This survey is dedicated to the memory of Professor Jiarong Yu,who recently passed away.It is concerned by a topic of which he was fond,an interest shared by myself:the analytic theory of Dirichlet series.
Analytical theories of the geodesic acoustic mode （GAM） are reviewed in the small- and large-orbit drift width limits, respectively. Different physics pictures in these two limits are displayed. As an example, these...Analytical theories of the geodesic acoustic mode （GAM） are reviewed in the small- and large-orbit drift width limits, respectively. Different physics pictures in these two limits are displayed. As an example, these two analytical methods are employed to investigate the plasma shaping effect on the frequency and collisionless damping rate of the GAM.展开更多
In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-...In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-function matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy. Numerical results show that the proposed new model can pass the Co- 1 patch test with excellent precision, does not exhibit extra zero energy modes and can cap- ture the scale effects of microstructure.展开更多
Study of the general theory of law,as an independent branch of legal research,originated in Germany in the mid to late 19th century,and thereafter became a widely propagated and well-developed subject in countries suc...Study of the general theory of law,as an independent branch of legal research,originated in Germany in the mid to late 19th century,and thereafter became a widely propagated and well-developed subject in countries such as the UK and the US.Scholars from the Soviet Union combined the general theory of law with Marxist philosophy and adapted it from an analytical legal theory to a social legal theory.The inheritance and development of the general theory of law in China went through three stages.Specifically,from the 1950s to the early 1960s,the jurisprudence community fully adopted the legal theories promoted by the Soviet Union;from the early 1980s to the late 1990s,the studies reflected upon past theories and sought advancement;and from the late 1990s to present,research has adopted a more open and innovative approach.In addition,the philosophy of law and other interdisciplinary subjects have gradually become dominant research paradigms.A review and compilation based on the evolution of theories of legal relations showed that the study of the general theory of law in China is closely associated to the historical rate of progress of the practice of rule of law and jurisprudence in China.The overall framework of the research is deeply influenced by the model of“theories of the Soviet+civil-law prototypes”.In addition,the research methods have evolved from investigations utilizing a single approach to processes combining various approaches.The general theory of law is far from a“relic of history,”and corresponding in-depth research is recommended for future jurisprudence study in China.展开更多
By using the iterative method in functional theory, an analytic expression of the Poisson-Boltzmann equation (PB eq.), which describes the distribution of the potential of electrical double layer of a spherical micell...By using the iterative method in functional theory, an analytic expression of the Poisson-Boltzmann equation (PB eq.), which describes the distribution of the potential of electrical double layer of a spherical micelle, has been carried out under the general potential condition for the first time. The method also can give the radius, the surface potential, and the thickness of the layer.展开更多
Textile-reinforced concrete(TRC)is a new high performance cementitious composite material,which not only has superior corrosion resistance but also can effectively limit the development of concrete cracks and make the...Textile-reinforced concrete(TRC)is a new high performance cementitious composite material,which not only has superior corrosion resistance but also can effectively limit the development of concrete cracks and make the crack width and spacing of concrete become smaller.However,due to the brittle feature of fiber materials,the TRC structural member has no distinct failure symptom when it arrives at its ultimate load.At the same time,ordinary reinforced concrete(RC)elements have large dead weight and can not efficiently restrict the expansion of the main crack of structures because of the restriction of their special cover thickness.In order to overcome the disadvantages of both the TRC and the RC,a new architecture reinforced with textile-combined steel is proposed in this study,making full use of the advantages of the above two structures.The cover concrete at the tension zone of an RC element is partially replaced with TRC and thus the steel reinforcements replaced with textiles are subtracted.Compared with the old one,the new structure has less dead weight and has the merits of service safety and good durability.The flexural development process of the proper beam with this new structure is investigated in this paper and based on the plane section assumption,analytical equations are derived by using nonlinear analysis theory,including the load-carrying capacity at different stages and moment-curvature relationship and mid-span deflection during the entire loading process.Comparison between the calculated and the experimental results reveals satisfactory agreement and thus verifies the feasibility of the equations.展开更多
