In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infin...In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.展开更多
In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-p...In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.展开更多
Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditi...Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.展开更多
A minimum-modified Debye-Hückel(DH)theory for electrolytes with size asymmetry is developed.Com-pared with the conventional DH theory,the minimum-modified DH theory only introduces an extra surface charge density...A minimum-modified Debye-Hückel(DH)theory for electrolytes with size asymmetry is developed.Com-pared with the conventional DH theory,the minimum-modified DH theory only introduces an extra surface charge density to capture the electrostatic effect of the size asymmetry of the electrolytes and hence facilitates a boundary element method for electrostatic potential calculation.This theory can distinguish the electrostat-ic energies and excess chemical potentials of ions with the same sizes but opposite charges,and is applied to a binary primitive electrolyte solution with moderate electrostatic coupling.Compared with the hyper-netted chain theory,the validity of this modified DH theory demonstrates significant improvement over the conventional DH theory.展开更多
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for shor...We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for short) classical incompressible Navier-Stokes equations and using techniques developed in(SIAM J Math Anal, 2020, 52(2): 1806–1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part Pu_0 and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.展开更多
By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive soluti...By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.展开更多
Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) ...Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.展开更多
In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational c...In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.展开更多
The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics th...The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.展开更多
^1H NMR chemical shifts of binary aqueous mixtures of acylamide, alcohol, dimethyl sulphoxide (DMSO), and acetone are correlated by statistical associating fluid theory (SAFT) association model. The comparison between...^1H NMR chemical shifts of binary aqueous mixtures of acylamide, alcohol, dimethyl sulphoxide (DMSO), and acetone are correlated by statistical associating fluid theory (SAFT) association model. The comparison between SAFT association model and Wilson equation shows that the former is better for dealing with aqueous solutions. Finally, the specialties of both models are discussed.展开更多
A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary a...A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.展开更多
This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has ...This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue delta0 is established.展开更多
On March 24th,2021,with the initiative of the Chinese government and the promotion of well-known scholars in public administration,the(qualitative)case study seminar of Tsinghua University initiated the case study mov...On March 24th,2021,with the initiative of the Chinese government and the promotion of well-known scholars in public administration,the(qualitative)case study seminar of Tsinghua University initiated the case study movement.The Case Study Seminar of Young Scholars was also held on November 16th 2021,and the Case Study Seminar of the Case Center of the Ministry of Education was held on November 17th 2021.If the three Minnowbrook Conferences of the United States were of epoch-making significance to the transformation of the paradigm of public administration theories and practices,then the three conferences also have the epoch-making significance of the paradigm transformation of case studies of public administration in China.Under the background of great changes in the global power contrast and profound reform in China,this review paper tries to use the interpretation and interpretation of critical discourse,especially to explain the Chinese theories which are in-depth,refined and transformed by the case study method of Chinese stories,and the Chinese solutions plausible for Chinese theories.In view of the diversity and complexity of Chinese theories and Chinese solutions,this paper mainly focuses on the realization of Chinese theoretical construction and the formulation of Chinese solutions through the discourse interpretation of Chinese case propositions.展开更多
On the basis of the Reddy's higher-order theory of composites, this paper introduces a displacement function Phi into it and transforms its three differential equations for symmetric cross-ply composites into only...On the basis of the Reddy's higher-order theory of composites, this paper introduces a displacement function Phi into it and transforms its three differential equations for symmetric cross-ply composites into only one eight-order differential equation generated by the displacement-function. When a proper Phi is chosen, both solutions are obtained, namely, the Navier-type solution of simply supported rectangular laminated plates and the Levy-type solution with the boundary condition where two opposite edges are simply supported and remains are arbitrary. The numerical examples show that the present results coincide well with the existing results in the references, thus validating that the present solving method is reliable. The higher-order theory of Reddy is simpler in calculation but has higher precision than the first-order shear deformation theory because the former has fewer unknows than the latter and requires no shear coefficients.展开更多
