To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical da...To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.展开更多
In this paper,we study a kind of dark energy models in the framework of the non-minimal coupling.With this kind of models,dark energy could cross the cosmological constant boundary,and at early time,dark energy could ...In this paper,we study a kind of dark energy models in the framework of the non-minimal coupling.With this kind of models,dark energy could cross the cosmological constant boundary,and at early time,dark energy could have 'tracking' behavior.展开更多
Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this pap...Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.展开更多
Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is con...Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.展开更多
This article deals with an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final time space discretized measurement using the optimization method with the ...This article deals with an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final time space discretized measurement using the optimization method with the help of the smooth interpolation technique.The main objective of the article is to analyse the asymptotic behavior of the solution of the inverse problem for the linearly coupled reaction diffusion system with respect to the homogeneous Dirichlet boundary condition.展开更多
Full annulus simulations of the flow which develops in a transonic centrifugal compressor are performed at two stable operating points （peak efficiency and near surge） and during the path to surge. At stable conditi...Full annulus simulations of the flow which develops in a transonic centrifugal compressor are performed at two stable operating points （peak efficiency and near surge） and during the path to surge. At stable conditions, the flow field properties are analyzed by comparisons with experimental data and numerical simulations using a phase lagged approach previously carried out. Regarding the stage overall performance, an excellent agreement is obtained between the numerical results （both with time lagged approach and full-annulus calculation） and the ex- periments. From the full-annnlus simulations, the change in flow pattern from peak efficiency to surge is found to be perfectly similar to that obtained from the simulations using the time lagged approach. In particular, pro- vided that the operating point is stable, the flow proves to be chorochronic. The full-annulus simulations were continued after a unique small change in the throttle law applied at the exit of the numerical domain. The mass flow, pressure ratio and efficiency then significantly drop all the more the time progresses. The simulation becomes unstable and the surge inception well underway. The path to surge is found to be due to the enlargement of the boundary layer separation on the suction side of the diffuser vanes in accordance with the conclusions drawn from the chorochronic simulations and experiments. But as the time progresses, the flow loses its chorochronic character. Stall cells rotating at around 7% of the rotor speed develop and lead to surge in around 5 revolutions.展开更多
Horseshoe vortex topological structure has been studied extensively in the past,traditional"saddle of separation"and new"attachment saddle point"topologies found in literature both have theoretical...Horseshoe vortex topological structure has been studied extensively in the past,traditional"saddle of separation"and new"attachment saddle point"topologies found in literature both have theoretical basis and experimental and computational evidences for support.The laminar incompressible juncture flows at low Reynolds numbers especially are observed to have new topology.Studies concerning the existence of the new topology though found in literature,the topological evolution and its dependency on various critical flow parameters require further investigation.A Particle Image Velocimetry based analysis is carried out to observe the effect of aspect ratio,?*/D and shape of the obstacle on laminar horseshoe vortex topology for small obstacles.Rise in aspect ratio evolves the topology from the traditional to new for all the cases observed.The circular cross section obstacles are found more apt to having the new topology compared to square cross sections.It is noted that the sweeping effect of the fluid above the vortex system in which horseshoe vortex is immersed plays a critical role in this evolution.Topological evolution is observed not only in the most upstream singular point region of horseshoe vortex system but also in the corner region.The corner vortex topology evolves from the traditional type to new one before the topological evolution of the most upstream singular point,resulting in a new topological pattern of the laminar juncture flows"separation-attachment combination".The study may help extend the understanding of the three-dimensional boundary layer separation phenomenon.展开更多
In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through a critical noz...In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through a critical nozzle. The Reynolds number effects are investigated with several nozzles with different throat diameter. Diffuser angle is varied to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that diffuser angle affects the critical pressure ratio.展开更多
A linear modelling of aeroacoustic waves propagation is discussed. The first point is an existence and uniqueness, theorem. But restrictive assumptions are required on the velocity of the flow. Then a counter example ...A linear modelling of aeroacoustic waves propagation is discussed. The first point is an existence and uniqueness, theorem. But restrictive assumptions are required on the velocity of the flow. Then a counter example proves that they are necessary.展开更多
基金supported by the National Program on Key Basic Research Project of China(973 Program)(No.2013CB036002,No.2014CB046901)the National Major Scientific Equipment Developed Special Project(No.51327802)+3 种基金National Natural Science Foundation of China(No.51139004,No.41102183)the Research Fund for the Doctoral Program of Higher Education of China(No.20110131120070)Natural Science Foundation of Shandong Province(No.ZR2011EEQ013)the Graduate Innovation Fund of Shandong University(No.YZC12083)
文摘To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.
