A model based on Watson’s power law for the species-area relationship predicts that full global warming, projected up to the year 2050, could provoke the disappearance of roughly one-quarter of existing species. Here...A model based on Watson’s power law for the species-area relationship predicts that full global warming, projected up to the year 2050, could provoke the disappearance of roughly one-quarter of existing species. Here, an alternative approach is worked out, based on the combination of two ecology laws: Taylor and Watson’s power laws, where the former relates species variability with their mean abundance. Just how severely global warming would affect not only the number but the diversity of the surviving species is addressed by this approach, while at the same time giving indications for the post-disaster fate of the remaining species (extinction or recovery).展开更多
This study generalizes the classical Taylor-Sedov framework to analyze finitesource spherical blast waves propagating through both uniform and power-law density media. Previous analyses have predominantly focused on t...This study generalizes the classical Taylor-Sedov framework to analyze finitesource spherical blast waves propagating through both uniform and power-law density media. Previous analyses have predominantly focused on the effects of varying initial conditions on blast dynamics. In contrast, this study investigates the primary shock wave evolution within different ambient gases, demonstrating the critical dependence on the initial density ratio between the blast sphere and the ambient medium, as well as the ambient density profile. We derive new scaling laws based on the density ratio, which accurately predict the dimensionless main shock distance. Furthermore, we systematically examine, for the first time, the conditions for uniform volume expansion, uniform surface area growth, and uniform shock wave propagation in power-law density media, revealing a key scaling relation associated with the power-law exponent. Numerical simulations validate these novel theoretical predictions, demonstrating excellent agreement with the normalized solutions. These findings provide new insights into blast wave dynamics in inhomogeneous media and have implications for astrophysical and laboratory plasma environments.展开更多
The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and...The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.展开更多
Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, t...Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.展开更多
Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers...Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.展开更多
Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the...Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations＇ daily precipitation series （from 1956 to 2000） in South China （SC） and North China （NC）, we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm （briefly BG algorithm）. For each station＇s precipitation series, we calculate the exponent of power-law tall （EPT） of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.展开更多
Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact as...Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact asymptotic field was found. Conclusion The exact analytic solution for the problem is available.展开更多
This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic(MHD)and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero na...This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic(MHD)and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero nanoparticle mass flux and convective heating.The nonlinear system of the governing equations is transformed and solved by Runge-Kutta-Fehlberg method.The impacts of the transverse magnetic field,bioconvection parameters,Lewis number,nanofluid parameters,Prandtl number and power-law index on the velocity,temperature,nanoparticle volume fraction,density of motile microorganism profiles is explored.In addition,the impacts of these parameters on local skin-friction coefficient,local Nusselt,local Sherwood numbers and local density number of the motile microorganisms are discussed.The results reveal that the power law index is considered an important factor in this study.Due to neglecting the buoyancy force term,the bioconvection and nanofluid parameters have slight effects on the velocity profiles.The resultant Lorentz force,from increasing the magnetic field parameter,try to decrease the velocity profiles and increase the rescaled density of motile microorganisms,temperature and nanoparticle volume fraction profiles.Physically,an augmentation of power-law index drops the reduced local skin-friction and reduced Sherwood number,while it increases reduced Nusselt number and reduced local density number of motile microorganisms.展开更多
