Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implemen...Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implementation,or configuration.To guarantee the durability&robustness of the software,vulnerability identification and fixation have become crucial areas of focus for developers,cybersecurity experts and industries.This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection.To uniquely model these processes,the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function.Furthermore,the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain.The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets,which offers a solid basis for the research conclusions.According to computational research,learning dynamics improves security response and results in more effective vulnerability management.The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment,software maintenance,and cybersecurity.This study helps create more robust software systems by increasing patch management effectiveness,which benefits developers,cybersecurity experts,and sectors looking to reduce security threats in a growing digital world.展开更多
To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based sim...To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based simulation(NNS)method with higher accuracy and better efficiency was proposed.The NNS method consisted of three main steps.First,the parameters of blast loads,including the peak pressures and impulses of cylindrical charges with different aspect ratios(L/D)at different stand-off distances and incident angles were obtained by two-dimensional numerical simulations.Subsequently,incident shape factors of cylindrical charges with arbitrary aspect ratios were predicted by a neural network.Finally,reflected shape factors were derived and implemented into the subroutine of the ABAQUS code to modify the CONWEP model,including modifications of impulse and overpressure.The reliability of the proposed NNS method was verified by related experimental results.Remarkable accuracy improvement was acquired by the proposed NNS method compared with the unmodified CONWEP model.Moreover,huge efficiency superiority was obtained by the proposed NNS method compared with the CEL method.The proposed NNS method showed good accuracy when the scaled distance was greater than 0.2 m/kg^(1/3).It should be noted that there is no need to generate a new dataset again since the blast loads satisfy the similarity law,and the proposed NNS method can be directly used to simulate the blast loads generated by different cylindrical charges.The proposed NNS method with high efficiency and accuracy can be used as an effective method to analyze the dynamic response of structures under blast loads,and it has significant application prospects in designing protective structures.展开更多
This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form c...This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications.The phase-field model,in particular,is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time.In this paper,we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths,limitations,stability,accuracy,and computational efficiency of each method.Traditional approaches such as Fourier spectral methods,finite difference methods and alternating direction explicit methods are reviewed,as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented.In addition,we introduce examples of the phase-field model,which are fingerprint image restoration and 3D printing.These examples demonstrate the extensive applicability of the reviewed methods and models.展开更多
Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,...Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes（grid-staggering,local-nesting and piecewise continuous integration） are designed to deal with the singularity of the Green＇s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential（or streamfunction） component to zero,the other component of the solution can be computed in two ways：（1） Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.（2） Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting（or piecewise continuous integration）,the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point（or along the entire boundary）.When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.展开更多
A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic c...A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic constitutive relationship of sand was established for three paths： the constant proportion of principle stress path, the conventional triaxial compression （CTC） path, and the p=constant （TC） path. The yield lines of plastic volumetric strain and plastic generalized shear strain were given. Through visualization, the three dimensional surface of the stress-strain relationship in the whole stress field （p, q） obtained under the three paths was plotted. Also, by comparing the stress-strain surfaces and yield locus of the three stress paths, the differences were found to be obvious, which demonstrates that the influence of the stress paths on constitutive law was not neglected. The numerical modeling method overcame the difficulty of finding an analytical expression for plastic potential. The results simulated the experimental data with an accuracy of 90% on average, so the constitutive model established in this paper provides an effective constitutive equation for this kind of engineering, reflecting the effect of practical stress paths that occur in sands.展开更多
In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic co...In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.展开更多
Nonlinear stochastic modeling plays a significant role in disciplines such as psychology,finance,physical sciences,engineering,econometrics,and biological sciences.Dynamical consistency,positivity,and boundedness are ...Nonlinear stochastic modeling plays a significant role in disciplines such as psychology,finance,physical sciences,engineering,econometrics,and biological sciences.Dynamical consistency,positivity,and boundedness are fundamental properties of stochastic modeling.A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation.Well-known explicit methods such as Euler Maruyama,stochastic Euler,and stochastic Runge–Kutta are investigated for the stochastic model.Regrettably,the above essential properties are not restored by existing methods.Hence,there is a need to construct essential properties preserving the computational method.The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model.The comparison of the results of deterministic and stochastic models is also presented.Our proposed efficient computational method well preserves the essential properties of the model.Comparison and convergence analyses of the method are presented.展开更多
A stuck drill string results in a major non-productive cost in extended reach drilling engineering. The first step is to determine the depth at which the sticking has occurred. Methods of measurement have been proved ...A stuck drill string results in a major non-productive cost in extended reach drilling engineering. The first step is to determine the depth at which the sticking has occurred. Methods of measurement have been proved useful for determining the stuck points, but these operations take considerable time. As a result of the limitation with the current operational practices, calculation methods are still preferred to estimate the stuck point depth. Current analytical methods do not consider friction and are only valid for vertical rather than extended reach wells. The numerical method is established to take full account of down hole friction, tool joint, upset end of drill pipe, combination drill strings and tubular materials so that it is valid to determine the stuck point in extended reach wells. The pull test, torsion test and combined test of rotation and pulling can be used to determine the stuck point. The results show that down hole friction, tool joint, upset end of drill pipe, tubular sizes and materials have significant effects on the pull length and/or the twist angle of the stuck drill string.展开更多
The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with de...The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSYS software. The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone.展开更多
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we ...Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train （expressed as wave train 2） leads to the energy focusing of the other short wave train （expressed as wave train 3）. This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.展开更多
Based directly on the original definition of K-S entropy, a new algorithm for calculating K-S entropy from chaotic time series is developed by using some techniques of coding and code operation.