The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-f...The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions. With all combinations of simplysupported (S) and clamped (C) boundary conditions applied to the natural mode, the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates, with the aid of which the normal modes and frequencies are solved exactly. It was believed that the exact eigensolutions for cases SSCC, SCCC and CCCC were unable to be obtained, however, they are successfully found in this paper. Comparisons between the present results and the FEM results validate the present exact solutions, which can thus be taken as the benchmark for verifying different approximate approaches.展开更多
A new unified analytical solution is presented for predicting the range of plastic zone and stress distributions around a deep circular tunnel in a homogeneous isotropic continuous medium. The rock mass, grouting zone...A new unified analytical solution is presented for predicting the range of plastic zone and stress distributions around a deep circular tunnel in a homogeneous isotropic continuous medium. The rock mass, grouting zone and lining are assumed as elastic-perfectly plastic and governed by the unified strength theory(UST). This new solution has made it possible to consider the interaction between seepage pressure, lining, grouting and rock mass, and the intermediate principal stress effect together. Moreover, parametric analysis is carried out to identify the influence of the related parameters on the plastic zone radius. Under the given conditions, the results show that the plastic zone radius decreases with an increasing cohesion, internal friction angle and hydraulic conductivity of lining and unified failure criterion parameter, respectively; whereas the plastic zone radius increases with the growth of elasticity modulus of lining. Comparison of results from the new solution and the other published one shows well agreement and provides confidence in the new solution proposed.展开更多
Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0...Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.展开更多
文摘In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.
基金partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100523,KJQN202000536)the National Natural Science Foundation of China(12001074)+3 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0606)supported by the National Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0278)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202100503)the Research Project of Chongqing Education Commission(CXQT21014)。
文摘In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.
文摘Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.
基金supported by the National Natural Science Foundation of China(No.21863001)a startup package from Guizhou Education University(to Tiejun Xiao)+1 种基金the Natural Science Foundation of de-partment of education of Guizhou province(No.QJKY[2015]483)a startup package from Guizhou Education University(to Yun Zhou).
文摘A minimum-modified Debye-Hückel(DH)theory for electrolytes with size asymmetry is developed.Com-pared with the conventional DH theory,the minimum-modified DH theory only introduces an extra surface charge density to capture the electrostatic effect of the size asymmetry of the electrolytes and hence facilitates a boundary element method for electrostatic potential calculation.This theory can distinguish the electrostat-ic energies and excess chemical potentials of ions with the same sizes but opposite charges,and is applied to a binary primitive electrolyte solution with moderate electrostatic coupling.Compared with the hyper-netted chain theory,the validity of this modified DH theory demonstrates significant improvement over the conventional DH theory.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金Zhai was partially supported by the Guangdong Provincial Natural Science Foundation (2022A1515011977)the Science and Technology Program of Shenzhen(20200806104726001)+1 种基金Zhong was partially supported by the NNSF of China (11901474, 12071359)the Exceptional Young Talents Project of Chongqing Talent (cstc2021ycjh-bgzxm0153)。
文摘We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for short) classical incompressible Navier-Stokes equations and using techniques developed in(SIAM J Math Anal, 2020, 52(2): 1806–1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part Pu_0 and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.
文摘By using the fixed point theorem under the case structure, we study the existence of sign-changing solutions of A class of second-order differential equations three-point boundary-value problems, and a positive solution and a negative solution are obtained respectively, so as to popularize and improve some results that have been known.
基金The authors gratefully a.cknowledge financial supportfrom th6 Natiol-al Natural Science Foundatiol- of CI-h-a. The number of
文摘Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.
文摘In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.
基金This work was supported by the National H-Tech Program under contract No.863-7152101
文摘The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.
基金Supported by the National Natural Science Foundation of China (No. 29976035)the Natural Science Foundation of Zhejiang Provincial (No. RC01051).
文摘^1H NMR chemical shifts of binary aqueous mixtures of acylamide, alcohol, dimethyl sulphoxide (DMSO), and acetone are correlated by statistical associating fluid theory (SAFT) association model. The comparison between SAFT association model and Wilson equation shows that the former is better for dealing with aqueous solutions. Finally, the specialties of both models are discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No 10475036)
文摘A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.