The Sierra de San Miguelito is a relatively uplifted area and is constituted by a large amount of silicic volcanic rocks with ages from middle to late Cenozoic. The normal faults of the Sierra de San Miguelito are Dom...The Sierra de San Miguelito is a relatively uplifted area and is constituted by a large amount of silicic volcanic rocks with ages from middle to late Cenozoic. The normal faults of the Sierra de San Miguelito are Domino-style and nearly parallel. The cumulative length and displacement of the faults obey power-law distribution. The fractal dimension of the fault traces is -1.49. Using the multi-line one-dimensional sampling, the calculated exponent of cumulative fault displacements is -0.66. A cumulative curve combining measurements of all four sections yielded a slope of -0.63. The displacement-length plot shows a non-linear relationship and large dispersion of data. The large dispersion in the plot is mainly due to the fault linkage during faulting. An estimation of extensional strain due to the normal faults is ca. 0.1830. The bed extension strain is always less than or equal to the horizontal extension strain. The deformation in the Sierra de San Miguelito occurred near the surface, producing pervasive faults and many faults are too small to appear in maps and sections at common scales. The stretching produced by small faults reach ca. 33% of the total horizontal elongation.展开更多
In order to investigate the flow characteristics of swirl injectors for gelled propellants,which actually behaved as non-Newtonian power-law fluid,a swirl axisymmetric model was established to solve Navier-Stokes equa...In order to investigate the flow characteristics of swirl injectors for gelled propellants,which actually behaved as non-Newtonian power-law fluid,a swirl axisymmetric model was established to solve Navier-Stokes equations and VOF(volume of fluid) equation,and the power-law constitutive equation was used to describe the rheology characteristics of the gelled propellants.The film thickness and velocity distribution in the swirl injector under different flow conditions were studied numerically.The simulation results show that the increased geometry characteristic parameter of the swirl injector contributes to the decrease of liquid film thickness.The liquid film thickness is almost independent of the pressure drop.The rheologic parameters have great influences on the inner flow of swirl injector: by increasing the fluid consistency index K and power index n,both the axial and the swirl velocities decrease dramatically;higher fluid consistency index K and power index n make the liquid film thickness increase.When the viscosity is large enough,the air core in the injector would vanish.展开更多
Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip ...Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.展开更多
This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolut...This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.展开更多
This paper aims at the elastic buckling of multilayered thin-walled conical shells with power-law distributed material properties under the axial load and lateral pressure based on the experimental study of palm trunk...This paper aims at the elastic buckling of multilayered thin-walled conical shells with power-law distributed material properties under the axial load and lateral pressure based on the experimental study of palm trunks. The material properties of the shells are assumed to vary continuously in the radial direction. Relations and analytical approaches for linear buckling response are presented by using the layer-wise shell theory. The buckling behaviors of the conical shells subjected to axial and transverse loads are investigated. Parametric study in geometry(relative thickness, relative stiffness and cone angle) is performed to enhance the overall buckling resistance and minimize the weight. Numerical results show the possibility to achieve larger load-carrying capacity by simultaneously optimizing the material and geometric parameters based on the structure of palm trunks.展开更多
A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. Th...A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.展开更多
Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood rou...Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood routing.While their use may guarantee a significant reduction of the computational effort,it is mandatory to define the conditions in which they may be confidently applied.The present paper investigates the applicability conditions of the kinematic,diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids.The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress,such as clay or kaolin suspensions,which are frequently encountered in Chinese rivers.In the framework of a linear analysis,the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one.Based on this comparison,applicability criteria for the different wave approximations for mud flood of power-law fluids are derived.The presented results provide guidelines for selecting the appropriate approximation for a given flow problem,and therefore they may represent a useful tool for engineering predictions.展开更多
基金supported by grants from FAPESP,CNEN and CNPq,Brazilian funding agencies for the promotion of science.
文摘A model based on Watson’s power law for the species-area relationship predicts that full global warming, projected up to the year 2050, could provoke the disappearance of roughly one-quarter of existing species. Here, an alternative approach is worked out, based on the combination of two ecology laws: Taylor and Watson’s power laws, where the former relates species variability with their mean abundance. Just how severely global warming would affect not only the number but the diversity of the surviving species is addressed by this approach, while at the same time giving indications for the post-disaster fate of the remaining species (extinction or recovery).