A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method.However,extra solutions would occur when solving the constraint equations of mechanism kinematics unless t...A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method.However,extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate.In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism,spherical analytical theory is employed to construct the constraint equations.Firstly,the mechanism is divided into a four-bar loop and a two-bar unit.On the basis of the decomposition,vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation.Secondly,the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism.Thirdly,the constraint equations are solved by using Bezout’ s elimination method for forward analysis and Sylvester’ s resultant elimination method for inverse kinematics respectively.By the aid of computer symbolic systems,Mathematica and Maple,symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained.Finally,numerical examples of forward and inverse analysis are presented to illustrate the proposed approach.The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature,and can be readily eliminated and solved.展开更多
By Green＇s function method we show that the water hammer （WH） can be analytically predicted for both laminar and turbulent flows （for the latter, with an eddy vis- cosity depending solely on the space coordinates...By Green＇s function method we show that the water hammer （WH） can be analytically predicted for both laminar and turbulent flows （for the latter, with an eddy vis- cosity depending solely on the space coordinates）, and thus its hazardous effect can be rationally controlled and mini- mized. To this end, we generalize a laminar water hammer equation of Wang et al. （J. Hydrodynamics, B2, 51, 1995） to include arbitrary initial condition and variable viscosity, and obtain its solution by Green＇s function method. The pre- dicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and, by adjusting the eddy viscosity coefficient, experimentally measured turbulent flow data. Optimal WH control principle is thereby constructed and demonstrated.展开更多
We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and...We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.展开更多
We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution.The general algorithms of analytical energy derivatives for the specific propert...We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution.The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory(TDDFT).The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown.It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency.The computational cost for a TDDFT excited-state Hessian calculation is only 2–3 times as that for the DFT ground-state Hessian calculation.With the low computational complexity of the developed analytical approaches,it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies,vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission,and resonance Raman spectroscopies for medium-to large-sized systems.展开更多
On the level of the time-dependent hybrid density functional theory, the one- and two-photon absorption properties of a series of symmetric 4-bis{2-[4-（2-aryl） phenyl]vinyl）-2,5-bisdialkoxybenzenes are studied resp...On the level of the time-dependent hybrid density functional theory, the one- and two-photon absorption properties of a series of symmetric 4-bis{2-[4-（2-aryl） phenyl]vinyl）-2,5-bisdialkoxybenzenes are studied respectively utilizing the analytic response theory and the few-state model methods. The calculated results show that the planarity of the geometrical structure plays a great role in enhancing the linear and nonlinear optical abilities of the molecule. However the effect of the length of the chain linked to the π-centre on the optical property is very little. For the investigated compounds, the A-π-A type charge-transfer molecules display more superior one- and two-photon absorption characteristics than the D-π-D type ones. Furthermore, the two-photon absorption results by use of few-state model are generally consistent with those by analytic response theory, demonstrating the reliability of the few-state model for evaluating the two-photon absorption cross section. The numerical simulations are in good agreement in tendency with the available experimental measurements.展开更多
