For a graphlike manifold whose contraction is a generalized cuneate figure,we deribve a formula in this paper to compute the number of homeomorphism classes of it by using twist operations and the combinatorial theory.
We conducted experiments on specially designed microfluidic chips that generate droplets through a microfluidic ow-focusing approach. The fluid flow in the microfluidic channel produced a shear flow field at low Reyno...We conducted experiments on specially designed microfluidic chips that generate droplets through a microfluidic ow-focusing approach. The fluid flow in the microfluidic channel produced a shear flow field at low Reynolds numbers. The droplets in the microfluidic system exhibited special droplet pattern formations similar to periodic crystal-like lattices because of the competition between shear forces and surface tension. By adjusting the flow rate ratio of the water （droplet phase） to oil （continuous phase） phases and changing the outlet channel widths, the droplets formed monolayer dispersion to double-layer formation to monolayer squeezing when the outlet channel widths were 250 or 300 μm. We also obtained droplets with monolayer dispersion, three-layer arrangements, double-layer squeezing, and monolayer squeezing when the outlet channel width was 350 μm. The outlet channel width was increased to 400 μm, and four-layer arrangements were observed. We also studied the translation of droplet formation, which resulted in a detailed strategy to control drop size and droplet pattern formation for emulsi cation in microfluidic devices. We expect that our strategy can provide theoretical guidance to synthesize dispersion or polydisperse colloid particles.展开更多
Hamiltonian of a one-dimensional Bose–Hubbard model is re-formulated by using differential realization of the boson algebra. Energy matrices can then be generated systematically by using a Mathematica package. The ou...Hamiltonian of a one-dimensional Bose–Hubbard model is re-formulated by using differential realization of the boson algebra. Energy matrices can then be generated systematically by using a Mathematica package. The output can be taken as the input of other diagonalization codes. As examples, exact energy eigenvalues and the corresponding wavefunctions for some cases are obtained with a Fortran diagonalization code. Phase transition of the model is analyzed.展开更多
文摘For a graphlike manifold whose contraction is a generalized cuneate figure,we deribve a formula in this paper to compute the number of homeomorphism classes of it by using twist operations and the combinatorial theory.
基金This work was supported by the National Natural Science Foundation of China （No.20934004 and No.91127046） and the National Basic Research Program of China （No.2012CB821500 and No.2010CB934500）.
文摘We conducted experiments on specially designed microfluidic chips that generate droplets through a microfluidic ow-focusing approach. The fluid flow in the microfluidic channel produced a shear flow field at low Reynolds numbers. The droplets in the microfluidic system exhibited special droplet pattern formations similar to periodic crystal-like lattices because of the competition between shear forces and surface tension. By adjusting the flow rate ratio of the water （droplet phase） to oil （continuous phase） phases and changing the outlet channel widths, the droplets formed monolayer dispersion to double-layer formation to monolayer squeezing when the outlet channel widths were 250 or 300 μm. We also obtained droplets with monolayer dispersion, three-layer arrangements, double-layer squeezing, and monolayer squeezing when the outlet channel width was 350 μm. The outlet channel width was increased to 400 μm, and four-layer arrangements were observed. We also studied the translation of droplet formation, which resulted in a detailed strategy to control drop size and droplet pattern formation for emulsi cation in microfluidic devices. We expect that our strategy can provide theoretical guidance to synthesize dispersion or polydisperse colloid particles.
基金The project supported by National Natural Science Foundation of China under Grant No.10175031the Natural Science Foundation of Liaoning Province of China under Grant No.2001101053
文摘Hamiltonian of a one-dimensional Bose–Hubbard model is re-formulated by using differential realization of the boson algebra. Energy matrices can then be generated systematically by using a Mathematica package. The output can be taken as the input of other diagonalization codes. As examples, exact energy eigenvalues and the corresponding wavefunctions for some cases are obtained with a Fortran diagonalization code. Phase transition of the model is analyzed.
