In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann op...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.展开更多
Hot deformation behavior of as-cast Mn18Cr18 N austenitic stainless steel was studied in the temperature range of 950-1200 ℃ and strain rate range of 0.001-1 s^（-1） using isothermal hot compression tests. The true ...Hot deformation behavior of as-cast Mn18Cr18 N austenitic stainless steel was studied in the temperature range of 950-1200 ℃ and strain rate range of 0.001-1 s^（-1） using isothermal hot compression tests. The true stress-strain curves of the steel were characterized by hardening and subsequent softening and varied with temperatures and strain rates. The hot deformation activation energy of the steel was calculated to be 657.4 k J/mol, which was higher than that of the corresponding wrought steel due to its as-cast coarse columnar grains and heterogeneous structure. Hot processing maps were developed at different plastic strains, which exhibited two domains with peak power dissipation efficiencies at 1150 ℃/0.001 s^（-1） and 1200 ℃/1 s^（-1）, respectively. The corresponding microstructures were analyzed by optical microscopy（OM）, scanning electron microscopy（SEM）, and electron backscatter diffraction（EBSD）. It has been confirmed that dynamic recrystallization（DRX） controlled by dislocation slipping and climbing mechanism occurs in the temperature and strain rate range of 1050-1200 ℃ and 0.001-0.01 s^（-1）; And DRX controlled by twinning mechanism occurs in the temperature and strain rate range of 1100-1200 ℃, 0.1-1 s^（-1）. These two DRX domains can serve as the hot working windows of the as-cast steel at lower strain rates and at higher strain rates, respectively. The processing maps at different strains also exhibit that the instability region decreases with increasing strain. The corresponding microstructures and the less tensile ductility in the instability region imply that the flow instability is attributed to flow localization accelerated by a few layers of very fine recrystallized grains along the original grain boundaries.展开更多
Laboratory-scale tests for magnesium ammonium phosphate（MAP）precipitation following urea hydrolysis of human urine were conducted using orthogonal experiment design.The effects of initial pH,temperature and the volu...Laboratory-scale tests for magnesium ammonium phosphate（MAP）precipitation following urea hydrolysis of human urine were conducted using orthogonal experiment design.The effects of initial pH,temperature and the volumetric ratios of stale urine to fresh urine,on urea hydrolysis in urine were studied to determine the final hydrolysis time to recover most nitrogen from separated human urine by MAP.With a volumetric ratio of stale to fresh urine>10% and at temperature≥20℃,urea hydrolysis could be completed in two days.Alkaline pH inhibited urea hydrolysis progress.The final pH values were all around 9.0 following urine hydrolysis,while the suspension pH might act as an indicator to detect the start and extent of urea hydrolysis.Over 95% of ammonium nitrogen and over 85% of phosphorus from hydrolyzed urine as MAP precipitate were obtained using MgCl;·6H;O and Na;HPO;·12H;O as precipitation agents at pH 8.5,molar ratio of Mg;:NH;-N:PO;-P at（1.2-1.3）:1:1,mixing speed of 120 r/min,and precipitation time and reaction time of 3 h and 15 min,respectively.The precipitate has a structure resembling pure MAP crystal.展开更多
As a parallel programming model, Map-Reduce is used for distributed computing of massive data. Map-Reduce model encapsulates the details of parallel implementation, fault-tolerant processing, local computing and load ...As a parallel programming model, Map-Reduce is used for distributed computing of massive data. Map-Reduce model encapsulates the details of parallel implementation, fault-tolerant processing, local computing and load balancing, etc., provides a simple but powerful interface. In case of having no clear idea about distributed and parallel programming, this interface can be utilized to save development time. This paper introduces the method of using Hadoop, the open-source Map-Reduce software platform, to combine PCs to carry out scalable parallel computing. Our experiment using 12 PCs to compute N-body problem based on Map-Reduce model shows that we can get a 9.8x speedup ratio. This work indicates that the Map-Reduce can be applied in scalable parallel computing.展开更多
In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficie...In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.展开更多
基金This work is supported by the National Natural Science Foundation of China(No.22103075,No.21827804,and No.22173089)the National Key R&D Program of China(No.2021YFA0716801andNo.2017YFA0303502).
