The paper proposes a new empirical correlation designed to complement the‘‘site laws"currently used to evaluate the attenuation in the rock masses of vibrations induced by rock blasting.The formula contains a d...The paper proposes a new empirical correlation designed to complement the‘‘site laws"currently used to evaluate the attenuation in the rock masses of vibrations induced by rock blasting.The formula contains a deformed exponential known as the K-exponential,which seems to well represent a large number of both natural and artificial phenomena ranging from astrophysics to quantum mechanics,with some extension in the field of economics and finance.Experimental validation of the formula was performed via the analysis of vibration data covering a number of case studies,which differed in terms of both operation and rock type.A total of 12 experimental cases were analysed and the proposed formulation exhibited a good performance in 11 of them.In particular,the proposed law,which was built using blast test data,produced very good approximations of the points representing the vibration measurements and would thus be useful in organising production blasts.However,the developed formula was found to work less well when a correlation obtained for a given site was applied to another presenting similar types of rocks and operations,and thus should not be employed in the absence of measurements from test data.展开更多
The authors study the functional equation f^[m]=1/f and analyze the featuresof its piecewise continuous solutions. All the piecewise continuous real solutions are obtained constructively. The results generalize the on...The authors study the functional equation f^[m]=1/f and analyze the featuresof its piecewise continuous solutions. All the piecewise continuous real solutions are obtained constructively. The results generalize the ones in [2]. Moreover, the conclusion is drawn that there is no circuit iterative roots for those functions not satisfying Babbage equation.展开更多
This paper is concerned with radially positive solutions of the k-Hessian equation involving a Matukuma-type source S_(k)(D^(2)(-φ))=|x|^(λ-2)/(1+|x|^(2))^(λ2)φ^(q),x∈Ω,where S_(k)(D^(2)(-φ))is the k-Hessian op...This paper is concerned with radially positive solutions of the k-Hessian equation involving a Matukuma-type source S_(k)(D^(2)(-φ))=|x|^(λ-2)/(1+|x|^(2))^(λ2)φ^(q),x∈Ω,where S_(k)(D^(2)(-φ))is the k-Hessian operator,q>k>1,λ>0,n>2k,k∈N,andΩis a suitable bounded do-main in R~n.It turns out that there are two different types of radially positive solutions for k>1,i.e.,M-solution(singular at r=0)and Esolution(regular at r=0),which is distinct from the case when k=1.For 1<q<[(n-2+λ)k](n-2k),we apply an iterative approach to improve accuracy of asymptotic expansions of M-solution step by step to the desired extend.In contrast to the case k=1,we require a more precise range of parameters due to repeated application of Taylor expansions,which also makes asymptotic expansions need more delicate investigation.展开更多
In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equati...In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.展开更多
This paper presents a numerical model that simulates the wind fields, turbulence fields, and dispersion of gaseous substances in urban areas on building to city block scales. A Computational Fluid Dynamics（CFD） appr...This paper presents a numerical model that simulates the wind fields, turbulence fields, and dispersion of gaseous substances in urban areas on building to city block scales. A Computational Fluid Dynamics（CFD） approach using the steady-state, Reynolds-Averaged Navier-Stokes（RANS） equations with the standard k-ε turbulence model within control volumes of non-uniform cuboid shapes has been employed. Dispersion field is computed by solving an unsteady transport equation of passive scalar. Another approach based on Gaussian plume model is used to correct the turbulent Schmidt number of tracer, in order to improve the dispersion simulation. The experimental data from a wind tunnel under neutral conditions are used to validate the numerical results of velocity, turbulence, and dispersion fields. The numerical results show a reasonable agreement with the wind tunnel data. The deviation of concentration between the simulation with corrected turbulent Schmidt number and the wind tunnel experiments may arise from 1） imperfect point sources, 2） heterogeneous turbulent difusivity, and 3） the constant turbulent Schmidt assumption used in the model.展开更多
文摘The paper proposes a new empirical correlation designed to complement the‘‘site laws"currently used to evaluate the attenuation in the rock masses of vibrations induced by rock blasting.The formula contains a deformed exponential known as the K-exponential,which seems to well represent a large number of both natural and artificial phenomena ranging from astrophysics to quantum mechanics,with some extension in the field of economics and finance.Experimental validation of the formula was performed via the analysis of vibration data covering a number of case studies,which differed in terms of both operation and rock type.A total of 12 experimental cases were analysed and the proposed formulation exhibited a good performance in 11 of them.In particular,the proposed law,which was built using blast test data,produced very good approximations of the points representing the vibration measurements and would thus be useful in organising production blasts.However,the developed formula was found to work less well when a correlation obtained for a given site was applied to another presenting similar types of rocks and operations,and thus should not be employed in the absence of measurements from test data.
基金the Youth Foundation of the Educational Department of Sichuan Province(No.072B042).
文摘The authors study the functional equation f^[m]=1/f and analyze the featuresof its piecewise continuous solutions. All the piecewise continuous real solutions are obtained constructively. The results generalize the ones in [2]. Moreover, the conclusion is drawn that there is no circuit iterative roots for those functions not satisfying Babbage equation.
基金Supported by the National Natural Science Foundation of China (11801436)the Research startup Foundation for Talent Introduction of Xi'an University of Science and Technology (2050123041)the Natural Science Basic Research Program of Shaanxi Province (2024JC-YBQN-0014)。
文摘This paper is concerned with radially positive solutions of the k-Hessian equation involving a Matukuma-type source S_(k)(D^(2)(-φ))=|x|^(λ-2)/(1+|x|^(2))^(λ2)φ^(q),x∈Ω,where S_(k)(D^(2)(-φ))is the k-Hessian operator,q>k>1,λ>0,n>2k,k∈N,andΩis a suitable bounded do-main in R~n.It turns out that there are two different types of radially positive solutions for k>1,i.e.,M-solution(singular at r=0)and Esolution(regular at r=0),which is distinct from the case when k=1.For 1<q<[(n-2+λ)k](n-2k),we apply an iterative approach to improve accuracy of asymptotic expansions of M-solution step by step to the desired extend.In contrast to the case k=1,we require a more precise range of parameters due to repeated application of Taylor expansions,which also makes asymptotic expansions need more delicate investigation.
文摘In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.
基金Supported by the China Meteorological Administration Special Public Welfare Research Fund (GYHY201106033)
文摘This paper presents a numerical model that simulates the wind fields, turbulence fields, and dispersion of gaseous substances in urban areas on building to city block scales. A Computational Fluid Dynamics（CFD） approach using the steady-state, Reynolds-Averaged Navier-Stokes（RANS） equations with the standard k-ε turbulence model within control volumes of non-uniform cuboid shapes has been employed. Dispersion field is computed by solving an unsteady transport equation of passive scalar. Another approach based on Gaussian plume model is used to correct the turbulent Schmidt number of tracer, in order to improve the dispersion simulation. The experimental data from a wind tunnel under neutral conditions are used to validate the numerical results of velocity, turbulence, and dispersion fields. The numerical results show a reasonable agreement with the wind tunnel data. The deviation of concentration between the simulation with corrected turbulent Schmidt number and the wind tunnel experiments may arise from 1） imperfect point sources, 2） heterogeneous turbulent difusivity, and 3） the constant turbulent Schmidt assumption used in the model.