This paper has theoretically designed a series of aggregate polymers on the basis of several para-nitroaniline monomers by hydrogen-bond interactions. At the level of time-dependent hybrid density functional theory, i...This paper has theoretically designed a series of aggregate polymers on the basis of several para-nitroaniline monomers by hydrogen-bond interactions. At the level of time-dependent hybrid density functional theory, it has optimized their geometrical structures and studied their two-photon absorption （TPA） properties by using analytical response theory. The calculated results exhibit that the aggregation effects not only bring out the conaiderable red shift of the excited energies but also greatly enhance the TPA intensities of the aggregate polymers in comparison with the para-nitroaniline monomer. The aggregate configurations also have an important influence on the TPA abilities of the polymers; the trimer has the largest TPA cross section. The electron transitions between the molecular orbits involving the strong TPA excitations of the trimer are depicted to illuminate the relationship between the intermolecular charge transfer and the TPA property.展开更多
The linear and nonlinear optical properties of two metalloporphyrin complexes formed by the complementary coordination of central zinc or magnesium ions to the ligand 5, 10, 15-tri-（p-tolyl）-20-phenylethynylporphyri...The linear and nonlinear optical properties of two metalloporphyrin complexes formed by the complementary coordination of central zinc or magnesium ions to the ligand 5, 10, 15-tri-（p-tolyl）-20-phenylethynylporphyrin are theo- retically investigated by using the analytic response theory at the density functional theory level. The results indicate that the studied complexes present more symmetric geometry structures than the ligand. The charge-transfer states of the two complexes in the lower energy region are all almost degenerate but those of the ligand are well separated. The ratio of the two-photon absorption cross sections of the ligand, zinc-porphyrin and magnesium-porphyrin com- plexes is 1.0：1.5：1.8, demonstrating that the two-photon absorption capability can be greatly increased when the ligand is coordinated with a metal ion. Moreover, several physical micro-mechanisms including electron transitions and in- tramolecular charge-transfer processes are discussed to explore the differences in optical property between the ligand and two complexes.展开更多
We provide analytical solutions to the problems of a circular bending of a beam in plane strain and the torsion of a non-circular cross-section beam, the beams obeying a second-gradient elasticity law proposed by the ...We provide analytical solutions to the problems of a circular bending of a beam in plane strain and the torsion of a non-circular cross-section beam, the beams obeying a second-gradient elasticity law proposed by the author, following a previous suggestion of delrlsola et al. （2009）. The motivation was to find benchmark analytical solutions that can serve to grasp the physical foundations of second gradient elasticity laws for heterogeneous materials. The analytical solution of the circular beam problem presents the additional advantage to establish some nice properties on the unknown second gradient elastic moduli introduced by Enakoutsa （2014） model and the classical elasticity constants for both incompressible and compressible heterogeneous elastic materials. A framework to find the elastic moduli of the new model is also proposed.展开更多
Is it possible that the current cosmic accelerating expansion will turn into a decelerating one？ Can this transition be realized by some viable theoretical model that is consistent with the standard Big Bang cosmolog...Is it possible that the current cosmic accelerating expansion will turn into a decelerating one？ Can this transition be realized by some viable theoretical model that is consistent with the standard Big Bang cosmology？ We study a class of phenomeno- logical models with a transient acceleration, based on a dynamical dark energy with a very general form of equation of state Pde = αPde -- βpdem. It mimics the cosmolog- ical constant αde → const for a small scale factor a, and behaves as a barotropic gas with pde → α-3（α＋1） with α 〉 0 for large a. The cosmic evolution of four models in the class has been examined in detail, and all yield a smooth transient acceleration. Depending on the specific model, the future universe may be dominated by either dark energy or by matter. In two models, the dynamical dark energy can be explicitly real- ized by a scalar field with an analytical potential V（O）. Moreover, a statistical analysis shows that the models can be as robust as ACDM in confronting the observational data of Type Ia supernovae, cosmic microwave background （CMB） and baryon acoustic os- cillation. As improvements over previous studies, our models overcome the problem of over-abundance of dark energy during early eras, and satisfy the constraints on dark energy from WMAP observations of CMB.展开更多
