The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the...The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the calculation domain. The mapping method deals with the irregular surface and the low-velocity layer underneath it using a fine grid. For the deeper high-velocity layers, the use of a fine grid causes local oversampling. In addition, when the irregular surface is transformed to horizontal, the flattened interface below the surface is transformed to curved, which produces inaccurate modeling results because of the presence of ladder-like burrs in the simulated seismic wave. Thus, we propose the mapping method based on the dual-variable finite-difference staggered grid. The proposed method uses different size grid spacings in different regions and locally variable time steps to match the size variability of grid spacings. Numerical examples suggest that the proposed method requires less memory storage capacity and improves the computational efficiency compared with forward modeling methods based on the conventional grid.展开更多
We present a finite difference (FD) method for the simulation of seismic wave fields in fractured medium with an irregular (non-fiat) free surface which is beneficial for interpreting exploration data acquired in ...We present a finite difference (FD) method for the simulation of seismic wave fields in fractured medium with an irregular (non-fiat) free surface which is beneficial for interpreting exploration data acquired in mountainous regions. Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded. To implement surface topography, we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one. We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations (in a curvilinear coordinate system) in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry (HTI). Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration. The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography. The scattered waves provoked by the topography are re-scattered by the fractures, especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures.展开更多
This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized...This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized coordinate which represents rotation around transversal main central axis of inertia of undercarriage.The excavator is described by a system of six nonlinear,nonhomogenous differential equations of the second kind.Numerical analysis of the differential equations has been done for BTH-600 hydraulic excavator with moving mechanism with pneumatic wheels.展开更多
The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation ar...The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.展开更多
The representation method of heterogeneous material information is one of the key technologies of heterogeneous object modeling, but almost all the existing methods cannot represent non-uniform rational B-spline (NU...The representation method of heterogeneous material information is one of the key technologies of heterogeneous object modeling, but almost all the existing methods cannot represent non-uniform rational B-spline (NURBS) entity. According to the characteristics of NURBS, a novel data structure, named NURBS material data structure, is proposed, in which the geometrical coordinates, weights and material coordinates of NURBS heterogene- ous objects can be represented simultaneously. Based on this data structure, both direct representation method and inverse construction method of heterogeneous NURBS objects are introduced. In the direct representation method, three forms of NURBS heterogeneous objects are introduced by giving the geometry and material information of con- trol points, among which the homogeneous coordinates form is employed for its brevity and easy programming. In the inverse construction method, continuous heterogeneous curves and surfaces can he obtained by interpolating discrete points and curves with specified material information. Some examples are given to show the effectiveness of the pro- posed methods.展开更多
This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green's functions of relevant boundary-value problems s...This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green's functions of relevant boundary-value problems stated in multiply-connected regions for Laplace equation written in geographical coordinates. Those are efficiently computed by a modification of the method of functional equations, with closed analytical forms preliminary obtained for Green's functions for the corresponding simply-connected regions.展开更多
Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, ...Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, either implicitly or explicitly. In order to calculate the effect of wind forcing on waves and currents, and vice versa, it is necessary to employ a consistent formula- tion of the energy and momentum balance within the airflow, wave field, and water column. It is very advantageous to apply sur- face-following coordinate systems, whereby the steep gradients in mean flow properties near the air-water interface in the cross-interface direction may be resolved over distances which are much smaller than the height of the waves themselves. We may account for the waves explicitly by employing a numerical spectral wave model, and applying a suitable theory of wave–mean flow interaction. If the mean flow is small compared with the wave phase speed, perturbation expansions of the hydrodynamic equations in a Lagrangian or generalized Lagrangian mean framework are useful: for stronger flows, such as for wind blowing over waves, the presence of critical levels where the mean flow velocity is equal to the wave phase speed necessitates the application of more general types of surface-following coordinate system. The interaction of the flow of air and water and associated differences in temperature and the concentration of various substances (such as gas species) gives rise to a complex boundary-layer structure at a wide range of vertical scales, from the sub-millimetre scales of gaseous diffusion, to several tens of metres for the turbulent Ekman layer. The bal- ance of momentum, heat, and mass is also affected significantly by breaking waves, which act to increase the effective area of the surface for mass transfer, and increase turbulent diffusive fluxes via the conversion of wave energy to turbulent kinetic energy.展开更多
