{"title":"一种扩散模型，基于杰弗里斯型方程","authors":"S. Rukolaine, A. Samsonov","doi":"10.1109/DD.2013.6712816","DOIUrl":null,"url":null,"abstract":"The diffusion equation (DE) is widely used for approximate description of non-anomalous diffusion and Brownian motion (BM). However, the DE is wrong in describing the mean-square displacement (MSD) of a particle at small values of time, where the MSD must be ballistic. We consider the equation of the Jeffreys type as a model equation for description of diffusion. We find that the MSD in the framework of this model is the same as that in the BM described by the standard Langevin equation.","PeriodicalId":340014,"journal":{"name":"Proceedings of the International Conference Days on Diffraction 2013","volume":"96 2-3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A model of diffusion, based on the equation of the Jeffreys type\",\"authors\":\"S. Rukolaine, A. Samsonov\",\"doi\":\"10.1109/DD.2013.6712816\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The diffusion equation (DE) is widely used for approximate description of non-anomalous diffusion and Brownian motion (BM). However, the DE is wrong in describing the mean-square displacement (MSD) of a particle at small values of time, where the MSD must be ballistic. We consider the equation of the Jeffreys type as a model equation for description of diffusion. We find that the MSD in the framework of this model is the same as that in the BM described by the standard Langevin equation.\",\"PeriodicalId\":340014,\"journal\":{\"name\":\"Proceedings of the International Conference Days on Diffraction 2013\",\"volume\":\"96 2-3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the International Conference Days on Diffraction 2013\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/DD.2013.6712816\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the International Conference Days on Diffraction 2013","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/DD.2013.6712816","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A model of diffusion, based on the equation of the Jeffreys type
The diffusion equation (DE) is widely used for approximate description of non-anomalous diffusion and Brownian motion (BM). However, the DE is wrong in describing the mean-square displacement (MSD) of a particle at small values of time, where the MSD must be ballistic. We consider the equation of the Jeffreys type as a model equation for description of diffusion. We find that the MSD in the framework of this model is the same as that in the BM described by the standard Langevin equation.
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