Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transfo...Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid(SSG) with interpolation, nonstaggered grid, rotated staggered grid(RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the firstorder stress–velocity equation in the curvilinear coordinates system and introduce the highprecision adaptive, unilateral mimetic finite-difference(UMFD) method to process the freeboundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.展开更多
The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the...The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its stag- gered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of nu- merical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.展开更多
Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a ...Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a dilemma arises in that conspicuous colors may not only attract mates,but also alert predators.The"private channels of communication"hypothesis proposes that some intraspecific signals may not be visible to heterospecific animals because of different visual systems.To better understand the evolution of plumage colors and sexual selection in birds,here we studied the chromatic difference and achromatic differences of melanin-and carotenoid-based plumage coloration in five minivet species(Pericrocotus spp.)under conspecific and predator visual systems.We found that either the chromatic or achromatic difference among male or female minivets’plumage was consistently higher under conspecific vision than under predator vision for all five studied species of minivets.This result indicated that individual differences in plumage colors of minivets were visible to the conspecific receivers and hidden from potential predators as a result of evolution under predation risk and conspecific communication.However,males were under a higher risk of predation because they were more conspicuous than females to the vision of a nocturnal predator.展开更多
In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate waves.The wave equations for both the viscoelastic model and the PML contain convolution operators.Ho...In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate waves.The wave equations for both the viscoelastic model and the PML contain convolution operators.However,convolution operator is intractable in finite-difference time-domain(FDTD)method.A great deal of progress has been made in using time stepping instead of convolution in FDTD.To incorporate PML into viscoelastic media,more memory variables need to be introduced,which increases the code complexity and computation costs.By modifying the nonsplitting PML formulation,I propose a viscoelastic model,which can be used as a viscoelastic material and/or a PML just by adjusting the parameters.The proposed viscoelastic model is essentially equivalent to a Maxwell model.Compared with existing PML methods,the proposed method requires less memory and its implementation in existing finite-difference codes is much easier.The attenuation and phase velocity of P-and S-waves are frequency independent in the viscoelastic model if the related quality factors(Q)are greater than 10.The numerical examples show that the method is stable for materials with high absorption(Q=1),and for heterogeneous media with large contrast of acoustic impedance and large contrast of viscosity.展开更多
We present a first-order finite difference scheme for approximating solutions of a mathematical model of cervical cancer induced by the human papillomavirus (HPV), which consists of four nonlinear partial differential...We present a first-order finite difference scheme for approximating solutions of a mathematical model of cervical cancer induced by the human papillomavirus (HPV), which consists of four nonlinear partial differential equations and a nonlinear first-order ordinary differential equation. The scheme is analyzed and used to provide an existence-uniqueness result. Numerical simulations are performed in order to demonstrate the first-order rate of convergence. A sensitivity analysis was done in order to compare the effects of two drug types, those that increase the death rate of HPV-infected cells, and those that increase the death rate of the precancerous cell population. The model predicts that treatments that affect the precancerous cell population by directly increasing the corresponding death rate are far more effective than those that increase the death rate of HPV-infected cells.展开更多
In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot's poroelastic equations will be e...In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot's poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.展开更多
