Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic diffe...Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.展开更多
Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter...Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.展开更多
This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifur...This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu (Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350(12), 4799-4838 (1998)).展开更多
A family of systems parameterized by H 〉 0, which describes the Langmuir turbulence, is considered. The asymptotic behavior of the solutions (E^H, nH) when H goes to zero is studied. The results of convergence of ...A family of systems parameterized by H 〉 0, which describes the Langmuir turbulence, is considered. The asymptotic behavior of the solutions (E^H, nH) when H goes to zero is studied. The results of convergence of (EH, nH) to the couple (E, n) which is the solution to the Zakharov equations are stated.展开更多
For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighb...For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighborhood of the origin are also given. The technique employed is essentially different from usual ones. The recursive formula for computation of critical point quantities is linear and then avoids complex integral operations. Some results show an interesting contrast with the related results on quadratic systems.展开更多
A simple and practical method to calculate the fractal dimension (FD) of amicron’s projective surface profile based on fractal theory is proposed. Taking Al(OH)3 material particles as an example, the scanning electro...A simple and practical method to calculate the fractal dimension (FD) of amicron’s projective surface profile based on fractal theory is proposed. Taking Al(OH)3 material particles as an example, the scanning electron microscope (SEM) photos of particles were processed using an image-processing software (IPS) Photoshop. Taking the pixel as a fixed yardstick with the enlargement of the size of the particle image, the box-dimension and circumference-area (C-S) methods were used to calculate the FD of the surface profile of the particle. The FD of 1.2623 of the classic Koch curve is obtained, which approximates the true value of 1.2628. The complexities of the object’s boundary and surface mi- cro-topography are simulated successfully by a generator method.展开更多
This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix ...This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.展开更多
The aim of this study is to apply the concept of functionally graded materials(FGMs) to cemented carbides and to develop high-performance rock drill buttons. Cobalt-gradient structure was introduced to the surface zon...The aim of this study is to apply the concept of functionally graded materials(FGMs) to cemented carbides and to develop high-performance rock drill buttons. Cobalt-gradient structure was introduced to the surface zone of the buttons by carburizing process. Finite element method and XRD measurement were used to decide the distribution of thermal residual stress. Constitutive parameters were determined by constraint factor. Numerical results show that residual stresses of gradient buttons mainly concentrate in cobalt-gradient zone. There is compressive stress in the surface zone and tensile stress in the cobalt-rich zone. The maximum value of surface compressive stress is 180 MPa for WC-6Co cemented carbides. And the numerical results agree with the results of XRD measurement.展开更多
Governing equations for a fully coupled flowing-reaction-deformation behavior with mass transfer in heap leaching are developed. The model equations are solved using an explicit finite difference method under the cond...Governing equations for a fully coupled flowing-reaction-deformation behavior with mass transfer in heap leaching are developed. The model equations are solved using an explicit finite difference method under the conditions of invariable application rate and constant hydraulic head. The distribution of the degree of the saturation, as well as the distributions of the concentration of the reagent and the solute is given. A cubic relationship between the mineral recovery and the leaching duration is obtained based on the numerical results. The relationship can be used to predict the recovery percentage of the valuable metal.展开更多
In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variation...In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.展开更多
For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using th...For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs.The corresponding results in[4,9]can be considered as its special cases.A relationship between the versal unfolding w.r.t.left-right equivalence and the versal deformation w.r.t.contact equivalence is established.展开更多
This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB(u)/dt + A(u) f, v0 ∈ B(u)(0), where the operator B is induced by a subgradient and A is pseudomonotone. Existe...This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB(u)/dt + A(u) f, v0 ∈ B(u)(0), where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.展开更多
In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide...In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.展开更多
Finite element model was developed to analyze thermal residual stress distribution of diamond coating on graded and homogeneous substrates.Graded cemented carbides were formed by carburizing pretreatment to reduce the...Finite element model was developed to analyze thermal residual stress distribution of diamond coating on graded and homogeneous substrates.Graded cemented carbides were formed by carburizing pretreatment to reduce the cobalt content in the surface layer and improve adhesion of diamond coating.The numerical calculation results show that the surface compressive stress of diamond coating is 950 MPa for graded substrate and 1 250 MPa for homogenous substrate,the thermal residual stress decreases by around 24% due to diamond coating.Carburizing pretreatment is good for diamond nucleation rate,and can increase the interface strength between diamond coating and substrate.展开更多
