Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as...Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as structure-damper systems. The approach,which is named the perturbation spectrum method,can provide a more accurate evaluation of a non-classically damped system's mean peak response in terms of the ground response spectrum. To account for the effect of non-classical damping,all elements are included in the proposed method for seismic analysis of structure,which is usually ap-proximated by ignoring the off-diagonal elements of the modal damping matrix. Moreover,as has been adopted in the traditional Complete Quadratic Combination (CQC) method,the white noise model is also used to simplify the expressions of perturbation correlation coefficients. Finally,numerical work is performed to examine the accuracy of the proposed method by comparing the approximate results with exact ones and to demonstrate the importance of the neglected off-diagonal elements of the modal damping matrix. In the examined cases,the proposed method shows good agreement with direct time-history integration. Also,the perturbation spectrum method leads to a more efficient and economical calculation by avoiding the integral and complex operation.展开更多
Purpose: The aim of this systematic review was to answer the question “Which treatment protocol, am- ong classical methods and/or various laser applica- tions is the most effective in root canal disinfection, in vitr...Purpose: The aim of this systematic review was to answer the question “Which treatment protocol, am- ong classical methods and/or various laser applica- tions is the most effective in root canal disinfection, in vitro”. Materials and Methods: A MEDLINE, a Co- chrane and an Embase search (three specified search- es) were conducted to identify randomized controlled trials (RCT) until June 2010, conducted on human teeth and published in English, German or French language, examining the root canal disinfection after the use of lasers with or without mechanical instru-mentation. Additionally, hand search was conducted and contact with authors, when needed. Results: The MEDLINE, the Cochrane and the EMBASE search identified 240, 28, and 35 published articles, respec-tively. Ten articles from the MEDLINE and 5 articles from the Cochrane search (that were also identified in the MEDLINE search) met the inclusion and va-lidity assessment criteria. In E. faecalis elimination, instrumentation of the root canal and diode laser/665 nanometer/1 Watt (diode laser/665 nm/1 W) irradia-tion with the combined effect of Methylene Blue (MB) as photosensitizing agent (logCFU/ml = 1636) seemed to be the best method. In P. aeruginosa and in A.naeslundii elimination, instrumentation of the root canal followed by irrigation with 5, 25% NaOCl (log-CFU/ml = 0) seemed to be the best method. In gen-eral, instrumentation of the root canal followed by irrigation with 5, 25% NaOCl (logCFU/ml = 0) and instrumentation of the root canal and Er: YAG laser/ 2940 nm/0.8 W irradiation (logCFU/ml = 1924) seemed to be the best (polymicrobial studies). Conclusions: There are treatment protocols with the assistance or not of laser irradiation that can eliminate E. faecalis, E. coli and S. aureus inside the root canal. However, there is a serious number of S. anginosus, F. nuclea-tum, A. naeslundii and P. aeruginosa that remain in-side the root canal even after laser irradiation. New research is needed in order to set a treatment proto-col effective in the root canal disinfection from all bac-teria that are related to endodontic origin pathology.展开更多
The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or obse...The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.展开更多
"Chinese Classical Philology" is a professional basic course for Chinese language and literature and related disciplines. Based on the analysis of the nature of the course and combined with teaching practice..."Chinese Classical Philology" is a professional basic course for Chinese language and literature and related disciplines. Based on the analysis of the nature of the course and combined with teaching practice, this paper summarizes the teaching methods such as teacher-student interaction, excellent pictures and texts, strengthening practice and combining with the present. For peer correction, for peer reference.展开更多
Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cann...Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.展开更多
The performance of a classical damping matrix, constructed either from the use of initial structural properties or current structural properties, in the step-by-step solution of a nonlinear multiple degree of freedom ...The performance of a classical damping matrix, constructed either from the use of initial structural properties or current structural properties, in the step-by-step solution of a nonlinear multiple degree of freedom （MDOF） system is analytically evaluated. The analytical results are confirmed by numerical examples. Consequently, some conclusions are drawn from these analytical results that might be considered as rough guidelines for practical applications. It is found that a classical damping matrix constructed from initial structural properties is adequate for practical applications, since it has approximately the same damping effect as obtained by current structural properties and is more efficient in terms of computing.展开更多