Reverse time migration and full waveform inversion involve the crosscorrelation of two wavefields,propagated in the forward-and reverse-time directions,respectively.As a result,the forward-propagated wavefield needs t...Reverse time migration and full waveform inversion involve the crosscorrelation of two wavefields,propagated in the forward-and reverse-time directions,respectively.As a result,the forward-propagated wavefield needs to be stored,and then accessed to compute the correlation with the backward-propagated wavefield.Boundary-value methods reconstruct the source wavefield using saved boundary wavefields and can significantly reduce the storage requirements.However,the existing boundary-value methods are based on the explicit finite-difference(FD)approximations of the spatial derivatives.Implicit FD methods exhibit greater accuracy and thus allow for a smaller operator length.We develop two(an accuracy-preserving and a memory-efficient)wavefield reconstruction schemes based on an implicit staggered-grid FD(SFD)operator.The former uses boundary wavefields at M layers of grid points and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield for a(2M+2)th-order implicit SFD operator.The latter applies boundary wavefields at N layers of grid points,a linear combination of wavefields at M–N layers of grid points,and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield(0≤N<M).The required memory of accuracy-preserving and memory-efficient schemes is(M+1)/M and(N+2)/M times,respectively,that of the explicit reconstruction scheme.Numerical results reveal that the accuracy-preserving scheme can achieve accurate reconstruction at the cost of storage.The memory-efficient scheme with N=2 can obtain plausible reconstructed wavefields and images,and the storage amount is 4/(M+1)of the accuracy-preserving scheme.展开更多
Numerical simulation in transverse isotropic media with tilted symmetry axis(TTI) using the standard staggered-grid finite-difference scheme(SSG)results in errors caused by averaging or interpolation. In order to ...Numerical simulation in transverse isotropic media with tilted symmetry axis(TTI) using the standard staggered-grid finite-difference scheme(SSG)results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme(RSG) is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme(CSG) is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme(RSGC). The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.展开更多
Strong ground motion of an earthquake is simulated by using both staggered grid finite difference method (FDM) and stochastic method, respectively. The acceleration time histories obtained from the both ways and their...Strong ground motion of an earthquake is simulated by using both staggered grid finite difference method (FDM) and stochastic method, respectively. The acceleration time histories obtained from the both ways and their response spectra are compared. The result demonstrates that the former is adequate to simulate the low-frequency seismic wave; the latter is adequate to simulate the high-frequency seismic wave. Moreover, the result obtained from FDM can better reflect basin effects.展开更多
Acoustic-elastic coupled media is often encountered in most marine explorations, and accurate simulation of acoustic-elastic coupled media is of great significance. At present, the study of acoustic-elastic coupled me...Acoustic-elastic coupled media is often encountered in most marine explorations, and accurate simulation of acoustic-elastic coupled media is of great significance. At present, the study of acoustic-elastic coupled media still assumes that the solid of the acoustic-elastic coupled media is isotropic, but this assumption is not in accordance with the actual situation. In this paper, we derive the solid media of acoustic-elastic coupled media from isotropic media to anisotropic media, and propose an acoustic-elastic coupled medium based ontransverse isotropic media with vertical symmetric axes(VTI) to improve the accuracy of forward modeling. Based on the relationship between the Thomsen parameter and the coefficient matrix of the anisotropic elastic wave equation, we transform the Thomson parameter into a velocity model with anisotropic properties. We use a staggered grid finite difference method to simulate the propagation of a wavefield in a three-dimensional acoustic-elastic coupled media. We obtain the snapshots of the wave field when the solid of the acoustic-elastic coupled media is an isotropic medium and a VTI media. When the solid of the acoustic-elastic coupled media is considered VTI media, we can observe the qP wave and qS wave that cannot be observed in the isotropic medium from the wave field snapshot. We can also find that the seismic records obtained by the method we use are more realistic. The algorithm proposed in this paper is of great significance for high-precision ocean numerical simulation.展开更多
Obsessive-compulsive disorder (OCD) is characterized by obsessions (intrusive thoughts, images etc.) and compulsions (repetitive, stereotyped and perseverant acts). Animal models of OCD are specifically devoted to sim...Obsessive-compulsive disorder (OCD) is characterized by obsessions (intrusive thoughts, images etc.) and compulsions (repetitive, stereotyped and perseverant acts). Animal models of OCD are specifically devoted to simulating compulsive features of the disorder. In OCD, compulsive behaviors are recognized as repetitive and maladaptive and symptoms relief can be experienced due to treatment with selective serotonin reuptake inhibitors. Many animal models of OCD are provided with some degree of validity. Genetically based differences in behavior in animal models of OCD are of great value, given that human OCD is reported to involve genetic factors. Some animal models of OCD were already used in studies for the evaluation of strain differences. These works were explored in the present review.展开更多