The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained: for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only...The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained: for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only if f1, f2, …, fm are pairwise weakly relatively prime with λ1, λ2, …, λm arbitrary non-negative integers; polynomial composition by θ = (θ1,θ2, …, θn) commutes with monomial-Grobner bases computation if and only if θ1, θ2, , θm are pairwise weakly relatively prime.展开更多
In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the f...In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.展开更多
The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x'(t) = g(x(t),x(qt))(q∈ (0, 1), t 〉 0) is investigated. A sufficient condition is presented to ensure that the...The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x'(t) = g(x(t),x(qt))(q∈ (0, 1), t 〉 0) is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.展开更多
The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-a...The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-associated with a pair of special standard processes which are in weak duality.展开更多
基金Project(06JJ30024) supported by the Natural Science Foundation of Hunan Province, ChinaProject(2004CB619206) supported by the Major State Basic Research and Development Program of China+1 种基金Project(50321402) supported by the National Science Fund for Innovative Research Groups of ChinaProject(06B052) supported by the Scientific Research Fund of Hunan Provincial Education Department of China
文摘Solute transmission in saturated ore heap was studied numerically and experimentally. The convection-diffusion equation (CDE) used to describe the mass transportation in porous media was solved by characteristic difference method to give the distribution of the concentration of ferrous ion in the ore column. To calibrate the computational model, a column test was performed using infiltration of sulfide ferrous solution (the initial concentration is c0=0.04 mol/L) on a 100 cm high column composed of ore particles smaller than 10 mm for 2.5 h. The numerical analysis shows that the results obtained from numerical modeling under the same operating conditions as used for column test are in good agreement with those from experimental procedure on the whole trend, which indicates that the model, the numerical method, and the parameters chosen can reflect the rule of ferrous ion transmission in ore heap.
基金Project supported by the National Natural Science Foundation of China(No.10671002)the Natural Science Foundation of Hunan Province of China(No.04JJ3072)the Science Foundation of the Education Department of Hunan Province of China(No.04C383)
文摘Based on the contact equivalent relation of smooth map-germs in singularity theory, the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameter symmetry is discussed. Some basic results are obtained. Transversality condition is used to characterize the stability of equavariant bifurcation problems.
基金Project supported by the National Natural Science Foundation of China (Nos. 10771215 and10771094)
文摘This paper investigates the dynamics of a TCP system described by a first- order nonlinear delay differential equation. By analyzing the associated characteristic transcendental equation, it is shown that a Hopf bifurcation sequence occurs at the pos- itive equilibrium as the delay passes through a sequence of critical values. The explicit algorithms for determining the Hopf bifurcation direction and the stability of the bifur- cating periodic solutions are derived with the normal form theory and the center manifold theory. The global existence of periodic solutions is also established with the method of Wu (Wu, J. H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society 350(12), 4799-4838 (1998)).
基金Project supported by the Scientific Research Fund of Hunan Provincial Education Department of China (No. 10C1056)
文摘A family of systems parameterized by H 〉 0, which describes the Langmuir turbulence, is considered. The asymptotic behavior of the solutions (E^H, nH) when H goes to zero is studied. The results of convergence of (EH, nH) to the couple (E, n) which is the solution to the Zakharov equations are stated.
文摘For a class of quintic systems, the first 16 critical point quantities are obtained by computer algebraic system Mathematica, and the necessary and sufficient conditions that there exists an exact integral in a neighborhood of the origin are also given. The technique employed is essentially different from usual ones. The recursive formula for computation of critical point quantities is linear and then avoids complex integral operations. Some results show an interesting contrast with the related results on quadratic systems.
基金Project 50474003 supported by the National Natural Science Foundation of China
文摘A simple and practical method to calculate the fractal dimension (FD) of amicron’s projective surface profile based on fractal theory is proposed. Taking Al(OH)3 material particles as an example, the scanning electron microscope (SEM) photos of particles were processed using an image-processing software (IPS) Photoshop. Taking the pixel as a fixed yardstick with the enlargement of the size of the particle image, the box-dimension and circumference-area (C-S) methods were used to calculate the FD of the surface profile of the particle. The FD of 1.2623 of the classic Koch curve is obtained, which approximates the true value of 1.2628. The complexities of the object’s boundary and surface mi- cro-topography are simulated successfully by a generator method.
基金This work was supported in part by the Doctor Subject Foundation of China (No. 20050533015)the National Science Foundation of China(No. 60425310,60574014).
文摘This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.
