In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
The hot compression deformation behavior of Mg-6Zn-1Mn-0.5Ca(ZM61-0.5Ca)and Mg-6Zn-1Mn-2Sn-0.5Ca(ZMT612-0.5Ca)alloys was investigated at deformation temperatures ranging from 250℃to 400℃and strain rates varying from...The hot compression deformation behavior of Mg-6Zn-1Mn-0.5Ca(ZM61-0.5Ca)and Mg-6Zn-1Mn-2Sn-0.5Ca(ZMT612-0.5Ca)alloys was investigated at deformation temperatures ranging from 250℃to 400℃and strain rates varying from 0.001 s^(-1) to 1 s^(-1).The results show that the addition of Sn promotes dynamic recrystallization(DRX),and CaMgSn phases can act as nucleation sites during the compression deformation.Flow stress increases with increasing the strain rate and decreasing the temperature.Both the ZM61-0.5Ca and ZMT612-0.5Ca alloys exhibit obvious DRX characteristics.CaMgSn phases can effectively inhibit dislocation motion with the addition of Sn,thus increasing the peak fl ow stress of the alloy.The addition of Sn increases the hot deformation activation energy of the ZM61-0.5Ca alloy from 199.654 kJ/mol to 276.649 kJ/mol,thus improving the thermal stability of the alloy.For the ZMT612-0.5Ca alloy,the optimal hot deformation parameters are determined to be a deformation temperature range of 350–400℃and a strain rate range of 0.001–0.01 s^(-1).展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challeng...Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.展开更多
Excessive unbalanced vibrations of rotor-bearing systems significantly affect the stability and safety of high-end rotating machinery,such as aero engines,turbo-generators,and high-end machine tools.To realize the on-...Excessive unbalanced vibrations of rotor-bearing systems significantly affect the stability and safety of high-end rotating machinery,such as aero engines,turbo-generators,and high-end machine tools.To realize the on-line self-recovery of unbalanced vibration faults in a rotor system,a self-recovery regulation method based on the grey wolf optimization-adaptive linear quadratic regulator(GWO-ALQR)is proposed.First,a self-recovery regulation system for unbalanced vibrations was constructed,with the state-space equation of the control system obtained and discretized based on the dynamic equation of the rotor-bearing system.Subsequently,a self-recovery regulation method for unbalanced vi-brations based on GWO-ALQR was designed based on the state-space equation.In this method,the parameters of the control system are optimized using grey wolf optimization(GwO),with the working conditions identified on-line.The optimization parameters were selected independently,while the control commands were generated through a linear quadratic regulator(LQR)to control the action of the actuator to achieve self-recovery of the unbalanced vibration.The experimental results indicate that the unbalanced vibration of the rotor system can be restrained below the expected vibration threshold by the self-recovery regulation system based on GWO-ALQR and the final vibration suppression effect can exceed 70%.展开更多
The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong ...The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.展开更多
The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix sp...The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.展开更多
Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in ...Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.展开更多
Tree plantations are globally significant,and therefore,growth-related challenges cannot be ignored.Canopy structure and light environment influence the growth of plantations,but the precise relationship remains uncle...Tree plantations are globally significant,and therefore,growth-related challenges cannot be ignored.Canopy structure and light environment influence the growth of plantations,but the precise relationship remains unclear.We selected seven-year-old poplar plantations of varying cultivars planted various densities and measured their growth,canopy structure,and light environment.The findings indicate that poplar plantations of different cultivars and at different planting densities showed variations in leaf area index(LAI),average leaf angle(ALA),crown length(CL),length ratio(CLR),roundness(CR)and surface area(CSA),which directly or indirectly affect growth,resulting in disparities in their growing conditions.Crown roundness directly impacted growth,while LAI,CLR and ALA influenced growth indirectly by affecting intercellular carbon dioxide concentration.LAI and CLR had a positive effect;ALA had a negative one.Crown length and surface area directly and indirectly influenced growth by affecting photo synthetically active radiation and net photo synthetic rate,with direct impacts being more pronounced.This research has clarified the regulatory role of canopy structure in plantations growth,providing valuable insights for developing more effective management strategies.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
