A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The resu...A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.展开更多
The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two-chmensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective...The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two-chmensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective for simulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.展开更多
Christopoulou Demetra（In his work, Hermann Weyl （1926） addresses the issue of abstraction principles, an issue that has been broadly discussed during the last decades with regard to the Neo-Fregean program. This pa...Christopoulou Demetra（In his work, Hermann Weyl （1926） addresses the issue of abstraction principles, an issue that has been broadly discussed during the last decades with regard to the Neo-Fregean program. This paper aims to show off the way Weyl＇s account of abstraction could offer a reply to Benacerraf＇s （1973） challenge to realism. Benacerraf argued that mathematical realism is not associated with a plausible epistemology about human access to abstract objects. Weyl deals with the method of abstraction by investigating certain cases of Fregean abstraction principles. He thinks that we can introduce shapes of geometrical images, integers mod m, circles, directions of lines etc. by means of certain creative acts of consciousness, especially intentionality towards proper relations between the elements of an initial domain. Weyl puts emphasis on intentions towards certain invariant characteristics of items that are involved in equivalence relations. Further, he claims that those invariants are transformed into ideal objects through a finite process that is involved in intuition. This paper, in the first place, attempts to make explicit Weyl＇s phenomenological leanings. Secondly, it argues that Weyl＇s explanation of how ideal mathematical objects become present to mind can address the epistemic issue concerning mathematical knowledge and can also be associated with a particular view which is implicit in his philosophy and retains realistic elements. Hence, it can address Benacerraf＇s problem.展开更多
An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different fr...An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.展开更多
We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the i...We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the integral system where G is the corresponding Green＇s function on the half space. More precisely, we show that every solution to （0.2） satisfies （0.1）, and we believe that the converse is also true. We establish a Liouville type theorem the non-existence of positive solutions to （0.2） under a very weak condition that u and v are only locally integrable. Some new ideas are involved in the proof, which can be applied to a system of more equations.展开更多
基金Supported by the National Nature Science Foundation of China(10472046)the Scientific Innova-tion Research of College Graduate in Jiangsu Province(CX08B-035Z)the Innovation and Excellence Foundation of Doctoral Dissertation of Nanjing University of Aeronautics and Astronautics(BCXJ08-01)~~
文摘A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.
文摘The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two-chmensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective for simulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.
文摘Christopoulou Demetra（In his work, Hermann Weyl （1926） addresses the issue of abstraction principles, an issue that has been broadly discussed during the last decades with regard to the Neo-Fregean program. This paper aims to show off the way Weyl＇s account of abstraction could offer a reply to Benacerraf＇s （1973） challenge to realism. Benacerraf argued that mathematical realism is not associated with a plausible epistemology about human access to abstract objects. Weyl deals with the method of abstraction by investigating certain cases of Fregean abstraction principles. He thinks that we can introduce shapes of geometrical images, integers mod m, circles, directions of lines etc. by means of certain creative acts of consciousness, especially intentionality towards proper relations between the elements of an initial domain. Weyl puts emphasis on intentions towards certain invariant characteristics of items that are involved in equivalence relations. Further, he claims that those invariants are transformed into ideal objects through a finite process that is involved in intuition. This paper, in the first place, attempts to make explicit Weyl＇s phenomenological leanings. Secondly, it argues that Weyl＇s explanation of how ideal mathematical objects become present to mind can address the epistemic issue concerning mathematical knowledge and can also be associated with a particular view which is implicit in his philosophy and retains realistic elements. Hence, it can address Benacerraf＇s problem.
基金Project(41074085)supported by the National Natural Science Foundation of ChinaProject(NCET-12-0551)supported by the Funds for New Century Excellent Talents in University,ChinaProject supported by Shenghua Yuying Program of Central South University,China
文摘An element-free Galerkin method(EFGM) is used to solve the two-dimensional(2D) ground penetrating radar(GPR)modelling problems, due to its simple pre-processing, the absence of elements and high accuracy. Different from element-based numerical methods, this approach makes nodes free from the elemental restraint and avoids the explicit mesh discretization. First, we derived the boundary value problem for the 2D GPR simulation problems. Second, a penalty function approach and a boundary condition truncated method were used to enforce the essential and the absorbing boundary conditions, respectively. A three-layered GPR model was used to verify our element-free approach. The numerical solutions show that our solutions have an excellent agreement with solutions of a finite element method(FEM). Then, we used the EFGM to simulate one more complex model to show its capability and limitations. Simulation results show that one obvious advantage of EFGM is the absence of element mesh, which makes the method very flexible. Due to the use of MLS fitting, a key feature of EFM, is that both the dependent variable and its gradient are continuous and have high precision.
基金supported by China Scholarship Council(Grant No.201206060010)
文摘We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the integral system where G is the corresponding Green＇s function on the half space. More precisely, we show that every solution to （0.2） satisfies （0.1）, and we believe that the converse is also true. We establish a Liouville type theorem the non-existence of positive solutions to （0.2） under a very weak condition that u and v are only locally integrable. Some new ideas are involved in the proof, which can be applied to a system of more equations.