General one-loop formulas for loop-induced processes gg/γγ → Φ_(i)Φ_(j) with Φ_(i)Φ_(j)= hh, hH, HH are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs E...General one-loop formulas for loop-induced processes gg/γγ → Φ_(i)Φ_(j) with Φ_(i)Φ_(j)= hh, hH, HH are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs Extensions of the Standard Model, e.g., Inert Doublet Higgs, Two Higgs Doublet, Zee-Babu, and Triplet Higgs Models. Analytic expressions for one-loop form factors are expressesd in terms of the basic scalar one-loop two-, three-, and fourpoint functions following the output format of the packages LoopTools and Collier. Hence, physical results can be evaluated numerically using one of these packages. The analytic results are tested using several checks such as the ultraviolet finiteness and infrared finiteness of the one-loop amplitudes. Furthermore, the amplitudes obey the ward identity due to massless gauge bosons in the initial states. This identity is also verified numerically. Regarding applications, we present the phenomenological results for the investigated processes in the Zee-Babu model as a typical example. In particular, production cross-sections for the processes γγ → hh are scanned over the parameter space of the Zee-Babu Model.展开更多
The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The ma...The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.展开更多
Given integers m and f,let Sn(m,f)be the set consisting of all integers e such that every n-vertex graph with e edges contains an m-vertex induced subgraph with f edges,and let σ(m,f)=lim sup_(n→∞)|S_(n)(m,f)|/(_(2...Given integers m and f,let Sn(m,f)be the set consisting of all integers e such that every n-vertex graph with e edges contains an m-vertex induced subgraph with f edges,and let σ(m,f)=lim sup_(n→∞)|S_(n)(m,f)|/(_(2)^(n)).As a natural extension of an extremal problem of Erdös,this was investigated by Erd˝os,Füredi,Rothschild and Sós 20 years ago.Their main result indicates that integers in S_(n)(m,f)are rare for most pairs(m,f),though they also found infinitely many pairs(m,f)whose σ(m,f)is a fixed positive constant.Here we aim to provide some improvements on this study.Our first result shows that σ(m,f)≤1/2 holds for all but finitely many pairs(m,f)and the constant 1/2 cannot be improved.This answers a question of Erdös et al.Our second result considers infinitely many pairs(m,f)of special forms,whose exact values of σ(m,f)were conjectured by Erdös et al.We partially solve this conjecture(only leaving two open cases)by making progress on some constructions which are related to number theory.Our proofs are based on the research of Erdös et al.and involve different arguments in number theory.We also discuss some related problems.展开更多
The iterative method in functional analysis is applied to looking for asolution of the Poisson-Boltzmann equation in order to describe the problems of the distribution ofthe potentials in the electric double layer(EDL...The iterative method in functional analysis is applied to looking for asolution of the Poisson-Boltzmann equation in order to describe the problems of the distribution ofthe potentials in the electric double layer(EDL)inside the water pool for a cylindrical inversemicelle.Potentials as a function of the position of a particular point in EDL are computed,whichdisplay a quantitative agreement with those from earlier calculation of Debye and Huckel in the caseof low potentials.But it is also shown that in the higher-potential range the iterativecalculations can give more accurate results.These results indicate the utility of this functionalanalysis technique in the description of the properties of EDL for a cylindrical inverse micelle.展开更多
文摘This survey is dedicated to the memory of Professor Jiarong Yu,who recently passed away.It is concerned by a topic of which he was fond,an interest shared by myself:the analytic theory of Dirichlet series.
基金supported by National Natural Science Foundation of China (No. 10990214)the Major State Basic Research Development Program of China (Nos. 2009GB105002, 2008GB717804)the JSPS-CAS Core University Program in Plasma and Nuclear Fusion
文摘Analytical theories of the geodesic acoustic mode （GAM） are reviewed in the small- and large-orbit drift width limits, respectively. Different physics pictures in these two limits are displayed. As an example, these two analytical methods are employed to investigate the plasma shaping effect on the frequency and collisionless damping rate of the GAM.
基金supported by the Fundamental Research Funds for the Central Universities (DUT16LK27,DUT17RC(4)59)the National Natural Science Foundation of China (No.11472071)
文摘In this paper, a 3-node triangular element for couple stress theory is proposed based on the assumed stress quasi-conforming method. The formulation starts from polynomial approx- imation of stresses. Then the stress-function matrix is treated as the weighted function to weaken the strain-displacement equations. Finally, the string-net functions are introduced to calculate strain integration and the stress smooth technique is adopted to improve the stress accuracy. Numerical results show that the proposed new model can pass the Co- 1 patch test with excellent precision, does not exhibit extra zero energy modes and can cap- ture the scale effects of microstructure.
基金the phased achievement of an ongoing project sponsored by the“Qian Duansheng Support Plan for Outstanding Scholars of China University of Political Science and Law”.
