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
This article reviews the application and progress of deep learning in efficient numerical computing methods.Deep learning,as an important branch of machine learning,provides new ideas for numerical computation by cons...This article reviews the application and progress of deep learning in efficient numerical computing methods.Deep learning,as an important branch of machine learning,provides new ideas for numerical computation by constructing multi-layer neural networks to simulate the learning process of the human brain.The article explores the application of deep learning in solving partial differential equations,optimizing problems,and data-driven modeling,and analyzes its advantages in computational efficiency,accuracy,and adaptability.At the same time,this article also points out the challenges faced by deep learning numerical computation methods in terms of computational efficiency,interpretability,and generalization ability,and proposes strategies and future development directions for integrating with traditional numerical methods.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
The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of t...The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
Tunnel construction is susceptible to accidents such as loosening, deformation, collapse, and water inrush, especiallyunder complex geological conditions like dense fault areas. These accidents can cause instability a...Tunnel construction is susceptible to accidents such as loosening, deformation, collapse, and water inrush, especiallyunder complex geological conditions like dense fault areas. These accidents can cause instability and damageto the tunnel. As a result, it is essential to conduct research on tunnel construction and grouting reinforcementtechnology in fault fracture zones to address these issues and ensure the safety of tunnel excavation projects. Thisstudy utilized the Xianglushan cross-fault tunnel to conduct a comprehensive analysis on the construction, support,and reinforcement of a tunnel crossing a fault fracture zone using the three-dimensional finite element numericalmethod. The study yielded the following research conclusions: The excavation conditions of the cross-fault tunnelarray were analyzed to determine the optimal construction method for excavation while controlling deformationand stress in the surrounding rock. The middle partition method (CD method) was found to be the most suitable.Additionally, the effects of advanced reinforcement grouting on the cross-fault fracture zone tunnel were studied,and the optimal combination of grouting reinforcement range (140°) and grouting thickness (1m) was determined.The stress and deformation data obtained fromon-site monitoring of the surrounding rock was slightly lower thanthe numerical simulation results. However, the change trend of both sets of data was found to be consistent. Theseresearch findings provide technical analysis and data support for the construction and design of cross-fault tunnels.展开更多
To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of...Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.展开更多
In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al...In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.展开更多
The best way to check the validity of our theories(models)is by direct comparison with the experiment(observations).However,this process suffers from numerical inaccuracies,which are not frequently studied and often r...The best way to check the validity of our theories(models)is by direct comparison with the experiment(observations).However,this process suffers from numerical inaccuracies,which are not frequently studied and often remain mostly unknown.In this study,we focus on addressing the numerical inaccuracies intrinsic to the process of comparing theory and observations.To achieve this goal,we built four-dimensional(4D)spectral grids for Wolf–Rayet stars(WC and WN spectral classes)and blue supergiants characterized by low metallicity similar to that of the Small Magellanic Cloud.In contrast to lighter(three-dimensional)grids,which rely on a priori assumptions about certain stellar parameters(e.g.,wind velocity)and thus have limited applicability,our 4D grids vary four independent parameters,enabling more flexible and broadly applicable spectral fitting.Utilizing these 4D grids,we developed and validated a fitting approach facilitating direct fits to observed spectra.Through rigorous testing on designated“test”models,we demonstrated that the numerical precision of derived essential stellar parameters,including effective temperature,mass-loss rate,luminosity,and wind velocity,is better than 0.05 dex.Furthermore,we explored the influence of unaccounted factors,including variations in the metal abundances,wind acceleration laws,and clumping,on the precision of the derived parameters.The results indicate that the first two factors have the strongest influence on the numerical accuracy of the derived stellar parameters.Variations in abundances predominantly influenced the mass-loss rate for weak-wind scenarios,while effective temperature and luminosity remained robust.We found that the wind acceleration law influences the numerical uncertainty of the derived wind parameters mostly for models with weak winds.Interestingly,different degrees of clumping demonstrated good precision for spectra with strong winds,contrasting with a decrease in the precision for weak-wind cases.We found also that the accuracy of our approach depends on spectral range and the inclusion of ultraviolet spectral range improves the precision of derived parameters,especially for an object with weak winds.展开更多
Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challeng...Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.展开更多
Atmospheric models are physical equations based on the ideal gas law. Applied to the atmosphere, this law yields equations for water, vapor (gas), ice, air, humidity, dryness, fire, and heat, thus defining the model o...Atmospheric models are physical equations based on the ideal gas law. Applied to the atmosphere, this law yields equations for water, vapor (gas), ice, air, humidity, dryness, fire, and heat, thus defining the model of key atmospheric parameters. The distribution of these parameters across the entire planet Earth is the origin of the formation of the climatic cycle, which is a normal climatic variation. To do this, the Earth is divided into eight (8) parts according to the number of key parameters to be defined in a physical representation of the model. Following this distribution, numerical models calculate the constants for the formation of water, vapor, ice, dryness, thermal energy (fire), heat, air, and humidity. These models vary in complexity depending on the indirect trigonometric direction and simplicity in the sum of neighboring models. Note that the constants obtained from the equations yield 275.156˚K (2.006˚C) for water, 273.1596˚K (0.00963˚C) for vapor, 273.1633˚K (0.0133˚C) for ice, 0.00365 in/s for atmospheric dryness, 1.996 in<sup>2</sup>/s for humidity, 2.993 in<sup>2</sup>/s for air, 1 J for thermal energy of fire, and 0.9963 J for heat. In summary, this study aims to define the main parameters and natural phenomena contributing to the modification of planetary climate. .展开更多
The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytica...The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.展开更多
This study investigates the flexural performance of ultra-high performance concrete(UHPC)in reinforced concrete T-beams,focusing on the effects of interfacial treatments.Three concrete T-beam specimens were fabricated...This study investigates the flexural performance of ultra-high performance concrete(UHPC)in reinforced concrete T-beams,focusing on the effects of interfacial treatments.Three concrete T-beam specimens were fabricated and tested:a control beam(RC-T),a UHPC-reinforced beam with a chiseled interface(UN-C-50F),and a UHPC-reinforced beam featuring both a chiseled interface and anchored steel rebars(UN-CS-50F).The test results indicated that both chiseling and the incorporation of anchored rebars effectively created a synergistic combination between the concrete T-beam and the UHPC reinforcement layer,with the UN-CS-50F exhibiting the highest flexural resistance.The cracking load and ultimate load of UN-CS-50F were 221.5%and 40.8%,respectively,higher than those of the RC-T.Finite element(FE)models were developed to provide further insights into the behavior of the UHPCreinforced T-beams,showing a maximumdeviation of just 8%when validated against experimental data.A parametric analysis varied the height,thickness,andmaterial strength of the UHPC reinforcement layer based on the validated FE model,revealing that increasing the UHPC layer thickness from 30 to 50 mm improved the ultimate resistance by 20%while reducing the UHPC reinforcement height from 440 to 300 mm led to a 10%decrease in bending resistance.The interfacial anchoring rebars significantly reduced crack propagation and enhanced stress redistribution,highlighting the importance of strengthening interfacial bonds and optimizing geometric parameters ofUHPCfor improved T-beam performance.These findings offer valuable insights for the design and retrofitting of UHPC-reinforced bridge girders.展开更多
Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vi...Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vironment and intensify carbon emissions.However,the use of microbially induced calcium carbonate pre-cipitation(MICP)to obtain bio-cement is a novel technique with the potential to induce soil stability,providing a low-carbon,environment-friendly,and sustainable integrated solution for some geotechnical engineering pro-blems in the environment.This paper presents a comprehensive review of the latest progress in soil improvement based on the MICP strategy.It systematically summarizes and overviews the mineralization mechanism,influ-encing factors,improved methods,engineering characteristics,and current field application status of the MICP.Additionally,it also explores the limitations and correspondingly proposes prospective applications via the MICP approach for soil improvement.This review indicates that the utilization of different environmental calcium-based wastes in MICP and combination of materials and MICP are conducive to meeting engineering and market demand.Furthermore,we recommend and encourage global collaborative study and practice with a view to commercializing MICP technique in the future.The current review purports to provide insights for engineers and interdisciplinary researchers,and guidance for future engineering applications.展开更多
We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of plana...We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.展开更多
In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume fram...In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving.展开更多
