For the solid blanket concept of helium cooled ceramic breeder (HCCB) demonstration fusion power plant (DEMO), a feasible blanket structure with configuration 2×X is proposed as considering relatively low tempera...For the solid blanket concept of helium cooled ceramic breeder (HCCB) demonstration fusion power plant (DEMO), a feasible blanket structure with configuration 2×X is proposed as considering relatively low temperature limit of neutron multiplier beryllium pebbles. Based on that, preliminary design for the typical blanket module of HCCB DEMO has been carried out and verified by thermal-hydraulic analysis and structural analysis. Furthermore, the specific relationship of maximum temperature depended on the surface heating of blanket key part first wall (FW) is also analyzed.展开更多
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearitie...The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.展开更多
This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional r...This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.展开更多
Computational techniques are invaluable to the continued success and development of Magnetic Resonance Imaging (MRI) and to its widespread applications. New processing methods are essential for addressing issues at ea...Computational techniques are invaluable to the continued success and development of Magnetic Resonance Imaging (MRI) and to its widespread applications. New processing methods are essential for addressing issues at each stage of MRI techniques. In this study, we present new sets of non-exponential generating functions representing the NMR transverse magnetizations and signals which are mathematically designed based on the theory and dynamics of the Bloch NMR flow equations. These signals are functions of many spinning nuclei of materials and can be used to obtain information observed in all flow systems. The Bloch NMR flow equations are solved using the Boubaker polynomial expansion scheme (BPES) and analytically connect most of the experimentally valuable NMR parameters in a simplified way for general analyses of magnetic resonance imaging with adiabatic condition.展开更多
As blockchain technology rapidly evolves,smart contracts have seen widespread adoption in financial transactions and beyond.However,the growing prevalence of malicious Ponzi scheme contracts presents serious security ...As blockchain technology rapidly evolves,smart contracts have seen widespread adoption in financial transactions and beyond.However,the growing prevalence of malicious Ponzi scheme contracts presents serious security threats to blockchain ecosystems.Although numerous detection techniques have been proposed,existing methods suffer from significant limitations,such as class imbalance and insufficient modeling of transaction-related semantic features.To address these challenges,this paper proposes an oversampling-based detection framework for Ponzi smart contracts.We enhance the Adaptive Synthetic Sampling(ADASYN)algorithm by incorporating sample proximity to decision boundaries and ensuring realistic sample distributions.This enhancement facilitates the generation of high-quality minority class samples and effectively mitigates class imbalance.In addition,we design a Contract Transaction Graph(CTG)construction algorithm to preserve key transactional semantics through feature extraction from contract code.A graph neural network(GNN)is then applied for classification.This study employs a publicly available dataset from the XBlock platform,consisting of 318 verified Ponzi contracts and 6498 benign contracts.Sourced from real Ethereum deployments,the dataset reflects diverse application scenarios and captures the varied characteristics of Ponzi schemes.Experimental results demonstrate that our approach achieves an accuracy of 96%,a recall of 92%,and an F1-score of 94%in detecting Ponzi contracts,outperforming state-of-the-art methods.展开更多
Clouds play an important role in global atmospheric energy and water vapor budgets, and the low cloud simulations suffer from large biases in many atmospheric general circulation models. In this study, cloud microphys...Clouds play an important role in global atmospheric energy and water vapor budgets, and the low cloud simulations suffer from large biases in many atmospheric general circulation models. In this study, cloud microphysical processes such as raindrop evaporation and cloud water accretion in a double-moment six-class cloud microphysics scheme were revised to enhance the simulation of low clouds using the Global-Regional Integrated Forecast System(GRIST)model. The validation of the revised scheme using a single-column version of the GRIST demonstrated a reasonable reduction in liquid water biases. The revised parameterization simulated medium-and low-level cloud fractions that were in better agreement with the observations