We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gor...We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.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
The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtra...The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtration and consequently has got, through various forms of limits, the exact analytical solutions of the three common reservoirs (fissure, homogeneous and the two-layered) pressure distribution under the conditions of three boundaries, i.e., infinite boundary, sealed finite boundary and the finite boundary at constant pressures.展开更多
By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we ...By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.展开更多
The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the un...The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region's differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.展开更多
Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, wi...Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.展开更多
The following partial differential equations are studied: generalized fifth-order KdV equation,water wave equation, Kupershmidt equation, couples KdV equation. The analytical solutions to these problems via using vari...The following partial differential equations are studied: generalized fifth-order KdV equation,water wave equation, Kupershmidt equation, couples KdV equation. The analytical solutions to these problems via using various ansatzes by introducing a second-order ordinary differential equation are found out.展开更多
Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green func...Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.展开更多
The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose...The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure <em>exact</em> (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the <em>exact</em> equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called <em>basic reproduction ratio</em>, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.展开更多
It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analyt...It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.展开更多
This paper presented a novel bond-slip model to better reveal the mechanical behavior of the bolt-grout interface for fully-grouted rockbolts under tensile loads by considering the non-linear response in the softening...This paper presented a novel bond-slip model to better reveal the mechanical behavior of the bolt-grout interface for fully-grouted rockbolts under tensile loads by considering the non-linear response in the softening stage.The exponential decay function is adopted for describing the non-linear response in the softening stage.Based on the improved bond-slip model,the corresponding analytical solutions for the interfacial shear stress and the axial force of the bolt under different loading stages are solved.Then,the validity of this proposed model was verified by comparing with the experimental results.The results show that compared with the linear softening model,the proposed model is more suitable for predicting the mechanical performance of fully-grouted rockbolts.Finally,a series of parametric studies are conducted to explore the effect of model parameters on the mechanical properties of fully-grouted rockbolts.The results indicate that compared with the anchor length,the bolt diameter and the bond strength of the bolt-grout interface have a significance influence on the ultimate load of bolt,especially for the elastic and softening stage.Moreover,it can be found that using the linear softening model maybe overestimates the supporting performance of grouted bolt,resulting in an unsafe design for bolt.展开更多
A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for...A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for solving the K-equation, using the truncated Gram-Charlier expansion (type A) of the concentration field and finite set equations for the corresponding moments. The other model (named ADMM: Analytical Dispersion Multilayers Model) is an semi- analytical solution to the time-dependent two-dimensional advection-diffusion equation based on a discretization of the PBL in N sub-layers;in each sub-layers the advection-diffusion equation is solved by the Laplace transform technique, considering an average value for eddy diffusivity and the wind speed. A preliminary performance evaluation is shown in the case of continuous emission from an elevated source in a variable boundary layer. Both models were able to correctly reproduce the concentration field measured and so to be used as operative air pollution models.展开更多
Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressibl...Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressible flow. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation assuming turbulence parameterization for realistic physical scenarios. We present the general time dependent three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.展开更多
According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each cont...According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived. The results show that when the drag force between twophasesdepends linearly on their relative velocity, the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall, and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.展开更多
Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Many ...Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation as- suming turbulence parameterization for realistic physical scenarios. We present the general steady three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.展开更多
