The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And...The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.展开更多
Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in prac...Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.展开更多
In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cell...In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.展开更多
This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So...This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.展开更多
A convenient method for methane(CH_(4))direct conversion to methanol(CH_(3)OH)is of great significance to use methane-rich resources,especially clathrates and stranded shale gas resources located in remote regions.The...A convenient method for methane(CH_(4))direct conversion to methanol(CH_(3)OH)is of great significance to use methane-rich resources,especially clathrates and stranded shale gas resources located in remote regions.Theoretically,the activation of CH_(4) and the selectivity to the CH_(3)OH product are challenging due to the extreme stability of CH_(4) and relatively high reactivity of CH_(3)OH.The state-of-the-art‘methane reforming-methanol synthesis’process adopts a two-step strategy to avoid the further reaction of CH_(3)OH under the harsh conditions required for CH_(4) activation.In the electrochemical field,researchers are trying to develop conversion pathways under mild conditions.They have found suitable catalysts to activate the C–H bonds in methane with the help of external charge and have designed the electrode reactions to continuously generate certain active oxygen species.These active oxygen species attack the activated methane and convert it to CH_(3)OH,with the benefit of avoiding over-oxidation of CH_(3)OH,and thus obtain a high conversion efficiency of CH_(4) to CH_(3)OH.This mini-review focuses on the advantages and challenges of electrochemical conversion of CH4 to CH_(3)OH,especially the strategies for supplying electro-generated active oxygen species in-situ to react with the activated methane.展开更多
Zeolite FAU composites with a macro/meso-microporous hierarchical structure were hydrothermally synthesized using macro-mesoporous γ-Al_2O_3 monolith as the substrate by means of the liquid crystallization directing...Zeolite FAU composites with a macro/meso-microporous hierarchical structure were hydrothermally synthesized using macro-mesoporous γ-Al_2O_3 monolith as the substrate by means of the liquid crystallization directing agent(LCDA) induced method. No template was needed throughout the synthesis processes. The structure and porosity of zeolite composites were analyzed by means of X-ray powder diffraction(XRD), scanning electron microscopy(SEM) and N_2adsorption-desorption isotherms. The results showed that the supported zeolite composites with varied zeolitic crystalline phases and different morphologies can be obtained by adjusting the crystallization parameters, such as the crystallization temperature, the composition and the alkalinity of the precursor solution. The presence of LCDA was defined as a determinant for synthesizing the zeolite composites. The mechanisms for formation of the hierarchically porous FAU zeolite composites in the LCDA induced synthesis process were discussed. The resulting monolithic zeolite with a trimodal-porous hierarchical structure shows potential applicability where facile diffusion is required.展开更多
A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous H...A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.展开更多
This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions an...This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.展开更多
A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be ...The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.展开更多
Silicoaluminophosphates SAPO-11 molecular sieves with small particle size and hierarchical pores were synthesized using the directing agent method.The effect of crystallization time on the particle structure,morpholog...Silicoaluminophosphates SAPO-11 molecular sieves with small particle size and hierarchical pores were synthesized using the directing agent method.The effect of crystallization time on the particle structure,morphology,pore structure properties,and acid properties of SAPO-11 molecular sieves were investigated.Unlike the SAPO-11 molecular sieves synthesized with the conventional method,the results of XRD,SEM,BET and NH3-TPD analyses showed that the SAPO-11 molecular sieves synthesized by the directing agent method in a shorter crystallization time exhibited fine and uniform morphology.By increasing the crystallization time,the particle size of SAPO-11 molecular sieve was significantly reduced,and the mesoporous structure(intercrystalline pores)was formed.Furthermore,the external specific surface area and the total specific surface area reached 81.7 m^2/g and 192.0 m^2/g,respectively,which effectively reduced the pore mass transfer resistance and significantly increased the number of acid sites.The results of n-dodecane hydroisomerization revealed that the Pt/SAPO-11 prepared with the novel method exhibited higher catalytic activity and better hydroisomerization selectivity than that synthesized by the conventional hydrothermal method.Thus,the small particle molecular sieve showed a promising industrial application prospect to be used as catalyst support.展开更多
Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explaine...Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width α 〉3/2/π≈ 0.3899, which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs–Thomson energy acting on the interface.展开更多
One of the essential points of the direct-method single-wavelength anomalous diffraction （SAD） phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respec...One of the essential points of the direct-method single-wavelength anomalous diffraction （SAD） phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respectively at φh″＋｜△φh｜ and φh″-｜△φh｜. The probability for △φh being positive （P＋） can be derived based on the Cochran distribution in direct methods. Hence the SAD phase ambiguity can be resolved by multiplying the Gaussian function peaked at φh″＋｜△φh｜ with P＋ and multiplying the Gaussian function peaked at φh″-｜△φh｜ with P_ （=1- P＋）. The direct-method SAD h phasing has been proved powerful in breaking SAD phase ambiguities, in particular when anomalous-scattering signals are weak. However, the approximation of bimodal phase distributions by the sum of two Gaussian functions introduces considerable errors. In this paper we show that a much better approximation can be achieved by replacing the two Gaussian functions with two von Mises distributions. Test results showed that this leads to significant improvement on the efficiency of direct-method SAD-phasing.展开更多