than the original scheme. Long-term global simulations indicate the mitigation of the originally overestimated low-level cloud fraction and cloud-water mixing ratio in mid-to high-latitude regions,primarily owing to enhanced accretion processes and weakened raindrop evaporation. The reduced low clouds with the revised scheme showed better consistency with satellite observations, particularly at mid-and high-latitudes. Further improvements can be observed in the simulated cloud shortwave radiative forcing and vertical distribution of total cloud cover. Annual precipitation in mid-latitude regions has also improved, particularly over the oceans, with significantly increased large-scale and decreased convective precipitation.展开更多
In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target ...In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.展开更多
This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, wher...The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.展开更多
Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-var...Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-variable cell population balance models (PBMs) offer the most general way to describe the complicated phenomena associated with cell growth, substrate consumption and product formation. For that reason, solving and understanding of such models are essential to predict and control cell growth in the processes of biotechnological interest. Such models typically consist of a partial integro-differential equation for describing cell growth and an ordinary integro-differential equation for representing substrate consumption. However, the involved mathematical complexities make their numerical solutions challenging for the given numerical scheme. In this article, the central upwind scheme is applied to solve the single-variate and bivariate cell population balance models considering equal and unequal partitioning of cellular materials. The validity of the developed algorithms is verified through several case studies. It was found that the suggested scheme is more reliable and effective.展开更多
In this paper,the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows,incl...In this paper,the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows,including inviscid LBFS Ⅰ,viscous LBFS Ⅱ,hybrid LBFS Ⅲ and hybrid LBFS Ⅳ.Hybrid LBFS can automatically realize the switch between inviscid LBFS Ⅰ and viscous LBFS Ⅱ through introducing a switch function.The resultant hybrid WENO-LBFS scheme absorbs the advantages of WENO scheme and hybrid LBFS.We investigate the performance of WENO scheme based on four kinds of LBFS systematically.Numerical results indicate that the devopled hybrid WENO-LBFS scheme has high accuracy,high resolution and no oscillations.It can not only accurately calculate smooth solutions,but also can effectively capture contact discontinuities and strong shock waves.展开更多
Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and ma...Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and mathematical sciences. In this paper we use three finite difference schemes in order to approximate the solution of stochastic parabolic partial differential equations. The conditions of the mean square convergence of the numerical solution are studied. Some case studies are discussed.展开更多
A filtering / extracting scheme for various timescale processes in short range climate model out-put is established by using the scale scattering method. And the climatological meanings as well as the impor-tance of t...A filtering / extracting scheme for various timescale processes in short range climate model out-put is established by using the scale scattering method. And the climatological meanings as well as the impor-tance of the filtered series are discussed. In the latter part of work, the effectiveness of the filtering method and the performance of the prediction model are analyzed through a real case.展开更多
The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence mod...The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.展开更多
Summary:Throughout the duration of the New Cooperative Medical Scheme(NCMS),it was found that an increasing number of rural patients were seeking out-of^county medical treatment,which posed a great burden on the NCMS ...Summary:Throughout the duration of the New Cooperative Medical Scheme(NCMS),it was found that an increasing number of rural patients were seeking out-of^county medical treatment,which posed a great burden on the NCMS fund.Our study was conducted to examine the prevalence of out-of^county hospitalizations and its related factors,and to provide a scientific basis for follow?up health insurance policies.A total of 215 counties in central and western China from 2008 to 2016 were selected.The total out-of-county hospitalization rate in nine years was 16.95%,which increased from 12.37%in 