基金Project supported by the National Natural Science Foundation of China.
文摘This paper deals with the solution of a parametric equation with generalized boundary condiiton in transport theory. It gives the distribution of parameter (so called delta-eigenvalue [1]) with which the equation has non-zero solution. A necessary and sufficient condition for the existence of; he control critical eigenvalue delta0 is established.
文摘On March 24th,2021,with the initiative of the Chinese government and the promotion of well-known scholars in public administration,the(qualitative)case study seminar of Tsinghua University initiated the case study movement.The Case Study Seminar of Young Scholars was also held on November 16th 2021,and the Case Study Seminar of the Case Center of the Ministry of Education was held on November 17th 2021.If the three Minnowbrook Conferences of the United States were of epoch-making significance to the transformation of the paradigm of public administration theories and practices,then the three conferences also have the epoch-making significance of the paradigm transformation of case studies of public administration in China.Under the background of great changes in the global power contrast and profound reform in China,this review paper tries to use the interpretation and interpretation of critical discourse,especially to explain the Chinese theories which are in-depth,refined and transformed by the case study method of Chinese stories,and the Chinese solutions plausible for Chinese theories.In view of the diversity and complexity of Chinese theories and Chinese solutions,this paper mainly focuses on the realization of Chinese theoretical construction and the formulation of Chinese solutions through the discourse interpretation of Chinese case propositions.
基金Supported by National Natural Science Foundation of China under Grant Nos.10775140,10975141Knowledge Innovation Funds of CAS under Grant No.KJCX3-SYW-S03
文摘有在严肃的 de 保姆计量器理论的模型的扭转的一个新静态的 de 保姆答案被获得。扭转仅仅包含 O (3 ) 对称的张肌部分根据无法缩减的分解。新答案的一些性质被讨论。
基金The project supported by National Natural Science Foundation of China under Grant No. 10375022 and the Scientific Research Fund of the Education Department of Hunan Province of China under Grant No. 05C414
文摘On the basis of the Reddy's higher-order theory of composites, this paper introduces a displacement function Phi into it and transforms its three differential equations for symmetric cross-ply composites into only one eight-order differential equation generated by the displacement-function. When a proper Phi is chosen, both solutions are obtained, namely, the Navier-type solution of simply supported rectangular laminated plates and the Levy-type solution with the boundary condition where two opposite edges are simply supported and remains are arbitrary. The numerical examples show that the present results coincide well with the existing results in the references, thus validating that the present solving method is reliable. The higher-order theory of Reddy is simpler in calculation but has higher precision than the first-order shear deformation theory because the former has fewer unknows than the latter and requires no shear coefficients.
基金supported by the National Natural Science Foundation of China (10772014)
文摘The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates, and formulation of the natural mode in closed form is performed. The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions. With all combinations of simplysupported (S) and clamped (C) boundary conditions applied to the natural mode, the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates, with the aid of which the normal modes and frequencies are solved exactly. It was believed that the exact eigensolutions for cases SSCC, SCCC and CCCC were unable to be obtained, however, they are successfully found in this paper. Comparisons between the present results and the FEM results validate the present exact solutions, which can thus be taken as the benchmark for verifying different approximate approaches.
基金Project(51378309)supported by National Natural Science Foundation of China
文摘A new unified analytical solution is presented for predicting the range of plastic zone and stress distributions around a deep circular tunnel in a homogeneous isotropic continuous medium. The rock mass, grouting zone and lining are assumed as elastic-perfectly plastic and governed by the unified strength theory(UST). This new solution has made it possible to consider the interaction between seepage pressure, lining, grouting and rock mass, and the intermediate principal stress effect together. Moreover, parametric analysis is carried out to identify the influence of the related parameters on the plastic zone radius. Under the given conditions, the results show that the plastic zone radius decreases with an increasing cohesion, internal friction angle and hydraulic conductivity of lining and unified failure criterion parameter, respectively; whereas the plastic zone radius increases with the growth of elasticity modulus of lining. Comparison of results from the new solution and the other published one shows well agreement and provides confidence in the new solution proposed.
文摘Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.