So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. Bu...So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou＇s direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.展开更多
The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal cohere...The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.展开更多
In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the disc...In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.展开更多
In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equation...In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.展开更多
The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolat...The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolation is not only reliable but also can save the amount of calculation by nearly 36%. Large amount of calculation and lacking strict theoretical bas is has been th e two disadvantage of direct method by new. If this defect is not overcome, they will not only s eriously affect the application of this method, but also hinder its further rese arch. Based on sufficient calculation practice, this article has made a primary discussion about the theory and method of reducing the amount of calculation, an d has achieved some satisfactory results.展开更多
Direct Monte Carlo(MC) simulation is a powerful probabilistic safety assessment method for accounting dynamics of the system.But it is not efficient at simulating rare events.A biasing transition rate method based on ...Direct Monte Carlo(MC) simulation is a powerful probabilistic safety assessment method for accounting dynamics of the system.But it is not efficient at simulating rare events.A biasing transition rate method based on direct MC simulation is proposed to solve the problem in this paper.This method biases transition rates of the components by adding virtual components to them in series to increase the occurrence probability of the rare event,hence the decrease in the variance of MC estimator.Several cases are used to benchmark this method.The results show that the method is effective at modeling system failure and is more efficient at collecting evidence of rare events than the direct MC simulation.The performance is greatly improved by the biasing transition rate method.展开更多
Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suf...Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.展开更多
文摘The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.
基金the National High Technology Research and Development Program of China(Grant No.2012AA011603)
文摘Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61105130 and 61175124)
文摘In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge^Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.
基金Project supported by the Natural Science Foundation of China(10371009)Research Fund for the Doctoral Program Higher Education
文摘This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.
基金support from National Science Foundation of China(No.22075012).
文摘A convenient method for methane(CH_(4))direct conversion to methanol(CH_(3)OH)is of great significance to use methane-rich resources,especially clathrates and stranded shale gas resources located in remote regions.Theoretically,the activation of CH_(4) and the selectivity to the CH_(3)OH product are challenging due to the extreme stability of CH_(4) and relatively high reactivity of CH_(3)OH.The state-of-the-art‘methane reforming-methanol synthesis’process adopts a two-step strategy to avoid the further reaction of CH_(3)OH under the harsh conditions required for CH_(4) activation.In the electrochemical field,researchers are trying to develop conversion pathways under mild conditions.They have found suitable catalysts to activate the C–H bonds in methane with the help of external charge and have designed the electrode reactions to continuously generate certain active oxygen species.These active oxygen species attack the activated methane and convert it to CH_(3)OH,with the benefit of avoiding over-oxidation of CH_(3)OH,and thus obtain a high conversion efficiency of CH_(4) to CH_(3)OH.This mini-review focuses on the advantages and challenges of electrochemical conversion of CH4 to CH_(3)OH,especially the strategies for supplying electro-generated active oxygen species in-situ to react with the activated methane.
基金the financial support from the National Natural Science Foundation of China(No.20973022 and No.11472048)the State Key Laboratory of Catalytic Materials and Reaction Engineering(RIPP,SINOPEC)(Serial No.33600000-14-ZC0607-0006)
文摘Zeolite FAU composites with a macro/meso-microporous hierarchical structure were hydrothermally synthesized using macro-mesoporous γ-Al_2O_3 monolith as the substrate by means of the liquid crystallization directing agent(LCDA) induced method. No template was needed throughout the synthesis processes. The structure and porosity of zeolite composites were analyzed by means of X-ray powder diffraction(XRD), scanning electron microscopy(SEM) and N_2adsorption-desorption isotherms. The results showed that the supported zeolite composites with varied zeolitic crystalline phases and different morphologies can be obtained by adjusting the crystallization parameters, such as the crystallization temperature, the composition and the alkalinity of the precursor solution. The presence of LCDA was defined as a determinant for synthesizing the zeolite composites. The mechanisms for formation of the hierarchically porous FAU zeolite composites in the LCDA induced synthesis process were discussed. The resulting monolithic zeolite with a trimodal-porous hierarchical structure shows potential applicability where facile diffusion is required.
文摘A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundations of China(Grant Nos.10735030,10475055,10675065 and 90503006)the National Basic Research Program of China(Grant No.2007CB814800)
文摘This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
基金Supported by the National Natural Science Foundation of China(Grant No.11971149,11871381)Natural Science Foundation of Henan Province for Youth(Grant No.202300410146)。
文摘The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.