2008 to 19.21%in 2016 with an average annual growth rate of 5.66%.Its related expenses and compensations were shown to increase each year,with those in the central region being higher than those in the western region.Stepwise logistic regression reveals that the increase in out-of-county hospitalization rate was associated with region(XI),rural population(X2),per capita per year net income(X3),per capita gross domestic product(GDP)(X4),per capita funding amount of NCMS(X5),compensation ratio of out-of^county hospitalization cost(X6),per time average in-county(X7)and out-of-county hospitalization cost(X8).According to Bayesian network(BN),the marginal probability of high out-of^county hospitalization rate was as high as 81.7%.Out-of^county hospitalizations were directly related to X8,X3,X4 and X6.The probability of high out-of-county hospitalization obtained based on hospitalization expenses factors,economy factors,regional characteristics and NCMS policy factors was 95.7%,91.1%,93.0% and 88.8%,respectively.And how these factors affect out-of-county hospitalization and their interrelationships were found out.Our findings suggest that more attention should be paid to the influence mechanism of these factors on out-of-county hospitalizations,and the increase of hospitalizations outside the county should be reasonably supervised and controlled and our results will be used to help guide the formulation of proper intervention policies.展开更多
This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics....This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics. We studied accuracy in term of L∞ error norm by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations.展开更多
The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase...The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.展开更多
This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpola...This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
基金supported by the National Special Project of China for magnetic confined nuclear fusion energy(2015GB108004)
文摘For the solid blanket concept of helium cooled ceramic breeder (HCCB) demonstration fusion power plant (DEMO), a feasible blanket structure with configuration 2×X is proposed as considering relatively low temperature limit of neutron multiplier beryllium pebbles. Based on that, preliminary design for the typical blanket module of HCCB DEMO has been carried out and verified by thermal-hydraulic analysis and structural analysis. Furthermore, the specific relationship of maximum temperature depended on the surface heating of blanket key part first wall (FW) is also analyzed.
基金partially supported by the National Natural Science Foundation of China(Grant No.12071073)financial support by the Jiangsu Provincial Scientific Research Center of Applied Mathematics(Grant No.BK20233002).
文摘The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.
文摘This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.
文摘Computational techniques are invaluable to the continued success and development of Magnetic Resonance Imaging (MRI) and to its widespread applications. New processing methods are essential for addressing issues at each stage of MRI techniques. In this study, we present new sets of non-exponential generating functions representing the NMR transverse magnetizations and signals which are mathematically designed based on the theory and dynamics of the Bloch NMR flow equations. These signals are functions of many spinning nuclei of materials and can be used to obtain information observed in all flow systems. The Bloch NMR flow equations are solved using the Boubaker polynomial expansion scheme (BPES) and analytically connect most of the experimentally valuable NMR parameters in a simplified way for general analyses of magnetic resonance imaging with adiabatic condition.
基金supported by the Key Project of Joint Fund of the National Natural Science Foundation of China“Research on Key Technologies and Demonstration Applications for Trusted and Secure Data Circulation and Trading”(U24A20241)the National Natural Science Foundation of China“Research on Trusted Theories and Key Technologies of Data Security Trading Based on Blockchain”(62202118)+4 种基金the Major Scientific and Technological Special Project of Guizhou Province([2024]014)Scientific and Technological Research Projects from the Guizhou Education Department(Qian jiao ji[2023]003)the Hundred-Level Innovative Talent Project of the Guizhou Provincial Science and Technology Department(Qiankehe Platform Talent-GCC[2023]018)the Major Project of Guizhou Province“Research and Application of Key Technologies for Trusted Large Models Oriented to Public Big Data”(Qiankehe Major Project[2024]003)the Guizhou Province Computational Power Network Security Protection Science and Technology Innovation Talent Team(Qiankehe Talent CXTD[2025]029).
