The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution ...The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.展开更多
In this article, the global existence and the large time behavior of smooth solutions to the initial boundary value problem for a degenerate compressible energy transport model are established.
This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domai...This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvaiue of the Stokes operator.展开更多
In this article, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be descri...In this article, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable ＂pressure＂ functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.展开更多
The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the ...The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.展开更多
We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system...We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws. When it is a perturbation of a constant state, the solution is shown time asymptotically approach- ing to predetermined diffusion waves, Pointwise estimates on the convergence details are obtained.展开更多
A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and...A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom（MDOF） system is approximated by using the modal energy-decomposition. Energybased base shear coefficients are verified by means of both pushover analysis and nonlinear time history（NLTH） analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.展开更多
The Cauchy problem of compressible Navier-Stokes-Korteweg system in R^(3) is considered here.Due to capillarity effect of material,we obtain the pointwise estimates of the solution in an H^(4)-framework,which is diffe...The Cauchy problem of compressible Navier-Stokes-Korteweg system in R^(3) is considered here.Due to capillarity effect of material,we obtain the pointwise estimates of the solution in an H^(4)-framework,which is different from the previous results for the compressible Navier-Stokes system in an H^(6)-framework[24,25].Our result mainly relies on two different descriptions of the singularity in the short wave of Green’s function for dealing initial propagation and nonlinear coupling respectively.Our pointwise results demonstrate the generalized Huygens’principle as the compressible Navier-Stokes system.As a corollary,we have an L^(p) estimate of the solution with p>1,which is a generalization for p≥2 in[33].展开更多
We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third ord...We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.展开更多
In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u...In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u,b)(t)‖χ^(1−2α)+‖(u,b)(t)‖χ^(1−2β)+‖(u,b)(t)‖χ^(2−2α)+‖(u,b)(t)‖χ^(2−2β)≤(1 t)^(-(5-4max{α,β}/4max{α,β})with 1/2≤α,β≤1 for the small global solution by using Fourier splitting method.The parametersαandβare the fractional dissipations corresponding to the velocity and magnetic field,respectively.展开更多
In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimension...In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.展开更多
SUMMARIES OF TOP NEWS STORIES CHINA Safeguarding Gaokao Fairness This year’s gaokao,China’s national college entrance exam,began on 7 June,with a record 13.35 million students taking part.As one of the country’s mo...SUMMARIES OF TOP NEWS STORIES CHINA Safeguarding Gaokao Fairness This year’s gaokao,China’s national college entrance exam,began on 7 June,with a record 13.35 million students taking part.As one of the country’s most important annual events,the 2025 gaokao has seen extensive nation-wide efforts to ensure fairness,safety,and support for all candidates.Authorities have implemented a range of security and logistical measures to safeguard exam integrity.AI-powered monitoring systems have been rolled out in provinces like Jiangxi,Hubei,and Guangdong,enabling real-time behaviour analysis and early warnings without human intervention.These tools reduce pressure on staff and strengthen fairness.展开更多
In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We p...In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.展开更多
A conveyor belt driven by wound rotor motors produces dynamic tension, velocity and accelerationduring starting. The terrible situation (such as resonance) in dynamic analysis and design is that system naturalfrequenc...A conveyor belt driven by wound rotor motors produces dynamic tension, velocity and accelerationduring starting. The terrible situation (such as resonance) in dynamic analysis and design is that system naturalfrequencies are equal to those for switching off electric resistances. This paper analyzes and determines systemnatural frequencies based on a modeling method of receptances with the analysis of sub-systems model and of theprinciple of their addition and conveyor loop closure. It also puts forward to calculate the time interval for switching off electric resistances. The starting of one conveyor is simulated by lumped-mass-spring-model software tofurther illustrate the influence of time interval for switching off electric resistances on conveyor dynamic behavior. Two methods are also compared. The receptance model is proved to be an excellent alternative.展开更多
In this paper,we consider the Cauchy problem for the Camassa-Holm-Novikov equation.First,we establish the local well-posedness and the blow-up scenario.Second,infinite propagation speed is obtained as the nontrivial s...In this paper,we consider the Cauchy problem for the Camassa-Holm-Novikov equation.First,we establish the local well-posedness and the blow-up scenario.Second,infinite propagation speed is obtained as the nontrivial solution u(x,t)does not have compact x-support for any t>0 in its lifespan,although the corresponding u0(x)is compactly supported.Then,the global existence and large time behavior for the support of the momentum density are considered.Finally,we study the persistence property of the solution in weighted Sobolev spaces.展开更多
In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetr...In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.展开更多
