By utilizing wave velocity imaging technology,the uniaxial multi-stage loading test was conducted on siltstone to attain wave velocity imagings during rock fracture.Based on the time series parameters of acoustic emis...By utilizing wave velocity imaging technology,the uniaxial multi-stage loading test was conducted on siltstone to attain wave velocity imagings during rock fracture.Based on the time series parameters of acoustic emissions(AE),joint response characteristics of the velocity field and AE during rock fracture were analyzed.Moreover,the localization effect of damage during rock fracture was explored by applying wave velocity imagings.The experimental result showed that the wave velocity imagings enable three-dimensional(3-D)visualization of the extent and spatial position of damage to the rock.A damaged zone has a low wave velocity and a zone where the low wave velocity is concentrated tends to correspond to a severely damaged zone.AE parameters and wave velocity imagings depict the changes in activity of cracks during rock fracture from temporal and spatial perspectives,respectively:the activity of cracks is strengthened,and the rate of AE events increases during rock fracture;correspondingly,the low-velocity zones are gradually aggregated and their area gradually increases.From the wave velocity imagings,the damaged zones in rock were divided into an initially damaged zone,a progressively damaged zone,and a fractured zone.During rock fracture,the progressively damaged zone and the fractured zone both develop around the initially damaged zone,showing a typical localization effect of the damage.By capturing the spatial development trends of the progressively damaged zone and fractured zone in wave velocity imagings,the development of microfractures can be predicted,exerting practical significance for determining the position of the main fracture.展开更多
The properties of the 8-wave for a quasl-free partide with position-dependent mass （PDM） have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the fr...The properties of the 8-wave for a quasl-free partide with position-dependent mass （PDM） have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle around the origin only occurs in two dimensions, the quasi-free particle with PDM can experience attractive forces in D dimensions except D = 1 when its mass function satisfies some conditions. The effective mass of a particle varying with its position can induce effective interaction, which may be attractive in some cases. The analytical expressions of the eigenfunctions and the corresponding probability densities for the 8-waves of the two- and three-dimensional systems with a special PDM are given, and the existences of localization around the origin for these systems are shown.展开更多
We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota＇s binary differ...We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota＇s binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized solutions of different but desired forms. For some specific external potentials and nonlinearity coefficients, we discuss features of the corresponding （2＋1）-dimensional multisolitonic solutions, including ring solitons, lump solitons, and soliton clusters.展开更多
A general class of(a,k)-regularized C-resolvent families is one of efficient research tools for dealing with non-degenerate abstract Volterra equations of scalar type.The main purpose of this expository paper is to pr...A general class of(a,k)-regularized C-resolvent families is one of efficient research tools for dealing with non-degenerate abstract Volterra equations of scalar type.The main purpose of this expository paper is to provide a detailed analysis of the above class in sequentially complete locally convex spaces.展开更多
This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized...This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.展开更多
The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn...The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn) is obtained.展开更多
The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response e...The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response eigenvalue problem by Bai and Li(2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4 dC G(ELOBP4dC G).Numerical results of the ELOBP4 dC G strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.展开更多
The heat transfer performance of a mist/air jet impingement on a constant-heat flux surface was experimentally investigated.Two objectives were outlined in the current study.The first objective is to assess the effect...The heat transfer performance of a mist/air jet impingement on a constant-heat flux surface was experimentally investigated.Two objectives were outlined in the current study.The first objective is to assess the effects of mist/air volumetric flow rate ratio,impinging mode and heat flux on the heat transfer characteristics of free mist/air jet impingement.The second objective is to assess the effect of swirl flow induced by the spinning grinding wheel on the mist/air jet impingement,simulating the heat transfer process on a grinding work-piece surface subjected to the mist/air jet impingement.The results show that the addition of dilute water droplets to air flow results in significant heat transfer enhancement.Once the mist/air ratio is increased to a certain value,the increase of heat transfer with the mist/air ratio becomes slow.For a given mist/air ratio,as the increase of heat flux,the contribution of droplet evaporation to the overall heat transfer is weakened relatively,resulting in a decrease of heat transfer enhancement in comparison to the lower heat flux case.The heat transfer coefficient in the stagnation region for the oblique jet is much lower than the normal mist/air jet impingement,while in the region away from the stagnation,the local heat transfer coefficient for the oblique jet is higher than the normal jet.As regards as the mist/air jet impingement in the vicinity of grinding zone is concerned,when the jet impinging direction is consistent with the rotating direction of rotating disk,the swirl flow induced by the rotating disk could entrain more droplets to enter the jet impinging stagnation zone,which is beneficial to convective heat transfer enhancement.Furthermore,as the rotational speed of disk increases,the temperature deceases in impinging jet stagnation zone.展开更多
基金Projects(51774138,51804122,51904105)supported by the National Natural Science Foundation of ChinaProjects(E2021209148,E2021209052)supported by the Natural Science Foundation of Hebei Province,China。
文摘By utilizing wave velocity imaging technology,the uniaxial multi-stage loading test was conducted on siltstone to attain wave velocity imagings during rock fracture.Based on the time series parameters of acoustic emissions(AE),joint response characteristics of the velocity field and AE during rock fracture were analyzed.Moreover,the localization effect of damage during rock fracture was explored by applying wave velocity imagings.The experimental result showed that the wave velocity imagings enable three-dimensional(3-D)visualization of the extent and spatial position of damage to the rock.A damaged zone has a low wave velocity and a zone where the low wave velocity is concentrated tends to correspond to a severely damaged zone.AE parameters and wave velocity imagings depict the changes in activity of cracks during rock fracture from temporal and spatial perspectives,respectively:the activity of cracks is strengthened,and the rate of AE events increases during rock fracture;correspondingly,the low-velocity zones are gradually aggregated and their area gradually increases.From the wave velocity imagings,the damaged zones in rock were divided into an initially damaged zone,a progressively damaged zone,and a fractured zone.During rock fracture,the progressively damaged zone and the fractured zone both develop around the initially damaged zone,showing a typical localization effect of the damage.By capturing the spatial development trends of the progressively damaged zone and fractured zone in wave velocity imagings,the development of microfractures can be predicted,exerting practical significance for determining the position of the main fracture.
