Edge detection is an image processing technique for finding the boundaries of objects within images. It is typically used to interpret gravity and magnetic data, and find the horizontal boundaries of geological bodies...Edge detection is an image processing technique for finding the boundaries of objects within images. It is typically used to interpret gravity and magnetic data, and find the horizontal boundaries of geological bodies. Large deviations between model and true edges are common because of the interference of depth and errors in computing the derivatives; thus, edge detection methods cannot provide information about the depth of the source. To simultaneously obtain the horizontal extent and depth of geophysical anomalies, we use normalized edge detection filters, which normalize the edge detection function at different depths, and the maxima that correspond to the location of the source. The errors between model and actual edges are minimized as the depth of the source decreases and the normalized edge detection method recognizes the extent of the source based on the maxima, allowing for reliable model results. We demonstrate the applicability of the normalized edge detection filters in defining the horizontal extent and depth using synthetic and actual aeromagnetic data.展开更多
This paper presents the one-dimensional(1D)viscoelastic consolidation system of saturated clayey soil under continuous drainage boundaries.The fractional-derivative Merchant(FDM)model has been introduced into the cons...This paper presents the one-dimensional(1D)viscoelastic consolidation system of saturated clayey soil under continuous drainage boundaries.The fractional-derivative Merchant(FDM)model has been introduced into the consolidation system to simulate the viscoelasticity.Swartzendruber’s flow law is also introduced to describe the non-Darcian flow characteristics simultaneously.The generalized numerical solution of the 1D consolidation under continuous boundaries is given by the finite difference scheme.Furthermore,to illustrate the effectiveness of the numerical method,two simplified cases are compared against the current analytical and numerical results.Finally,the effects of boundary parameters and model parameters on the viscoelastic consolidation were illustrated and discussed.The results indicated that the boundary parameters have a significant influence on consolidation.The larger the values of boundary parameters,the faster the whole dissipation of the excess pore-water pressure and soils’settlement rate.Fractional-order and viscosity parameter have little effect on consolidation,which are primarily significant in the middle and late consolidation phases.With the increase of the modulus ratio,the whole consolidation process becomes faster.Moreover,considering Swartzendruber’s flow delays the consolidation rate of the soil layer.展开更多
There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle th...There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.展开更多
This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.
The effective thermal conductivity of composites with ellipsoidal fillers is analyzed by using a homogenization method that is able to represent the microstructure precisely.In this study,various parameters such as th...The effective thermal conductivity of composites with ellipsoidal fillers is analyzed by using a homogenization method that is able to represent the microstructure precisely.In this study,various parameters such as the volume fraction,shape,and distribution of the filler are quantitatively estimated to understand the mechanisms of heat transfer in the composite.First,thermal boundary resistance between resin and filler is important for obtaining composites with higher thermal conductivity.Second,the anisotropy of the effective thermal conductivity arises from contact between filler in the case of ellipsoidal filler and produces lower thermal resistance.Finally,the filler network and thermal resistance are essential for the heat transfer in composites because the path of thermal conduction is improved by contact between neighboring filler particles.展开更多
This paper is devoted to the study of fractional(q, p)-Sobolev-Poincar′e inequalities in irregular domains. In particular, the author establishes(essentially) sharp fractional(q, p)-Sobolev-Poincar′e inequalities in...This paper is devoted to the study of fractional(q, p)-Sobolev-Poincar′e inequalities in irregular domains. In particular, the author establishes(essentially) sharp fractional(q, p)-Sobolev-Poincar′e inequalities in s-John domains and in domains satisfying the quasihyperbolic boundary conditions. When the order of the fractional derivative tends to 1, our results tend to the results for the usual derivatives. Furthermore, the author verifies that those domains which support the fractional(q, p)-Sobolev-Poincar′e inequalities together with a separation property are s-diam John domains for certain s, depending only on the associated data. An inaccurate statement in [Buckley, S. and Koskela, P.,Sobolev-Poincar′e implies John, Math. Res. Lett., 2(5), 1995, 577–593] is also pointed out.展开更多
The dynamics of the laser-induced bubble at different ambient pressures was numerically studied by Finite Volume Method (FVM). The velocity of the bubble wall, the liquid jet velocity at collapse, and the pressure of ...The dynamics of the laser-induced bubble at different ambient pressures was numerically studied by Finite Volume Method (FVM). The velocity of the bubble wall, the liquid jet velocity at collapse, and the pressure of the water hammer while the liquid jet impacting onto the boundary are found to increase nonlinearly with increasing ambient pressure. The collapse time and the formation time of the liquid jet are found to decrease nonlinearly with increasing ambient pressure. The ratios of the jet formation time to the collapse time, and the displacement of the bubble center to the maximal radius while the jet formation stay invariant when ambient pressure changes. These ratios are independent of ambient pressure.展开更多
The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity...The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.展开更多
A forward-facing step (FFS) immersed in a subsonic boundary layer is studied through a high-order flux reconstruction (FR) method to highlight the flow transition induced by the step. The step height is a third of the...A forward-facing step (FFS) immersed in a subsonic boundary layer is studied through a high-order flux reconstruction (FR) method to highlight the flow transition induced by the step. The step height is a third of the local boundary-layer thickness. The Reynolds number based on the step height is 720. Inlet disturbances are introduced giving rise to streamwise vortices upstream of the step. It is observed that these small-scale streamwise structures interact with the step and hairpin vortices are quickly developed after the step leading to flow transition in the boundary layer.展开更多
基金supported by the China Postdoctoral Science Foundation (No.2014M551188)the Deep Exploration in China Sinoprobe-09-01 (No.201011078)
文摘Edge detection is an image processing technique for finding the boundaries of objects within images. It is typically used to interpret gravity and magnetic data, and find the horizontal boundaries of geological bodies. Large deviations between model and true edges are common because of the interference of depth and errors in computing the derivatives; thus, edge detection methods cannot provide information about the depth of the source. To simultaneously obtain the horizontal extent and depth of geophysical anomalies, we use normalized edge detection filters, which normalize the edge detection function at different depths, and the maxima that correspond to the location of the source. The errors between model and actual edges are minimized as the depth of the source decreases and the normalized edge detection method recognizes the extent of the source based on the maxima, allowing for reliable model results. We demonstrate the applicability of the normalized edge detection filters in defining the horizontal extent and depth using synthetic and actual aeromagnetic data.
