In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,br...In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.展开更多
The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann cond...The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann conditions is proposed. The scheme is based on the modified Adomian decomposition method and the inverse linear operator theorem. Several differential equations with Neumann boundary conditions are solved to demonstrate the high accuracy and efficiency of the proposed scheme.展开更多
The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic material...The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic materials,the direct applications of the traditional single edge notched beam(SENB)method that ignores those typical structural characters may cause errors.To measure the surface fracture toughness more accurately,the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered.In this paper,a modified single edge V-notched beam(MSEVNB)method with typical structural characters is developed.According to the finite element analysis(FEA),the geometry factor of the multilayer structure is recalculated.Owing to the narrower V-notches,a more accurate critical fracture stress is obtained.Based on the Griffith energy balance,the reduction of the crack surface caused by micro-defects is corrected.The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.展开更多
In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the n...In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the next generation matrix method. We also used the Lyaponuv method to show the global stability of both the disease free and endemic equilibrium points. The results showed that the disease-free equilibrium point is globally asymptotically stable if R<sub>C</sub> R<sub>C</sub> > 1. We further used the Adomian decomposition method and the modified Adomian decomposition method to obtain the solutions of the model. Numerical analysis of the model was done using Sagemath 9.0 software.展开更多
In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 eq...In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.展开更多
The modified suction caisson(MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wi...The modified suction caisson(MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wind turbine foundation subjected to larger lateral loads compared with the imposed vertical loads. Determination of the lateral bearing capacity is a key issue for the MSC design. The formula estimating the lateral bearing capacity of the MSC was proposed in terms of the limit equilibrium method and was verified by the test results. Parametric studies on the lateral bearing capacity were also carried out. It was found that the lateral bearing capacity of the MSC increases with the increasing length and radius of the external skirt, and the lateral bearing capacity increases linearly with the increasing coefficient of subgrade reaction. The maximum lateral bearing capacity of the MSC is attained when the ratio of the radii of the internal compartment to the external skirt equals 0.82 and the ratio of the lengths of the external skirt to the internal compartment equals 0.48, provided that the steel usage of the MSC is kept constant.展开更多
A modified domain reduction method(MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numeric...A modified domain reduction method(MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numerical test is designed. The numerical results of the MDRM and DRM are compared using an extended meshed model. The results show that the MDRM significantly improved the computational accuracy of the DRM. Then, the MDRM is compared with two existing conventional methods, namely Liao's transmitting boundary and viscous-spring boundary with Liu's method. The MDRM shows its great advancement in computational accuracy, stability and range of applications. This paper also discusses the influence of boundary location on computational accuracy. It can be concluded that smaller models tend to have larger errors. By introducing two dimensionless parameters, φ_1 and φ_2, the rational distance between the observation point and the MDRM boundary is suggested. When φ_1 >2 or φ_2>13, the relative PGA error can be limited to 5%. In practice, the appropriate model size can be chosen based on these two parameters to achieve desired computational accuracy.展开更多
The stiffness spreading method (SSM) was initially proposed for layout optimization of truss structures,in which an artificial elastic material of low modulus is uniformly distributed in the design domain to create co...The stiffness spreading method (SSM) was initially proposed for layout optimization of truss structures,in which an artificial elastic material of low modulus is uniformly distributed in the design domain to create connections between discrete members.In this paper,a modified stiffness spreading method is proposed by replacing the artificial elastic material with auxiliary bars to connect real members of the truss structure.Since the background continuum mesh for the elastic material is no longer required,the computational cost is significantly reduced.Like SSM,the new method is advantageous in that an initial design may consist of disconnected bars allocated in the design domain,and mathematical programming methods can be applied for the efficient solution of the formulated optimization problem.A number of solution strategies are also developed to achieve more practical designs with lower computational cost.Numerical examples of both 2-D and 3-D truss structures are presented to demonstrate the feasibility,robustness and effectiveness of the proposed method.展开更多
In earthquake prone areas,understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures.In this study,the limit equilibrium method is used ...In earthquake prone areas,understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures.In this study,the limit equilibrium method is used for estimation of critical seismic passive earth resistance for an inclined wall supporting horizontal cohesionless backfill.A composite failure surface is considered in the present analysis.Seismic forces are computed assuming the backfill soil as a viscoelastic material overlying a rigid stratum and the rigid stratum is subjected to a harmonic shaking.The present method satisfies the boundary conditions.The amplification of acceleration depends on the properties of the backfill soil and on the characteristics of the input motion.The acceleration distribution along the depth of the backfill is found to be nonlinear in nature.The present study shows that the horizontal and vertical acceleration distribution in the backfill soil is not always in-phase for the critical value of the seismic passive earth pressure coefficient.The effect of different parameters on the seismic passive earth pressure is studied in detail.A comparison of the present method with other theories is also presented,which shows the merits of the present study.展开更多