文摘As blockchain technology rapidly evolves,smart contracts have seen widespread adoption in financial transactions and beyond.However,the growing prevalence of malicious Ponzi scheme contracts presents serious security threats to blockchain ecosystems.Although numerous detection techniques have been proposed,existing methods suffer from significant limitations,such as class imbalance and insufficient modeling of transaction-related semantic features.To address these challenges,this paper proposes an oversampling-based detection framework for Ponzi smart contracts.We enhance the Adaptive Synthetic Sampling(ADASYN)algorithm by incorporating sample proximity to decision boundaries and ensuring realistic sample distributions.This enhancement facilitates the generation of high-quality minority class samples and effectively mitigates class imbalance.In addition,we design a Contract Transaction Graph(CTG)construction algorithm to preserve key transactional semantics through feature extraction from contract code.A graph neural network(GNN)is then applied for classification.This study employs a publicly available dataset from the XBlock platform,consisting of 318 verified Ponzi contracts and 6498 benign contracts.Sourced from real Ethereum deployments,the dataset reflects diverse application scenarios and captures the varied characteristics of Ponzi schemes.Experimental results demonstrate that our approach achieves an accuracy of 96%,a recall of 92%,and an F1-score of 94%in detecting Ponzi contracts,outperforming state-of-the-art methods.
基金National Natural Science Foundation of China(42375153,42105153,42205157)Development of Science and Technology at Chinese Academy of Meteorological Sciences(2023KJ038)。
文摘Clouds play an important role in global atmospheric energy and water vapor budgets, and the low cloud simulations suffer from large biases in many atmospheric general circulation models. In this study, cloud microphysical processes such as raindrop evaporation and cloud water accretion in a double-moment six-class cloud microphysics scheme were revised to enhance the simulation of low clouds using the Global-Regional Integrated Forecast System(GRIST)model. The validation of the revised scheme using a single-column version of the GRIST demonstrated a reasonable reduction in liquid water biases. The revised parameterization simulated medium-and low-level cloud fractions that were in better agreement with the observations than the original scheme. Long-term global simulations indicate the mitigation of the originally overestimated low-level cloud fraction and cloud-water mixing ratio in mid-to high-latitude regions,primarily owing to enhanced accretion processes and weakened raindrop evaporation. The reduced low clouds with the revised scheme showed better consistency with satellite observations, particularly at mid-and high-latitudes. Further improvements can be observed in the simulated cloud shortwave radiative forcing and vertical distribution of total cloud cover. Annual precipitation in mid-latitude regions has also improved, particularly over the oceans, with significantly increased large-scale and decreased convective precipitation.
基金supported by the National Natural Science Foundation of China(Grant No.11571181)by the Natural Science Foundation of Jiangsu Province(Grant No.BK20171454).
文摘In this paper,we propose and analyze two second-order accurate finite difference schemes for the one-dimensional heat equation with concentrated capacity on a computa-tional domain=[a,b].We first transform the target equation into the standard heat equation on the domain excluding the singular point equipped with an inner interface matching(IIM)condition on the singular point x=ξ∈(a,b),then adopt Taylor’s ex-pansion to approximate the IIM condition at the singular point and apply second-order finite difference method to approximate the standard heat equation at the nonsingular points.This discrete procedure allows us to choose different grid sizes to partition the two sub-domains[a,ξ]and[ξ,b],which ensures that x=ξ is a grid point,and hence the pro-posed schemes can be generalized to the heat equation with more than one concentrated capacities.We prove that the two proposed schemes are uniquely solvable.And through in-depth analysis of the local truncation errors,we rigorously prove that the two schemes are second-order accurate both in temporal and spatial directions in the maximum norm without any constraint on the grid ratio.Numerical experiments are carried out to verify our theoretical conclusions.
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
基金Project supported by the National Natural Science Foundation of China(Grant No.11471262)Henan University of Technology High-level Talents Fund,China(Grant No.2018BS039)
文摘The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.
文摘Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Because of the included level of details, multi-variable cell population balance models (PBMs) offer the most general way to describe the complicated phenomena associated with cell growth, substrate consumption and product formation. For that reason, solving and understanding of such models are essential to predict and control cell growth in the processes of biotechnological interest. Such models typically consist of a partial integro-differential equation for describing cell growth and an ordinary integro-differential equation for representing substrate consumption. However, the involved mathematical complexities make their numerical solutions challenging for the given numerical scheme. In this article, the central upwind scheme is applied to solve the single-variate and bivariate cell population balance models considering equal and unequal partitioning of cellular materials. The validity of the developed algorithms is verified through several case studies. It was found that the suggested scheme is more reliable and effective.