Arid and semi-arid ecosystems are prone to extensive fires due to specific climatic conditions,sparse vegetation cover,and high density of fine fuels.Understanding the flammability characteristics of land covers is es...Arid and semi-arid ecosystems are prone to extensive fires due to specific climatic conditions,sparse vegetation cover,and high density of fine fuels.Understanding the flammability characteristics of land covers is essential for fire management and designing land restoration programs in arid and semi-arid ecosystems.This study provided a new approach to evaluate the flammability of shrublands and woodlands using flammability indices(FIs)including time to ignition(TI),duration of combustion(DC),and flame height(FH)of plant species and their relative frequencies in the Dalfard Basin of southeastern Iran.The results showed that there was a significant difference in FIs between land covers.Shrublands had higher flammability potential compared with woodlands.Plant moisture content had a negative relationship with TI(P<0.010)and no significant relationship with DC and FH(P>0.050).Artemisia spp.,Astragalus gossypinus Fischer,Amygdalus scoparia Spach,and Cymbopogon jwarancusa(Jones)Schult.had the highest FI.Tree species such as Rhazya stricta Decne.,and Pistacia atlantica Desf.showed greater resistance to fire.Using principal component analysis,the relationship between species and FIs was examined,and TI of wet fuel was the most important FI in relation to species.Structural equation model showed that life form(P<0.001)was the most important flammability driver.Precipitation(P<0.010)and legume species(P<0.010)were significantly related to the flammability in arid land.This study emphasizes the importance of managing high-risk species and using resistant species in vegetation restoration and shows that combining species FIs with their abundance is an effective tool for assessing fire risk and fuel management at the plant community scale.展开更多
The paper considers the initial value problem of inhomogeneous fourth-order Schr¨odinger equation with potential in energy space H^(2)(R^(d)).The global well-posedness is obtained in dimensions d≥5 resorting to ...The paper considers the initial value problem of inhomogeneous fourth-order Schr¨odinger equation with potential in energy space H^(2)(R^(d)).The global well-posedness is obtained in dimensions d≥5 resorting to contractive mapping principle,Strichartz estimates,Caffarelli-Kohn-Nirenberg-type inequality and the continuity method.展开更多
Understanding spatial patterns of plant species diversity and the factors(e.g.,climate and human)that drive these patterns is essential for biodiversity conservation.We used data from 1700.1-ha forest plots in the She...Understanding spatial patterns of plant species diversity and the factors(e.g.,climate and human)that drive these patterns is essential for biodiversity conservation.We used data from 1700.1-ha forest plots in the Shettihalli tropical forest landscape of the Western Ghats biodiversity hotspot,India,to analyse tree community composition and the drivers ofα-diversity(Shannon)andβ-diversity(LCBD).Compositional patterns were visualized using Non-Metric Multidimensional Scaling(NMDS),and hybrid feature selection with structural equation modeling(SEM)was employed to evaluate the direct and indirect effects of environmental variables on diversity.NMDS identified four distinct forest types in the Shettihalli landscape:semi-evergreen,dry deciduous,moist deciduous,and plantation forests,each with distinct plant composition.Shannon diversity and ecological uniqueness was significantly higher in semi-evergreen forest than in deciduous forest plots.The SEMs explained about 79%and 39–45%of the variation inα-diversity andβ-diversity.Our analysis indicated that current diversity patterns result from multiple processes,with structure,disturbance,and edaphic parameters exerting the strongest direct and indirect effects onα-diversity.β-diversity,in contrast,was largely influenced by climate,topography,stand structure,and edaphic factors.Overall,our findings indicate that various factors(e.g.,climate,topography,and human disturbance)interact to shape tree diversity patterns in tropical forests.These findings will help develop unique conservation and management strategies for distinct forest types in tropical forest ecosystems.展开更多
It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of...It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.展开更多
We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
Explosive cyclones(ECs) are rapidly intensifying subtropical cyclones that can develop within a short time and pose considerable threats to coastal areas in middle and high latitudes.Gaining a comprehensive understand...Explosive cyclones(ECs) are rapidly intensifying subtropical cyclones that can develop within a short time and pose considerable threats to coastal areas in middle and high latitudes.Gaining a comprehensive understanding of their formation,evolution,and mechanisms of explosive development is essential for improving forecasts of extreme weather events and mitigating associated impacts.Potential vorticity(PV),which is closely related to cyclone dynamics,serves as a valuable diagnostic tool in the study of ECs.In this study,two wintertime ECs of differing intensity over the Northwestern Pacific Ocean are analyzed to examine how different atmospheric processes influence PV generation and the rapid development of ECs.The maximum deepening rates of the two ECs are 2.81 Bergeron(called EC1) and 1.52 Bergeron(referred to as EC2).Results indicate that different stages of EC evolution are closely associated with PV tendency changes at different atmospheric levels.Using the PV tendency equation,during the explosive development of EC1,latent heat release may trigger the downward propagation of upper-level PV.For EC2,latent heat release notably enhances low-level PV,directly contributing to its rapid intensification.To validate these findings,sensitivity tests are conducted using the Weather Research and Forecasting model,with latent heat release turned off in the microphysical scheme for both cases.The results confirm the crucial role of latent heat release in generating low-level PV,further revealing that latent heat release contributes more to the explosive development of EC2 than that of EC1.展开更多