The graded density impactor(GDI)dynamic loading technique is crucial for acquiring the dynamic physical property parameters of materials used in weapons.The accuracy and timeliness of GDI structural design are key to ...The graded density impactor(GDI)dynamic loading technique is crucial for acquiring the dynamic physical property parameters of materials used in weapons.The accuracy and timeliness of GDI structural design are key to achieving controllable stress-strain rate loading.In this study,we have,for the first time,combined one-dimensional fluid computational software with machine learning methods.We first elucidated the mechanisms by which GDI structures control stress and strain rates.Subsequently,we constructed a machine learning model to create a structure-property response surface.The results show that altering the loading velocity and interlayer thickness has a pronounced regulatory effect on stress and strain rates.In contrast,the impedance distribution index and target thickness have less significant effects on stress regulation,although there is a matching relationship between target thickness and interlayer thickness.Compared with traditional design methods,the machine learning approach offers a10^(4)—10^(5)times increase in efficiency and the potential to achieve a global optimum,holding promise for guiding the design of GDI.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
Rock is geometrically and mechanically multiscale in nature,and the traditional phenomenological laws at the macroscale cannot render a quantitative relationship between microscopic damage of rocks and overall rock st...Rock is geometrically and mechanically multiscale in nature,and the traditional phenomenological laws at the macroscale cannot render a quantitative relationship between microscopic damage of rocks and overall rock structural degradation.This may lead to problems in the evaluation of rock structure stability and safe life.Multiscale numerical modeling is regarded as an effective way to gain insight into factors affecting rock properties from a cross-scale view.This study compiles the history of theoretical developments and numerical techniques related to rock multiscale issues according to different modeling architectures,that is,the homogenization theory,the hierarchical approach,and the concurrent approach.For these approaches,their benefits,drawbacks,and application scope are underlined.Despite the considerable attempts that have been made,some key issues still result in multiple challenges.Therefore,this study points out the perspectives of rock multiscale issues so as to provide a research direction for the future.The review results show that,in addition to numerical techniques,for example,high-performance computing,more attention should be paid to the development of an advanced constitutive model with consideration of fine geometrical descriptions of rock to facilitate solutions to multiscale problems in rock mechanics and rock engineering.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.
文摘This article reviews the application and progress of deep learning in efficient numerical computing methods.Deep learning,as an important branch of machine learning,provides new ideas for numerical computation by constructing multi-layer neural networks to simulate the learning process of the human brain.The article explores the application of deep learning in solving partial differential equations,optimizing problems,and data-driven modeling,and analyzes its advantages in computational efficiency,accuracy,and adaptability.At the same time,this article also points out the challenges faced by deep learning numerical computation methods in terms of computational efficiency,interpretability,and generalization ability,and proposes strategies and future development directions for integrating with traditional numerical methods.
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.
文摘The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
基金the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.KYCX22_0621)the National Natural Science Foundation of China(Grant No.52209130)Jiangsu Funding Program for Excellent Postdoctoral Talent.
文摘Tunnel construction is susceptible to accidents such as loosening, deformation, collapse, and water inrush, especiallyunder complex geological conditions like dense fault areas. These accidents can cause instability and damageto the tunnel. As a result, it is essential to conduct research on tunnel construction and grouting reinforcementtechnology in fault fracture zones to address these issues and ensure the safety of tunnel excavation projects. Thisstudy utilized the Xianglushan cross-fault tunnel to conduct a comprehensive analysis on the construction, support,and reinforcement of a tunnel crossing a fault fracture zone using the three-dimensional finite element numericalmethod. The study yielded the following research conclusions: The excavation conditions of the cross-fault tunnelarray were analyzed to determine the optimal construction method for excavation while controlling deformationand stress in the surrounding rock. The middle partition method (CD method) was found to be the most suitable.Additionally, the effects of advanced reinforcement grouting on the cross-fault fracture zone tunnel were studied,and the optimal combination of grouting reinforcement range (140°) and grouting thickness (1m) was determined.The stress and deformation data obtained fromon-site monitoring of the surrounding rock was slightly lower thanthe numerical simulation results. However, the change trend of both sets of data was found to be consistent. Theseresearch findings provide technical analysis and data support for the construction and design of cross-fault tunnels.
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
基金Supported by the National Natural Science Foundation of China(12001395)the special fund for Science and Technology Innovation Teams of Shanxi Province(202204051002018)+1 种基金Research Project Supported by Shanxi Scholarship Council of China(2022-169)Graduate Education Innovation Project of Taiyuan Normal University(SYYJSYC-2314)。
文摘Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.
基金supported by the National Science Foundation grant DMS-1818998.
文摘In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.