In this paper, a six-order nonlinear dynamic model with three degrees of freedom is presented for the study of the 'fishtail' motion of a Single Point Mooring System. The effect of parameter variations on the ...In this paper, a six-order nonlinear dynamic model with three degrees of freedom is presented for the study of the 'fishtail' motion of a Single Point Mooring System. The effect of parameter variations on the equilibrium state of the system is analyzed. In order to study the stability of the equilibrium state, the mooring-line length l is chosen as a bifurcation parameter, so that all eigenvalues of the Jacobian matrix under different parameters can be worked out, and then the Hopf-bifurcation point can be found. Finally, the Hopf-bifurcation periodic solution of the system is computed.展开更多
In this paper,we consider the Rayleigh-Stokes problem for a heated generalized second grade fluid（RSP-HGSGF）with fractional derivative.An effective numerical method for approximating RSP-HGSGF in a bounded domain is...In this paper,we consider the Rayleigh-Stokes problem for a heated generalized second grade fluid（RSP-HGSGF）with fractional derivative.An effective numerical method for approximating RSP-HGSGF in a bounded domain is presented.The stability and convergence of the method are analyzed.Numerical examples are presented to show the application of the present technique.展开更多
A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, spl...A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration.展开更多
The crack tip strain gauge method in the compliance technique was used to determine the opening load of notched crack of axle steel,and the nonlinear finite element ADINA program, to which the cyclic stress-strain cur...The crack tip strain gauge method in the compliance technique was used to determine the opening load of notched crack of axle steel,and the nonlinear finite element ADINA program, to which the cyclic stress-strain curve of axle steel was applied,was used to analyze the stress-strain field ahead of the crack tip and the opening load of notched crack.The results of both the compliance technique and the numerical method were in good agreement.In this pa- per,the concept of the sensitive point is proposed and the key to the determination of the crack opening load in the experiment is to place a strain gauge at sensitive point.It is certified by both experimental and numerical methods that the sensitive point has the best linear relation- ship character and the value of strain is much greater.展开更多
An equation describing the state of weak acid mixtures was derived from the relationships between mole balance and charge balance. The equation was solved with numerical method and the compositions of the acid mixture...An equation describing the state of weak acid mixtures was derived from the relationships between mole balance and charge balance. The equation was solved with numerical method and the compositions of the acid mixtures were determined. The advantages of this treatment were demonstrated by analyzing binary mixtures of chloroacetic, formic and acetic acids.展开更多
A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro_differential equation includin...A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro_differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application,motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method. Then the new numerical method is used to solve a class of weakly singular Volterra integro_differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close.展开更多
This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this un...This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.展开更多
An 8-channel HCN laser interferometer will be installed on HL-2A in near term. In order to get the spatial profile of the electron density Barr numerical method is adopted to realize the Abel inversion. In this articl...An 8-channel HCN laser interferometer will be installed on HL-2A in near term. In order to get the spatial profile of the electron density Barr numerical method is adopted to realize the Abel inversion. In this article the result of the Abel inversion by Matlab GUI is given which can be updated to process the measured data of the 8-channel laser interferometer and provide the spatial distribution of the electron density.展开更多
Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be ...Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.展开更多
基金supported by grants received by the first author and third author from the Institute of Eminence,Delhi University,Delhi,India,as part of the Faculty Research Program via Ref.No./IoE/2024-25/12/FRP.