The radiative heat flux of the plume from reusable rockets is a critical parameter during the launch and return processes.This paper proposes a method for calculating radiative heat flux with higher accuracy than prev...The radiative heat flux of the plume from reusable rockets is a critical parameter during the launch and return processes.This paper proposes a method for calculating radiative heat flux with higher accuracy than previously reported for a recoverable nine-engine liquid-propellant rocket.Based on the Radiative Transfer Equation(RTE),this study employs the discrete transfer method to solve the transient RTE problem using physical properties to describe the problem while avoiding the need to directly solve mathematical equations.The proposed method can effectively determine the radiative heat flux of the flow field and is applicable to problems involving various geometries.Calculations reveal that during the ascent phase of the rocket,the radiative heat flux at the base of the vehicle reaches its maximum in the initial stages of the lift-off,reaching a maximum of~50 kW/m^(2),which is 2.24 times the maximum value during the return phase.During the deceleration stage of re-entry into the atmosphere,the maximum radiative heat flux recorded on the sidewall of the rocket is 29.1 kW/m^(2);the maximum heat flux on the bottom surface is approximately 22.3 kW/m^(2),accounting for 76.6%of that on the rocket's sidewall.This provides a basis for the thermal protection design of the rocket's bottom and walls as well as for the thermal management of cryogenic propellant tanks.Future research will involve ground engine testing and flight experiments to further validate the proposed model.展开更多
The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical pe...The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.展开更多
In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of th...In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.展开更多
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金Sichuan Science and Technology Program(2025ZNSFSC1341)Fundamental Research Funds for the Central Universities(J2022-090,25CAFUC04087)。
文摘The hot compression deformation behavior of Mg-6Zn-1Mn-0.5Ca(ZM61-0.5Ca)and Mg-6Zn-1Mn-2Sn-0.5Ca(ZMT612-0.5Ca)alloys was investigated at deformation temperatures ranging from 250℃to 400℃and strain rates varying from 0.001 s^(-1) to 1 s^(-1).The results show that the addition of Sn promotes dynamic recrystallization(DRX),and CaMgSn phases can act as nucleation sites during the compression deformation.Flow stress increases with increasing the strain rate and decreasing the temperature.Both the ZM61-0.5Ca and ZMT612-0.5Ca alloys exhibit obvious DRX characteristics.CaMgSn phases can effectively inhibit dislocation motion with the addition of Sn,thus increasing the peak fl ow stress of the alloy.The addition of Sn increases the hot deformation activation energy of the ZM61-0.5Ca alloy from 199.654 kJ/mol to 276.649 kJ/mol,thus improving the thermal stability of the alloy.For the ZMT612-0.5Ca alloy,the optimal hot deformation parameters are determined to be a deformation temperature range of 350–400℃and a strain rate range of 0.001–0.01 s^(-1).
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Supported by National Natural Science Foundation of China(Grant No.62173161).
文摘Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.
基金Supported by National Natural Science Foundation of China(Grant No.51875031)Beijing Municipal Natural Science Foundation of China(Grant No.3212010).
文摘Excessive unbalanced vibrations of rotor-bearing systems significantly affect the stability and safety of high-end rotating machinery,such as aero engines,turbo-generators,and high-end machine tools.To realize the on-line self-recovery of unbalanced vibration faults in a rotor system,a self-recovery regulation method based on the grey wolf optimization-adaptive linear quadratic regulator(GWO-ALQR)is proposed.First,a self-recovery regulation system for unbalanced vibrations was constructed,with the state-space equation of the control system obtained and discretized based on the dynamic equation of the rotor-bearing system.Subsequently,a self-recovery regulation method for unbalanced vi-brations based on GWO-ALQR was designed based on the state-space equation.In this method,the parameters of the control system are optimized using grey wolf optimization(GwO),with the working conditions identified on-line.The optimization parameters were selected independently,while the control commands were generated through a linear quadratic regulator(LQR)to control the action of the actuator to achieve self-recovery of the unbalanced vibration.The experimental results indicate that the unbalanced vibration of the rotor system can be restrained below the expected vibration threshold by the self-recovery regulation system based on GWO-ALQR and the final vibration suppression effect can exceed 70%.