In this paper, we prove the existence of global classical solutions to time-dependent Ginzburg-Landau（TDGL） equations. By the properties of Besov and Sobolev spaces, together with the energy method, we establish the...In this paper, we prove the existence of global classical solutions to time-dependent Ginzburg-Landau（TDGL） equations. By the properties of Besov and Sobolev spaces, together with the energy method, we establish the global existence and uniqueness of classical solutions to the initial boundary value problem for time-dependent Ginzburg-Landau equations.展开更多
This paper uses the classical ensemble method to study the double ionization of a 2-dimensional （2D） model helium atom interacting with an elliptically polarized laser pulse. The classical ensemble calculation demon...This paper uses the classical ensemble method to study the double ionization of a 2-dimensional （2D） model helium atom interacting with an elliptically polarized laser pulse. The classical ensemble calculation demonstrates that the ratio of double to single ionization decreases with the increasing ellipticity of the driving field. The classical scenario shows that there are hardly any e--e recollisions with the circularly polarized laser pulse. The double ionization probability is studied for linearly and circularly polarized laser pulses. The classical numerical results are consistent with the semiclassical rescattering mechanism and in agreement with the experimental results and the quantum calculations qualitatively.展开更多
In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation(δ2 gij)/δt2+μ/((1 + t)λ)(δ gij)/δt=-2 Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ ≤ 1, μ ...In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation(δ2 gij)/δt2+μ/((1 + t)λ)(δ gij)/δt=-2 Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ ≤ 1, μ 〉 λ + 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R(t, x) of the solution metric gij remains uniformly bounded.展开更多
This paper explores some problems concerning ancient Chinese classical linguistics. It is maintained that there are both similarities and obvious differences between it and western philology. The development of ancien...This paper explores some problems concerning ancient Chinese classical linguistics. It is maintained that there are both similarities and obvious differences between it and western philology. The development of ancient Chinese linguistics from the Pre-Qin Period to the Qing Dynasty can be divided into five stages: the embryonic stage, the stage for laying the foundation, the preparatory stage, the stage of growth, and the stage of overall revival and prosperity. The literature produced during this period can be grouped in six categories: gloss exegesis, orthographical form and meaning, phonological form and meaning, historical phonology, grammar on function words, and rhetoric. It is pointed out that, in researching the theoretical history of ancient Chinese linguistics, great importance should be attached to the consistency between history and theoretical logic, cultural background as reference, and textual research methodology.展开更多
In recent years,with the prevailing of Chinese traditional culture,the related“classic education(经典教育jingdianjiaoyu)”debate ensued.Some scholars strongly oppose the“classical education”and think that make chil...In recent years,with the prevailing of Chinese traditional culture,the related“classic education(经典教育jingdianjiaoyu)”debate ensued.Some scholars strongly oppose the“classical education”and think that make children memorize mechanicallyand forced recite,without understand about Confucian classes deviate from the modern“children’s center-based education”and“ideas violate scientific”and to be“an ancient and retrogression”,“ignorance of cultural conservatism”.They advocating that“things other than children’s lives cannot be forcibly entered into the lives of children,”otherwise it will be“a killing of childhood innocence and stifling the lives of children”,and imprisonment of children’s life.To sum up this fierce argument,the main issues of debate are generally not out of the following four aspects:(1)why do we need classic enlightenment?(2)the purpose and utility of the classic enlightenment?(3)the content and methods of classic enlightenment?(4)the timing of the classic enlightenment?In response to these four points of view,Mr.Wangfuzhi,who was 400 years ago,also put forward his own ideas.This article is not intended to participate in this controversy.Instead,it wants to understand Wangfuzhi’s“ideas of classical enlightenment”to understand how the ancients advocated these four issues.For modern people’s reference.展开更多