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.
基金Funded by the National Natural Science Foundation of China(No.51575372)
文摘Hot deformation behavior of as-cast Mn18Cr18 N austenitic stainless steel was studied in the temperature range of 950-1200 ℃ and strain rate range of 0.001-1 s^（-1） using isothermal hot compression tests. The true stress-strain curves of the steel were characterized by hardening and subsequent softening and varied with temperatures and strain rates. The hot deformation activation energy of the steel was calculated to be 657.4 k J/mol, which was higher than that of the corresponding wrought steel due to its as-cast coarse columnar grains and heterogeneous structure. Hot processing maps were developed at different plastic strains, which exhibited two domains with peak power dissipation efficiencies at 1150 ℃/0.001 s^（-1） and 1200 ℃/1 s^（-1）, respectively. The corresponding microstructures were analyzed by optical microscopy（OM）, scanning electron microscopy（SEM）, and electron backscatter diffraction（EBSD）. It has been confirmed that dynamic recrystallization（DRX） controlled by dislocation slipping and climbing mechanism occurs in the temperature and strain rate range of 1050-1200 ℃ and 0.001-0.01 s^（-1）; And DRX controlled by twinning mechanism occurs in the temperature and strain rate range of 1100-1200 ℃, 0.1-1 s^（-1）. These two DRX domains can serve as the hot working windows of the as-cast steel at lower strain rates and at higher strain rates, respectively. The processing maps at different strains also exhibit that the instability region decreases with increasing strain. The corresponding microstructures and the less tensile ductility in the instability region imply that the flow instability is attributed to flow localization accelerated by a few layers of very fine recrystallized grains along the original grain boundaries.
文摘Laboratory-scale tests for magnesium ammonium phosphate（MAP）precipitation following urea hydrolysis of human urine were conducted using orthogonal experiment design.The effects of initial pH,temperature and the volumetric ratios of stale urine to fresh urine,on urea hydrolysis in urine were studied to determine the final hydrolysis time to recover most nitrogen from separated human urine by MAP.With a volumetric ratio of stale to fresh urine>10% and at temperature≥20℃,urea hydrolysis could be completed in two days.Alkaline pH inhibited urea hydrolysis progress.The final pH values were all around 9.0 following urine hydrolysis,while the suspension pH might act as an indicator to detect the start and extent of urea hydrolysis.Over 95% of ammonium nitrogen and over 85% of phosphorus from hydrolyzed urine as MAP precipitate were obtained using MgCl;·6H;O and Na;HPO;·12H;O as precipitation agents at pH 8.5,molar ratio of Mg;:NH;-N:PO;-P at（1.2-1.3）:1:1,mixing speed of 120 r/min,and precipitation time and reaction time of 3 h and 15 min,respectively.The precipitate has a structure resembling pure MAP crystal.
基金Project supported by the Shanghai Leading Academic Discipline Project(Grant No.J50103)the National High-Technology Research and Development Program of China(Grant No.2009AA012201)+1 种基金the Major Technology R&D Program of Shanghai(Grant No.08DZ501600)the Science and Technology Pillar Project of Jiangxi(Grant No.2010BGB00604)
文摘As a parallel programming model, Map-Reduce is used for distributed computing of massive data. Map-Reduce model encapsulates the details of parallel implementation, fault-tolerant processing, local computing and load balancing, etc., provides a simple but powerful interface. In case of having no clear idea about distributed and parallel programming, this interface can be utilized to save development time. This paper introduces the method of using Hadoop, the open-source Map-Reduce software platform, to combine PCs to carry out scalable parallel computing. Our experiment using 12 PCs to compute N-body problem based on Map-Reduce model shows that we can get a 9.8x speedup ratio. This work indicates that the Map-Reduce can be applied in scalable parallel computing.
文摘In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for the Schrödinger equation in 3-dimensional. We numerically implement the coefficients of the explicit formulas. In this work, Lipschitz type stability is established near the edge of the domain with giving estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neuman map.
