In[Liu L.,Chen S.,Feng L.,Wang J.,Zhang S.,Chen Y.,Si X.,Zheng L.,Analysis of the anomalous diffusion in comb structure with absorbing boundary conditions,J.Comput.Phys.490:112315,2023],an anomalous diffusion model in...In[Liu L.,Chen S.,Feng L.,Wang J.,Zhang S.,Chen Y.,Si X.,Zheng L.,Analysis of the anomalous diffusion in comb structure with absorbing boundary conditions,J.Comput.Phys.490:112315,2023],an anomalous diffusion model in comb structure is simulated by finite difference method,which exhibits a low convergence rate in time compared to space.It inspires us to enhance temporal convergence accuracy for this interesting problem.In this paper,we first consider the finite difference method of normal diffusion equation in comb structure which can be viewed as a natural generalization of the anomalous diffusion case.Then we use finite difference method to solve the above anomalous diffusion problem.Unlike the existed work which employs L1 method to discrete the fractional derivative of the considered equation,the Crank-Nicolson method is used for integer-order problem and L2-1σmethod is used for fractional problem here.For these two proposed numerical schemes,their stability and convergence are discussed,respectively.For the fractional problem,the present convergence result shows that the accuracy in time has been obviously improved compared with the existed work.Finally,the obtained theoretical results are verified by some numerical tests.展开更多
Micromachined comb-drive electrostatic resonators with folded-cantilever beams were designed and fabricated. A combination of Rayleigh＇s method and finite-element analysis was used to calculate the resonant frequency...Micromachined comb-drive electrostatic resonators with folded-cantilever beams were designed and fabricated. A combination of Rayleigh＇s method and finite-element analysis was used to calculate the resonant frequency drift as we adjusted the device geometry and material parameters. Three micromachined lateral resonant resonators with different beam widths were fabricated. Their resonant frequencies were experimentally measured to be 64.5,147.2, and 255.5kHz, respectively, which are in good agreement with the simulated resonant frequency. It is shown that an improved frequency performance could be obtained on the poly 3C-SiC based device structural material systems with high Young＇s modulus.展开更多
FELiChEM is an infrared free electron laser（FEL） facility currently under construction, which consists of two oscillators generating middle-infrared and far-infrared laser covering the spectral range of 2.5–200 μm...FELiChEM is an infrared free electron laser（FEL） facility currently under construction, which consists of two oscillators generating middle-infrared and far-infrared laser covering the spectral range of 2.5–200 μm. In this paper, we numerically study the output characteristics of the middle-infrared oscillator with accurate cavity length detuning. Emphasis is put on the temporal structure of the micropulse and the corresponding spectral bandwidth.Taking the radiation wavelengths of 50 μm and 5 μm as examples, we show that the output pulse duration can be tuned in the range of 1–6 ps with corresponding bandwidth of 13%–0.2% by adjusting the cavity length detuning.In addition, a special discussion on the comb structure is presented, and it is indicated that the comb structure may arise in the output optical pulse when the normalized slippage length is much smaller than unity. This work has reference value for the operation of FELiChEM and other FEL oscillators.展开更多
Construction of macro-materials with highly oriented microstructures and well-connected interfaces between building blocks is significant for a variety of applications. However, it is still challenging to confine the ...Construction of macro-materials with highly oriented microstructures and well-connected interfaces between building blocks is significant for a variety of applications. However, it is still challenging to confine the desired structures. Thus, well-defined building blocks would be crucial to address this issue. Herein, we present a facile process based on 1.8 nm Pd nanoclusters （NCs） to achieve centimeter-size assemblages with aligned honeycomb structures, where the diameter of a single tubular moiety is -4 μm. Layered and disordered porous assemblages were also obtained by modulating the temperature in this system. The reconciled interactions between the NCs were crucial to the assemblages. As a comparison, 14 nm Pd nanoparticles formed only aggregates. This work highlights the approach of confining the size of the building blocks in order to better control the assembly process and improve the stability of the structures.展开更多
基金supported by the Research Foundation of Education Commission of Hunan Province of China(Grant No.23A0126)supported by the National Natural Science Foundation of China(Grant No.12301533).
文摘In[Liu L.,Chen S.,Feng L.,Wang J.,Zhang S.,Chen Y.,Si X.,Zheng L.,Analysis of the anomalous diffusion in comb structure with absorbing boundary conditions,J.Comput.Phys.490:112315,2023],an anomalous diffusion model in comb structure is simulated by finite difference method,which exhibits a low convergence rate in time compared to space.It inspires us to enhance temporal convergence accuracy for this interesting problem.In this paper,we first consider the finite difference method of normal diffusion equation in comb structure which can be viewed as a natural generalization of the anomalous diffusion case.Then we use finite difference method to solve the above anomalous diffusion problem.Unlike the existed work which employs L1 method to discrete the fractional derivative of the considered equation,the Crank-Nicolson method is used for integer-order problem and L2-1σmethod is used for fractional problem here.For these two proposed numerical schemes,their stability and convergence are discussed,respectively.For the fractional problem,the present convergence result shows that the accuracy in time has been obviously improved compared with the existed work.Finally,the obtained theoretical results are verified by some numerical tests.
文摘Micromachined comb-drive electrostatic resonators with folded-cantilever beams were designed and fabricated. A combination of Rayleigh＇s method and finite-element analysis was used to calculate the resonant frequency drift as we adjusted the device geometry and material parameters. Three micromachined lateral resonant resonators with different beam widths were fabricated. Their resonant frequencies were experimentally measured to be 64.5,147.2, and 255.5kHz, respectively, which are in good agreement with the simulated resonant frequency. It is shown that an improved frequency performance could be obtained on the poly 3C-SiC based device structural material systems with high Young＇s modulus.
基金Supported by National Natural Science Foundation of China(21327901,11205156)
文摘FELiChEM is an infrared free electron laser（FEL） facility currently under construction, which consists of two oscillators generating middle-infrared and far-infrared laser covering the spectral range of 2.5–200 μm. In this paper, we numerically study the output characteristics of the middle-infrared oscillator with accurate cavity length detuning. Emphasis is put on the temporal structure of the micropulse and the corresponding spectral bandwidth.Taking the radiation wavelengths of 50 μm and 5 μm as examples, we show that the output pulse duration can be tuned in the range of 1–6 ps with corresponding bandwidth of 13%–0.2% by adjusting the cavity length detuning.In addition, a special discussion on the comb structure is presented, and it is indicated that the comb structure may arise in the output optical pulse when the normalized slippage length is much smaller than unity. This work has reference value for the operation of FELiChEM and other FEL oscillators.
文摘Construction of macro-materials with highly oriented microstructures and well-connected interfaces between building blocks is significant for a variety of applications. However, it is still challenging to confine the desired structures. Thus, well-defined building blocks would be crucial to address this issue. Herein, we present a facile process based on 1.8 nm Pd nanoclusters （NCs） to achieve centimeter-size assemblages with aligned honeycomb structures, where the diameter of a single tubular moiety is -4 μm. Layered and disordered porous assemblages were also obtained by modulating the temperature in this system. The reconciled interactions between the NCs were crucial to the assemblages. As a comparison, 14 nm Pd nanoparticles formed only aggregates. This work highlights the approach of confining the size of the building blocks in order to better control the assembly process and improve the stability of the structures.
