In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the ...In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.展开更多
We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β ...We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β = 1.33, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on the theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be α = 0.33, which is confirmed by a simple numerical calculation.展开更多
A local alternating segment explicit - implicit method for the solution of 2D diffusion equations is presented in this paper .The method is unconditionally stable and has the obvious property of parallelism. Some nume...A local alternating segment explicit - implicit method for the solution of 2D diffusion equations is presented in this paper .The method is unconditionally stable and has the obvious property of parallelism. Some numerical experiments show the method is not only simple but also more accurate.展开更多
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for th...In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.展开更多
Rational designing of one-dimensional(1D)magnetic alloy to facilitate electromagnetic(EM)wave attenuation capability in low-frequency(2-6 GHz)microwave absorption field is highly desired but remains a significant chal...Rational designing of one-dimensional(1D)magnetic alloy to facilitate electromagnetic(EM)wave attenuation capability in low-frequency(2-6 GHz)microwave absorption field is highly desired but remains a significant challenge.In this study,a composite EM wave absorber made of a FeCoNi medium-entropy alloy embedded in a 1D carbon matrix framework is rationally designed through an improved electrospinning method.The 1D-shaped FeCoNi alloy embedded composite demonstrates the high-density and continuous magnetic network using off-axis electronic holography technique,indicating the excellent magnetic loss ability under an external EM field.Then,the in-depth analysis shows that many factors,including 1D anisotropy and intrinsic physical features of the magnetic medium-entropy alloy,primarily contribute to the enhanced EM wave absorption performance.Therefore,the fabricated EM wave absorber shows an increasing effective absorption band of 1.3 GHz in the low-frequency electromagnetic field at an ultrathin thickness of 2 mm.Thus,this study opens up a new method for the design and preparation of high-performance 1D magnetic EM absorbers.展开更多
To analyze previous experimental data of suspended sediment concentration for silty sediment with different sediment particle sizes due to waves, a new stratification correction coefficient is presented. The suspended...To analyze previous experimental data of suspended sediment concentration for silty sediment with different sediment particle sizes due to waves, a new stratification correction coefficient is presented. The suspended sediment concentration gradient and sediment particle diameter are selected as parameters. Furthermore, a diffusion coefficient model with a stratification effect over the whole water depth for silty sediment suspension under waves is developed. The comparison between the suspended sediment concentration calculated by the presented model and several groups of experimental data shows that the model can reasonably reflect the vertical distribution of silty sediment suspension.The stratification effect calculated by the present model decreases with an increase in the sediment particle diameter,which indicates that the model can be extended to describe the suspended sediment concentration of fine to medium sand when the near-bottom sediment concentration is not very high. Although the original model needs to be iteratively solved, the approximate method without iteration is recommended for applications when the near bottom sediment concentration is between 10 and 20 kg/m~3 due to the small difference between the non-iterative and iterative solution for near bed layer suspended sediment concentration, which plays a major role in sediment transport.展开更多
We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of th...We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.展开更多
We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous...We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.展开更多
Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous...Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stability analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.展开更多
Flood wave propagation modeling is of critical importance to advancing water resources management and protecting human life and property. In this study, we investigated how the advection-diffusion routing model perfor...Flood wave propagation modeling is of critical importance to advancing water resources management and protecting human life and property. In this study, we investigated how the advection-diffusion routing model performed in flood wave propagation on a 16 km long downstream section of the Big Piney River, MO. Model performance was based on gaging station data at the upstream and downstream cross sections. We demonstrated with advection-diffusion theory that for small differences in watershed drainage area between the two river cross sections, inflow along the reach mainly contributes to the downstream hydrograph＇s rising limb and not to the falling limb. The downstream hydrograph＇s falling limb is primarily determined by the propagated flood wave originating at the upstream cross section. This research suggests the parameter for the advectiondiffusion routing model can be calibrated by fitting the hydrograph falling limb. Application of the advection diffusion model to the flood wave of January 29, 2013 supports our theoretical finding that the propagated flood wave determines the downstream cross section falling limb, and the model has good performance in our test examples.展开更多
The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear...The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments.展开更多
The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical...The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.展开更多
This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme...This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.展开更多
In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas ...In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified Fisher equation and find the approximation of minimum wave speed analytically, by using the eigenvalues of the stationary states, and numerically by using COMSOL (a commercial finite element solver). The results reveal that the minimum wave speed depends on the parameter values involved in the model. We observe that when diffusion is moderately non-linear, the eigenvalue method correctly predicts the minimum wave speed in our numerical calculations, but when diffusion is strongly non-linear the eigenvalues method gives the wrong answer.展开更多