In non-classical thermoelastic solids incorporating internal rotation and conjugate Cauchy moment tensor the mechanical deformation is reversible. This suggests that within the realm of linear mathematical models that...In non-classical thermoelastic solids incorporating internal rotation and conjugate Cauchy moment tensor the mechanical deformation is reversible. This suggests that within the realm of linear mathematical models that only consider small strains and small deformation the mechanical deformation is reversible. Hence, it is possible to recast the conservation and balance laws along with constitutive theories in a form that adjoint A* of the differential operator A in mathematical model is same as the differential operator A. This holds regardless of whether we consider an initial value problem (IVP) (when the integrals over open boundary are neglected) or boundary value problem (BVP). Thus, in such cases Galerkin method with weak form (GM/WF) for BVPs and space-time Galerkin method with weak form (STGM/WF) for IVPs are highly meritorious due to the fact that: 1) the integral form for BVPs is variationally consistent (VC) and 2) the space-time integral forms for IVP are space time variationally consistent (STVC). The consequence of VC and STVC integral forms is that the resulting coefficient matrices are symmetric and positive definite ensuring unconditionally stable computational processes for both BVPs and IVPs. Other benefits of GM/WF and space-time GM/WF are simplicity of specifying boundary conditions and initial conditions, especially traction boundary conditions and initial conditions on curved boundaries due to self-equilibrating nature of the sum of secondary variables that only exist in GM/WF due to concomitant. In fact, zero traction conditions are automatically satisfied in GM/WF, hence need not be specified at all. While VC and STVC feature also exists in least squares process (LSP) and space-time least squares finite element processes (STLSP) for BVPs and IVPs, the ease of specifying traction boundary conditions feature in GM/WF and STGM/WF is highly meritorious compared to LSP and STLSP in which zero traction conditions need to be explicitly specified. A disadvantage of GM/WF and STGM/ WF is that the mathematical models (momentum equations) needed in the desired form contain higher order derivatives of displacements (upto fourth order), hence necessitate use of higher order spaces in their solution. As well known, this problem can be easily overcome in LSP and STLSP by introduction of auxiliary equations and auxiliary variables, thus keeping the highest orders of the derivatives of the dependent variables to one or any other desired order. A serious disadvantage of this approach in LSP is the significant increase in the number of dependent variables, hence poor computational efficiency. In this paper we consider non-classical continuum models for internally polar linear elastic solids in which internal rotations due to displacement gradient tensor (hence internal polar physics) are considered in the conservation and the balance laws and the constitutive theories. For simplicity, we only consider isothermal case;hence energy equation is not part of mathematical model. When using mathematical models derived in displacements in GM/WF and LSP in constructing integral forms, we note that in GM/WF the number of dependent variables is reduced drastically (only three in R3), whereas in case of first order systems used in LSP and STLSP we may have as many as 22 dependent variables for isothermal case. Thus, GM/WF results in dramatic improvement in computational efficiency as well as accuracy when minimally conforming spaces are used for approximations. In this paper we only consider mathematical model in R2 for BVPs (for simplicity). Mathematical models for IVP and BVP in R3 will be considered in subsequent paper. The integral form is derived in R2 using GM/WF. Numerical examples are presented using GM/WF and LSP to demonstrate advantages of finite element process derived using integral form based on GM/WF for non-classical linear theories for solids incorporating internal rotations due to displacement gradient tensor.展开更多
Realizing “carbon peaking” and “carbon neutrality” is a major strategic decision made by China to coordinate domestic and international situations.In order to achieve the “double carbon” goal,it is also necessar...Realizing “carbon peaking” and “carbon neutrality” is a major strategic decision made by China to coordinate domestic and international situations.In order to achieve the “double carbon” goal,it is also necessary for relevant practitioners to actively put into practice to improve the participation of residents and advocate low carbon life while formulating the policy action plan.Community is an important place for human activities and one of the main spatial types of carbon emissions in cities.Doing a good job in planning energy conservation and emission reduction in the community plays an important role in achieving the “double carbon” goal.Through the analysis of classic low carbon community practice cases at home and abroad,6 planning and design methods for low carbon community are concluded,and the development status of low carbon community in China is reflected and summarized.展开更多
