To confirm sub-regular solution model valid for predicting the activity of component in binary oxide systems, seven systems in the whole concentration and twelve systems presenting saturation concentration have been s...To confirm sub-regular solution model valid for predicting the activity of component in binary oxide systems, seven systems in the whole concentration and twelve systems presenting saturation concentration have been studied. The total average relative errors of component 1 and 2 are 3.2 % and 4.1% respectively by application of the sub-regular solution model into the systems within the whole concentration. However, the total average relative errors are 16 % and 1088 % in the systems presenting saturation concentration. The results show that sub-regular solu- tion model is not good for predicting the systems presenting saturation concentration, especially for the systems con- taining acidic or neutral oxide. The reason may be that the influence of the two types of oxide on the configuration is greater in binary oxide systems. These oxides can be present in the form of complex anion partly, Si-O, Al-O, Ti-O and so on, for example （SiO4）4-. That is contrary to sub-regular solution model which is supposed that the oxide systems consist of cation and O2-. But compared with regular solution model and quasi-regular solution model, sub- regular solution model is closer to the characteristics of actual solution and the calculated results are superior.展开更多
In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave so...In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.展开更多
This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that...This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.展开更多
In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asympt...In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.展开更多
The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were...The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were investigated using in-situ neutron diffraction and the EVPSC-TDT model.Neutron diffraction was used to quantitatively track grain-level lattice strains and diffraction intensity changes(related to mechanical twinning)in differently oriented grains of each alloy during cyclic tensile/compressive loadings.These measurements were accurately captured by the model.The stress-strain curves of Mg-1 wt%Zn and Mg-2 wt%Zn alloys show as-expected solid solution strengthening from the addition of Zn compared to pure Mg.The macroscopic yielding and hardening behaviors are explained by alternating slip and twinning modes as calculated by the model.The solid solution's influence on individual deformation modes,including basal〈a〉slip,prismatic〈a〉slip,and extension twinning,was then quantitatively assessed in terms of activity,yielding behavior,and hardening response by combining neutron diffraction results with crystal plasticity predictions.The Mg-1 wt%Zn alloy displays distinct yielding and hardening behavior due to solid solution softening of prismatic〈a〉slip.Additionally,the dependence of extension twinning,in terms of the twinning volume fraction,on Zn content exhibits opposite trends under tensile and compressive loadings.展开更多
This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution ...This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.展开更多
The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 a...The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.展开更多
The thermodynamic properties of the most important NaOH-NaAI（OH）4-H20 system in Bayer process for alumina production were investigated. A theoretical model for calculating the equilibrium constant of gibbsite dissol...The thermodynamic properties of the most important NaOH-NaAI（OH）4-H20 system in Bayer process for alumina production were investigated. A theoretical model for calculating the equilibrium constant of gibbsite dissolved in sodium hydroxide solution was proposed. New Pitzer model parameters and mixing parameters for the system NaOH-NaAI（OH）4-H20 were yielded and tested in the temperature range of 298.15-373.15 K. The results show that the proposed model for calculating the equilibrium constant of gibbsite dissolution is applicable and accurate. The obtained Pitzer model parameters of β（0）（NaAl（OH）4）、β（1）（NaAl（OH）4）和CΦ（NaAl（OH）4）,Al（OH）4 for NaAI（OH）4, the binary mixing parameter of θ（OH-Al（OH）4-） with OH-, and the ternary mixing parameter of ψ（Na＋OH-Al（OH）4-） for AI（OH）4- with OH- and Na＋ are temperature-dependent. The prediction of the equilibrium solubility of gibbsite dissolved in sodium hydroxide solution was feasible in the temperature range of 298.15-373.15 K.展开更多
A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexi...A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexistence theory and verified in four kinds of binary aqueous solutions and two kinds of ternary aqueous solutions. The calculated mass action concentrations of structural units or ion couples in four binary aqueous solutions and two ternary solutions at 298.15 K have good agreement with the reported activity data from literatures after shifting the standard state and concentration unit. Therefore, the calculated mass action concentrations of structural units or ion couples from the developed universal thermodynamic model for ternary and binary aqueous solutions can be applied to predict reaction ability of components in ternary and binary strong electrolyte aqueous solutions. It is also proved that the assumptions applied in the developed thermodynamic model are correct and reasonable, i.e., strong electrolyte aqueous solution is composed of cations and anions as simple ions, H2O as simple molecule and other hydrous salt compounds as complex molecules. The calculated mass action concentrations of structural units or ion couples in ternary and binary strong electrolyte aqueous solutions strictly follow the mass action law.展开更多