A historical run(1993–2014)of a global,eddy-permitting,hybrid coordinate ocean model(HYCOM)is evaluated against observations.The authors evaluate several metrics in the model,including the spatial distribution of sea...A historical run(1993–2014)of a global,eddy-permitting,hybrid coordinate ocean model(HYCOM)is evaluated against observations.The authors evaluate several metrics in the model,including the spatial distribution of sea surface temperature(SST),the zonally averaged seasonal cycle of SST,the variability of the sea level anomaly(SLA),the zonally and meridionally averaged temperature and salinity,and the equatorial undercurrent.It is found that the simulated seasonal cycle of SST is 0.2–0.8 stronger than observed at midlatitudes.The modeled SST is 0.29°C warmer than the observed for the global ocean.the structure of the subsurface temperature and salinity is similar to the observed.moreover,the variability of SLA exhibits the same pattern as observed.The modeled equatorial undercurrent in the pacific ocean is weaker than observed,but stronger than the ecco reanalysis product.overall,the model can reproduce the large-scale ocean states,and is suitable for analyses seeking to better understand the dynamics and thermodynamics of the upper ocean,as well as ocean variability.展开更多
Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the mean...Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.展开更多
We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering oper...We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion, which is elegant in form and has many applications in deriving new operator identities. This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.展开更多
基金financially supported by the National Natural Science Foundation of China(Nos.41104069 and 41274124)the National 973 Project(Nos.2014CB239006 and 2011CB202402)+1 种基金the Shandong Natural Science Foundation of China(No.ZR2011DQ016)Fundamental Research Funds for Central Universities(No.R1401005A)
文摘The mapping method is a forward-modeling method that transforms the irregular surface to horizontal by mapping the rectangular grid as curved; moreover, the wave field calculations move from the physical domain to the calculation domain. The mapping method deals with the irregular surface and the low-velocity layer underneath it using a fine grid. For the deeper high-velocity layers, the use of a fine grid causes local oversampling. In addition, when the irregular surface is transformed to horizontal, the flattened interface below the surface is transformed to curved, which produces inaccurate modeling results because of the presence of ladder-like burrs in the simulated seismic wave. Thus, we propose the mapping method based on the dual-variable finite-difference staggered grid. The proposed method uses different size grid spacings in different regions and locally variable time steps to match the size variability of grid spacings. Numerical examples suggest that the proposed method requires less memory storage capacity and improves the computational efficiency compared with forward modeling methods based on the conventional grid.
基金sponsored by the Knowledge Innovation Program of the Chinese Academy of Sciences No.KZCX2-YW-132)the Important National Science and Technology Specific Projects(No.2008ZX05008-006)the National Natural Science Foundation of China Nos.41074033,40721003,40830315,and 40874041)
文摘We present a finite difference (FD) method for the simulation of seismic wave fields in fractured medium with an irregular (non-fiat) free surface which is beneficial for interpreting exploration data acquired in mountainous regions. Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded. To implement surface topography, we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one. We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations (in a curvilinear coordinate system) in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry (HTI). Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration. The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography. The scattered waves provoked by the topography are re-scattered by the fractures, especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures.
文摘This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized coordinate which represents rotation around transversal main central axis of inertia of undercarriage.The excavator is described by a system of six nonlinear,nonhomogenous differential equations of the second kind.Numerical analysis of the differential equations has been done for BTH-600 hydraulic excavator with moving mechanism with pneumatic wheels.
基金Supported by National Natural Science Foundation of China (No10872141)Doctoral Foundation of Ministry of Education of China (No20060056005)Natural Science Foundation of Tianjin University of Science and Technology (No20070210)
文摘The normal forms of generalized Neimark-Sacker bifurcation are extensively studied using normal form theory of dynamic system. It is well known that if the normal forms of the generalized Neimark-Sacker bifurcation are expressed in polar coordinates, then all odd order terms must, in general, remain in the normal forms. In this paper, five theorems are presented to show that the conventional Neimark-Sacker bifurcation can be further simplified. The simplest normal forms of generalized Neimark-Sacker bifurcation are calculated. Based on the conventional normal form, using appropriate nonlinear transformations, it is found that the generalized Neimark-Sacker bifurcation has at most two nonlinear terms remaining in the amplitude equations of the simplest normal forms up to any order. There are two kinds of simplest normal forms. Their algebraic expression formulas of the simplest normal forms in terms of the coefficients of the generalized Neimark-Sacker bifurcation systems are given.
