The transformations, which are similar to Mangler's transformations, are given in this paper. They change the entrance region flow of axially symmetrical laminar boundary layer between two parallel spherical surfa...The transformations, which are similar to Mangler's transformations, are given in this paper. They change the entrance region flow of axially symmetrical laminar boundary layer between two parallel spherical surfaces into the flow of two-dimensional boundary layer, and simplify the problems. The simplified equations can be solved by the two-dimensional boundary layer theory and numerical methods. Therefore, a new way is opened up to solve the diffusive laminar flow in the entrance region between two parallel spherical surfaces.展开更多
In this paper, a polymer spherical symmetry GRIN sphere lens were prepared by the suspension-diffusion-copolymerization(SDC) technique, selecting methyl methacrylate(MMA) as monomer M1 and acrylic 2,2,2-trifluoroethyl...In this paper, a polymer spherical symmetry GRIN sphere lens were prepared by the suspension-diffusion-copolymerization(SDC) technique, selecting methyl methacrylate(MMA) as monomer M1 and acrylic 2,2,2-trifluoroethyl ester(3FEA) as M2. The radial distribution of refractive index of the lens was measured by the shearing interference method, which demonstrated that the quadratic refractive-index distribution was formed in the sphere lens, and its Δn=0.019.展开更多
We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To b...We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.展开更多
In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous c...In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids.We prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.展开更多
In this paper,we give a review of our theoretical and experimental progress in octahedral spherical hohlraum study.From our theoretical study,the octahedral spherical hohlraums with 6 Laser Entrance Holes(LEHs)of octa...In this paper,we give a review of our theoretical and experimental progress in octahedral spherical hohlraum study.From our theoretical study,the octahedral spherical hohlraums with 6 Laser Entrance Holes(LEHs)of octahedral symmetry have robust high symmetry during the capsule implosion at hohlraum-to-capsule radius ratio larger than 3.7.In addition,the octahedral spherical hohlraums also have potential superiority on low backscattering without supplementary technology.We studied the laser arrangement and constraints of the octahedral spherical hohlraums,and gave a design on the laser arrangement for ignition octahedral hohlraums.As a result,the injection angle of laser beams of 50°-60°was proposed as the optimum candidate range for the octahedral spherical hohlraums.We proposed a novel octahedral spherical hohlraum with cylindrical LEHs and LEH shields,in order to increase the laser coupling efficiency and improve the capsule symmetry and to mitigate the influence of the wall blowoff on laser transport.We studied on the sensitivity of the octahedral spherical hohlraums to random errors and compared the sensitivity among the octahedral spherical hohlraums,the rugby hohlraums and the cylindrical hohlraums,and the results show that the octahedral spherical hohlraums are robust to these random errors while the cylindrical hohlraums are the most sensitive.Up till to now,we have carried out three experiments on the spherical hohlraum with 2 LEHs on Shenguang(SG)laser facilities,including demonstration of improving laser transport by using the cylindrical LEHs in the spherical hohlraums,spherical hohlraum energetics on the SGIII prototype laser facility,and comparisons of laser plasma instabilities between the spherical hohlraums and the cylindrical hohlraums on the SGIII laser facility.展开更多
We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving...We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.展开更多
To kinetically model implosion- and explosion-related phenomena, we present a theoretical framework for constructing a discrete Boltzmann model （DBM） with spherical symmetry in spherical coordinates. To achieve this...To kinetically model implosion- and explosion-related phenomena, we present a theoretical framework for constructing a discrete Boltzmann model （DBM） with spherical symmetry in spherical coordinates. To achieve this goal, a key technique is to use local Cartesian coordinates to describe the particle velocity in the kinetic model. Therefore, geometric effects, such as divergence and convergence, are described as a ＂force term＂. To better access the nonequilibrium behavior, even though the corre- sponding hydrodynamic model is one-dimensional, the DBM uses a discrete velocity model （DVM） with three dimensions. A new scheme is introduced so that the DBM can use the same DVM regard- less of whether or not there are extra degrees of freedom. As an example, a DVM with 26 velocities is formulated to construct the DBM at the Navier-Stokes level. Via the DBM, one can study simulta- neously the hydrodynamic and thermodynamic nonequilibrium behaviors in implosion and explosion processes that are not very close to the spherical center. The extension of the current model to a multiple-relaxation-time version is straightforward.展开更多
We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameteri...We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.展开更多