Assessing the slope deformation is significant for landslide prediction. Many researchers have studied the slope displacement based on field data from the inclinometer in combination with complicated numerical analysi...Assessing the slope deformation is significant for landslide prediction. Many researchers have studied the slope displacement based on field data from the inclinometer in combination with complicated numerical analysis. They found that there was a shear zone above the slip surface, and they usually focused on the distribution of velocity and displacement within the shear zone. In this paper,two simple methods are proposed to analyze the distribution of displacement and velocity along the whole profile of a slope from the slip surface to the slope surface during slow movement. In the empirical method, the slope soil above the shear zone is assumed as a rigid body. Dual or triple piecewise fitting functions are empirically proposed for the distribution of velocity along the profile of a slope. In the analytical method, the slope soil is not assumed as a rigid body but as a deformable material. Continuous functions of the velocity and displacement along the profile of a slope are directly obtained by solving the Newton's equation of motion associated with the Bingham model. Using the two proposed methods respectively, the displacement and velocity along the slope profiles of three slopes are determined. A reasonable agreement between the measured data and the calculated results of the two proposed methods has been reached. In comparison with the empirical method, the analytical method would be more beneficial for slope deformation analysis in slope engineering, because the parameters are material constants in the analytical solution independent of time t, and the nonlinear viscosity of the soil can be considered.展开更多
The Cahn, Lücke and Stüwe theory remains the backbone of more complex analysis dealing with solute drag, however, the mathematical treatment is rather involved. A new approach based on solute pinning the bou...The Cahn, Lücke and Stüwe theory remains the backbone of more complex analysis dealing with solute drag, however, the mathematical treatment is rather involved. A new approach based on solute pinning the boundary has therefore recently been suggested, which has the main advantage of a simpler mathematical treatment. In the present paper this approach has been generalized to take into account the influence of different types of solute atoms in the high solute content/low driving force regime.展开更多
This research investigates water-wave scattering via a horizontal perforated plate fixed at the still water level through analytical studies and physical model tests.The velocity potential decomposition method is comb...This research investigates water-wave scattering via a horizontal perforated plate fixed at the still water level through analytical studies and physical model tests.The velocity potential decomposition method is combined with an efficient iterative algorithm to develop an analytical solution in which the quadratic pressure drop condition is imposed on the horizontal perforated plate.The analytical results are in good agreement with the results of an independently developed iterative boundary element method(BEM)solution.Experimental tests are carried out in a wave flume to measure the reflection coefficient and transmission coefficient of the horizontal perforated plate,and the analytical results agree reasonably well with the experimental data.The influence of various structural parameters of the horizontal perforated plate on the hydrodynamic parameters of reflection coefficient,transmission coefficient,energy-loss coefficient,and wave force are analyzed on the basis of the analytical solution.Useful results for the practical engineering application of horizontal perforated plates are also presented.展开更多
Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required.Cellular materials subjected to high impact loading result in a compaction type deformation,us...Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required.Cellular materials subjected to high impact loading result in a compaction type deformation,usually modeled using continuum-based shock theory.The resulting governing differential equation of the shock model is nonlinear,and the density gradient further complicates the problem.Earlier studies have employed numerical methods to obtain the solution.In this study,an analytical closed-form solution is proposed to predict the response of density-graded cellular materials subjected to a rigid body impact.Solutions for the velocity of the impinging rigid body mass,energy absorption capacity of the cellular material,and the incident stress are obtained for a single shock propagation.The results obtained are in excellent agreement with the existing numerical solutions found in the literature.The proposed analytical solution can be potentially used for parametric studies and for effectively designing graded structures to mitigate impact.展开更多
文摘We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.
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.
文摘The present study has obtained the new model of the reservoir filtration problem by taking into account the effect of wellbore storage and skin and by making use of the coupled equations of doubled porous media filtration and consequently has got, through various forms of limits, the exact analytical solutions of the three common reservoirs (fissure, homogeneous and the two-layered) pressure distribution under the conditions of three boundaries, i.e., infinite boundary, sealed finite boundary and the finite boundary at constant pressures.
基金Project supported in part by the Natural Science Foundation of China (Grant Nos. 10575040,90503010,10634060 and 10874050)by National Basic Research Program of China (Grant No. 2005CB724508)+1 种基金the Foundation from the ministry of the National Education of China (Grant No. 200804870051)the Science Innovation Foundation of Huazhong University of Science and Technology (Grant No. HF-06-010-08-012)
文摘By using a two-mode mean-field approximation, we study the dynamics of the microcavities containing semiconductor quantum wells. The exact analytical solutions are obtained in this study. Based on these solutions, we show that the emission from the microcavity manifests periodic oscillation behaviour and the oscillation can be suppressed under a certain condition.
