Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respecti...Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended -expansion method, substituting the solutions obtained into the corresponding transformation of variables, the decay mode solutions of the three (2 + 1)-dimensional equations have been obtained successfully.展开更多
Real-time atomic force microscopy (AFM) imaging revealed for the first time, the detailed growth/dissolution mechanism of Lauryl glycol (LG) or 1, 2 dodecanediol molecules on HOPG at the nano-level after recrystallizi...Real-time atomic force microscopy (AFM) imaging revealed for the first time, the detailed growth/dissolution mechanism of Lauryl glycol (LG) or 1, 2 dodecanediol molecules on HOPG at the nano-level after recrystallizing them from chloroform solution. At the early stage of recrystallization, parallelogram-like-structures having lengths of several microns and distinct widths (between ~ 100 - 400 nm) were observed. Growth/dissolution behavior of these parallelogram-like-structures as a function of time was investigated. While dissolution occurred along all three dimensions, growth was found to be strictly two dimensional. Both the growth and dissolution process were found to be logarithmic in nature. The average growth rates along their length and width were found to be 11 nm/min and 1.5 nm/min respectively. Average dissolution rate in percentage on HOPG surface was found to be ~ 0.078%/min. Based upon the recrystallization of LG molecules schematics are drawn for a better understanding of the recrystallization process.展开更多
文摘Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended -expansion method, substituting the solutions obtained into the corresponding transformation of variables, the decay mode solutions of the three (2 + 1)-dimensional equations have been obtained successfully.
文摘Real-time atomic force microscopy (AFM) imaging revealed for the first time, the detailed growth/dissolution mechanism of Lauryl glycol (LG) or 1, 2 dodecanediol molecules on HOPG at the nano-level after recrystallizing them from chloroform solution. At the early stage of recrystallization, parallelogram-like-structures having lengths of several microns and distinct widths (between ~ 100 - 400 nm) were observed. Growth/dissolution behavior of these parallelogram-like-structures as a function of time was investigated. While dissolution occurred along all three dimensions, growth was found to be strictly two dimensional. Both the growth and dissolution process were found to be logarithmic in nature. The average growth rates along their length and width were found to be 11 nm/min and 1.5 nm/min respectively. Average dissolution rate in percentage on HOPG surface was found to be ~ 0.078%/min. Based upon the recrystallization of LG molecules schematics are drawn for a better understanding of the recrystallization process.