文摘The best way to check the validity of our theories(models)is by direct comparison with the experiment(observations).However,this process suffers from numerical inaccuracies,which are not frequently studied and often remain mostly unknown.In this study,we focus on addressing the numerical inaccuracies intrinsic to the process of comparing theory and observations.To achieve this goal,we built four-dimensional(4D)spectral grids for Wolf–Rayet stars(WC and WN spectral classes)and blue supergiants characterized by low metallicity similar to that of the Small Magellanic Cloud.In contrast to lighter(three-dimensional)grids,which rely on a priori assumptions about certain stellar parameters(e.g.,wind velocity)and thus have limited applicability,our 4D grids vary four independent parameters,enabling more flexible and broadly applicable spectral fitting.Utilizing these 4D grids,we developed and validated a fitting approach facilitating direct fits to observed spectra.Through rigorous testing on designated“test”models,we demonstrated that the numerical precision of derived essential stellar parameters,including effective temperature,mass-loss rate,luminosity,and wind velocity,is better than 0.05 dex.Furthermore,we explored the influence of unaccounted factors,including variations in the metal abundances,wind acceleration laws,and clumping,on the precision of the derived parameters.The results indicate that the first two factors have the strongest influence on the numerical accuracy of the derived stellar parameters.Variations in abundances predominantly influenced the mass-loss rate for weak-wind scenarios,while effective temperature and luminosity remained robust.We found that the wind acceleration law influences the numerical uncertainty of the derived wind parameters mostly for models with weak winds.Interestingly,different degrees of clumping demonstrated good precision for spectra with strong winds,contrasting with a decrease in the precision for weak-wind cases.We found also that the accuracy of our approach depends on spectral range and the inclusion of ultraviolet spectral range improves the precision of derived parameters,especially for an object with weak winds.
基金Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Project under Grant Number RGP2/302/45supported by the Deanship of Scientific Research,Vice Presidency forGraduate Studies and Scientific Research,King Faisal University,Saudi Arabia(Grant Number A426).
文摘Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.
文摘Atmospheric models are physical equations based on the ideal gas law. Applied to the atmosphere, this law yields equations for water, vapor (gas), ice, air, humidity, dryness, fire, and heat, thus defining the model of key atmospheric parameters. The distribution of these parameters across the entire planet Earth is the origin of the formation of the climatic cycle, which is a normal climatic variation. To do this, the Earth is divided into eight (8) parts according to the number of key parameters to be defined in a physical representation of the model. Following this distribution, numerical models calculate the constants for the formation of water, vapor, ice, dryness, thermal energy (fire), heat, air, and humidity. These models vary in complexity depending on the indirect trigonometric direction and simplicity in the sum of neighboring models. Note that the constants obtained from the equations yield 275.156˚K (2.006˚C) for water, 273.1596˚K (0.00963˚C) for vapor, 273.1633˚K (0.0133˚C) for ice, 0.00365 in/s for atmospheric dryness, 1.996 in<sup>2</sup>/s for humidity, 2.993 in<sup>2</sup>/s for air, 1 J for thermal energy of fire, and 0.9963 J for heat. In summary, this study aims to define the main parameters and natural phenomena contributing to the modification of planetary climate. .
基金supported by the National Natural Science Foundation of China(12172023).
文摘The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.
基金The National Natural Science Foundation of China(Grant#52278161)the Science and Technology Project of Guangzhou(Grant#2024A04J9888)the Guangdong Basic and Applied Basic Research Foundation(Grant#2023A1515010535).
文摘This study investigates the flexural performance of ultra-high performance concrete(UHPC)in reinforced concrete T-beams,focusing on the effects of interfacial treatments.Three concrete T-beam specimens were fabricated and tested:a control beam(RC-T),a UHPC-reinforced beam with a chiseled interface(UN-C-50F),and a UHPC-reinforced beam featuring both a chiseled interface and anchored steel rebars(UN-CS-50F).The test results indicated that both chiseling and the incorporation of anchored rebars effectively created a synergistic combination between the concrete T-beam and the UHPC reinforcement layer,with the UN-CS-50F exhibiting the highest flexural resistance.The cracking load and ultimate load of UN-CS-50F were 221.5%and 40.8%,respectively,higher than those of the RC-T.Finite element(FE)models were developed to provide further insights into the behavior of the UHPCreinforced T-beams,showing a maximumdeviation of just 8%when validated against experimental data.A parametric analysis varied the height,thickness,andmaterial strength of the UHPC reinforcement layer based on the validated FE model,revealing that increasing the UHPC layer thickness from 30 to 50 mm improved the ultimate resistance by 20%while reducing the UHPC reinforcement height from 440 to 300 mm led to a 10%decrease in bending resistance.The interfacial anchoring rebars significantly reduced crack propagation and enhanced stress redistribution,highlighting the importance of strengthening interfacial bonds and optimizing geometric parameters ofUHPCfor improved T-beam performance.These findings offer valuable insights for the design and retrofitting of UHPC-reinforced bridge girders.
