Визначення параметрів субдиффузійного рівняння на підставі даних SPT експерименту
A method is proposed of determining the subdiffuson equation parameters. The method is based on a single particle tracking experiment data analysis. The combination of random barriers model and random traps model is considered as a model of subdiffusion. Subdiffusion equation related to this model c...
Збережено в:
| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine
2016
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| Теми: | |
| Онлайн доступ: | https://www.cpts.com.ua/index.php/cpts/article/view/377 |
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| Назва журналу: | Chemistry, Physics and Technology of Surface |
Репозитарії
Chemistry, Physics and Technology of Surface| Резюме: | A method is proposed of determining the subdiffuson equation parameters. The method is based on a single particle tracking experiment data analysis. The combination of random barriers model and random traps model is considered as a model of subdiffusion. Subdiffusion equation related to this model contains two memory functions as a parameters. The first function characterizes the distribution of the heights of barriers, the other one characterizes the distribution of the depths of traps. Within the framework of the model under consideration, expressions are derived for the mean square displacement of particles averaged over time and over the ensemble. Expressions are derived for random walks in unlimited space and in a restricted domain of arbitrary shape with the reflectiing boundary. It has been shown that the derived expressions allow us to determine the memory functions appearing in subdiffusion equation. For this purpose, single particle tracking experiment data should be approximated by using these expressions. The method proposed can be used for modeling the diffusion controlled reactions in disordered media. |
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