On the basis of the previous researches and the ecological footprint theory,we use the cross-sectional data of Chinese energy consumption in 2007 to calculate the regional differences of energy consumption footprint o...On the basis of the previous researches and the ecological footprint theory,we use the cross-sectional data of Chinese energy consumption in 2007 to calculate the regional differences of energy consumption footprint of 30 provinces in China;by using the method of EEF calculation method,we calculate the regional distribution of EFI and analyze its law;through the construction of STIRPAT model,we reveal the relationship between EEF and factors of population and economy.The results show that provinces with higher EEF mainly concentrate in the Middle Eastern China,which have a developed industry,such as Shandong,Hebei,Liaoning Province and so on.However,provinces with lower EEF mainly concentrate in the Western China,which have a relatively poor economy,such as Ningxia,Qinghai Province and so on.These results are in accordance with the area distribution of China's economic development level.The EFI decreases gradually from west to east.As the level of regional economy is improved,the EFI has the downward trend.The quantity of population shows notable impact on EFI.The per capita GDP does not show the nagative relationship with EFI,which can not prove the existence of Environmental Kuznets Curve.展开更多
In this paper, an efficient computational algorithm is proposed to solve the nonlinear optimal control problem. In our approach, the linear quadratic optimal control model, which is adding the adjusted parameters into...In this paper, an efficient computational algorithm is proposed to solve the nonlinear optimal control problem. In our approach, the linear quadratic optimal control model, which is adding the adjusted parameters into the model used, is employed. The aim of applying this model is to take into account the differences between the real plant and the model used during the calculation procedure. In doing so, an expanded optimal control problem is introduced such that system optimization and parameter estimation are mutually interactive. Accordingly, the optimality conditions are derived after the Hamiltonian function is defined. Specifically, the modified model-based optimal control problem is resulted. Here, the conjugate gradient approach is used to solve the modified model-based optimal control problem, where the optimal solution of the model used is calculated repeatedly, in turn, to update the adjusted parameters on each iteration step. When the convergence is achieved, the iterative solution approaches to the correct solution of the original optimal control problem, in spite of model-reality differences. For illustration, an economic growth problem is solved by using the algorithm proposed. The results obtained demonstrate the efficiency of the algorithm proposed. In conclusion, the applicability of the algorithm proposed is highly recommended.展开更多
Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real pla...Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.展开更多
This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip veloci...This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.展开更多
D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration a...D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration are used to solve seismic wave equation, which means difference scheme for space domain and analytic integration for time domain. Both the principle and algorithm of this method are introduced in the paper. Based on the theory, the numerical examples prove that this hybrid method can lead to higher accuracy than the traditional finite difference method and the solution is very close to the exact one. Also the seismic modeling examples show the good performance of this method even in the case of complex surface conditions and complicated structures.展开更多
The Tazhong paleouplift is divided into the upper and the lower structural layers, bounded by the unconformity surface at the top of the Ordovician carbonate rock. The reservoirs in the two layers from different parts...The Tazhong paleouplift is divided into the upper and the lower structural layers, bounded by the unconformity surface at the top of the Ordovician carbonate rock. The reservoirs in the two layers from different parts vary in number, type and reserves, but the mechanism was rarely researched before. Therefore, an explanation of the mechanism will promote petroleum exploration in Tazhong paleouplift. After studying the evolution and reservoir distribution of the Tazhong paleouplift, it is concluded that the evolution in late Caledonian, late Hercynian and Himalayan periods resulted in the upper and the lower structural layers. It is also defined that in the upper structural layer, structural and stratigraphic overlap reservoirs are developed at the top and the upper part of the paleouplift, which are dominated by oil reservoirs, while for the lower structural layer, lithological reservoirs are developed