The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution ...The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.展开更多
In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model w...In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.展开更多
The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, pe...The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.展开更多
A sea-air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Nino-southern oscillation （ENSO） model. Employing the perturbed method, an asymptotic sol...A sea-air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Nino-southern oscillation （ENSO） model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature （SST） anomaly and the related physical quantities.展开更多
A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the correspon...A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.展开更多
This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions fo...This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established.展开更多
In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A...In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.展开更多
The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contami...The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid_solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure_saturation_permeability in laboratory.展开更多
In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical b...In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.展开更多
According to the physiological and anatomical characteristics of small intestine,neglecting the effect of its motility on the distribution and absorption of drug and nutrient,Y.Miyamoto et al.proposed a model of two-d...According to the physiological and anatomical characteristics of small intestine,neglecting the effect of its motility on the distribution and absorption of drug and nutrient,Y.Miyamoto et al.proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drugby numerical analysis.In this paper,we give a steady-state analytical solution of the above model including deactivationterm.The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence pro- vides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments.展开更多
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ...Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.展开更多
基金Item Sponsored by National Natural Science Foundation of China(50764006,50574045)Yunnan Basic Applied Research Foundation of China(2006E0021M)
文摘To confirm sub-regular solution model valid for predicting the activity of component in binary oxide systems, seven systems in the whole concentration and twelve systems presenting saturation concentration have been studied. The total average relative errors of component 1 and 2 are 3.2 % and 4.1% respectively by application of the sub-regular solution model into the systems within the whole concentration. However, the total average relative errors are 16 % and 1088 % in the systems presenting saturation concentration. The results show that sub-regular solu- tion model is not good for predicting the systems presenting saturation concentration, especially for the systems con- taining acidic or neutral oxide. The reason may be that the influence of the two types of oxide on the configuration is greater in binary oxide systems. These oxides can be present in the form of complex anion partly, Si-O, Al-O, Ti-O and so on, for example （SiO4）4-. That is contrary to sub-regular solution model which is supposed that the oxide systems consist of cation and O2-. But compared with regular solution model and quasi-regular solution model, sub- regular solution model is closer to the characteristics of actual solution and the calculated results are superior.
基金Supported by the National Natural Science Foundation of China(12261050)Science and Technology Project of Department of Education of Jiangxi Province(GJJ2201612 and GJJ211027)Natural Science Foundation of Jiangxi Province of China(20212BAB202021)。
文摘In this paper,we investigate the periodic traveling wave solutions problem for a single population model with advection and distributed delay.By the bifurcation analysis method,we can obtain periodic traveling wave solutions for this model under the influence of advection term and distributed delay.The obtained results indicate that weak kernel and strong kernel can both deduce the existence of periodic traveling wave solutions.Finally,we apply the main results in this paper to Logistic model and Nicholson’s blowflies model.
文摘This work focuses on a Keller-Segel chemotaxis model, with an emphasis on its conservation laws. Through a new approach combined with the multiplier method, called the mixed method, we obtain conservation vectors that are related and unrelated to symmetric information. In addition, some exact solutions with particular forms are obtained according to the method of conservation laws. These particular solutions are different from the group-invariant solutions.