文摘Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implementation,or configuration.To guarantee the durability&robustness of the software,vulnerability identification and fixation have become crucial areas of focus for developers,cybersecurity experts and industries.This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection.To uniquely model these processes,the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function.Furthermore,the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain.The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets,which offers a solid basis for the research conclusions.According to computational research,learning dynamics improves security response and results in more effective vulnerability management.The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment,software maintenance,and cybersecurity.This study helps create more robust software systems by increasing patch management effectiveness,which benefits developers,cybersecurity experts,and sectors looking to reduce security threats in a growing digital world.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52271317 and 52071149)the Fundamental Research Funds for the Central Universities(HUST:2019kfy XJJS007)。
文摘To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based simulation(NNS)method with higher accuracy and better efficiency was proposed.The NNS method consisted of three main steps.First,the parameters of blast loads,including the peak pressures and impulses of cylindrical charges with different aspect ratios(L/D)at different stand-off distances and incident angles were obtained by two-dimensional numerical simulations.Subsequently,incident shape factors of cylindrical charges with arbitrary aspect ratios were predicted by a neural network.Finally,reflected shape factors were derived and implemented into the subroutine of the ABAQUS code to modify the CONWEP model,including modifications of impulse and overpressure.The reliability of the proposed NNS method was verified by related experimental results.Remarkable accuracy improvement was acquired by the proposed NNS method compared with the unmodified CONWEP model.Moreover,huge efficiency superiority was obtained by the proposed NNS method compared with the CEL method.The proposed NNS method showed good accuracy when the scaled distance was greater than 0.2 m/kg^(1/3).It should be noted that there is no need to generate a new dataset again since the blast loads satisfy the similarity law,and the proposed NNS method can be directly used to simulate the blast loads generated by different cylindrical charges.The proposed NNS method with high efficiency and accuracy can be used as an effective method to analyze the dynamic response of structures under blast loads,and it has significant application prospects in designing protective structures.
文摘This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications.The phase-field model,in particular,is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time.In this paper,we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths,limitations,stability,accuracy,and computational efficiency of each method.Traditional approaches such as Fourier spectral methods,finite difference methods and alternating direction explicit methods are reviewed,as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented.In addition,we introduce examples of the phase-field model,which are fingerprint image restoration and 3D printing.These examples demonstrate the extensive applicability of the reviewed methods and models.
基金supported by the Office of Naval Research (Grant No.N000141010778) to the University of Oklahomathe National Natural Sciences Foundation of China (Grant Nos. 40930950,41075043,and 4092116037) to the Institute of Atmospheric Physicsprovided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement No. (NA17RJ1227),U.S. Department of Commerce
文摘Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary（around a data hole） inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes（grid-staggering,local-nesting and piecewise continuous integration） are designed to deal with the singularity of the Green＇s function encountered in numerical calculations.For the externally induced part,by setting the velocity potential（or streamfunction） component to zero,the other component of the solution can be computed in two ways：（1） Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.（2） Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting（or piecewise continuous integration）,the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point（or along the entire boundary）.When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.
文摘A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic constitutive relationship of sand was established for three paths： the constant proportion of principle stress path, the conventional triaxial compression （CTC） path, and the p=constant （TC） path. The yield lines of plastic volumetric strain and plastic generalized shear strain were given. Through visualization, the three dimensional surface of the stress-strain relationship in the whole stress field （p, q） obtained under the three paths was plotted. Also, by comparing the stress-strain surfaces and yield locus of the three stress paths, the differences were found to be obvious, which demonstrates that the influence of the stress paths on constitutive law was not neglected. The numerical modeling method overcame the difficulty of finding an analytical expression for plastic potential. The results simulated the experimental data with an accuracy of 90% on average, so the constitutive model established in this paper provides an effective constitutive equation for this kind of engineering, reflecting the effect of practical stress paths that occur in sands.
基金Supported by National Key R&D Program of China(Grant No.2019YFB1505301)National Natural Science Foundation of China(Grant No.U1937602)+1 种基金Aeronautical Science Foundation of China(Grant No.201907058001)Open Research Fund of State Key Laboratory of Smart Manufacturing for Special Vehicles and Transmission System(Grant No.GZ2019KF013).
文摘In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.
基金the Research and initiative center COVID-19-DES-2020-65,Prince Sultan University.
文摘Nonlinear stochastic modeling plays a significant role in disciplines such as psychology,finance,physical sciences,engineering,econometrics,and biological sciences.Dynamical consistency,positivity,and boundedness are fundamental properties of stochastic modeling.A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation.Well-known explicit methods such as Euler Maruyama,stochastic Euler,and stochastic Runge–Kutta are investigated for the stochastic model.Regrettably,the above essential properties are not restored by existing methods.Hence,there is a need to construct essential properties preserving the computational method.The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model.The comparison of the results of deterministic and stochastic models is also presented.Our proposed efficient computational method well preserves the essential properties of the model.Comparison and convergence analyses of the method are presented.