基金Projects(51879104,52078206)supported by the National Natural Science Foundation of China。
文摘This paper presents the one-dimensional(1D)viscoelastic consolidation system of saturated clayey soil under continuous drainage boundaries.The fractional-derivative Merchant(FDM)model has been introduced into the consolidation system to simulate the viscoelasticity.Swartzendruber’s flow law is also introduced to describe the non-Darcian flow characteristics simultaneously.The generalized numerical solution of the 1D consolidation under continuous boundaries is given by the finite difference scheme.Furthermore,to illustrate the effectiveness of the numerical method,two simplified cases are compared against the current analytical and numerical results.Finally,the effects of boundary parameters and model parameters on the viscoelastic consolidation were illustrated and discussed.The results indicated that the boundary parameters have a significant influence on consolidation.The larger the values of boundary parameters,the faster the whole dissipation of the excess pore-water pressure and soils’settlement rate.Fractional-order and viscosity parameter have little effect on consolidation,which are primarily significant in the middle and late consolidation phases.With the increase of the modulus ratio,the whole consolidation process becomes faster.Moreover,considering Swartzendruber’s flow delays the consolidation rate of the soil layer.
文摘There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.
基金Supported the National Natural Science Foundation of China（10471080） Supported by the Natural Science Foundation of Henan Province（2004110008）
文摘This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.
文摘The effective thermal conductivity of composites with ellipsoidal fillers is analyzed by using a homogenization method that is able to represent the microstructure precisely.In this study,various parameters such as the volume fraction,shape,and distribution of the filler are quantitatively estimated to understand the mechanisms of heat transfer in the composite.First,thermal boundary resistance between resin and filler is important for obtaining composites with higher thermal conductivity.Second,the anisotropy of the effective thermal conductivity arises from contact between filler in the case of ellipsoidal filler and produces lower thermal resistance.Finally,the filler network and thermal resistance are essential for the heat transfer in composites because the path of thermal conduction is improved by contact between neighboring filler particles.
文摘This paper is devoted to the study of fractional(q, p)-Sobolev-Poincar′e inequalities in irregular domains. In particular, the author establishes(essentially) sharp fractional(q, p)-Sobolev-Poincar′e inequalities in s-John domains and in domains satisfying the quasihyperbolic boundary conditions. When the order of the fractional derivative tends to 1, our results tend to the results for the usual derivatives. Furthermore, the author verifies that those domains which support the fractional(q, p)-Sobolev-Poincar′e inequalities together with a separation property are s-diam John domains for certain s, depending only on the associated data. An inaccurate statement in [Buckley, S. and Koskela, P.,Sobolev-Poincar′e implies John, Math. Res. Lett., 2(5), 1995, 577–593] is also pointed out.
基金supported by the Nanjing University of Science & Technology Research Funding (Grant No. 2010ZDJH09)
文摘The dynamics of the laser-induced bubble at different ambient pressures was numerically studied by Finite Volume Method (FVM). The velocity of the bubble wall, the liquid jet velocity at collapse, and the pressure of the water hammer while the liquid jet impacting onto the boundary are found to increase nonlinearly with increasing ambient pressure. The collapse time and the formation time of the liquid jet are found to decrease nonlinearly with increasing ambient pressure. The ratios of the jet formation time to the collapse time, and the displacement of the bubble center to the maximal radius while the jet formation stay invariant when ambient pressure changes. These ratios are independent of ambient pressure.
基金supported by the National Natural Science Foundation of China(No.11201292)Shanghai Natural Science Foundation(No.12ZR1444300)the Key Discipline"Applied Mathematics"of Shanghai Second Polytechnic University(No.XXKZD1304)
文摘The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.
文摘A forward-facing step (FFS) immersed in a subsonic boundary layer is studied through a high-order flux reconstruction (FR) method to highlight the flow transition induced by the step. The step height is a third of the local boundary-layer thickness. The Reynolds number based on the step height is 720. Inlet disturbances are introduced giving rise to streamwise vortices upstream of the step. It is observed that these small-scale streamwise structures interact with the step and hairpin vortices are quickly developed after the step leading to flow transition in the boundary layer.