基金The project supported by National Natural Science Foundation of China for Distinguished Young Scientists under Grant No. 10125521, the Doctoral Fund of Ministry of Education of China under Grant No. 20010284036, the State Key Basic Research Development Program under Grant No. G2000077400, the Knowledge Innovation Project of the Chinese Academy of Sciences under Grant No. KJCX2-SW-N02, and National Natural Science Foundation of China under Grant No. 60371013
文摘The properties of the 8-wave for a quasl-free partide with position-dependent mass （PDM） have been discussed in details. Differed from the system with constant mass in which the localization of the s-wave for the free quantum particle around the origin only occurs in two dimensions, the quasi-free particle with PDM can experience attractive forces in D dimensions except D = 1 when its mass function satisfies some conditions. The effective mass of a particle varying with its position can induce effective interaction, which may be attractive in some cases. The analytical expressions of the eigenfunctions and the corresponding probability densities for the 8-waves of the two- and three-dimensional systems with a special PDM are given, and the existences of localization around the origin for these systems are shown.
基金Supported by the Natural Science Foundation of Guangdong Province under Grant No. 1015283001000000,Chinasupported by the NPRP 09-462-1-074 project with the Qatar National Research Foundation
文摘We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrodinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota＇s binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized solutions of different but desired forms. For some specific external potentials and nonlinearity coefficients, we discuss features of the corresponding （2＋1）-dimensional multisolitonic solutions, including ring solitons, lump solitons, and soliton clusters.
基金supported by Ministry of Science and Technological Development,Republic of Serbia (Grant No. 144016)
文摘A general class of(a,k)-regularized C-resolvent families is one of efficient research tools for dealing with non-degenerate abstract Volterra equations of scalar type.The main purpose of this expository paper is to provide a detailed analysis of the above class in sequentially complete locally convex spaces.
基金Project supported by the National Natural Science Foundation of China(No.10071063)
文摘This paper presents a geometric characterization of convex sets in locally convex spaces onwhich a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem ofw* Asplund spaces a localized setting.
文摘The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn) is obtained.
基金supported by National Science Foundation of USA(Grant Nos.DMS1522697,CCF-1527091,DMS-1317330 and CCF-1527091)National Natural Science Foundation of China(Grant No.11428104)
文摘The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by Bai and Li(2013) and later was extended to the generalized linear response eigenvalue problem by Bai and Li(2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4 dC G(ELOBP4dC G).Numerical results of the ELOBP4 dC G strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.
基金supported by the National Natural Science Foundation of China(Grant No.51076063)
文摘The heat transfer performance of a mist/air jet impingement on a constant-heat flux surface was experimentally investigated.Two objectives were outlined in the current study.The first objective is to assess the effects of mist/air volumetric flow rate ratio,impinging mode and heat flux on the heat transfer characteristics of free mist/air jet impingement.The second objective is to assess the effect of swirl flow induced by the spinning grinding wheel on the mist/air jet impingement,simulating the heat transfer process on a grinding work-piece surface subjected to the mist/air jet impingement.The results show that the addition of dilute water droplets to air flow results in significant heat transfer enhancement.Once the mist/air ratio is increased to a certain value,the increase of heat transfer with the mist/air ratio becomes slow.For a given mist/air ratio,as the increase of heat flux,the contribution of droplet evaporation to the overall heat transfer is weakened relatively,resulting in a decrease of heat transfer enhancement in comparison to the lower heat flux case.The heat transfer coefficient in the stagnation region for the oblique jet is much lower than the normal mist/air jet impingement,while in the region away from the stagnation,the local heat transfer coefficient for the oblique jet is higher than the normal jet.As regards as the mist/air jet impingement in the vicinity of grinding zone is concerned,when the jet impinging direction is consistent with the rotating direction of rotating disk,the swirl flow induced by the rotating disk could entrain more droplets to enter the jet impinging stagnation zone,which is beneficial to convective heat transfer enhancement.Furthermore,as the rotational speed of disk increases,the temperature deceases in impinging jet stagnation zone.