The Ca＋CH3I→CaI＋CH3 reaction system has been studied with the quasi-classical trajectory method on the extended Lond-Eyring-Polanyi-Sato（LEPS） potential energy surface. At collision energy Ecol=10.78 kJ/mol, the ...The Ca＋CH3I→CaI＋CH3 reaction system has been studied with the quasi-classical trajectory method on the extended Lond-Eyring-Polanyi-Sato（LEPS） potential energy surface. At collision energy Ecol=10.78 kJ/mol, the calculated results show that the CaI vibrational population peaks are located at v=2. The calculated cross section decreases slowly with the collision energy increasing. The angle product distributions tend toward backward scattering. The calculated （P2（J^1·K）） values deviate slightly from-0.5 and decrease with increasing collision energy. The Quasiclassical trajectory calculation（QCT） results are in reasonable agreement with experimental data. Moreover, the dynamics of the reaction has been discussed.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
基金Project supported by the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0518)the Program of Introducing Talents of Discipline to Universities (No. B08014), China
文摘Fundamental principles from structural dynamics,random theory and perturbation methods are adopted to develop a new response spectrum combination rule for the seismic analysis of non-classically damped systems,such as structure-damper systems. The approach,which is named the perturbation spectrum method,can provide a more accurate evaluation of a non-classically damped system's mean peak response in terms of the ground response spectrum. To account for the effect of non-classical damping,all elements are included in the proposed method for seismic analysis of structure,which is usually ap-proximated by ignoring the off-diagonal elements of the modal damping matrix. Moreover,as has been adopted in the traditional Complete Quadratic Combination (CQC) method,the white noise model is also used to simplify the expressions of perturbation correlation coefficients. Finally,numerical work is performed to examine the accuracy of the proposed method by comparing the approximate results with exact ones and to demonstrate the importance of the neglected off-diagonal elements of the modal damping matrix. In the examined cases,the proposed method shows good agreement with direct time-history integration. Also,the perturbation spectrum method leads to a more efficient and economical calculation by avoiding the integral and complex operation.
文摘Purpose: The aim of this systematic review was to answer the question “Which treatment protocol, am- ong classical methods and/or various laser applica- tions is the most effective in root canal disinfection, in vitro”. Materials and Methods: A MEDLINE, a Co- chrane and an Embase search (three specified search- es) were conducted to identify randomized controlled trials (RCT) until June 2010, conducted on human teeth and published in English, German or French language, examining the root canal disinfection after the use of lasers with or without mechanical instru-mentation. Additionally, hand search was conducted and contact with authors, when needed. Results: The MEDLINE, the Cochrane and the EMBASE search identified 240, 28, and 35 published articles, respec-tively. Ten articles from the MEDLINE and 5 articles from the Cochrane search (that were also identified in the MEDLINE search) met the inclusion and va-lidity assessment criteria. In E. faecalis elimination, instrumentation of the root canal and diode laser/665 nanometer/1 Watt (diode laser/665 nm/1 W) irradia-tion with the combined effect of Methylene Blue (MB) as photosensitizing agent (logCFU/ml = 1636) seemed to be the best method. In P. aeruginosa and in A.naeslundii elimination, instrumentation of the root canal followed by irrigation with 5, 25% NaOCl (log-CFU/ml = 0) seemed to be the best method. In gen-eral, instrumentation of the root canal followed by irrigation with 5, 25% NaOCl (logCFU/ml = 0) and instrumentation of the root canal and Er: YAG laser/ 2940 nm/0.8 W irradiation (logCFU/ml = 1924) seemed to be the best (polymicrobial studies). Conclusions: There are treatment protocols with the assistance or not of laser irradiation that can eliminate E. faecalis, E. coli and S. aureus inside the root canal. However, there is a serious number of S. anginosus, F. nuclea-tum, A. naeslundii and P. aeruginosa that remain in-side the root canal even after laser irradiation. New research is needed in order to set a treatment proto-col effective in the root canal disinfection from all bac-teria that are related to endodontic origin pathology.
文摘The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
文摘"Chinese Classical Philology" is a professional basic course for Chinese language and literature and related disciplines. Based on the analysis of the nature of the course and combined with teaching practice, this paper summarizes the teaching methods such as teacher-student interaction, excellent pictures and texts, strengthening practice and combining with the present. For peer correction, for peer reference.
基金国家杰出青年科学基金，the Research Fund for the Doctoral Program of Higher Education of China
文摘Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.