In this paper,we consider a Cauchy problem of the time fractional diffusion equation(TFDE)in x∈[0,L].This problem is ubiquitous in science and engineering applications.The illposedness of the Cauchy problem is explai...In this paper,we consider a Cauchy problem of the time fractional diffusion equation(TFDE)in x∈[0,L].This problem is ubiquitous in science and engineering applications.The illposedness of the Cauchy problem is explained by its solution in frequency domain.Furthermore,the problem is formulated into a minimization problem with a modified Tikhonov regularization method.The gradient of the regularization functional based on an adjoint problem is deduced and the standard conjugate gradient method is presented for solving the minimization problem.The error estimates for the regularized solutions are obtained under Hp norm priori bound assumptions.Finally,numerical examples illustrate the effectiveness of the proposed method.展开更多
A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term ...A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.展开更多
A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the clas...A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the classical multi-scale method(MSM)and the method of variation of parameters.Assuming that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional MSM.Then,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation.To certify the correctness and precision of the proposed analytical method,the van der Pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)responses.The approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.展开更多
In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its app...In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.展开更多
Background: The deep understanding of pathogenesis is a key moment in the formation of the modern strategy of modern medicine. We conducted the thorough analysis of the microscopic processes occurring in the bodies of...Background: The deep understanding of pathogenesis is a key moment in the formation of the modern strategy of modern medicine. We conducted the thorough analysis of the microscopic processes occurring in the bodies of patients with purulent-septic complications. The modified pathogenetic concept of the diagnostic and treatment model of diseases with septic complications is presented. The obtained information about the mechanisms of origin and development of these diseases is fundamentally important for finding the modern effective methods of treating patients. The aim of the research is to modify treatment tactics for patients with sepsis and burn injuries based on the modified pathogenetic concept using modern diagnostics, i.e. the method of fluorescence spectroscopy (MFS) and biomarkers. Materials and Methods: The proposed modified pathogenetic concept of the diagnostic and treatment model of diseases with purulent-septic complications along with standard methods was used successfully for effective treatment of 15 patients with sepsis and 25 with burn injuries. Results: 3 main scenarios of behaviour of spectral-fluorescence characteristics of patients with sepsis are illustrated. Spectral-fluorescence markers of sepsis were studied, which are informative 24 to 48 hours before the appearance of obvious clinical and laboratory signs of significant changes in the general somatic status of patients. Conclusions: The proposed diagnostic and therapeutic approach is new and fundamentally important for diagnostics and monitoring of the process of treatment of patients with purulent-septic diseases and burn injuries. An in-depth understanding of the dynamics of septic complications and the corresponding changes of the main markers of these diseases during treatment is especially relevant. The use of infusion therapy with solutions of donor albumin as an effective pathogenetic treatment is scientifically justified.展开更多
In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales...In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.展开更多
The modified configuration interaction method is extended to double electronic systems in magnetic fields.Eigen-values and binding energies of ground state of H^(-) ion and He atom in uniform magnetic fields are calcu...The modified configuration interaction method is extended to double electronic systems in magnetic fields.Eigen-values and binding energies of ground state of H^(-) ion and He atom in uniform magnetic fields are calculated.In a range running from low to intermediate magnetic fields,the best results with relative errors of 1.0×10^(-5) and 1.4×10^(-6) for H^(-) and He,respectively,are obtained.The accuracy of our results are almost 2 orders of magnitude better than those obtained by the other methods.展开更多
Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus,the studies on machining deformation rules induced by residual stresses largely de...Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus,the studies on machining deformation rules induced by residual stresses largely depend on correctly and efficiently measuring the residual stresses of workpieces. A modified layer-removal method is proposed to measure residual stress by analysing the characteristics of a traditional layer-removal method. The coefficients of strain release are then deduced according to the simulation results using the finite element method( FEM). Moreover,the residual stress in a 7075T651 aluminium alloy plate is measured using the proposed method,and the results are then analyzed and compared with the data obtained by the traditional methods. The analysis indicates that the modified layer-removal method is effective and practical for measuring the residual stress distribution in pre-stretched aluminium alloy plates.展开更多
In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex trans...In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation method has been implemented, to find the exact solutions of these equations, in the sense of modified Riemann-Liouville derivative. For applications, the exact solutions of time-space fractional derivative Burgers’ equation and time-space fractional derivative foam drainage equation have been discussed. Moreover, it can also be concluded that the proposed method is easy, direct and concise as compared to other existing methods.展开更多
This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems...This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems, known as unit commitment (UC) scheduling. The UC scheduling problem is a mixed-integer nonlinear problem, highly-dimensional and extremely constrained. Existing meta-heuristic UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to large-scale, heavily-constrained UC applications. In the first step of the proposed method, initial hourly optimum solutions of UC are obtained by Modified Priority List (MPL);however, the obtained UC solution may still be possible to be further improved. Therefore, in the second step, the CSS is utilized to achieve higher quality solutions. The UC is formulated as mixed integer linear programming to ensure the tractability of the results. The proposed method is successfully applied to a popular test system up to 100 units generators for both 24-hr and 168-hr system. Computational results show that both solution cost and execution time are superior to those of published methods.展开更多
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
文摘In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.