We study the large time behavior of the solution to the initial value problem for a nonlinear pseudoparabolic equation with strong nonlinear terms. The Fourier transform, integral estimate, and the splitting of the fr...We study the large time behavior of the solution to the initial value problem for a nonlinear pseudoparabolic equation with strong nonlinear terms. The Fourier transform, integral estimate, and the splitting of the frequency domain are used.展开更多
In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique...In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper.展开更多
Solid propellant is a high-energy composite material composed of solid particles,which can exhibit time dependent behaviors such as creep and stress relaxation during long-term storage.To model and analyze time depend...Solid propellant is a high-energy composite material composed of solid particles,which can exhibit time dependent behaviors such as creep and stress relaxation during long-term storage.To model and analyze time dependent behavior of solid propellants,the modified soft-bond model(MSBM)based on the rate process theory(RPT)was implemented in Particle Flow Code(PFC).Numerical results show the predicted creep and stress relaxation behaviors by MSBM are in good agreement with experimental data,demonstrating that the MSBM can accurately capture time dependent behaviors in solid propellants.Furthermore,three categories of DEM samples were generated by varying formulations such as particle size,volume fraction and gradation,and a damage parameter was constructed to assess the characteristics of creep and stress relaxation.Among all formulations,the DEM simulation identified the graded formulation exhibiting the minimal damage parameter and optimal creep and stress relaxation resistance.These findings provide guidance for formula design of solid propellant.展开更多
The reverse iontophoresis-based glucose monitoring circumstance is similar to the small-volume solution in which mass diffusion controls the current response of the electrochemical biosensors.In this study,the law of ...The reverse iontophoresis-based glucose monitoring circumstance is similar to the small-volume solution in which mass diffusion controls the current response of the electrochemical biosensors.In this study,the law of mass transfer in this type of solution was analyzed and a mathematic model was established to depict the current-time behavior of the fabricated planar electrode used in the non-invasive meter designed by ourselves.A small-volume glucose solution was directly constructed on the electrode to simulate the reverse iontophoresis-based sensing condition.The correctness of the model was demonstrated by chronoamperometry.Animal assay was subsequently carried out to verify the practicality of the model in determination of blood glucose.The results processed by the new method accurately traced the authentic value,confirming the advantage of the new method and the potential in clinical analysis.展开更多
基金This work was supported by the National Science Foundation of China(10271034)
文摘The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.
基金Supported by the Foundation for Talents of Beijing (20081D0501500171)the Funds of Beijing University of Technology
文摘In this article, the global existence and the large time behavior of smooth solutions to the initial boundary value problem for a degenerate compressible energy transport model are established.
文摘This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvaiue of the Stokes operator.
基金supported by the NSFC(11571177)the Priority Academic Program Development of Jiangsu Higher Education Institutionssupported by the Fundamental Research Funds for the Central Universities(2014B14014)
文摘In this article, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable ＂pressure＂ functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.
文摘The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.
文摘We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws. When it is a perturbation of a constant state, the solution is shown time asymptotically approach- ing to predetermined diffusion waves, Pointwise estimates on the convergence details are obtained.
文摘A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom（MDOF） system is approximated by using the modal energy-decomposition. Energybased base shear coefficients are verified by means of both pushover analysis and nonlinear time history（NLTH） analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.
基金Supported by Natural Science Foundation of China(11971100)Natural Science Foundation of Shanghai(22ZR1402300).
文摘The Cauchy problem of compressible Navier-Stokes-Korteweg system in R^(3) is considered here.Due to capillarity effect of material,we obtain the pointwise estimates of the solution in an H^(4)-framework,which is different from the previous results for the compressible Navier-Stokes system in an H^(6)-framework[24,25].Our result mainly relies on two different descriptions of the singularity in the short wave of Green’s function for dealing initial propagation and nonlinear coupling respectively.Our pointwise results demonstrate the generalized Huygens’principle as the compressible Navier-Stokes system.As a corollary,we have an L^(p) estimate of the solution with p>1,which is a generalization for p≥2 in[33].
基金partially supported by the National Nature Science Foundation of China(12271114)the Guangxi Natural Science Foundation(2023JJD110009,2019JJG110003,2019AC20214)+2 种基金the Innovation Project of Guangxi Graduate Education(JGY2023061)the Key Laboratory of Mathematical Model and Application(Guangxi Normal University)the Education Department of Guangxi Zhuang Autonomous Region。
文摘We are concerned with the large-time behavior of 3D quasilinear hyperbolic equations with nonlinear damping.The main novelty of this paper is two-fold.First,we prove the optimal decay rates of the second and third order spatial derivatives of the solution,which are the same as those of the heat equation,and in particular,are faster than ones of previous related works.Second,for well-chosen initial data,we also show that the lower optimal L^(2) convergence rate of the k(∈[0,3])-order spatial derivatives of the solution is(1+t)^(-(2+2k)/4).Therefore,our decay rates are optimal in this sense.The proofs are based on the Fourier splitting method,low-frequency and high-frequency decomposition,and delicate energy estimates.