基金support from the national projects(Grant No.:2011ZX05009-005and2010CB226703)
文摘A stuck drill string results in a major non-productive cost in extended reach drilling engineering. The first step is to determine the depth at which the sticking has occurred. Methods of measurement have been proved useful for determining the stuck points, but these operations take considerable time. As a result of the limitation with the current operational practices, calculation methods are still preferred to estimate the stuck point depth. Current analytical methods do not consider friction and are only valid for vertical rather than extended reach wells. The numerical method is established to take full account of down hole friction, tool joint, upset end of drill pipe, combination drill strings and tubular materials so that it is valid to determine the stuck point in extended reach wells. The pull test, torsion test and combined test of rotation and pulling can be used to determine the stuck point. The results show that down hole friction, tool joint, upset end of drill pipe, tubular sizes and materials have significant effects on the pull length and/or the twist angle of the stuck drill string.
文摘The purpose of this study was to investigate the effect of bolt profile on load transfer mechanism of fully grouted bolts in jointed rocks using analytical and numerical methods. Based on the analytical method with development of methods, a new model is presented. To validate the analytical model, five different profiles modeled by ANSYS software. The profile of rock bolts T3 and T4with load transfer capacity,respectively 180 and 195 kN in the jointed rocks was selected as the optimum profiles. Finally, the selected profiles were examined in Tabas Coal Mine. FLAC analysis indicates that patterns 6+7 with2 NO flexi bolt 4 m better than other patterns within the faulted zone.
基金Project supported by the National High Technology Research and Development Program of China (Grant No 2007AA12Z170)the Major Research Plan of the National Natural Science Foundation of China (Grant No 40706058)+1 种基金the Science-Technology Chenguang foundation for Young Scientist of Wuhan,China (Grant No 200850731388)the Canadian Space Agency Government Related Initiatives Program (GRIP) entitled Building Satellite Data into Fisheries and Oceans Operational Systems
文摘Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train （expressed as wave train 2） leads to the energy focusing of the other short wave train （expressed as wave train 3）. This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.
基金The project supported by National Natural Science Foundation of China
文摘Based directly on the original definition of K-S entropy, a new algorithm for calculating K-S entropy from chaotic time series is developed by using some techniques of coding and code operation.
文摘In this paper, a six-order nonlinear dynamic model with three degrees of freedom is presented for the study of the 'fishtail' motion of a Single Point Mooring System. The effect of parameter variations on the equilibrium state of the system is analyzed. In order to study the stability of the equilibrium state, the mooring-line length l is chosen as a bifurcation parameter, so that all eigenvalues of the Jacobian matrix under different parameters can be worked out, and then the Hopf-bifurcation point can be found. Finally, the Hopf-bifurcation periodic solution of the system is computed.
文摘In this paper,we consider the Rayleigh-Stokes problem for a heated generalized second grade fluid（RSP-HGSGF）with fractional derivative.An effective numerical method for approximating RSP-HGSGF in a bounded domain is presented.The stability and convergence of the method are analyzed.Numerical examples are presented to show the application of the present technique.
基金supported by the Chinese National Research Program of Science and Technology under Project! 85-903-03-04.
文摘A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration.
文摘The crack tip strain gauge method in the compliance technique was used to determine the opening load of notched crack of axle steel,and the nonlinear finite element ADINA program, to which the cyclic stress-strain curve of axle steel was applied,was used to analyze the stress-strain field ahead of the crack tip and the opening load of notched crack.The results of both the compliance technique and the numerical method were in good agreement.In this pa- per,the concept of the sensitive point is proposed and the key to the determination of the crack opening load in the experiment is to place a strain gauge at sensitive point.It is certified by both experimental and numerical methods that the sensitive point has the best linear relation- ship character and the value of strain is much greater.
文摘An equation describing the state of weak acid mixtures was derived from the relationships between mole balance and charge balance. The equation was solved with numerical method and the compositions of the acid mixtures were determined. The advantages of this treatment were demonstrated by analyzing binary mixtures of chloroacetic, formic and acetic acids.
文摘A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro_differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application,motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method. Then the new numerical method is used to solve a class of weakly singular Volterra integro_differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close.
基金supported by the National Natural Science Foundation of China (NSFC) (10872155)
文摘This paper first analyzes the features of two classes of numerical methods for global analysis of nonlinear dynamical systems, which regard state space respectively as continuous and discrete ones. On basis of this understanding it then points out that the previously proposed method of point mapping under cell reference (PMUCR), has laid a frame work for the development of a two scaled numerical method suitable for the global analysis of high dimensional nonlinear systems, which may take the advantages of both classes of single scaled methods but will release the difficulties induced by the disadvantages of them. The basic ideas and main steps of implementation of the two scaled method, namely extended PMUCR, are elaborated. Finally, two examples are presented to demonstrate the capabilities of the proposed method.
文摘An 8-channel HCN laser interferometer will be installed on HL-2A in near term. In order to get the spatial profile of the electron density Barr numerical method is adopted to realize the Abel inversion. In this article the result of the Abel inversion by Matlab GUI is given which can be updated to process the measured data of the 8-channel laser interferometer and provide the spatial distribution of the electron density.
文摘Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.