基金supported by the National Natural Science Foundation of China(Nos.12422208,12432011,12421002,and 12372220)。
文摘This study generalizes the classical Taylor-Sedov framework to analyze finitesource spherical blast waves propagating through both uniform and power-law density media. Previous analyses have predominantly focused on the effects of varying initial conditions on blast dynamics. In contrast, this study investigates the primary shock wave evolution within different ambient gases, demonstrating the critical dependence on the initial density ratio between the blast sphere and the ambient medium, as well as the ambient density profile. We derive new scaling laws based on the density ratio, which accurately predict the dimensionless main shock distance. Furthermore, we systematically examine, for the first time, the conditions for uniform volume expansion, uniform surface area growth, and uniform shock wave propagation in power-law density media, revealing a key scaling relation associated with the power-law exponent. Numerical simulations validate these novel theoretical predictions, demonstrating excellent agreement with the normalized solutions. These findings provide new insights into blast wave dynamics in inhomogeneous media and have implications for astrophysical and laboratory plasma environments.
基金supported by the Guangdong Province Introduced Innovative R&D Team of Big Data-Mathematical Earth Sciences and Extreme Geological Events Team(grant number 2021ZT09H399)the National Natural Science Foundation of China(grant number 42430111,42050103).
文摘The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.
文摘Aim To determine numerically the field characteristics in the vied at the tip of a place crack growing steadily in a power-law hardening material. Meteods. Methods on the Euler mode and small-scale yield assumption, the numerical results were given by nonlinear finite element analysis. Results The numerical results of the shape of the active plastic sone, the angular distribution of stresseses and Clack tip opening displacement (CTOD) in the vicinity at the hp of the steadily groWing CraCk are determined. Conclusion The comparison between the numerical results given by the present wort and those given by analytic asymptotic analysis shows that the present work reached a very high accuracy.
文摘Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.
基金supported by the National Natural Science Foundation of China (Grant No 40675044)the State Key development program for Basic Research (Grant No 2006CB400503)
文摘Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations＇ daily precipitation series （from 1956 to 2000） in South China （SC） and North China （NC）, we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm （briefly BG algorithm）. For each station＇s precipitation series, we calculate the exponent of power-law tall （EPT） of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series.
文摘Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact asymptotic field was found. Conclusion The exact analytic solution for the problem is available.
基金the Deanship of Scientific Research at King Khalid University for funding this work through Big Group Research Project under grant number(R.G.P2/16/40).
文摘This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic(MHD)and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero nanoparticle mass flux and convective heating.The nonlinear system of the governing equations is transformed and solved by Runge-Kutta-Fehlberg method.The impacts of the transverse magnetic field,bioconvection parameters,Lewis number,nanofluid parameters,Prandtl number and power-law index on the velocity,temperature,nanoparticle volume fraction,density of motile microorganism profiles is explored.In addition,the impacts of these parameters on local skin-friction coefficient,local Nusselt,local Sherwood numbers and local density number of the motile microorganisms are discussed.The results reveal that the power law index is considered an important factor in this study.Due to neglecting the buoyancy force term,the bioconvection and nanofluid parameters have slight effects on the velocity profiles.The resultant Lorentz force,from increasing the magnetic field parameter,try to decrease the velocity profiles and increase the rescaled density of motile microorganisms,temperature and nanoparticle volume fraction profiles.Physically,an augmentation of power-law index drops the reduced local skin-friction and reduced Sherwood number,while it increases reduced Nusselt number and reduced local density number of motile microorganisms.
文摘The Sierra de San Miguelito is a relatively uplifted area and is constituted by a large amount of silicic volcanic rocks with ages from middle to late Cenozoic. The normal faults of the Sierra de San Miguelito are Domino-style and nearly parallel. The cumulative length and displacement of the faults obey power-law distribution. The fractal dimension of the fault traces is -1.49. Using the multi-line one-dimensional sampling, the calculated exponent of cumulative fault displacements is -0.66. A cumulative curve combining measurements of all four sections yielded a slope of -0.63. The displacement-length plot shows a non-linear relationship and large dispersion of data. The large dispersion in the plot is mainly due to the fault linkage during faulting. An estimation of extensional strain due to the normal faults is ca. 0.1830. The bed extension strain is always less than or equal to the horizontal extension strain. The deformation in the Sierra de San Miguelito occurred near the surface, producing pervasive faults and many faults are too small to appear in maps and sections at common scales. The stretching produced by small faults reach ca. 33% of the total horizontal elongation.