基金the National Natural Science Foundation of China(Nos.50679061,50709025and50749031)
文摘The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region's differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.
文摘Practical resolution of consolidation problems that we often face requires an extensive and solid knowledge of the different parameters highlighted by the Terzaghi one-dimensional consolidation theory. This theory, with its assumptions, leads to a partial differential equation of second order in space and first order in time of pore water pressure. Analytical and numerical resolutions of this equation allow determining the water pressure variation before and after the application of a charge. Numerical modeling has enabled the simulation of the whole results obtained by the two methods of resolution (pressure, degree of consolidation, time factor, among others) to have a physical analysis and a lawful observation that lead to a suitable understanding of the phenomenon of Terzaghi one-dimensional consolidation.
文摘The following partial differential equations are studied: generalized fifth-order KdV equation,water wave equation, Kupershmidt equation, couples KdV equation. The analytical solutions to these problems via using various ansatzes by introducing a second-order ordinary differential equation are found out.
基金Project supported by the National Natural Science Foundation of China (No. 50776097)
文摘Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.
文摘The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure <em>exact</em> (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the <em>exact</em> equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called <em>basic reproduction ratio</em>, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.
文摘It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.
基金This work was financially supported by the National Key Research and Development Program of China(No.2021YFC2902103)Meanwhile,the authors would also like to acknowledge the support provided by Beijing Gold-Bridge Funds and Beijing Excellent Young Engineer Innovation Studio.
文摘This paper presented a novel bond-slip model to better reveal the mechanical behavior of the bolt-grout interface for fully-grouted rockbolts under tensile loads by considering the non-linear response in the softening stage.The exponential decay function is adopted for describing the non-linear response in the softening stage.Based on the improved bond-slip model,the corresponding analytical solutions for the interfacial shear stress and the axial force of the bolt under different loading stages are solved.Then,the validity of this proposed model was verified by comparing with the experimental results.The results show that compared with the linear softening model,the proposed model is more suitable for predicting the mechanical performance of fully-grouted rockbolts.Finally,a series of parametric studies are conducted to explore the effect of model parameters on the mechanical properties of fully-grouted rockbolts.The results indicate that compared with the anchor length,the bolt diameter and the bond strength of the bolt-grout interface have a significance influence on the ultimate load of bolt,especially for the elastic and softening stage.Moreover,it can be found that using the linear softening model maybe overestimates the supporting performance of grouted bolt,resulting in an unsafe design for bolt.
文摘A comparison between a non-Gaussian puff model and an advanced time-dependent model to simulate the pollutant dispersion in the Planetary Boundary Layer is presented. The puff model is based on a general technique for solving the K-equation, using the truncated Gram-Charlier expansion (type A) of the concentration field and finite set equations for the corresponding moments. The other model (named ADMM: Analytical Dispersion Multilayers Model) is an semi- analytical solution to the time-dependent two-dimensional advection-diffusion equation based on a discretization of the PBL in N sub-layers;in each sub-layers the advection-diffusion equation is solved by the Laplace transform technique, considering an average value for eddy diffusivity and the wind speed. A preliminary performance evaluation is shown in the case of continuous emission from an elevated source in a variable boundary layer. Both models were able to correctly reproduce the concentration field measured and so to be used as operative air pollution models.
文摘Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressible flow. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation assuming turbulence parameterization for realistic physical scenarios. We present the general time dependent three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.
文摘According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived. The results show that when the drag force between twophasesdepends linearly on their relative velocity, the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall, and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.