in the lower part of the paleouplift, which are dominated by gas reservoirs, and more reserves are discovered in the lower structural layer than the upper. Through a comparative analysis of accumulation conditions of the upper and the lower structural layers, the mechanism of enrichment differences is clearly explained. The reservoir and seal conditions of the lower structural layer are better than those of the upper layer, which is the reason why more reservoirs have been found in the former. The differences in the carrier system types, trap types and charging periods between the upper and the lower structural layers lead to differences in the reservoir types and distribution. An accumulation model is established for the Tazhong paleouplift. For the upper structural layer, the structural reservoirs and the stratigraphic overlap reservoirs are formed at the upper part of the paleouplift, while for the lower structural layer, the weathering crust reservoirs are formed at the top, the reef-flat reservoirs are formed on the lateral margin, the karst and inside reservoirs are formed in the lower part of the paleouplift.展开更多
Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with ...Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.展开更多
In this paper, a new lattice hydrodynamic model based on Nagatani's model INagatani T 1998 Physica A 261 5991 is presented by introducing the flow difference effect. The stability condition for the new model is obtai...In this paper, a new lattice hydrodynamic model based on Nagatani's model INagatani T 1998 Physica A 261 5991 is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink -antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.展开更多
A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordin...A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.展开更多
基金supported by the National Nature Science Foundation of China(Nos.41504102 and 41604037)National Science and Technology Major Project(No.2016ZX05015-006)Yangtze University Youth Found(No.2015cqn32)
文摘Finite-difference(FD) methods are widely used in seismic forward modeling owing to their computational efficiency but are not readily applicable to irregular topographies. Thus, several FD methods based on the transformation to curvilinear coordinates using body-fitted grids have been proposed, e.g., stand staggered grid(SSG) with interpolation, nonstaggered grid, rotated staggered grid(RSG), and fully staggered. The FD based on the RSG is somewhat superior to others because it satisfies the spatial distribution of the wave equation without additional memory and computational requirements; furthermore, it is simpler to implement. We use the RSG FD method to transform the firstorder stress–velocity equation in the curvilinear coordinates system and introduce the highprecision adaptive, unilateral mimetic finite-difference(UMFD) method to process the freeboundary conditions of an irregular surface. The numerical results suggest that the precision of the solution is higher than that of the vacuum formalism. When the minimum wavelength is low, UMFD avoids the surface wave dispersion. We compare FD methods based on RSG, SEM, and nonstaggered grid and infer that all simulation results are consistent but the computational efficiency of the RSG FD method is higher than the rest.
基金Fund Project of Key Lab of Geophysical Exploration of China National Petroleum Corporation (GPR0408).
文摘The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its stag- gered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of nu- merical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.
基金supported by the National Natural Science Foundation of China(32260127)the Education Department of Hainan Province(HnjgY2022-12)+1 种基金the Hainan Provincial Natural Science Foundation of China(320CXTD437)the Hainan Provincial Innovative Research Program for Graduates(Qhys2022-241)。
文摘Adaptive mate choice has been accepted as the leading theory to explain the colorful plumage of birds.This theory hypothesizes that conspicuous colors act as signals to advertise the qualities of the owners.However,a dilemma arises in that conspicuous colors may not only attract mates,but also alert predators.The"private channels of communication"hypothesis proposes that some intraspecific signals may not be visible to heterospecific animals because of different visual systems.To better understand the evolution of plumage colors and sexual selection in birds,here we studied the chromatic difference and achromatic differences of melanin-and carotenoid-based plumage coloration in five minivet species(Pericrocotus spp.)under conspecific and predator visual systems.We found that either the chromatic or achromatic difference among male or female minivets’plumage was consistently higher under conspecific vision than under predator vision for all five studied species of minivets.This result indicated that individual differences in plumage colors of minivets were visible to the conspecific receivers and hidden from potential predators as a result of evolution under predation risk and conspecific communication.However,males were under a higher risk of predation because they were more conspicuous than females to the vision of a nocturnal predator.