基金supported by the National Natural Science Foundation of China(Grant Nos.12475003 and11705284)by the Natural Science Foundation of Beijing Municipality(Grant Nos.1232022 and 1212007)。
文摘In this paper,the N-soliton solutions for the massive Thirring model(MTM)in laboratory coordinates are analyzed via the Riemann-Hilbert(RH)approach.The direct scattering including the analyticity,symmetries,and asymptotic behaviors of the Jost solutions as|λ|→∞andλ→0 are given.Considering that the scattering coefficients have simple zeros,the matrix RH problem,reconstruction formulas and corresponding trace formulas are also derived.Further,the N-soliton solutions in the reflectionless case are obtained explicitly in the form of determinants.The propagation characteristics of one-soliton solutions and interaction properties of two-soliton solutions are discussed.In particular,the asymptotic expressions of two-soliton solutions as|t|→∞are obtained,which show that the velocities and amplitudes of the asymptotic solitons do not change before and after interaction except the position shifts.In addition,three types of bounded states for two-soliton solutions are presented with certain parametric conditions.
基金supported by the National Research Foundation grant funded by the Korean government(No,2023R1A2C2007190,RS-2024-00398068)partially funded by the Natural Science Foundation of Shandong Province,China(No.ZR2022QE206).
文摘The effects of solid solution on the deformation behavior of binary Mg-xZn(x=0,1,2 wt%)alloys featuring a designated texture that enables extension twinning under tension parallel to the basal pole in most grains,were investigated using in-situ neutron diffraction and the EVPSC-TDT model.Neutron diffraction was used to quantitatively track grain-level lattice strains and diffraction intensity changes(related to mechanical twinning)in differently oriented grains of each alloy during cyclic tensile/compressive loadings.These measurements were accurately captured by the model.The stress-strain curves of Mg-1 wt%Zn and Mg-2 wt%Zn alloys show as-expected solid solution strengthening from the addition of Zn compared to pure Mg.The macroscopic yielding and hardening behaviors are explained by alternating slip and twinning modes as calculated by the model.The solid solution's influence on individual deformation modes,including basal〈a〉slip,prismatic〈a〉slip,and extension twinning,was then quantitatively assessed in terms of activity,yielding behavior,and hardening response by combining neutron diffraction results with crystal plasticity predictions.The Mg-1 wt%Zn alloy displays distinct yielding and hardening behavior due to solid solution softening of prismatic〈a〉slip.Additionally,the dependence of extension twinning,in terms of the twinning volume fraction,on Zn content exhibits opposite trends under tensile and compressive loadings.
基金supported by the Anhui Provincial Natural Science Foundation(2408085QA031)the third author's work was supported by the National Natural Science Foundation of China(12001033).
文摘This paper studies the global existence and large-time behaviors of weak solutions to the kinetic particle model coupled with the incompressible Navier-Stokes equations in IR3.First,we obtain the global weak solution using the characteristic and energy methods.Then,under the small assumption of the mass of the particle,we show that the solutions decay at the algebraic time-decay rate.Finally,it is also proved that the above rate is optimal.It should be remarked that if the particle in the coupled system vanishes(i.e.f=O),our works coincide with the classical results by Schonbek[32](J Amer Math Soc,1991,4:423-449),which can be regarded as a generalization from a single fuid model to the two-phase fluid one.
文摘The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.
基金Project (2005CB6237) supported by the National Basic Research Program of China
文摘The thermodynamic properties of the most important NaOH-NaAI（OH）4-H20 system in Bayer process for alumina production were investigated. A theoretical model for calculating the equilibrium constant of gibbsite dissolved in sodium hydroxide solution was proposed. New Pitzer model parameters and mixing parameters for the system NaOH-NaAI（OH）4-H20 were yielded and tested in the temperature range of 298.15-373.15 K. The results show that the proposed model for calculating the equilibrium constant of gibbsite dissolution is applicable and accurate. The obtained Pitzer model parameters of β（0）（NaAl（OH）4）、β（1）（NaAl（OH）4）和CΦ（NaAl（OH）4）,Al（OH）4 for NaAI（OH）4, the binary mixing parameter of θ（OH-Al（OH）4-） with OH-, and the ternary mixing parameter of ψ（Na＋OH-Al（OH）4-） for AI（OH）4- with OH- and Na＋ are temperature-dependent. The prediction of the equilibrium solubility of gibbsite dissolved in sodium hydroxide solution was feasible in the temperature range of 298.15-373.15 K.