文摘Atmospheric air pollution turbulent fluxes can be assumed to be proportional to the mean concentration gradient. This assumption, along with the equation of continuity, leads to the advection-diffusion equation. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation as- suming turbulence parameterization for realistic physical scenarios. We present the general steady three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.
基金supported by the National Natural Science Foundation of China(Grant No.51579167)the Public Non-profit Welfare Project from China Ministry of Water Resources(Grant No.201301022)the Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-rock Dam of the Ministry of Water Resources(Grant No.YK915003)
文摘Assessing the slope deformation is significant for landslide prediction. Many researchers have studied the slope displacement based on field data from the inclinometer in combination with complicated numerical analysis. They found that there was a shear zone above the slip surface, and they usually focused on the distribution of velocity and displacement within the shear zone. In this paper,two simple methods are proposed to analyze the distribution of displacement and velocity along the whole profile of a slope from the slip surface to the slope surface during slow movement. In the empirical method, the slope soil above the shear zone is assumed as a rigid body. Dual or triple piecewise fitting functions are empirically proposed for the distribution of velocity along the profile of a slope. In the analytical method, the slope soil is not assumed as a rigid body but as a deformable material. Continuous functions of the velocity and displacement along the profile of a slope are directly obtained by solving the Newton's equation of motion associated with the Bingham model. Using the two proposed methods respectively, the displacement and velocity along the slope profiles of three slopes are determined. A reasonable agreement between the measured data and the calculated results of the two proposed methods has been reached. In comparison with the empirical method, the analytical method would be more beneficial for slope deformation analysis in slope engineering, because the parameters are material constants in the analytical solution independent of time t, and the nonlinear viscosity of the soil can be considered.
基金supported by a KMB project(project number:193179/I40),in Norwayfinancial support by the Research Council of Norway and the industrial partners,Hydro Aluminium and Sapa Technology is gratefully acknowledged.
文摘The Cahn, Lücke and Stüwe theory remains the backbone of more complex analysis dealing with solute drag, however, the mathematical treatment is rather involved. A new approach based on solute pinning the boundary has therefore recently been suggested, which has the main advantage of a simpler mathematical treatment. In the present paper this approach has been generalized to take into account the influence of different types of solute atoms in the high solute content/low driving force regime.
基金supported by the National Natural Science Foundation of China(Nos.51725903 and 52001293)the Taishan Scholar Program of Shandong Province(No.ts20190915).
文摘This research investigates water-wave scattering via a horizontal perforated plate fixed at the still water level through analytical studies and physical model tests.The velocity potential decomposition method is combined with an efficient iterative algorithm to develop an analytical solution in which the quadratic pressure drop condition is imposed on the horizontal perforated plate.The analytical results are in good agreement with the results of an independently developed iterative boundary element method(BEM)solution.Experimental tests are carried out in a wave flume to measure the reflection coefficient and transmission coefficient of the horizontal perforated plate,and the analytical results agree reasonably well with the experimental data.The influence of various structural parameters of the horizontal perforated plate on the hydrodynamic parameters of reflection coefficient,transmission coefficient,energy-loss coefficient,and wave force are analyzed on the basis of the analytical solution.Useful results for the practical engineering application of horizontal perforated plates are also presented.
基金the financial support provided by the US Army Research Office under grant number W911NF-18-1-0023.
文摘Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required.Cellular materials subjected to high impact loading result in a compaction type deformation,usually modeled using continuum-based shock theory.The resulting governing differential equation of the shock model is nonlinear,and the density gradient further complicates the problem.Earlier studies have employed numerical methods to obtain the solution.In this study,an analytical closed-form solution is proposed to predict the response of density-graded cellular materials subjected to a rigid body impact.Solutions for the velocity of the impinging rigid body mass,energy absorption capacity of the cellular material,and the incident stress are obtained for a single shock propagation.The results obtained are in excellent agreement with the existing numerical solutions found in the literature.The proposed analytical solution can be potentially used for parametric studies and for effectively designing graded structures to mitigate impact.