文摘In numerical simulation of wave propagation,both viscoelastic materials and perfectly matched layers(PMLs)attenuate waves.The wave equations for both the viscoelastic model and the PML contain convolution operators.However,convolution operator is intractable in finite-difference time-domain(FDTD)method.A great deal of progress has been made in using time stepping instead of convolution in FDTD.To incorporate PML into viscoelastic media,more memory variables need to be introduced,which increases the code complexity and computation costs.By modifying the nonsplitting PML formulation,I propose a viscoelastic model,which can be used as a viscoelastic material and/or a PML just by adjusting the parameters.The proposed viscoelastic model is essentially equivalent to a Maxwell model.Compared with existing PML methods,the proposed method requires less memory and its implementation in existing finite-difference codes is much easier.The attenuation and phase velocity of P-and S-waves are frequency independent in the viscoelastic model if the related quality factors(Q)are greater than 10.The numerical examples show that the method is stable for materials with high absorption(Q=1),and for heterogeneous media with large contrast of acoustic impedance and large contrast of viscosity.
文摘We present a first-order finite difference scheme for approximating solutions of a mathematical model of cervical cancer induced by the human papillomavirus (HPV), which consists of four nonlinear partial differential equations and a nonlinear first-order ordinary differential equation. The scheme is analyzed and used to provide an existence-uniqueness result. Numerical simulations are performed in order to demonstrate the first-order rate of convergence. A sensitivity analysis was done in order to compare the effects of two drug types, those that increase the death rate of HPV-infected cells, and those that increase the death rate of the precancerous cell population. The model predicts that treatments that affect the precancerous cell population by directly increasing the corresponding death rate are far more effective than those that increase the death rate of HPV-infected cells.
基金Project supported by the "100 Talents Project" of the Chinese Academy of Sciences and the Major Program of the National Natural Science Foundation of China (Grant No 10534040).
文摘In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot's poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.
基金partially supported by National Key R&D Program of China(2021YFA0716902)the National Natural Science Foundation of China(42174156)the Fundamental Research Funds for the Central Universities,CHD(300102261107)。
文摘Reverse time migration and full waveform inversion involve the crosscorrelation of two wavefields,propagated in the forward-and reverse-time directions,respectively.As a result,the forward-propagated wavefield needs to be stored,and then accessed to compute the correlation with the backward-propagated wavefield.Boundary-value methods reconstruct the source wavefield using saved boundary wavefields and can significantly reduce the storage requirements.However,the existing boundary-value methods are based on the explicit finite-difference(FD)approximations of the spatial derivatives.Implicit FD methods exhibit greater accuracy and thus allow for a smaller operator length.We develop two(an accuracy-preserving and a memory-efficient)wavefield reconstruction schemes based on an implicit staggered-grid FD(SFD)operator.The former uses boundary wavefields at M layers of grid points and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield for a(2M+2)th-order implicit SFD operator.The latter applies boundary wavefields at N layers of grid points,a linear combination of wavefields at M–N layers of grid points,and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield(0≤N<M).The required memory of accuracy-preserving and memory-efficient schemes is(M+1)/M and(N+2)/M times,respectively,that of the explicit reconstruction scheme.Numerical results reveal that the accuracy-preserving scheme can achieve accurate reconstruction at the cost of storage.The memory-efficient scheme with N=2 can obtain plausible reconstructed wavefields and images,and the storage amount is 4/(M+1)of the accuracy-preserving scheme.
文摘Numerical simulation in transverse isotropic media with tilted symmetry axis(TTI) using the standard staggered-grid finite-difference scheme(SSG)results in errors caused by averaging or interpolation. In order to eliminate the errors, a method of rotated staggered-grid finite-difference scheme(RSG) is proposed. However, the RSG brings serious numerical dispersion. The compact staggered-grid finite-difference scheme(CSG) is an implicit difference scheme, which use fewer grid points to suppress dispersion more effectively than the SSG. This paper combines the CSG with the RSG to derive a rotated staggered-grid compact finite-difference scheme(RSGC). The numerical experiments indicate that the RSGC has weaker numerical dispersion and better accuracy than the RSG.