文摘The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.
基金The National Natural Science Foundations of China (12202219)the Natural Science Foundations of Ningxia (2024AAC02009, 2023AAC05001)the Ningxia Youth Top Talents Training Project。
文摘The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.
基金Supported by the Development and Application Project of Ship CAE Software.
文摘Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.
基金supported by the National Key Research and Development Program of China(Grant No.2021YFD2201203)the financial support of the National Natural Science Foundation of China(32001311)。
文摘Tree plantations are globally significant,and therefore,growth-related challenges cannot be ignored.Canopy structure and light environment influence the growth of plantations,but the precise relationship remains unclear.We selected seven-year-old poplar plantations of varying cultivars planted various densities and measured their growth,canopy structure,and light environment.The findings indicate that poplar plantations of different cultivars and at different planting densities showed variations in leaf area index(LAI),average leaf angle(ALA),crown length(CL),length ratio(CLR),roundness(CR)and surface area(CSA),which directly or indirectly affect growth,resulting in disparities in their growing conditions.Crown roundness directly impacted growth,while LAI,CLR and ALA influenced growth indirectly by affecting intercellular carbon dioxide concentration.LAI and CLR had a positive effect;ALA had a negative one.Crown length and surface area directly and indirectly influenced growth by affecting photo synthetically active radiation and net photo synthetic rate,with direct impacts being more pronounced.This research has clarified the regulatory role of canopy structure in plantations growth,providing valuable insights for developing more effective management strategies.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
文摘Arid and semi-arid ecosystems are prone to extensive fires due to specific climatic conditions,sparse vegetation cover,and high density of fine fuels.Understanding the flammability characteristics of land covers is essential for fire management and designing land restoration programs in arid and semi-arid ecosystems.This study provided a new approach to evaluate the flammability of shrublands and woodlands using flammability indices(FIs)including time to ignition(TI),duration of combustion(DC),and flame height(FH)of plant species and their relative frequencies in the Dalfard Basin of southeastern Iran.The results showed that there was a significant difference in FIs between land covers.Shrublands had higher flammability potential compared with woodlands.Plant moisture content had a negative relationship with TI(P<0.010)and no significant relationship with DC and FH(P>0.050).Artemisia spp.,Astragalus gossypinus Fischer,Amygdalus scoparia Spach,and Cymbopogon jwarancusa(Jones)Schult.had the highest FI.Tree species such as Rhazya stricta Decne.,and Pistacia atlantica Desf.showed greater resistance to fire.Using principal component analysis,the relationship between species and FIs was examined,and TI of wet fuel was the most important FI in relation to species.Structural equation model showed that life form(P<0.001)was the most important flammability driver.Precipitation(P<0.010)and legume species(P<0.010)were significantly related to the flammability in arid land.This study emphasizes the importance of managing high-risk species and using resistant species in vegetation restoration and shows that combining species FIs with their abundance is an effective tool for assessing fire risk and fuel management at the plant community scale.
基金Supported by National Natural Science Foundation of China(Grant No.11601122).
文摘The paper considers the initial value problem of inhomogeneous fourth-order Schr¨odinger equation with potential in energy space H^(2)(R^(d)).The global well-posedness is obtained in dimensions d≥5 resorting to contractive mapping principle,Strichartz estimates,Caffarelli-Kohn-Nirenberg-type inequality and the continuity method.
基金supported by the Department of Biotechnology,Ministry of Science and Technology,Govt.India,under grant No.BT/Coord.II/10/02/2016/22.03.2018the Indian Council of Social Science Research,New Delhi,India,for providing a short-term doctoral fellowship(RFD/Short-Term/2022-23/ENV/ST/66).