基金Supported by the National Natural Science Foundation of China(11871305)
文摘In this paper,we investigate the large time behavior of solutions to the three dimensional generalized Hall-magnetohydrodynamics(Hall-MHD)system in the spacesχ^(s)(R^(3)).We obtain that the temporal decay rate is‖(u,b)(t)‖χ^(1−2α)+‖(u,b)(t)‖χ^(1−2β)+‖(u,b)(t)‖χ^(2−2α)+‖(u,b)(t)‖χ^(2−2β)≤(1 t)^(-(5-4max{α,β}/4max{α,β})with 1/2≤α,β≤1 for the small global solution by using Fourier splitting method.The parametersαandβare the fractional dissipations corresponding to the velocity and magnetic field,respectively.
文摘In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.
文摘SUMMARIES OF TOP NEWS STORIES CHINA Safeguarding Gaokao Fairness This year’s gaokao,China’s national college entrance exam,began on 7 June,with a record 13.35 million students taking part.As one of the country’s most important annual events,the 2025 gaokao has seen extensive nation-wide efforts to ensure fairness,safety,and support for all candidates.Authorities have implemented a range of security and logistical measures to safeguard exam integrity.AI-powered monitoring systems have been rolled out in provinces like Jiangxi,Hubei,and Guangdong,enabling real-time behaviour analysis and early warnings without human intervention.These tools reduce pressure on staff and strengthen fairness.
基金supported by the Jilin Scientific and Technological Development Program(20210101466JC).
文摘In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.
文摘A conveyor belt driven by wound rotor motors produces dynamic tension, velocity and accelerationduring starting. The terrible situation (such as resonance) in dynamic analysis and design is that system naturalfrequencies are equal to those for switching off electric resistances. This paper analyzes and determines systemnatural frequencies based on a modeling method of receptances with the analysis of sub-systems model and of theprinciple of their addition and conveyor loop closure. It also puts forward to calculate the time interval for switching off electric resistances. The starting of one conveyor is simulated by lumped-mass-spring-model software tofurther illustrate the influence of time interval for switching off electric resistances on conveyor dynamic behavior. Two methods are also compared. The receptance model is proved to be an excellent alternative.
基金partially supported by the National Natural Science Foundation of China(12071439)the Zhejiang Provincial Natural Science Foundation of China(LY19A010016)the Natural Science Foundation of Jiangxi Province(20212BAB201016)。
文摘In this paper,we consider the Cauchy problem for the Camassa-Holm-Novikov equation.First,we establish the local well-posedness and the blow-up scenario.Second,infinite propagation speed is obtained as the nontrivial solution u(x,t)does not have compact x-support for any t>0 in its lifespan,although the corresponding u0(x)is compactly supported.Then,the global existence and large time behavior for the support of the momentum density are considered.Finally,we study the persistence property of the solution in weighted Sobolev spaces.
基金Supported by CNPq-Conselho Nacional de Desenvolvimento Cient'fico e Tecnológico
文摘In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.
文摘We study the large time behavior of the solution to the initial value problem for a nonlinear pseudoparabolic equation with strong nonlinear terms. The Fourier transform, integral estimate, and the splitting of the frequency domain are used.
基金National Natural Science Foundation of China(No.11571373)
文摘In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper.
基金The authors acknowledge the support from the National Natural Science Foundation of China(grant Nos.12172263 and 11772237).
文摘Solid propellant is a high-energy composite material composed of solid particles,which can exhibit time dependent behaviors such as creep and stress relaxation during long-term storage.To model and analyze time dependent behavior of solid propellants,the modified soft-bond model(MSBM)based on the rate process theory(RPT)was implemented in Particle Flow Code(PFC).Numerical results show the predicted creep and stress relaxation behaviors by MSBM are in good agreement with experimental data,demonstrating that the MSBM can accurately capture time dependent behaviors in solid propellants.Furthermore,three categories of DEM samples were generated by varying formulations such as particle size,volume fraction and gradation,and a damage parameter was constructed to assess the characteristics of creep and stress relaxation.Among all formulations,the DEM simulation identified the graded formulation exhibiting the minimal damage parameter and optimal creep and stress relaxation resistance.These findings provide guidance for formula design of solid propellant.
基金sponsored by Hi-Tech R. & D. Program of China (2007AA042105 & 2007AA04Z326)CAS Innovative Program (KGCX2-YU-916)
文摘The reverse iontophoresis-based glucose monitoring circumstance is similar to the small-volume solution in which mass diffusion controls the current response of the electrochemical biosensors.In this study,the law of mass transfer in this type of solution was analyzed and a mathematic model was established to depict the current-time behavior of the fabricated planar electrode used in the non-invasive meter designed by ourselves.A small-volume glucose solution was directly constructed on the electrode to simulate the reverse iontophoresis-based sensing condition.The correctness of the model was demonstrated by chronoamperometry.Animal assay was subsequently carried out to verify the practicality of the model in determination of blood glucose.The results processed by the new method accurately traced the authentic value,confirming the advantage of the new method and the potential in clinical analysis.