In this paper, an integrated model based on Finite Element Method (FEM) and Geographical Information Systems (GIS) has been presented for the runoff simulation of small watersheds. Interception is estimated by an expo...In this paper, an integrated model based on Finite Element Method (FEM) and Geographical Information Systems (GIS) has been presented for the runoff simulation of small watersheds. Interception is estimated by an exponential model based on Leaf Area Index (LAI). Philip two term model has been used for the estima-tion of infiltration in the watershed. For runoff estimation, diffusion wave equations solved by FEM are used. Interflow has been simulated using FEM based model. The developed integrated model has been applied to Peacheater Creek watershed in USA. Sensitivity analysis of the model has been carried out for various pa-rameters. From the results, it is seen that the model is able to simulate the hydrographs with reasonable ac-curacy. The presented model is useful for runoff estimation in small watersheds.展开更多
We present a general homogenization method a periodic heterogeneous material with piecewise constants for diffusion, heat conduction, and wave propagation in The method is relevant to the frequently encountered upsca...We present a general homogenization method a periodic heterogeneous material with piecewise constants for diffusion, heat conduction, and wave propagation in The method is relevant to the frequently encountered upscaling issues for heterogeneous materials. The dispersion relation for each problem is first expressed in the general form where the frequency co （or wavenumber k） is expanded in terms of the wavenumber k （or frequency ω）. A general homogenization model can be directly obtained with any given dispersion relation. Next step we study the unit cell of the heterogeneous material and derive the exact dispersion relation. The final homogenized equations include both leading order terms （effective properties） and high order contributions that represent the effect of the microscopic heterogeneity on the macroscopic behavior. That effect can be lumped into a single dimensionless heterogeneity parameter β, which is bounded between -1/12≤β≤ 0 and has a universal expression for all three problems. Numerical examples validate the proposed method and demonstrate a significant computational saving.展开更多
An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower sol...An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.展开更多
We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth tr...We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods.Moreover,we show the existence and regularity of an original solution via a compactness analysis.Finally,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.展开更多
The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for th...The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.展开更多
Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Men...Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are;1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia;2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front , τ = Xp;4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.展开更多
基金Supported by the National Natural Science Foundation of China(11171223)
文摘In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10605020)the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605376.)
文摘We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β = 1.33, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on the theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be α = 0.33, which is confirmed by a simple numerical calculation.
文摘A local alternating segment explicit - implicit method for the solution of 2D diffusion equations is presented in this paper .The method is unconditionally stable and has the obvious property of parallelism. Some numerical experiments show the method is not only simple but also more accurate.
基金Supported by the National Natural Sciences Foundation of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)the Natural Science Foundation of Zeijiang,China(Y606268).
文摘In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
基金supported by the National Natural Science Foundation of China(Nos.51725101,11727807,51672050,61790581,22088101)the Ministry of Science and Technology of China(973 Project Nos.2018YFA0209102 and 2021YFA1200600)Infrastructure and Facility Construction Project of Zhejiang Laboratory.
文摘Rational designing of one-dimensional(1D)magnetic alloy to facilitate electromagnetic(EM)wave attenuation capability in low-frequency(2-6 GHz)microwave absorption field is highly desired but remains a significant challenge.In this study,a composite EM wave absorber made of a FeCoNi medium-entropy alloy embedded in a 1D carbon matrix framework is rationally designed through an improved electrospinning method.The 1D-shaped FeCoNi alloy embedded composite demonstrates the high-density and continuous magnetic network using off-axis electronic holography technique,indicating the excellent magnetic loss ability under an external EM field.Then,the in-depth analysis shows that many factors,including 1D anisotropy and intrinsic physical features of the magnetic medium-entropy alloy,primarily contribute to the enhanced EM wave absorption performance.Therefore,the fabricated EM wave absorber shows an increasing effective absorption band of 1.3 GHz in the low-frequency electromagnetic field at an ultrathin thickness of 2 mm.Thus,this study opens up a new method for the design and preparation of high-performance 1D magnetic EM absorbers.
基金financially supported by NSFC—Shandong Joint Fund Project (Grant No. U1906231)。
文摘To analyze previous experimental data of suspended sediment concentration for silty sediment with different sediment particle sizes due to waves, a new stratification correction coefficient is presented. The suspended sediment concentration gradient and sediment particle diameter are selected as parameters. Furthermore, a diffusion coefficient model with a stratification effect over the whole water depth for silty sediment suspension under waves is developed. The comparison between the suspended sediment concentration calculated by the presented model and several groups of experimental data shows that the model can reasonably reflect the vertical distribution of silty sediment suspension.The stratification effect calculated by the present model decreases with an increase in the sediment particle diameter,which indicates that the model can be extended to describe the suspended sediment concentration of fine to medium sand when the near-bottom sediment concentration is not very high. Although the original model needs to be iteratively solved, the approximate method without iteration is recommended for applications when the near bottom sediment concentration is between 10 and 20 kg/m~3 due to the small difference between the non-iterative and iterative solution for near bed layer suspended sediment concentration, which plays a major role in sediment transport.
基金supported by"the Fundamental Research Funds for the Central Universities"
文摘We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.
文摘We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.
文摘Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stability analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.