基金National Natural Science Foundation of China (5048003) and DAAD of Munich University, Germany.
文摘Strong ground motion of an earthquake is simulated by using both staggered grid finite difference method (FDM) and stochastic method, respectively. The acceleration time histories obtained from the both ways and their response spectra are compared. The result demonstrates that the former is adequate to simulate the low-frequency seismic wave; the latter is adequate to simulate the high-frequency seismic wave. Moreover, the result obtained from FDM can better reflect basin effects.
基金Supported by Major Project of National Science and Technology of China(No.2016ZX05026-002-003)National Natural Science Foundation of China(No.41374108)
文摘Acoustic-elastic coupled media is often encountered in most marine explorations, and accurate simulation of acoustic-elastic coupled media is of great significance. At present, the study of acoustic-elastic coupled media still assumes that the solid of the acoustic-elastic coupled media is isotropic, but this assumption is not in accordance with the actual situation. In this paper, we derive the solid media of acoustic-elastic coupled media from isotropic media to anisotropic media, and propose an acoustic-elastic coupled medium based ontransverse isotropic media with vertical symmetric axes(VTI) to improve the accuracy of forward modeling. Based on the relationship between the Thomsen parameter and the coefficient matrix of the anisotropic elastic wave equation, we transform the Thomson parameter into a velocity model with anisotropic properties. We use a staggered grid finite difference method to simulate the propagation of a wavefield in a three-dimensional acoustic-elastic coupled media. We obtain the snapshots of the wave field when the solid of the acoustic-elastic coupled media is an isotropic medium and a VTI media. When the solid of the acoustic-elastic coupled media is considered VTI media, we can observe the qP wave and qS wave that cannot be observed in the isotropic medium from the wave field snapshot. We can also find that the seismic records obtained by the method we use are more realistic. The algorithm proposed in this paper is of great significance for high-precision ocean numerical simulation.
文摘Obsessive-compulsive disorder (OCD) is characterized by obsessions (intrusive thoughts, images etc.) and compulsions (repetitive, stereotyped and perseverant acts). Animal models of OCD are specifically devoted to simulating compulsive features of the disorder. In OCD, compulsive behaviors are recognized as repetitive and maladaptive and symptoms relief can be experienced due to treatment with selective serotonin reuptake inhibitors. Many animal models of OCD are provided with some degree of validity. Genetically based differences in behavior in animal models of OCD are of great value, given that human OCD is reported to involve genetic factors. Some animal models of OCD were already used in studies for the evaluation of strain differences. These works were explored in the present review.
基金Supported by Anhui Province Key Project of Natural Science Foundation((KJ2010A316)Project of Natural Science of Suzhou university(2009YZK01)
文摘On the basis of the previous researches and the ecological footprint theory,we use the cross-sectional data of Chinese energy consumption in 2007 to calculate the regional differences of energy consumption footprint of 30 provinces in China;by using the method of EEF calculation method,we calculate the regional distribution of EFI and analyze its law;through the construction of STIRPAT model,we reveal the relationship between EEF and factors of population and economy.The results show that provinces with higher EEF mainly concentrate in the Middle Eastern China,which have a developed industry,such as Shandong,Hebei,Liaoning Province and so on.However,provinces with lower EEF mainly concentrate in the Western China,which have a relatively poor economy,such as Ningxia,Qinghai Province and so on.These results are in accordance with the area distribution of China's economic development level.The EFI decreases gradually from west to east.As the level of regional economy is improved,the EFI has the downward trend.The quantity of population shows notable impact on EFI.The per capita GDP does not show the nagative relationship with EFI,which can not prove the existence of Environmental Kuznets Curve.
