We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with...We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with a special rate kernel. For the system without monomer input, the concentration aj（t） of the Aj clusters （j 〉 1） asymptotically retains a nonzero quantity, while for the system with monomer input, it decays with time and vanishes finally. We also investigate the kinetics of an interesting model with fixed-rate monomer adsorption. For the ease without monomer source, the evolution of the system will halt at a finite time; while the system evolves infinitely in time in the case with monomer source. Finally, we also suggest a connection between the fixed-rate monomer adsorption systems and growing networks.展开更多
To improve design capabilities for the knitted fabric pattern,a preliminary study is carried out for the design method.Based on mathematical theory,pattern could be created automatically by computer with inputting dif...To improve design capabilities for the knitted fabric pattern,a preliminary study is carried out for the design method.Based on mathematical theory,pattern could be created automatically by computer with inputting different parameters for mathematical functions.The knitted fabric simulation is realized by M1 CAD pattern preparation system of STOLL Company.In the pattern,different color unit is replaced by obverse stitch with different color,or by obverse stitch and reverse stitch with the same color separately,after that the effects of knitted fabrics could be simulated.Designing with this method,it would not only help to acquire a great of diversity patterns,but also improve design efficiency and save cost.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10775104 and 10305009
文摘We propose a monomer adsorption model, in which only the monomers are allowed to diffuse and adsorb onto other clusters. By means of the generalized rate equation we investigate the kinetic behavior of the system with a special rate kernel. For the system without monomer input, the concentration aj（t） of the Aj clusters （j 〉 1） asymptotically retains a nonzero quantity, while for the system with monomer input, it decays with time and vanishes finally. We also investigate the kinetics of an interesting model with fixed-rate monomer adsorption. For the ease without monomer source, the evolution of the system will halt at a finite time; while the system evolves infinitely in time in the case with monomer source. Finally, we also suggest a connection between the fixed-rate monomer adsorption systems and growing networks.
基金Doctoral fundation of Tianjin Polytechnic University,China(No.029066)
文摘To improve design capabilities for the knitted fabric pattern,a preliminary study is carried out for the design method.Based on mathematical theory,pattern could be created automatically by computer with inputting different parameters for mathematical functions.The knitted fabric simulation is realized by M1 CAD pattern preparation system of STOLL Company.In the pattern,different color unit is replaced by obverse stitch with different color,or by obverse stitch and reverse stitch with the same color separately,after that the effects of knitted fabrics could be simulated.Designing with this method,it would not only help to acquire a great of diversity patterns,but also improve design efficiency and save cost.