In this paper,we consider the initial boundary value problem of a coupled compressible Navier-Stokes/Allen-Cahn system which is described the motion of a mixture of two viscous compressible fluids in 3D.Our aim is to ...In this paper,we consider the initial boundary value problem of a coupled compressible Navier-Stokes/Allen-Cahn system which is described the motion of a mixture of two viscous compressible fluids in 3D.Our aim is to show the existence and uniqueness of local classical solution under the assumption of spherically symmetric condition for initial dataρ0 without vacuum state.展开更多
The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar p...The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.展开更多
In[14],Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates.These schemes use a node-based discretization of the numerical flu...In[14],Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates.These schemes use a node-based discretization of the numerical fluxes.The control volume version has several distinguished properties,including the conservation of mass,momentum and total energy and compatibility with the geometric conservation law(GCL).However it also has a limitation in that it cannot preserve spherical symmetry for one-dimensional spherical flow.An alternative is also given to use the first order area-weighted approach which can ensure spherical symmetry,at the price of sacrificing conservation of momentum.In this paper,we apply the methodology proposed in our recent work[8]to the first order control volume scheme of Maire in[14]to obtain the spherical symmetry property.The modified scheme can preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid,andmeanwhile itmaintains its original good properties such as conservation and GCL.Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of symmetry,non-oscillation and robustness properties.展开更多
文摘The transformations, which are similar to Mangler's transformations, are given in this paper. They change the entrance region flow of axially symmetrical laminar boundary layer between two parallel spherical surfaces into the flow of two-dimensional boundary layer, and simplify the problems. The simplified equations can be solved by the two-dimensional boundary layer theory and numerical methods. Therefore, a new way is opened up to solve the diffusive laminar flow in the entrance region between two parallel spherical surfaces.
文摘In this paper, a polymer spherical symmetry GRIN sphere lens were prepared by the suspension-diffusion-copolymerization(SDC) technique, selecting methyl methacrylate(MMA) as monomer M1 and acrylic 2,2,2-trifluoroethyl ester(3FEA) as M2. The radial distribution of refractive index of the lens was measured by the shearing interference method, which demonstrated that the quadratic refractive-index distribution was formed in the sphere lens, and its Δn=0.019.
文摘We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.
基金Supported by the NNSF of China(Grant Nos.12171438,11801133)the Natural Science Foundation of Henan Province(Grant No.152300410227)the grant from the Special Project of Basic Scientific Research Business Expenses of Zhongyuan University of Technology(Grant No.K2020TD004)。
文摘In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible fluids.We prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.
基金supported by the National Fundamental Research Program of China(Contact No.11475033 and 11405011)CAEP(Contact No.2013A0102002).
文摘In this paper,we give a review of our theoretical and experimental progress in octahedral spherical hohlraum study.From our theoretical study,the octahedral spherical hohlraums with 6 Laser Entrance Holes(LEHs)of octahedral symmetry have robust high symmetry during the capsule implosion at hohlraum-to-capsule radius ratio larger than 3.7.In addition,the octahedral spherical hohlraums also have potential superiority on low backscattering without supplementary technology.We studied the laser arrangement and constraints of the octahedral spherical hohlraums,and gave a design on the laser arrangement for ignition octahedral hohlraums.As a result,the injection angle of laser beams of 50°-60°was proposed as the optimum candidate range for the octahedral spherical hohlraums.We proposed a novel octahedral spherical hohlraum with cylindrical LEHs and LEH shields,in order to increase the laser coupling efficiency and improve the capsule symmetry and to mitigate the influence of the wall blowoff on laser transport.We studied on the sensitivity of the octahedral spherical hohlraums to random errors and compared the sensitivity among the octahedral spherical hohlraums,the rugby hohlraums and the cylindrical hohlraums,and the results show that the octahedral spherical hohlraums are robust to these random errors while the cylindrical hohlraums are the most sensitive.Up till to now,we have carried out three experiments on the spherical hohlraum with 2 LEHs on Shenguang(SG)laser facilities,including demonstration of improving laser transport by using the cylindrical LEHs in the spherical hohlraums,spherical hohlraum energetics on the SGIII prototype laser facility,and comparisons of laser plasma instabilities between the spherical hohlraums and the cylindrical hohlraums on the SGIII laser facility.
