys. Lett."},{"key":"23_CR25","doi-asserted-by":"crossref","first-page":"17.1","DOI":"10.62721\/diffusion-fundamentals.7.159","volume":"7","author":"S. Zschiegner","year":"2007","unstructured":"Zschiegner, S., Russ, S., Bunde, A., Coppens, M.-O., K\u00e4rger, J.: Normal and anomalous Knudsen diffusion in 2D and 3D channel pores. Diffus. Fundam 7, 17.1\u201317.2 (2007)","journal-title":"Diffus. Fundam"},{"key":"23_CR26","first-page":"109","volume":"161","author":"S. Zschiegner","year":"2008","unstructured":"Zschiegner, S., Russ, S., Valiullin, R., Coppens, M.-O., Dammers, A.-J., Bunde, A., K\u00e4rger, J.: Normal and anomalous diffusion of non-interacting particles in linear nanopores. Eur. Phys. J. 161, 109 (2008)","journal-title":"Eur. Phys. J."}],"container-title":["Journal of Statistical Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-010-0023-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10955-010-0023-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-010-0023-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,23]],"date-time":"2025-02-23T10:32:08Z","timestamp":1740306728000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10955-010-0023-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,27]]},"references-count":26,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["23"],"URL":"https:\/\/doi.org\/10.1007\/s10955-010-0023-8","relation":{},"ISSN":["0022-4715","1572-9613"],"issn-type":[{"value":"0022-4715","type":"print"},{"value":"1572-9613","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,27]]}}}