基金Supported by the Natural Science Foundation of Shandong Province under Grant No.ZR2009AL001
文摘In this paper,we study a kind of dark energy models in the framework of the non-minimal coupling.With this kind of models,dark energy could cross the cosmological constant boundary,and at early time,dark energy could have 'tracking' behavior.
文摘Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.
基金CHEN Min's work is supported by Grant No. 70221001 and No. 70331001 from NNSFC and Grant No. KZCX2-SW-118 from CAS.
文摘Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.
基金supported by the Council of Scientific and Industrial Research(CSIR),India(No.09/472(0143)/2010-EMR-I)
文摘This article deals with an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final time space discretized measurement using the optimization method with the help of the smooth interpolation technique.The main objective of the article is to analyse the asymptotic behavior of the solution of the inverse problem for the linearly coupled reaction diffusion system with respect to the homogeneous Dirichlet boundary condition.
基金the HPC resources of CINES under the allocation 2012- 2a6356 and 2013-2a6356
文摘Full annulus simulations of the flow which develops in a transonic centrifugal compressor are performed at two stable operating points （peak efficiency and near surge） and during the path to surge. At stable conditions, the flow field properties are analyzed by comparisons with experimental data and numerical simulations using a phase lagged approach previously carried out. Regarding the stage overall performance, an excellent agreement is obtained between the numerical results （both with time lagged approach and full-annulus calculation） and the ex- periments. From the full-annnlus simulations, the change in flow pattern from peak efficiency to surge is found to be perfectly similar to that obtained from the simulations using the time lagged approach. In particular, pro- vided that the operating point is stable, the flow proves to be chorochronic. The full-annulus simulations were continued after a unique small change in the throttle law applied at the exit of the numerical domain. The mass flow, pressure ratio and efficiency then significantly drop all the more the time progresses. The simulation becomes unstable and the surge inception well underway. The path to surge is found to be due to the enlargement of the boundary layer separation on the suction side of the diffuser vanes in accordance with the conclusions drawn from the chorochronic simulations and experiments. But as the time progresses, the flow loses its chorochronic character. Stall cells rotating at around 7% of the rotor speed develop and lead to surge in around 5 revolutions.
基金supported by the National Natural Science Foundation of China(Grant No.11372027)
文摘Horseshoe vortex topological structure has been studied extensively in the past,traditional"saddle of separation"and new"attachment saddle point"topologies found in literature both have theoretical basis and experimental and computational evidences for support.The laminar incompressible juncture flows at low Reynolds numbers especially are observed to have new topology.Studies concerning the existence of the new topology though found in literature,the topological evolution and its dependency on various critical flow parameters require further investigation.A Particle Image Velocimetry based analysis is carried out to observe the effect of aspect ratio,?*/D and shape of the obstacle on laminar horseshoe vortex topology for small obstacles.Rise in aspect ratio evolves the topology from the traditional to new for all the cases observed.The circular cross section obstacles are found more apt to having the new topology compared to square cross sections.It is noted that the sweeping effect of the fluid above the vortex system in which horseshoe vortex is immersed plays a critical role in this evolution.Topological evolution is observed not only in the most upstream singular point region of horseshoe vortex system but also in the corner region.The corner vortex topology evolves from the traditional type to new one before the topological evolution of the most upstream singular point,resulting in a new topological pattern of the laminar juncture flows"separation-attachment combination".The study may help extend the understanding of the three-dimensional boundary layer separation phenomenon.
文摘In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through a critical nozzle. The Reynolds number effects are investigated with several nozzles with different throat diameter. Diffuser angle is varied to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that diffuser angle affects the critical pressure ratio.
文摘A linear modelling of aeroacoustic waves propagation is discussed. The first point is an existence and uniqueness, theorem. But restrictive assumptions are required on the velocity of the flow. Then a counter example proves that they are necessary.