文摘In order to investigate the flow characteristics of swirl injectors for gelled propellants,which actually behaved as non-Newtonian power-law fluid,a swirl axisymmetric model was established to solve Navier-Stokes equations and VOF(volume of fluid) equation,and the power-law constitutive equation was used to describe the rheology characteristics of the gelled propellants.The film thickness and velocity distribution in the swirl injector under different flow conditions were studied numerically.The simulation results show that the increased geometry characteristic parameter of the swirl injector contributes to the decrease of liquid film thickness.The liquid film thickness is almost independent of the pressure drop.The rheologic parameters have great influences on the inner flow of swirl injector: by increasing the fluid consistency index K and power index n,both the axial and the swirl velocities decrease dramatically;higher fluid consistency index K and power index n make the liquid film thickness increase.When the viscosity is large enough,the air core in the injector would vanish.
基金Project supported by the National Natural Science Foundation of China(No.11302024)the Fundamental Research Funds for the Central Universities(No.FRF-TP-12-108A)the Foundation of the China Scholarship Council in 2014(No.154201406465041)
文摘Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.
基金supported by the National Natural Science Foundation of China(Grant No.70871082)the Shanghai Leading Academic Discipline Project,China(Grant No.S30504)
文摘This paper studies and predicts the number growth of China＇s mobile users by using the power-law regression. We find that the number growth of the mobile users follows a power law. Motivated by the data on the evolution of the mobile users, we consider scenarios of self-organization of accelerating growth networks into scale-free structures and propose a directed network model, in which the nodes grow following a power-law acceleration. The expressions for the transient and the stationary average degree distributions are obtained by using the Poisson process. This result shows that the model generates appropriate power-law connectivity distributions. Therefore, we find a power-law acceleration invariance of the scale-free networks. The numerical simulations of the models agree with the analytical results well.
基金the National Natural Science Foundation of China(No.50975090)the Torch Program of Ministry of Science and Technology of China(No.2012GH571660)
文摘This paper aims at the elastic buckling of multilayered thin-walled conical shells with power-law distributed material properties under the axial load and lateral pressure based on the experimental study of palm trunks. The material properties of the shells are assumed to vary continuously in the radial direction. Relations and analytical approaches for linear buckling response are presented by using the layer-wise shell theory. The buckling behaviors of the conical shells subjected to axial and transverse loads are investigated. Parametric study in geometry(relative thickness, relative stiffness and cone angle) is performed to enhance the overall buckling resistance and minimize the weight. Numerical results show the possibility to achieve larger load-carrying capacity by simultaneously optimizing the material and geometric parameters based on the structure of palm trunks.
文摘A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.
文摘Simplified wave models- such as kinematic,diffusion and quasi-steady- are widely employed as a convenient replacement of the full dynamic one in the analysis of unsteady open-channel flows,and especially for flood routing.While their use may guarantee a significant reduction of the computational effort,it is mandatory to define the conditions in which they may be confidently applied.The present paper investigates the applicability conditions of the kinematic,diffusion and quasisteady dynamic shallow wave models for mud flows of power-law fluids.The power-law model describes in an adequate and convenient way fluids that at low shear rates fluids do not posses yield stress,such as clay or kaolin suspensions,which are frequently encountered in Chinese rivers.In the framework of a linear analysis,the propagation characteristics of a periodic perturbation of an initial steady uniform flow predicted by the simplified models are compared with those of the full dynamic one.Based on this comparison,applicability criteria for the different wave approximations for mud flood of power-law fluids are derived.The presented results provide guidelines for selecting the appropriate approximation for a given flow problem,and therefore they may represent a useful tool for engineering predictions.