基金Project supported by Publication Foundation of National Science and Technology Academic Books of China
文摘A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexistence theory and verified in four kinds of binary aqueous solutions and two kinds of ternary aqueous solutions. The calculated mass action concentrations of structural units or ion couples in four binary aqueous solutions and two ternary solutions at 298.15 K have good agreement with the reported activity data from literatures after shifting the standard state and concentration unit. Therefore, the calculated mass action concentrations of structural units or ion couples from the developed universal thermodynamic model for ternary and binary aqueous solutions can be applied to predict reaction ability of components in ternary and binary strong electrolyte aqueous solutions. It is also proved that the assumptions applied in the developed thermodynamic model are correct and reasonable, i.e., strong electrolyte aqueous solution is composed of cations and anions as simple ions, H2O as simple molecule and other hydrous salt compounds as complex molecules. The calculated mass action concentrations of structural units or ion couples in ternary and binary strong electrolyte aqueous solutions strictly follow the mass action law.
文摘The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.
文摘In this research, LINGO is used successfully to solve the water supply system′s optimal operation model. Firstly, the language of LINGO and the using method were studied intensively, on the basis of which the model was transformed to LINGO form and solved successfully. Secondly, the research on the interface between LINGO and the popular office software was made. The optimization software was developed, which had Excel as the workspace and LINGO as the core of computation. Through practice, this software was found stable, easy to use and suitable for the application to the water supply corporations.
基金supported by the National Outstanding Young Scientist Foundation of China (Grant 11225213)the Key Subject "Computational Solid Mechanics" of China Academy of Engineering Physics
文摘The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.
基金Project supported by the National Natural Science Foundation of China (Grant No.40876010)the Natural Science Foundation of Zhejiang Province of China (Grant No.Y6110502)+2 种基金the Natural Science Foundation of the Education Bureau of Anhui Province of China (Grant Nos.KJ2011A135 and KJ2011Z003)the LASG State Key Laboratory Special Fund of Chinathe Foundation of E-Institutes of Shanghai Municipal Education Commission,China (Grant No.E03004)
文摘A sea-air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Nino-southern oscillation （ENSO） model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature （SST） anomaly and the related physical quantities.
基金Project supported by the National Basic Research Program of China (Grant No. 2011CB403501)the National Natural Science Foundation of China (GrantNos. 41175058,41275062,and 11202106)
文摘A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.
文摘This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11562014,11762011,11671101,71471020,51839002the Natural Science Foundation of Inner Mongolia under Grant No.2017MS0108+4 种基金Hunan Provincial Natural Science Foundation of China under Grant No.2016JJ2061the Scientific Research Fund of Hunan Provincial Education Department under Grant No.18A325the Construct Program of the Key Discipline in Hunan Province under Grant No.201176the Aid Program for Science and Technology Innovative Research Team in Higher Educational Instituions of Hunan Province under Grant No.2014207Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering of Changsha University of Science and Technology under Grant No.018MMAEZD191
文摘In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect.Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.
文摘The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid_solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure_saturation_permeability in laboratory.
文摘In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.
基金The project supported by NSF of Shandong Province
文摘According to the physiological and anatomical characteristics of small intestine,neglecting the effect of its motility on the distribution and absorption of drug and nutrient,Y.Miyamoto et al.proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drugby numerical analysis.In this paper,we give a steady-state analytical solution of the above model including deactivationterm.The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence pro- vides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments.
基金国家自然科学基金，NKBRD of China，Doctor Foundation of Education Commission of China
文摘Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.