基金We thank the National Natural Science Fund of China(2016-Z0030)Natural Science Foundation of Liaoning Province(L2017 LQN008,L2019014).
文摘Silicoaluminophosphates SAPO-11 molecular sieves with small particle size and hierarchical pores were synthesized using the directing agent method.The effect of crystallization time on the particle structure,morphology,pore structure properties,and acid properties of SAPO-11 molecular sieves were investigated.Unlike the SAPO-11 molecular sieves synthesized with the conventional method,the results of XRD,SEM,BET and NH3-TPD analyses showed that the SAPO-11 molecular sieves synthesized by the directing agent method in a shorter crystallization time exhibited fine and uniform morphology.By increasing the crystallization time,the particle size of SAPO-11 molecular sieve was significantly reduced,and the mesoporous structure(intercrystalline pores)was formed.Furthermore,the external specific surface area and the total specific surface area reached 81.7 m^2/g and 192.0 m^2/g,respectively,which effectively reduced the pore mass transfer resistance and significantly increased the number of acid sites.The results of n-dodecane hydroisomerization revealed that the Pt/SAPO-11 prepared with the novel method exhibited higher catalytic activity and better hydroisomerization selectivity than that synthesized by the conventional hydrothermal method.Thus,the small particle molecular sieve showed a promising industrial application prospect to be used as catalyst support.
基金Project supported by the National Basic Research Program of China(Grant No.2011CB610401)the National Natural Science Foundation of China(Grant No.51371151)the Free Research Fund of State Key Laboratory of Solidification Processing,China(Grant No.100-QP-2014)
文摘Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width α 〉3/2/π≈ 0.3899, which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs–Thomson energy acting on the interface.
基金Project supported by the Innovation Foundation of the Chinese Academy of Sciences and by the National Basic Research Program of China(Grant No.2002CB713801)
文摘One of the essential points of the direct-method single-wavelength anomalous diffraction （SAD） phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respectively at φh″＋｜△φh｜ and φh″-｜△φh｜. The probability for △φh being positive （P＋） can be derived based on the Cochran distribution in direct methods. Hence the SAD phase ambiguity can be resolved by multiplying the Gaussian function peaked at φh″＋｜△φh｜ with P＋ and multiplying the Gaussian function peaked at φh″-｜△φh｜ with P_ （=1- P＋）. The direct-method SAD h phasing has been proved powerful in breaking SAD phase ambiguities, in particular when anomalous-scattering signals are weak. However, the approximation of bimodal phase distributions by the sum of two Gaussian functions introduces considerable errors. In this paper we show that a much better approximation can be achieved by replacing the two Gaussian functions with two von Mises distributions. Test results showed that this leads to significant improvement on the efficiency of direct-method SAD-phasing.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10575087 and 10875106)
文摘So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou＇s direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.
基金supported by the National Natural Science Foundations of China (Grant Nos 10735030,10475055,10675065 and 90503006)National Basic Research Program of China (Grant No 2007CB814800)+2 种基金PCSIRT (Grant No IRT0734)the Research Fund of Postdoctoral of China (Grant No 20070410727)Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070248120)
文摘The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.
基金Project supported by the National Natural Science Foundation of China （Grant No 11171038）.
文摘In this work, we present the direct discontinuous Galerkin （DDG） method for the one-dimensional coupled nonlinear Schr5dinger （CNLS） equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.
基金Project was supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University
文摘In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.
文摘The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolation is not only reliable but also can save the amount of calculation by nearly 36%. Large amount of calculation and lacking strict theoretical bas is has been th e two disadvantage of direct method by new. If this defect is not overcome, they will not only s eriously affect the application of this method, but also hinder its further rese arch. Based on sufficient calculation practice, this article has made a primary discussion about the theory and method of reducing the amount of calculation, an d has achieved some satisfactory results.
基金supported by the Special Projects of International Thermonuclear Experimental Reactor(2015GB116000)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA03040000)+1 种基金the Informatizational Special Projects of Chinese Academy of Sciences(No.XXH12504-1-09)the Major/Innovative Program of Development Foundation of Hefei Center for Physical Science and Technology(No.2014FXCX004)
文摘Direct Monte Carlo(MC) simulation is a powerful probabilistic safety assessment method for accounting dynamics of the system.But it is not efficient at simulating rare events.A biasing transition rate method based on direct MC simulation is proposed to solve the problem in this paper.This method biases transition rates of the components by adding virtual components to them in series to increase the occurrence probability of the rare event,hence the decrease in the variance of MC estimator.Several cases are used to benchmark this method.The results show that the method is effective at modeling system failure and is more efficient at collecting evidence of rare events than the direct MC simulation.The performance is greatly improved by the biasing transition rate method.
基金National Natural Science Foundation of China(61973037)National 173 Program Project(2019-JCJQ-ZD-324)。
文摘Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.