基金Science Council,Taipei 106-08,Chinese Taipei,under Grant No. NSC-99-2221-E-027-029
文摘The performance of a classical damping matrix, constructed either from the use of initial structural properties or current structural properties, in the step-by-step solution of a nonlinear multiple degree of freedom （MDOF） system is analytically evaluated. The analytical results are confirmed by numerical examples. Consequently, some conclusions are drawn from these analytical results that might be considered as rough guidelines for practical applications. It is found that a classical damping matrix constructed from initial structural properties is adequate for practical applications, since it has approximately the same damping effect as obtained by current structural properties and is more efficient in terms of computing.
基金Supported by National Natural Science Foundation of China(11201415,11571159)Program for New Century Excellent Talents in Fujian Province University(JA14191)
文摘In this paper, we prove the existence of global classical solutions to time-dependent Ginzburg-Landau（TDGL） equations. By the properties of Besov and Sobolev spaces, together with the energy method, we establish the global existence and uniqueness of classical solutions to the initial boundary value problem for time-dependent Ginzburg-Landau equations.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10974068 and 10574057)
文摘This paper uses the classical ensemble method to study the double ionization of a 2-dimensional （2D） model helium atom interacting with an elliptically polarized laser pulse. The classical ensemble calculation demonstrates that the ratio of double to single ionization decreases with the increasing ellipticity of the driving field. The classical scenario shows that there are hardly any e--e recollisions with the circularly polarized laser pulse. The double ionization probability is studied for linearly and circularly polarized laser pulses. The classical numerical results are consistent with the semiclassical rescattering mechanism and in agreement with the experimental results and the quantum calculations qualitatively.
基金supported in part by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)the Science Foundation in Higher Education of Henan(18A110036)
文摘In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation(δ2 gij)/δt2+μ/((1 + t)λ)(δ gij)/δt=-2 Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ ≤ 1, μ 〉 λ + 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R(t, x) of the solution metric gij remains uniformly bounded.
文摘This paper explores some problems concerning ancient Chinese classical linguistics. It is maintained that there are both similarities and obvious differences between it and western philology. The development of ancient Chinese linguistics from the Pre-Qin Period to the Qing Dynasty can be divided into five stages: the embryonic stage, the stage for laying the foundation, the preparatory stage, the stage of growth, and the stage of overall revival and prosperity. The literature produced during this period can be grouped in six categories: gloss exegesis, orthographical form and meaning, phonological form and meaning, historical phonology, grammar on function words, and rhetoric. It is pointed out that, in researching the theoretical history of ancient Chinese linguistics, great importance should be attached to the consistency between history and theoretical logic, cultural background as reference, and textual research methodology.
文摘In recent years,with the prevailing of Chinese traditional culture,the related“classic education(经典教育jingdianjiaoyu)”debate ensued.Some scholars strongly oppose the“classical education”and think that make children memorize mechanicallyand forced recite,without understand about Confucian classes deviate from the modern“children’s center-based education”and“ideas violate scientific”and to be“an ancient and retrogression”,“ignorance of cultural conservatism”.They advocating that“things other than children’s lives cannot be forcibly entered into the lives of children,”otherwise it will be“a killing of childhood innocence and stifling the lives of children”,and imprisonment of children’s life.To sum up this fierce argument,the main issues of debate are generally not out of the following four aspects:(1)why do we need classic enlightenment?(2)the purpose and utility of the classic enlightenment?(3)the content and methods of classic enlightenment?(4)the timing of the classic enlightenment?In response to these four points of view,Mr.Wangfuzhi,who was 400 years ago,also put forward his own ideas.This article is not intended to participate in this controversy.Instead,it wants to understand Wangfuzhi’s“ideas of classical enlightenment”to understand how the ancients advocated these four issues.For modern people’s reference.