基金Project(50323008) supported by the National Natural Science Foundation of China
文摘The aim of this study is to apply the concept of functionally graded materials(FGMs) to cemented carbides and to develop high-performance rock drill buttons. Cobalt-gradient structure was introduced to the surface zone of the buttons by carburizing process. Finite element method and XRD measurement were used to decide the distribution of thermal residual stress. Constitutive parameters were determined by constraint factor. Numerical results show that residual stresses of gradient buttons mainly concentrate in cobalt-gradient zone. There is compressive stress in the surface zone and tensile stress in the cobalt-rich zone. The maximum value of surface compressive stress is 180 MPa for WC-6Co cemented carbides. And the numerical results agree with the results of XRD measurement.
基金Project supported by the National Basic Research and Development Program of China (No.2004CB619206)the National Science Fund for Distinguished Young Scholars (No.50325415)+1 种基金the National Science Fund for Innovative Research Group (No.50321402)the Natural Science Foundation of Hunan Province (No.06JJ30024)
文摘Governing equations for a fully coupled flowing-reaction-deformation behavior with mass transfer in heap leaching are developed. The model equations are solved using an explicit finite difference method under the conditions of invariable application rate and constant hydraulic head. The distribution of the degree of the saturation, as well as the distributions of the concentration of the reagent and the solute is given. A cubic relationship between the mineral recovery and the leaching duration is obtained based on the numerical results. The relationship can be used to predict the recovery percentage of the valuable metal.
基金supported financially by the National Natural Science Foundation of China(10971019)supported financially by the Scientific Research Fund of Hunan Provincial Educational Department(09C852)
文摘In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.
文摘For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry,the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs.The corresponding results in[4,9]can be considered as its special cases.A relationship between the versal unfolding w.r.t.left-right equivalence and the versal deformation w.r.t.contact equivalence is established.
基金supported by NSFC (10971019)Scientific Research Fund of Guangxi Education Department (201012MS067)Hunan Provincial Innovation Foundation For Postgraduate (CX2010B117)
文摘This paper deals with the initial-value problem of nonlinear evolution inclusions of the form dB(u)/dt + A(u) f, v0 ∈ B(u)(0), where the operator B is induced by a subgradient and A is pseudomonotone. Existence theorem is established via the time discretization technique and the regularization method. In contrast to the previous results, here we impose a weaker coerciveness condition on A and remove the strong monotonicity from B.
基金supported by the National Natural Science Foundation (11071258, 60874083, 10872119, 10901164)
文摘In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.
基金Project(50323008) supported by the National Natural Science Foundation of China
文摘Finite element model was developed to analyze thermal residual stress distribution of diamond coating on graded and homogeneous substrates.Graded cemented carbides were formed by carburizing pretreatment to reduce the cobalt content in the surface layer and improve adhesion of diamond coating.The numerical calculation results show that the surface compressive stress of diamond coating is 950 MPa for graded substrate and 1 250 MPa for homogenous substrate,the thermal residual stress decreases by around 24% due to diamond coating.Carburizing pretreatment is good for diamond nucleation rate,and can increase the interface strength between diamond coating and substrate.
基金Supported by the NSFC (10771058, 11071062, 10871205), NSFH (10JJ3065)Scientific Research Fund of Hunan Provincial Education Department (10A033)Hunan Provincial Degree and Education of Graduate Student Foundation (JG2009A017)
文摘The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained: for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only if f1, f2, …, fm are pairwise weakly relatively prime with λ1, λ2, …, λm arbitrary non-negative integers; polynomial composition by θ = (θ1,θ2, …, θn) commutes with monomial-Grobner bases computation if and only if θ1, θ2, , θm are pairwise weakly relatively prime.
基金Project(10471153) supported by the National Natural Science Foundation of China project supported by the Natural Science Foundation of Central South University
文摘In this paper, we apply a cone theoretic fixed point theorem to obtain sufficient conditions for the existence of multiple positive periodic solutions to the higher-dimensional functional difference equations of the form:x(n+ 1) =A(n)x(n) +λh(n)f(x(n- τ(n))), n∈ Z.
基金This work is supported by the National Natural Science Foundation of China(Grant No.10571147).
文摘The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x'(t) = g(x(t),x(qt))(q∈ (0, 1), t 〉 0) is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.
文摘The hh-transforms of positivity preserving semigroups and their associated Markov processes are investigated in this paper. In particular, it is shown that any quasi-regular positivity preserving coercive form is hh-associated with a pair of special standard processes which are in weak duality.