文摘In this paper, an efficient computational algorithm is proposed to solve the nonlinear optimal control problem. In our approach, the linear quadratic optimal control model, which is adding the adjusted parameters into the model used, is employed. The aim of applying this model is to take into account the differences between the real plant and the model used during the calculation procedure. In doing so, an expanded optimal control problem is introduced such that system optimization and parameter estimation are mutually interactive. Accordingly, the optimality conditions are derived after the Hamiltonian function is defined. Specifically, the modified model-based optimal control problem is resulted. Here, the conjugate gradient approach is used to solve the modified model-based optimal control problem, where the optimal solution of the model used is calculated repeatedly, in turn, to update the adjusted parameters on each iteration step. When the convergence is achieved, the iterative solution approaches to the correct solution of the original optimal control problem, in spite of model-reality differences. For illustration, an economic growth problem is solved by using the algorithm proposed. The results obtained demonstrate the efficiency of the algorithm proposed. In conclusion, the applicability of the algorithm proposed is highly recommended.
文摘Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.
文摘This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.
基金This project is sponsored by the Specialized Prophasic Basic Research of the"973"Programme,contract No:2001cca02300
文摘D seismic modeling can be used to study the propagation of seismic wave exactly and it is also a tool of 3-D seismic data processing and interpretation. In this paper the arbitrary difference and precise integration are used to solve seismic wave equation, which means difference scheme for space domain and analytic integration for time domain. Both the principle and algorithm of this method are introduced in the paper. Based on the theory, the numerical examples prove that this hybrid method can lead to higher accuracy than the traditional finite difference method and the solution is very close to the exact one. Also the seismic modeling examples show the good performance of this method even in the case of complex surface conditions and complicated structures.
基金supported by the National 973 Key Development Program for Basic Research of China(S/N: 2006CB202308)the National Natural Science Foundation of China(Grant No.40972088)
文摘The Tazhong paleouplift is divided into the upper and the lower structural layers, bounded by the unconformity surface at the top of the Ordovician carbonate rock. The reservoirs in the two layers from different parts vary in number, type and reserves, but the mechanism was rarely researched before. Therefore, an explanation of the mechanism will promote petroleum exploration in Tazhong paleouplift. After studying the evolution and reservoir distribution of the Tazhong paleouplift, it is concluded that the evolution in late Caledonian, late Hercynian and Himalayan periods resulted in the upper and the lower structural layers. It is also defined that in the upper structural layer, structural and stratigraphic overlap reservoirs are developed at the top and the upper part of the paleouplift, which are dominated by oil reservoirs, while for the lower structural layer, lithological reservoirs are developed in the lower part of the paleouplift, which are dominated by gas reservoirs, and more reserves are discovered in the lower structural layer than the upper. Through a comparative analysis of accumulation conditions of the upper and the lower structural layers, the mechanism of enrichment differences is clearly explained. The reservoir and seal conditions of the lower structural layer are better than those of the upper layer, which is the reason why more reservoirs have been found in the former. The differences in the carrier system types, trap types and charging periods between the upper and the lower structural layers lead to differences in the reservoir types and distribution. An accumulation model is established for the Tazhong paleouplift. For the upper structural layer, the structural reservoirs and the stratigraphic overlap reservoirs are formed at the upper part of the paleouplift, while for the lower structural layer, the weathering crust reservoirs are formed at the top, the reef-flat reservoirs are formed on the lateral margin, the karst and inside reservoirs are formed in the lower part of the paleouplift.
基金supported by China Scholarship Council and partially by the National "863" Program of China under contract No. 2007AA06Z218.
文摘Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.
基金Project supported by the National Basic Research Program of China (Grant No. G2006CB705500)the National Natural Science Foundation of China (Grant Nos. 70501004,70701004 and 70631001)Program for New Century Excellent Talents in University(Grant No. NCET-07-0057)
文摘In this paper, a new lattice hydrodynamic model based on Nagatani's model INagatani T 1998 Physica A 261 5991 is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink -antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.
基金The National Natural Science Foundation of China (No10471023)
文摘A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.