文摘In non-classical thermoelastic solids incorporating internal rotation and conjugate Cauchy moment tensor the mechanical deformation is reversible. This suggests that within the realm of linear mathematical models that only consider small strains and small deformation the mechanical deformation is reversible. Hence, it is possible to recast the conservation and balance laws along with constitutive theories in a form that adjoint A* of the differential operator A in mathematical model is same as the differential operator A. This holds regardless of whether we consider an initial value problem (IVP) (when the integrals over open boundary are neglected) or boundary value problem (BVP). Thus, in such cases Galerkin method with weak form (GM/WF) for BVPs and space-time Galerkin method with weak form (STGM/WF) for IVPs are highly meritorious due to the fact that: 1) the integral form for BVPs is variationally consistent (VC) and 2) the space-time integral forms for IVP are space time variationally consistent (STVC). The consequence of VC and STVC integral forms is that the resulting coefficient matrices are symmetric and positive definite ensuring unconditionally stable computational processes for both BVPs and IVPs. Other benefits of GM/WF and space-time GM/WF are simplicity of specifying boundary conditions and initial conditions, especially traction boundary conditions and initial conditions on curved boundaries due to self-equilibrating nature of the sum of secondary variables that only exist in GM/WF due to concomitant. In fact, zero traction conditions are automatically satisfied in GM/WF, hence need not be specified at all. While VC and STVC feature also exists in least squares process (LSP) and space-time least squares finite element processes (STLSP) for BVPs and IVPs, the ease of specifying traction boundary conditions feature in GM/WF and STGM/WF is highly meritorious compared to LSP and STLSP in which zero traction conditions need to be explicitly specified. A disadvantage of GM/WF and STGM/ WF is that the mathematical models (momentum equations) needed in the desired form contain higher order derivatives of displacements (upto fourth order), hence necessitate use of higher order spaces in their solution. As well known, this problem can be easily overcome in LSP and STLSP by introduction of auxiliary equations and auxiliary variables, thus keeping the highest orders of the derivatives of the dependent variables to one or any other desired order. A serious disadvantage of this approach in LSP is the significant increase in the number of dependent variables, hence poor computational efficiency. In this paper we consider non-classical continuum models for internally polar linear elastic solids in which internal rotations due to displacement gradient tensor (hence internal polar physics) are considered in the conservation and the balance laws and the constitutive theories. For simplicity, we only consider isothermal case;hence energy equation is not part of mathematical model. When using mathematical models derived in displacements in GM/WF and LSP in constructing integral forms, we note that in GM/WF the number of dependent variables is reduced drastically (only three in R3), whereas in case of first order systems used in LSP and STLSP we may have as many as 22 dependent variables for isothermal case. Thus, GM/WF results in dramatic improvement in computational efficiency as well as accuracy when minimally conforming spaces are used for approximations. In this paper we only consider mathematical model in R2 for BVPs (for simplicity). Mathematical models for IVP and BVP in R3 will be considered in subsequent paper. The integral form is derived in R2 using GM/WF. Numerical examples are presented using GM/WF and LSP to demonstrate advantages of finite element process derived using integral form based on GM/WF for non-classical linear theories for solids incorporating internal rotations due to displacement gradient tensor.
基金Sponsored by General Project of Natural Science Foundation of Beijing (8202017)Youth Talent Support Program of 2018 Beijing Municipal University Academic Human Resources Development (PXM2018_014212_000043)。
文摘Realizing “carbon peaking” and “carbon neutrality” is a major strategic decision made by China to coordinate domestic and international situations.In order to achieve the “double carbon” goal,it is also necessary for relevant practitioners to actively put into practice to improve the participation of residents and advocate low carbon life while formulating the policy action plan.Community is an important place for human activities and one of the main spatial types of carbon emissions in cities.Doing a good job in planning energy conservation and emission reduction in the community plays an important role in achieving the “double carbon” goal.Through the analysis of classic low carbon community practice cases at home and abroad,6 planning and design methods for low carbon community are concluded,and the development status of low carbon community in China is reflected and summarized.
基金Supported by the National Natural Science Foundation of China(No10604012)
文摘The Ca＋CH3I→CaI＋CH3 reaction system has been studied with the quasi-classical trajectory method on the extended Lond-Eyring-Polanyi-Sato（LEPS） potential energy surface. At collision energy Ecol=10.78 kJ/mol, the calculated results show that the CaI vibrational population peaks are located at v=2. The calculated cross section decreases slowly with the collision energy increasing. The angle product distributions tend toward backward scattering. The calculated （P2（J^1·K）） values deviate slightly from-0.5 and decrease with increasing collision energy. The Quasiclassical trajectory calculation（QCT） results are in reasonable agreement with experimental data. Moreover, the dynamics of the reaction has been discussed.
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.