文摘The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann conditions is proposed. The scheme is based on the modified Adomian decomposition method and the inverse linear operator theorem. Several differential equations with Neumann boundary conditions are solved to demonstrate the high accuracy and efficiency of the proposed scheme.
基金Project supported by the National Natural Science Foundation of China(Nos.12172048 and 12027901)the National Science and Technology Major Project of China(Nos.2019-Ⅶ-0007-0147 and 2017-Ⅵ-0020-0093)。
文摘The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic materials,the direct applications of the traditional single edge notched beam(SENB)method that ignores those typical structural characters may cause errors.To measure the surface fracture toughness more accurately,the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered.In this paper,a modified single edge V-notched beam(MSEVNB)method with typical structural characters is developed.According to the finite element analysis(FEA),the geometry factor of the multilayer structure is recalculated.Owing to the narrower V-notches,a more accurate critical fracture stress is obtained.Based on the Griffith energy balance,the reduction of the crack surface caused by micro-defects is corrected.The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.
文摘In this study, we constructed and analysed a mathematical model of COVID-19 in order to comprehend the transmission dynamics of the disease. The reproduction number (R<sub>C</sub>) was calculated via the next generation matrix method. We also used the Lyaponuv method to show the global stability of both the disease free and endemic equilibrium points. The results showed that the disease-free equilibrium point is globally asymptotically stable if R<sub>C</sub> R<sub>C</sub> > 1. We further used the Adomian decomposition method and the modified Adomian decomposition method to obtain the solutions of the model. Numerical analysis of the model was done using Sagemath 9.0 software.
文摘In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51639002 and 51379118)Shandong University of Science and Technology Scientific Found(Grant No.2015TDJH104)
文摘The modified suction caisson(MSC) adds a short-skirted structure around the regular suction caissons to increase the lateral bearing capacity and limit the deflection. The MSC is suitable for acting as the offshore wind turbine foundation subjected to larger lateral loads compared with the imposed vertical loads. Determination of the lateral bearing capacity is a key issue for the MSC design. The formula estimating the lateral bearing capacity of the MSC was proposed in terms of the limit equilibrium method and was verified by the test results. Parametric studies on the lateral bearing capacity were also carried out. It was found that the lateral bearing capacity of the MSC increases with the increasing length and radius of the external skirt, and the lateral bearing capacity increases linearly with the increasing coefficient of subgrade reaction. The maximum lateral bearing capacity of the MSC is attained when the ratio of the radii of the internal compartment to the external skirt equals 0.82 and the ratio of the lengths of the external skirt to the internal compartment equals 0.48, provided that the steel usage of the MSC is kept constant.
