One dimensional periodic hopping model is useful to understand the motion of microscopic particles in thermal noise environment. In this research, by formal calculation and based on detailed balance, the explicit expr...One dimensional periodic hopping model is useful to understand the motion of microscopic particles in thermal noise environment. In this research, by formal calculation and based on detailed balance, the explicit expressions of the limits of mean velocity and diffusion constant of this model as the number of internal mechanochemical sates tend to infinity are obtained.These results will be helpful to understand the limit of the one dimensional hopping model.At the same time, the work can be used to get more useful results in continuous form from the corresponding ones obtained by discrete models.展开更多
The periodic one-dimensional hopping model is useful for studying the motion of microscopic particles in the thermal noise environment. Based on the explicit formulations of mean velocity, mean first passage time and ...The periodic one-dimensional hopping model is useful for studying the motion of microscopic particles in the thermal noise environment. Based on the explicit formulations of mean velocity, mean first passage time and effective diffusion constant, a general N internal states or even infinite internal states model can be approximated by a one state model that retains the basic properties of the original process. This effective description aids the analysis of biochemical and biophysical problems. This effective description also implies that, to some extent, many processes can be well described by simple two-state models, or even one-state models.展开更多
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.10701029） and the Shanghai Key Laboratory for Contemporary Applied Mathematics （No.SGST09DZ2272900）.
文摘One dimensional periodic hopping model is useful to understand the motion of microscopic particles in thermal noise environment. In this research, by formal calculation and based on detailed balance, the explicit expressions of the limits of mean velocity and diffusion constant of this model as the number of internal mechanochemical sates tend to infinity are obtained.These results will be helpful to understand the limit of the one dimensional hopping model.At the same time, the work can be used to get more useful results in continuous form from the corresponding ones obtained by discrete models.
基金the National Natural Science Foundation of China(Grant No. 10701029)
文摘The periodic one-dimensional hopping model is useful for studying the motion of microscopic particles in the thermal noise environment. Based on the explicit formulations of mean velocity, mean first passage time and effective diffusion constant, a general N internal states or even infinite internal states model can be approximated by a one state model that retains the basic properties of the original process. This effective description aids the analysis of biochemical and biophysical problems. This effective description also implies that, to some extent, many processes can be well described by simple two-state models, or even one-state models.