基金funded by the National Natural Science Foundation of China(No.41962016)the Natural Science Foundation of NingXia(Nos.2023AAC02023,2023A1218,and 2021AAC02006).
文摘Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vironment and intensify carbon emissions.However,the use of microbially induced calcium carbonate pre-cipitation(MICP)to obtain bio-cement is a novel technique with the potential to induce soil stability,providing a low-carbon,environment-friendly,and sustainable integrated solution for some geotechnical engineering pro-blems in the environment.This paper presents a comprehensive review of the latest progress in soil improvement based on the MICP strategy.It systematically summarizes and overviews the mineralization mechanism,influ-encing factors,improved methods,engineering characteristics,and current field application status of the MICP.Additionally,it also explores the limitations and correspondingly proposes prospective applications via the MICP approach for soil improvement.This review indicates that the utilization of different environmental calcium-based wastes in MICP and combination of materials and MICP are conducive to meeting engineering and market demand.Furthermore,we recommend and encourage global collaborative study and practice with a view to commercializing MICP technique in the future.The current review purports to provide insights for engineers and interdisciplinary researchers,and guidance for future engineering applications.
基金Project supported by the National Natural Science Foundation of China(Nos.12471367 and12361076)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Nos.NJZY19186,NJZY22036,and NJZY23003)。
文摘We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.
基金supported in part by the NSF grant DMS-2208438.The work of M.Herty was supported in part by the DFG(German Research Foundation)through 20021702/GRK2326,333849990/IRTG-2379,HE5386/18-1,19-2,22-1,23-1under Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612+1 种基金The work of A.Kurganov was supported in part by the NSFC grant 12171226the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design,China(No.2019B030301001).
文摘In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving.
基金supported by the Guangdong Major Project of Basic and Applied Basic Research(Grant No.2021B0301030001)the National Key Research and Development Program of China(Grant No.2021YFB3802300)the Foundation of National Key Laboratory of Shock Wave and Detonation Physics(Grant No.JCKYS2022212004)。
文摘The graded density impactor(GDI)dynamic loading technique is crucial for acquiring the dynamic physical property parameters of materials used in weapons.The accuracy and timeliness of GDI structural design are key to achieving controllable stress-strain rate loading.In this study,we have,for the first time,combined one-dimensional fluid computational software with machine learning methods.We first elucidated the mechanisms by which GDI structures control stress and strain rates.Subsequently,we constructed a machine learning model to create a structure-property response surface.The results show that altering the loading velocity and interlayer thickness has a pronounced regulatory effect on stress and strain rates.In contrast,the impedance distribution index and target thickness have less significant effects on stress regulation,although there is a matching relationship between target thickness and interlayer thickness.Compared with traditional design methods,the machine learning approach offers a10^(4)—10^(5)times increase in efficiency and the potential to achieve a global optimum,holding promise for guiding the design of GDI.
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.
基金National Natural Science Foundation of China,Grant/Award Numbers:52192691,52192690。
文摘Rock is geometrically and mechanically multiscale in nature,and the traditional phenomenological laws at the macroscale cannot render a quantitative relationship between microscopic damage of rocks and overall rock structural degradation.This may lead to problems in the evaluation of rock structure stability and safe life.Multiscale numerical modeling is regarded as an effective way to gain insight into factors affecting rock properties from a cross-scale view.This study compiles the history of theoretical developments and numerical techniques related to rock multiscale issues according to different modeling architectures,that is,the homogenization theory,the hierarchical approach,and the concurrent approach.For these approaches,their benefits,drawbacks,and application scope are underlined.Despite the considerable attempts that have been made,some key issues still result in multiple challenges.Therefore,this study points out the perspectives of rock multiscale issues so as to provide a research direction for the future.The review results show that,in addition to numerical techniques,for example,high-performance computing,more attention should be paid to the development of an advanced constitutive model with consideration of fine geometrical descriptions of rock to facilitate solutions to multiscale problems in rock mechanics and rock engineering.