基金National Natural Science Foundation of China under Grant Nos.91315301,51478279the State Key Laboratory Basic Theory Foundation of the Ministry of Science and Technology of China under the Grant SLDRCE08-A-07
文摘A modified domain reduction method(MDRM) that introduces damping terms to the original DRM is presented in this paper. To verify the proposed MDRM and compare the computational accuracy of these two methods, a numerical test is designed. The numerical results of the MDRM and DRM are compared using an extended meshed model. The results show that the MDRM significantly improved the computational accuracy of the DRM. Then, the MDRM is compared with two existing conventional methods, namely Liao's transmitting boundary and viscous-spring boundary with Liu's method. The MDRM shows its great advancement in computational accuracy, stability and range of applications. This paper also discusses the influence of boundary location on computational accuracy. It can be concluded that smaller models tend to have larger errors. By introducing two dimensionless parameters, φ_1 and φ_2, the rational distance between the observation point and the MDRM boundary is suggested. When φ_1 >2 or φ_2>13, the relative PGA error can be limited to 5%. In practice, the appropriate model size can be chosen based on these two parameters to achieve desired computational accuracy.
基金The authors gratefully acknowledge the financial support provided by the National Science and Technology Major Project of the Ministry of Science and Technology of China(Grant 2016YFB0200605)the National Natural Science Foundation of China(Grant 11372004).
文摘The stiffness spreading method (SSM) was initially proposed for layout optimization of truss structures,in which an artificial elastic material of low modulus is uniformly distributed in the design domain to create connections between discrete members.In this paper,a modified stiffness spreading method is proposed by replacing the artificial elastic material with auxiliary bars to connect real members of the truss structure.Since the background continuum mesh for the elastic material is no longer required,the computational cost is significantly reduced.Like SSM,the new method is advantageous in that an initial design may consist of disconnected bars allocated in the design domain,and mathematical programming methods can be applied for the efficient solution of the formulated optimization problem.A number of solution strategies are also developed to achieve more practical designs with lower computational cost.Numerical examples of both 2-D and 3-D truss structures are presented to demonstrate the feasibility,robustness and effectiveness of the proposed method.
文摘In earthquake prone areas,understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures.In this study,the limit equilibrium method is used for estimation of critical seismic passive earth resistance for an inclined wall supporting horizontal cohesionless backfill.A composite failure surface is considered in the present analysis.Seismic forces are computed assuming the backfill soil as a viscoelastic material overlying a rigid stratum and the rigid stratum is subjected to a harmonic shaking.The present method satisfies the boundary conditions.The amplification of acceleration depends on the properties of the backfill soil and on the characteristics of the input motion.The acceleration distribution along the depth of the backfill is found to be nonlinear in nature.The present study shows that the horizontal and vertical acceleration distribution in the backfill soil is not always in-phase for the critical value of the seismic passive earth pressure coefficient.The effect of different parameters on the seismic passive earth pressure is studied in detail.A comparison of the present method with other theories is also presented,which shows the merits of the present study.
基金Supported by the National Natural Science Foundation of China(Grant No.11471253 and No.11571311)
文摘In this paper,we consider a Cauchy problem of the time fractional diffusion equation(TFDE)in x∈[0,L].This problem is ubiquitous in science and engineering applications.The illposedness of the Cauchy problem is explained by its solution in frequency domain.Furthermore,the problem is formulated into a minimization problem with a modified Tikhonov regularization method.The gradient of the regularization functional based on an adjoint problem is deduced and the standard conjugate gradient method is presented for solving the minimization problem.The error estimates for the regularized solutions are obtained under Hp norm priori bound assumptions.Finally,numerical examples illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(Grants11632008 and 11872189)
文摘A modified slow-fast analysis method is presented for the periodically excited non-autonomous dynamical system with an order gap between the exciting frequency and the natural frequency.By regarding the exciting term as a slow-varying parameter,a generalized autonomous fast subsystem can be defined,the equilibrium branches as well as the bifurcations of which can be employed to account for the mechanism of the bursting oscillations by combining the transformed phase portrait introduced.As an example,a typical periodically excited Hartley model is used to demonstrate the validness of the method,in which the exciting frequency is far less than the natural frequency.The equilibrium branches and their bifurcations of the fast subsystem with the variation of the slow-varying parameter are presented.Bursting oscillations for two typical cases are considered,which reveals that,fold bifurcation may cause the the trajectory to jump between different equilibrium branches,while Hopf bifurcation may cause the trajectory to oscillate around the stable limit cycle.