基金Supported by National Natural Science Foundation of China (No. 60973079)Natural Science Foundation of Hebei Province (No. E2006000039)
文摘The representation method of heterogeneous material information is one of the key technologies of heterogeneous object modeling, but almost all the existing methods cannot represent non-uniform rational B-spline (NURBS) entity. According to the characteristics of NURBS, a novel data structure, named NURBS material data structure, is proposed, in which the geometrical coordinates, weights and material coordinates of NURBS heterogene- ous objects can be represented simultaneously. Based on this data structure, both direct representation method and inverse construction method of heterogeneous NURBS objects are introduced. In the direct representation method, three forms of NURBS heterogeneous objects are introduced by giving the geometry and material information of con- trol points, among which the homogeneous coordinates form is employed for its brevity and easy programming. In the inverse construction method, continuous heterogeneous curves and surfaces can he obtained by interpolating discrete points and curves with specified material information. Some examples are given to show the effectiveness of the pro- posed methods.
文摘This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green's functions of relevant boundary-value problems stated in multiply-connected regions for Laplace equation written in geographical coordinates. Those are efficiently computed by a modification of the method of functional equations, with closed analytical forms preliminary obtained for Green's functions for the corresponding simply-connected regions.
文摘Surface waves comprise an important aspect of the interaction between the atmosphere and the ocean, so a dynamically consistent framework for modelling atmosphere-ocean interaction must take account of surface waves, either implicitly or explicitly. In order to calculate the effect of wind forcing on waves and currents, and vice versa, it is necessary to employ a consistent formula- tion of the energy and momentum balance within the airflow, wave field, and water column. It is very advantageous to apply sur- face-following coordinate systems, whereby the steep gradients in mean flow properties near the air-water interface in the cross-interface direction may be resolved over distances which are much smaller than the height of the waves themselves. We may account for the waves explicitly by employing a numerical spectral wave model, and applying a suitable theory of wave–mean flow interaction. If the mean flow is small compared with the wave phase speed, perturbation expansions of the hydrodynamic equations in a Lagrangian or generalized Lagrangian mean framework are useful: for stronger flows, such as for wind blowing over waves, the presence of critical levels where the mean flow velocity is equal to the wave phase speed necessitates the application of more general types of surface-following coordinate system. The interaction of the flow of air and water and associated differences in temperature and the concentration of various substances (such as gas species) gives rise to a complex boundary-layer structure at a wide range of vertical scales, from the sub-millimetre scales of gaseous diffusion, to several tens of metres for the turbulent Ekman layer. The bal- ance of momentum, heat, and mass is also affected significantly by breaking waves, which act to increase the effective area of the surface for mass transfer, and increase turbulent diffusive fluxes via the conversion of wave energy to turbulent kinetic energy.
基金supported by the National Key R&D Program of China [Grant No.2016YFC1401705]the National Natural Science Foundation of China [Grant Nos.41176015 and41776041]+2 种基金the Chinese Academy Sciences Project ‘Western Pacific Ocean System:Structure,Dynamics and Consequences’[Grant No.XDA11010203]confidencial military project [Grant No.315030401]the State Key Laboratory of Tropical Oceanography,South China Sea Institute of Oceanology,Chinese Academy of Sciences [Project No.LTO1501]
文摘A historical run(1993–2014)of a global,eddy-permitting,hybrid coordinate ocean model(HYCOM)is evaluated against observations.The authors evaluate several metrics in the model,including the spatial distribution of sea surface temperature(SST),the zonally averaged seasonal cycle of SST,the variability of the sea level anomaly(SLA),the zonally and meridionally averaged temperature and salinity,and the equatorial undercurrent.It is found that the simulated seasonal cycle of SST is 0.2–0.8 stronger than observed at midlatitudes.The modeled SST is 0.29°C warmer than the observed for the global ocean.the structure of the subsurface temperature and salinity is similar to the observed.moreover,the variability of SLA exhibits the same pattern as observed.The modeled equatorial undercurrent in the pacific ocean is weaker than observed,but stronger than the ecco reanalysis product.overall,the model can reproduce the large-scale ocean states,and is suitable for analyses seeking to better understand the dynamics and thermodynamics of the upper ocean,as well as ocean variability.
基金supported by the National Natural Science Foundation of China (Grant No. 11175113)
文摘Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.
基金supported by the National Natural Science Foundation of China (Grant Nos.10775097 and 10874174)the Special Funds of the National Natural Science Foundation of China (Grant No.10947017/A05)+1 种基金the Higher School Fund of Outstanding Young Talent (Grant No.2010SQRL132)the Scientific Research Starting Foundation of Chizhou University (Grant No.2010RC036)
文摘We show that the quantum-mechanical fundamental representations, say, the coordinate representation, the coherent state representation, the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion, which is elegant in form and has many applications in deriving new operator identities. This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.