基金supported by funding from the USDA Forest Service Northern Research Station iTree Spatial Simulation (No. PL-5937)the National Urban and Community Forest Advisory Council iT ree Tool (No. 11-DG-11132544340)The SUNY ESF Department of Environmental Resources Engineering provided computing facilities and logistical support
文摘Flood wave propagation modeling is of critical importance to advancing water resources management and protecting human life and property. In this study, we investigated how the advection-diffusion routing model performed in flood wave propagation on a 16 km long downstream section of the Big Piney River, MO. Model performance was based on gaging station data at the upstream and downstream cross sections. We demonstrated with advection-diffusion theory that for small differences in watershed drainage area between the two river cross sections, inflow along the reach mainly contributes to the downstream hydrograph＇s rising limb and not to the falling limb. The downstream hydrograph＇s falling limb is primarily determined by the propagated flood wave originating at the upstream cross section. This research suggests the parameter for the advectiondiffusion routing model can be calibrated by fitting the hydrograph falling limb. Application of the advection diffusion model to the flood wave of January 29, 2013 supports our theoretical finding that the propagated flood wave determines the downstream cross section falling limb, and the model has good performance in our test examples.
文摘The motion of organization center of three_dimensional untwisted scroll waves in excitable media with single diffusion is studied by singular perturbation method in this paper. The relation of curvature and the linear law are derived for untwisted organization center. These results have explicit physical meaning and are in good agreement with experiments.
基金Council of Scientific and Industrial Research(CSIR)
文摘The present paper is devoted to the study of Rayleigh wave propagation in a homogeneous, transversely isotropic, thermoelastic diffusive half-space, subject to stress free, thermally insulated/isothermal, and chemical potential boundary conditions in the context of the generalized thermoelastic diffusion theory. The Green-Lindsay（GL） theory is used in the study. In this theory, thermodiffusion and thermodiffusion mechanical relaxations are governed by four different time constants. Secular equations for surface wave propagation in the considered media are derived. Anisotropy and diffusion effects on the phase velocity, attenuation coefficient are graphically presented in order to present the analytical results and make comparison. Some special cases of frequency equations are derived from the present investigation.
基金Supported by the Natural Science Foundation of China (11171120)the Doctoral Program of Higher Education of China (20094407110001)Natural Science Foundation of Guangdong Province (10151063101000003)
文摘This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.
文摘In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified Fisher equation and find the approximation of minimum wave speed analytically, by using the eigenvalues of the stationary states, and numerically by using COMSOL (a commercial finite element solver). The results reveal that the minimum wave speed depends on the parameter values involved in the model. We observe that when diffusion is moderately non-linear, the eigenvalue method correctly predicts the minimum wave speed in our numerical calculations, but when diffusion is strongly non-linear the eigenvalues method gives the wrong answer.
文摘In this paper, an integrated model based on Finite Element Method (FEM) and Geographical Information Systems (GIS) has been presented for the runoff simulation of small watersheds. Interception is estimated by an exponential model based on Leaf Area Index (LAI). Philip two term model has been used for the estima-tion of infiltration in the watershed. For runoff estimation, diffusion wave equations solved by FEM are used. Interflow has been simulated using FEM based model. The developed integrated model has been applied to Peacheater Creek watershed in USA. Sensitivity analysis of the model has been carried out for various pa-rameters. From the results, it is seen that the model is able to simulate the hydrographs with reasonable ac-curacy. The presented model is useful for runoff estimation in small watersheds.
文摘We present a general homogenization method a periodic heterogeneous material with piecewise constants for diffusion, heat conduction, and wave propagation in The method is relevant to the frequently encountered upscaling issues for heterogeneous materials. The dispersion relation for each problem is first expressed in the general form where the frequency co （or wavenumber k） is expanded in terms of the wavenumber k （or frequency ω）. A general homogenization model can be directly obtained with any given dispersion relation. Next step we study the unit cell of the heterogeneous material and derive the exact dispersion relation. The final homogenized equations include both leading order terms （effective properties） and high order contributions that represent the effect of the microscopic heterogeneity on the macroscopic behavior. That effect can be lumped into a single dimensionless heterogeneity parameter β, which is bounded between -1/12≤β≤ 0 and has a universal expression for all three problems. Numerical examples validate the proposed method and demonstrate a significant computational saving.
基金Supported by the National Natural Science Foundation of China（11371368） Supported by the Natural Science Foundation of Hebei Province（A2013506012） Supported by the Foundation of Shijiazhuang Mechanical Engineering College（JCB1201, YJJXM13008）
文摘An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
基金partially supported by the NSFC(11971179,12371205)partially supported by the National Key R&D Program of China(2021YFA1002900)+1 种基金the Guangdong Province Basic and Applied Basic Research Fund(2021A1515010235)the Guangzhou City Basic and Applied Basic Research Fund(2024A04J6336)。
文摘We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods.Moreover,we show the existence and regularity of an original solution via a compactness analysis.Finally,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.
文摘The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.
文摘Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are;1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia;2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front , τ = Xp;4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.