文摘Understanding spatial patterns of plant species diversity and the factors(e.g.,climate and human)that drive these patterns is essential for biodiversity conservation.We used data from 1700.1-ha forest plots in the Shettihalli tropical forest landscape of the Western Ghats biodiversity hotspot,India,to analyse tree community composition and the drivers ofα-diversity(Shannon)andβ-diversity(LCBD).Compositional patterns were visualized using Non-Metric Multidimensional Scaling(NMDS),and hybrid feature selection with structural equation modeling(SEM)was employed to evaluate the direct and indirect effects of environmental variables on diversity.NMDS identified four distinct forest types in the Shettihalli landscape:semi-evergreen,dry deciduous,moist deciduous,and plantation forests,each with distinct plant composition.Shannon diversity and ecological uniqueness was significantly higher in semi-evergreen forest than in deciduous forest plots.The SEMs explained about 79%and 39–45%of the variation inα-diversity andβ-diversity.Our analysis indicated that current diversity patterns result from multiple processes,with structure,disturbance,and edaphic parameters exerting the strongest direct and indirect effects onα-diversity.β-diversity,in contrast,was largely influenced by climate,topography,stand structure,and edaphic factors.Overall,our findings indicate that various factors(e.g.,climate,topography,and human disturbance)interact to shape tree diversity patterns in tropical forests.These findings will help develop unique conservation and management strategies for distinct forest types in tropical forest ecosystems.
基金Supported by National Natural Science Foundation of China(Grant No.12171140).
文摘It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
文摘We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
基金financially supported by the National Key R&D Program of China (No. 2022YFC3004204)the National Natural Science Foundation of China (No. 42275001)the Natural Science Foundation of Shandong Province (No. ZR2022MD038)。
文摘Explosive cyclones(ECs) are rapidly intensifying subtropical cyclones that can develop within a short time and pose considerable threats to coastal areas in middle and high latitudes.Gaining a comprehensive understanding of their formation,evolution,and mechanisms of explosive development is essential for improving forecasts of extreme weather events and mitigating associated impacts.Potential vorticity(PV),which is closely related to cyclone dynamics,serves as a valuable diagnostic tool in the study of ECs.In this study,two wintertime ECs of differing intensity over the Northwestern Pacific Ocean are analyzed to examine how different atmospheric processes influence PV generation and the rapid development of ECs.The maximum deepening rates of the two ECs are 2.81 Bergeron(called EC1) and 1.52 Bergeron(referred to as EC2).Results indicate that different stages of EC evolution are closely associated with PV tendency changes at different atmospheric levels.Using the PV tendency equation,during the explosive development of EC1,latent heat release may trigger the downward propagation of upper-level PV.For EC2,latent heat release notably enhances low-level PV,directly contributing to its rapid intensification.To validate these findings,sensitivity tests are conducted using the Weather Research and Forecasting model,with latent heat release turned off in the microphysical scheme for both cases.The results confirm the crucial role of latent heat release in generating low-level PV,further revealing that latent heat release contributes more to the explosive development of EC2 than that of EC1.
文摘The radiative heat flux of the plume from reusable rockets is a critical parameter during the launch and return processes.This paper proposes a method for calculating radiative heat flux with higher accuracy than previously reported for a recoverable nine-engine liquid-propellant rocket.Based on the Radiative Transfer Equation(RTE),this study employs the discrete transfer method to solve the transient RTE problem using physical properties to describe the problem while avoiding the need to directly solve mathematical equations.The proposed method can effectively determine the radiative heat flux of the flow field and is applicable to problems involving various geometries.Calculations reveal that during the ascent phase of the rocket,the radiative heat flux at the base of the vehicle reaches its maximum in the initial stages of the lift-off,reaching a maximum of~50 kW/m^(2),which is 2.24 times the maximum value during the return phase.During the deceleration stage of re-entry into the atmosphere,the maximum radiative heat flux recorded on the sidewall of the rocket is 29.1 kW/m^(2);the maximum heat flux on the bottom surface is approximately 22.3 kW/m^(2),accounting for 76.6%of that on the rocket's sidewall.This provides a basis for the thermal protection design of the rocket's bottom and walls as well as for the thermal management of cryogenic propellant tanks.Future research will involve ground engine testing and flight experiments to further validate the proposed model.
基金supported by the National Nature Science Foundation of China under Grant No.11902332。
文摘The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.
基金supported by the NSFC(12461012)and the NSF of Chongqing(CSTB2024NSCQ-MSX1246).
文摘In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.
