In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's m...In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.展开更多
This work aimed to quantify the physical and mechanical behavior of three-dimensional microstructures in rocks under uniaxial compression.A high-precision in situ XCT(X-ray transmission computed tomography)technology ...This work aimed to quantify the physical and mechanical behavior of three-dimensional microstructures in rocks under uniaxial compression.A high-precision in situ XCT(X-ray transmission computed tomography)technology was applied to investigating the behavior of mineral grains in sandstone:the movement,the rotation deformation,and the principal strains between fault zone and non-fault zone.The results indicate that after unloading,the shear strain of mineral grains is periodic in the radial direction,the strain of mineral grains in the fracture zone is about 30 times of the macro strain of the specimen,which is about 5 times in the non-fracture zone,and the shear strain near the fault zone is larger than the compressive strain,and there is the shear stress concentration feature.展开更多
This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the cor...This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.展开更多
Resonance enhancement has been increasingly employed in the emergent felntosecond stimu- lated Raman spectroscopy （FSRS） to selectively monitor molecular structure and dynamics with improved spectral and temporal re...Resonance enhancement has been increasingly employed in the emergent felntosecond stimu- lated Raman spectroscopy （FSRS） to selectively monitor molecular structure and dynamics with improved spectral and temporal resolutions and signal-to-noise ratios. Such joint eflforts by the technique- and application-oriented scientists and engineers have laid the foundation for exploiting the tunable FSRS methodology to investigate a great variety of photosensitive systems and elucidate the underlying functional mechanisms on molecular time scales. Dur- ing spectral analysis, peak line shapes remain a major concern with an intricate dependence on resonance conditions. Here, we present a comprehensive study of line shapes by tuning the Rarnan pump wavelength from red to blue side of the ground-state absorption band of the fluorescent dye rhodarnine 6G in solution. Distinct line shape patterns in Stokes and anti-Stokes FSRS as well as from the low to high-frequency modes highlight the competition between multiple third-order and higher-order nonlinear pathways, governed by difl^rent res- onance conditions achieved by Raman pump and probe pulses. In particular, the resonance condition of probe wavelength is revealed to play an important role in generating circular line shape changes through oppositely phased dispersion via hot luminescence （HL） pathways. Meanwhile, on-resonance conditions of the Rarnan pump could promote excited-state vibrational modes which are broadened and red-shifted from the coincident ground-state vibrational modes, posing challenges for spectral analysis. Certain strategies in tuning the Raman pump and probe to characteristic regions across an electronic transition band are discussed to improve the FSRS usability and versatility as a powerful structural dynamics toolset to advance chemical, physical, materials, and biological sciences.展开更多
文摘In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.
基金financially supported in part by the National Key Research and Development Program of China(No.2017YFC0602901)。
文摘This work aimed to quantify the physical and mechanical behavior of three-dimensional microstructures in rocks under uniaxial compression.A high-precision in situ XCT(X-ray transmission computed tomography)technology was applied to investigating the behavior of mineral grains in sandstone:the movement,the rotation deformation,and the principal strains between fault zone and non-fault zone.The results indicate that after unloading,the shear strain of mineral grains is periodic in the radial direction,the strain of mineral grains in the fracture zone is about 30 times of the macro strain of the specimen,which is about 5 times in the non-fracture zone,and the shear strain near the fault zone is larger than the compressive strain,and there is the shear stress concentration feature.
基金Supported by Natural Science Foundation of China(1077107410771139)+1 种基金Supported by the NSF of Wenzhou University(2007L024)Supported by the NSF of Zhejiang Province(Y6080077)
文摘This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R^2. The authors prove the existence of L^2-global attractor and Hi-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.
基金supported by the U.S.National Science Foundation CAREER grant(CHE-1455353)the Oregon State University(OSU) Research Equipment Reserve Fund(Spring 2014)to C.Fang(USTC9603)the Wei Family Private Foundation in supporting C.Chen(USTC 0903) during his graduate studies at OSU Chemistry
文摘Resonance enhancement has been increasingly employed in the emergent felntosecond stimu- lated Raman spectroscopy （FSRS） to selectively monitor molecular structure and dynamics with improved spectral and temporal resolutions and signal-to-noise ratios. Such joint eflforts by the technique- and application-oriented scientists and engineers have laid the foundation for exploiting the tunable FSRS methodology to investigate a great variety of photosensitive systems and elucidate the underlying functional mechanisms on molecular time scales. Dur- ing spectral analysis, peak line shapes remain a major concern with an intricate dependence on resonance conditions. Here, we present a comprehensive study of line shapes by tuning the Rarnan pump wavelength from red to blue side of the ground-state absorption band of the fluorescent dye rhodarnine 6G in solution. Distinct line shape patterns in Stokes and anti-Stokes FSRS as well as from the low to high-frequency modes highlight the competition between multiple third-order and higher-order nonlinear pathways, governed by difl^rent res- onance conditions achieved by Raman pump and probe pulses. In particular, the resonance condition of probe wavelength is revealed to play an important role in generating circular line shape changes through oppositely phased dispersion via hot luminescence （HL） pathways. Meanwhile, on-resonance conditions of the Rarnan pump could promote excited-state vibrational modes which are broadened and red-shifted from the coincident ground-state vibrational modes, posing challenges for spectral analysis. Certain strategies in tuning the Raman pump and probe to characteristic regions across an electronic transition band are discussed to improve the FSRS usability and versatility as a powerful structural dynamics toolset to advance chemical, physical, materials, and biological sciences.
