A variable-order fractal derivative model for anomalous diffusion
Апстракт
This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the previous mentioned anomalous diffusion (or transport) processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior, and heavy tail phenomena of the new model, and variable-order fractional derivative model are also offered.
Кључне речи:
variable-order fractal derivative / stretced Gaussian distribution / porosity-gradient / anomalous diffusionИзвор:
Thermal Science, 2017, 21, 1, 51-59Издавач:
- Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd
Финансирање / пројекти:
- National Science Foundation of China [11572112, 11528205]
- Serbia-China bilateral project [3-12
DOI: 10.2298/TSCI160415244L
ISSN: 0354-9836
WoS: 000396378300007
Scopus: 2-s2.0-85015698419
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Liu, Xiaoting AU - Sun, HongGuang AU - Lazarević, Mihailo AU - Fu, Zhuojia PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2558 AB - This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the previous mentioned anomalous diffusion (or transport) processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior, and heavy tail phenomena of the new model, and variable-order fractional derivative model are also offered. PB - Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd T2 - Thermal Science T1 - A variable-order fractal derivative model for anomalous diffusion EP - 59 IS - 1 SP - 51 VL - 21 DO - 10.2298/TSCI160415244L ER -
@article{ author = "Liu, Xiaoting and Sun, HongGuang and Lazarević, Mihailo and Fu, Zhuojia", year = "2017", abstract = "This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the previous mentioned anomalous diffusion (or transport) processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior, and heavy tail phenomena of the new model, and variable-order fractional derivative model are also offered.", publisher = "Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd", journal = "Thermal Science", title = "A variable-order fractal derivative model for anomalous diffusion", pages = "59-51", number = "1", volume = "21", doi = "10.2298/TSCI160415244L" }
Liu, X., Sun, H., Lazarević, M.,& Fu, Z.. (2017). A variable-order fractal derivative model for anomalous diffusion. in Thermal Science Univerzitet u Beogradu - Institut za nuklearne nauke Vinča, Beograd., 21(1), 51-59. https://doi.org/10.2298/TSCI160415244L
Liu X, Sun H, Lazarević M, Fu Z. A variable-order fractal derivative model for anomalous diffusion. in Thermal Science. 2017;21(1):51-59. doi:10.2298/TSCI160415244L .
Liu, Xiaoting, Sun, HongGuang, Lazarević, Mihailo, Fu, Zhuojia, "A variable-order fractal derivative model for anomalous diffusion" in Thermal Science, 21, no. 1 (2017):51-59, https://doi.org/10.2298/TSCI160415244L . .