基金the National Natural Science Foundation of China(Nos.11672191,11772206,and U1934201)the Hundred Excellent Innovative Talents Support Program in Hebei University(No.SLRC2017053)。
文摘A simple,yet accurate modi?ed multi-scale method(MMSM)for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed.This method depends on the classical multi-scale method(MSM)and the method of variation of parameters.Assuming that the forced excitation is a constant,one could easily obtain the approximate analytical solution of the simpli?ed system based on the traditional MSM.Then,this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation.To certify the correctness and precision of the proposed analytical method,the van der Pol system with two scales subject to slowly periodic excitation is investigated;this system presents rich dynamical phenomena such as spiking(SP),spiking-quiescence(SP-QS),and quiescence(QS)responses.The approximate analytical expressions of the three types of responses are given by the MMSM,and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method(HBM).The results obtained by the present method are considerably better than those obtained by traditional methods,quantitatively and qualitatively,particularly when the excitation frequency is far less than the natural frequency of the system.
文摘In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.
文摘Background: The deep understanding of pathogenesis is a key moment in the formation of the modern strategy of modern medicine. We conducted the thorough analysis of the microscopic processes occurring in the bodies of patients with purulent-septic complications. The modified pathogenetic concept of the diagnostic and treatment model of diseases with septic complications is presented. The obtained information about the mechanisms of origin and development of these diseases is fundamentally important for finding the modern effective methods of treating patients. The aim of the research is to modify treatment tactics for patients with sepsis and burn injuries based on the modified pathogenetic concept using modern diagnostics, i.e. the method of fluorescence spectroscopy (MFS) and biomarkers. Materials and Methods: The proposed modified pathogenetic concept of the diagnostic and treatment model of diseases with purulent-septic complications along with standard methods was used successfully for effective treatment of 15 patients with sepsis and 25 with burn injuries. Results: 3 main scenarios of behaviour of spectral-fluorescence characteristics of patients with sepsis are illustrated. Spectral-fluorescence markers of sepsis were studied, which are informative 24 to 48 hours before the appearance of obvious clinical and laboratory signs of significant changes in the general somatic status of patients. Conclusions: The proposed diagnostic and therapeutic approach is new and fundamentally important for diagnostics and monitoring of the process of treatment of patients with purulent-septic diseases and burn injuries. An in-depth understanding of the dynamics of septic complications and the corresponding changes of the main markers of these diseases during treatment is especially relevant. The use of infusion therapy with solutions of donor albumin as an effective pathogenetic treatment is scientifically justified.
文摘In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.
基金Supported by the National Natural Science Foundation of China under Grant No.19674064.
文摘The modified configuration interaction method is extended to double electronic systems in magnetic fields.Eigen-values and binding energies of ground state of H^(-) ion and He atom in uniform magnetic fields are calculated.In a range running from low to intermediate magnetic fields,the best results with relative errors of 1.0×10^(-5) and 1.4×10^(-6) for H^(-) and He,respectively,are obtained.The accuracy of our results are almost 2 orders of magnitude better than those obtained by the other methods.
基金Sponsored by the National Science and Technology Major Project(Grant No.2014ZX04001011)
文摘Residual stress is one of the factors affecting the machining deformation of monolithic structure parts in the aviation industry. Thus,the studies on machining deformation rules induced by residual stresses largely depend on correctly and efficiently measuring the residual stresses of workpieces. A modified layer-removal method is proposed to measure residual stress by analysing the characteristics of a traditional layer-removal method. The coefficients of strain release are then deduced according to the simulation results using the finite element method( FEM). Moreover,the residual stress in a 7075T651 aluminium alloy plate is measured using the proposed method,and the results are then analyzed and compared with the data obtained by the traditional methods. The analysis indicates that the modified layer-removal method is effective and practical for measuring the residual stress distribution in pre-stretched aluminium alloy plates.
文摘In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation method has been implemented, to find the exact solutions of these equations, in the sense of modified Riemann-Liouville derivative. For applications, the exact solutions of time-space fractional derivative Burgers’ equation and time-space fractional derivative foam drainage equation have been discussed. Moreover, it can also be concluded that the proposed method is easy, direct and concise as compared to other existing methods.
文摘This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems, known as unit commitment (UC) scheduling. The UC scheduling problem is a mixed-integer nonlinear problem, highly-dimensional and extremely constrained. Existing meta-heuristic UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to large-scale, heavily-constrained UC applications. In the first step of the proposed method, initial hourly optimum solutions of UC are obtained by Modified Priority List (MPL);however, the obtained UC solution may still be possible to be further improved. Therefore, in the second step, the CSS is utilized to achieve higher quality solutions. The UC is formulated as mixed integer linear programming to ensure the tractability of the results. The proposed method is successfully applied to a popular test system up to 100 units generators for both 24-hr and 168-hr system. Computational results show that both solution cost and execution time are superior to those of published methods.