文摘We start with a recently introduced spherically symmetric geodesic fluid model (arXiv: 1601.07030) whose energy-momentum tensor (EMT) in the comoving frame is dust-like with nontrivial energy flux. In the non-comoving energy frame (vanishing energy flux), the same EMT contains besides dust only radial pressure. We present Einstein’s equations together with the matter equations in static spherically symmetric coordinates. These equations are self-contained (four equations for four unknowns). We solve them analytically except for a resulting nonlinear ordinary differential equation (ODE) for the gravitational potential. This ODE can be rewritten as a Lienard differential equation which, however, may be transformed into a rational Abel differential equation of the first kind. Finally, we list some open mathematical problems and outline possible physical applications (galactic halos, dark energy stars) and related open problems.
文摘To kinetically model implosion- and explosion-related phenomena, we present a theoretical framework for constructing a discrete Boltzmann model （DBM） with spherical symmetry in spherical coordinates. To achieve this goal, a key technique is to use local Cartesian coordinates to describe the particle velocity in the kinetic model. Therefore, geometric effects, such as divergence and convergence, are described as a ＂force term＂. To better access the nonequilibrium behavior, even though the corre- sponding hydrodynamic model is one-dimensional, the DBM uses a discrete velocity model （DVM） with three dimensions. A new scheme is introduced so that the DBM can use the same DVM regard- less of whether or not there are extra degrees of freedom. As an example, a DVM with 26 velocities is formulated to construct the DBM at the Navier-Stokes level. Via the DBM, one can study simulta- neously the hydrodynamic and thermodynamic nonequilibrium behaviors in implosion and explosion processes that are not very close to the spherical center. The extension of the current model to a multiple-relaxation-time version is straightforward.
基金Project supported by the National Natural Science Foundation of China (Nos. 60673006 and 60533060)the Program for New Century Excellent Talents in University (No. NCET-05-0275), Chinathe IDeA Network of Biomedical Research Excellence Grant (No. 5P20RR01647206) from National Institutes of Health (NIH), USA
文摘We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
基金the NNSF of China(11671367,11801133)the Natural Science Foundation of He'nan Province(Grant No.152300410227)the grant from the Key Research Projects of He'nan Higher Education Institutions(18A110038).
文摘In this paper,we consider the initial boundary value problem of a coupled compressible Navier-Stokes/Allen-Cahn system which is described the motion of a mixture of two viscous compressible fluids in 3D.Our aim is to show the existence and uniqueness of local classical solution under the assumption of spherically symmetric condition for initial dataρ0 without vacuum state.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11105097,10975075,and 11175089the National Basic Research Program of China under Grant No.2012CB921900the National Research Foundation and Ministry of Education,Singapore under Grant No.WBS:R-710-000-008-271
文摘The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.
基金J.Cheng is supported in part byNSFC grants 10972043 and 10931004Additional support is provided by theNational Basic Research Programof China under grant 2011CB309702C.-W.Shu is supported in part by ARO grant W911NF-08-1-0520 and NSF grant DMS-0809086.
文摘In[14],Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates.These schemes use a node-based discretization of the numerical fluxes.The control volume version has several distinguished properties,including the conservation of mass,momentum and total energy and compatibility with the geometric conservation law(GCL).However it also has a limitation in that it cannot preserve spherical symmetry for one-dimensional spherical flow.An alternative is also given to use the first order area-weighted approach which can ensure spherical symmetry,at the price of sacrificing conservation of momentum.In this paper,we apply the methodology proposed in our recent work[8]to the first order control volume scheme of Maire in[14]to obtain the spherical symmetry property.The modified scheme can preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid,andmeanwhile itmaintains its original good properties such as conservation and GCL.Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of symmetry,non-oscillation and robustness properties.