基金This study was supported by the National Natural Science Foundation of China(Grants 11372168,11772179).
文摘In this paper,the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows,including inviscid LBFS Ⅰ,viscous LBFS Ⅱ,hybrid LBFS Ⅲ and hybrid LBFS Ⅳ.Hybrid LBFS can automatically realize the switch between inviscid LBFS Ⅰ and viscous LBFS Ⅱ through introducing a switch function.The resultant hybrid WENO-LBFS scheme absorbs the advantages of WENO scheme and hybrid LBFS.We investigate the performance of WENO scheme based on four kinds of LBFS systematically.Numerical results indicate that the devopled hybrid WENO-LBFS scheme has high accuracy,high resolution and no oscillations.It can not only accurately calculate smooth solutions,but also can effectively capture contact discontinuities and strong shock waves.
文摘Stochastic partial differential equations (SPDEs) describe the dynamics of stochastic processes depending on space-time continuum. These equations have been widely used to model many applications in engineering and mathematical sciences. In this paper we use three finite difference schemes in order to approximate the solution of stochastic parabolic partial differential equations. The conditions of the mean square convergence of the numerical solution are studied. Some case studies are discussed.
文摘A filtering / extracting scheme for various timescale processes in short range climate model out-put is established by using the scale scattering method. And the climatological meanings as well as the impor-tance of the filtered series are discussed. In the latter part of work, the effectiveness of the filtering method and the performance of the prediction model are analyzed through a real case.
基金Projects(59375211,10771178,10676031) supported by the National Natural Science Foundation of ChinaProject(07A068) supported by the Key Project of Hunan Education CommissionProject(2005CB321702) supported by the National Key Basic Research Program of China
文摘The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.
基金This work was supported by the National Natural Science Foundation of China(No.71573192 and No.81573262)the Fundamental Research Funds for the Central Universities,HUST(No.2016YXZD042).
文摘Summary:Throughout the duration of the New Cooperative Medical Scheme(NCMS),it was found that an increasing number of rural patients were seeking out-of^county medical treatment,which posed a great burden on the NCMS fund.Our study was conducted to examine the prevalence of out-of^county hospitalizations and its related factors,and to provide a scientific basis for follow?up health insurance policies.A total of 215 counties in central and western China from 2008 to 2016 were selected.The total out-of-county hospitalization rate in nine years was 16.95%,which increased from 12.37%in 2008 to 19.21%in 2016 with an average annual growth rate of 5.66%.Its related expenses and compensations were shown to increase each year,with those in the central region being higher than those in the western region.Stepwise logistic regression reveals that the increase in out-of-county hospitalization rate was associated with region(XI),rural population(X2),per capita per year net income(X3),per capita gross domestic product(GDP)(X4),per capita funding amount of NCMS(X5),compensation ratio of out-of^county hospitalization cost(X6),per time average in-county(X7)and out-of-county hospitalization cost(X8).According to Bayesian network(BN),the marginal probability of high out-of^county hospitalization rate was as high as 81.7%.Out-of^county hospitalizations were directly related to X8,X3,X4 and X6.The probability of high out-of-county hospitalization obtained based on hospitalization expenses factors,economy factors,regional characteristics and NCMS policy factors was 95.7%,91.1%,93.0% and 88.8%,respectively.And how these factors affect out-of-county hospitalization and their interrelationships were found out.Our findings suggest that more attention should be paid to the influence mechanism of these factors on out-of-county hospitalizations,and the increase of hospitalizations outside the county should be reasonably supervised and controlled and our results will be used to help guide the formulation of proper intervention policies.
文摘This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics. We studied accuracy in term of L∞ error norm by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations.
文摘The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.
文摘This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