文摘Study of the general theory of law,as an independent branch of legal research,originated in Germany in the mid to late 19th century,and thereafter became a widely propagated and well-developed subject in countries such as the UK and the US.Scholars from the Soviet Union combined the general theory of law with Marxist philosophy and adapted it from an analytical legal theory to a social legal theory.The inheritance and development of the general theory of law in China went through three stages.Specifically,from the 1950s to the early 1960s,the jurisprudence community fully adopted the legal theories promoted by the Soviet Union;from the early 1980s to the late 1990s,the studies reflected upon past theories and sought advancement;and from the late 1990s to present,research has adopted a more open and innovative approach.In addition,the philosophy of law and other interdisciplinary subjects have gradually become dominant research paradigms.A review and compilation based on the evolution of theories of legal relations showed that the study of the general theory of law in China is closely associated to the historical rate of progress of the practice of rule of law and jurisprudence in China.The overall framework of the research is deeply influenced by the model of“theories of the Soviet+civil-law prototypes”.In addition,the research methods have evolved from investigations utilizing a single approach to processes combining various approaches.The general theory of law is far from a“relic of history,”and corresponding in-depth research is recommended for future jurisprudence study in China.
基金We wish to thank to the National Natural Science Foundation of China(to grant No,29903006 and 29973023)the Visiting Scholar Foundation of Key Laboratory in University of China for financial suppor.
文摘By using the iterative method in functional theory, an analytic expression of the Poisson-Boltzmann equation (PB eq.), which describes the distribution of the potential of electrical double layer of a spherical micelle, has been carried out under the general potential condition for the first time. The method also can give the radius, the surface potential, and the thickness of the layer.
基金support from the Key Program of the National Natural Science Foundation of China(Grant No.50438010)
文摘Textile-reinforced concrete(TRC)is a new high performance cementitious composite material,which not only has superior corrosion resistance but also can effectively limit the development of concrete cracks and make the crack width and spacing of concrete become smaller.However,due to the brittle feature of fiber materials,the TRC structural member has no distinct failure symptom when it arrives at its ultimate load.At the same time,ordinary reinforced concrete(RC)elements have large dead weight and can not efficiently restrict the expansion of the main crack of structures because of the restriction of their special cover thickness.In order to overcome the disadvantages of both the TRC and the RC,a new architecture reinforced with textile-combined steel is proposed in this study,making full use of the advantages of the above two structures.The cover concrete at the tension zone of an RC element is partially replaced with TRC and thus the steel reinforcements replaced with textiles are subtracted.Compared with the old one,the new structure has less dead weight and has the merits of service safety and good durability.The flexural development process of the proper beam with this new structure is investigated in this paper and based on the plane section assumption,analytical equations are derived by using nonlinear analysis theory,including the load-carrying capacity at different stages and moment-curvature relationship and mid-span deflection during the entire loading process.Comparison between the calculated and the experimental results reveals satisfactory agreement and thus verifies the feasibility of the equations.
基金supported by National Natural Science Foundation of China(Grant No.50975186)
文摘A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method.However,extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate.In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism,spherical analytical theory is employed to construct the constraint equations.Firstly,the mechanism is divided into a four-bar loop and a two-bar unit.On the basis of the decomposition,vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation.Secondly,the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism.Thirdly,the constraint equations are solved by using Bezout’ s elimination method for forward analysis and Sylvester’ s resultant elimination method for inverse kinematics respectively.By the aid of computer symbolic systems,Mathematica and Maple,symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained.Finally,numerical examples of forward and inverse analysis are presented to illustrate the proposed approach.The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature,and can be readily eliminated and solved.
基金supported in part by the National Natural Science Foundation of China,Key Project (10532010)the Ministry of Science and Technology of China’s Turbulence Program(2009CB724101)+1 种基金the National Basic Research Program of China(2007CB714600)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(10921202/A0204)
文摘By Green＇s function method we show that the water hammer （WH） can be analytically predicted for both laminar and turbulent flows （for the latter, with an eddy vis- cosity depending solely on the space coordinates）, and thus its hazardous effect can be rationally controlled and mini- mized. To this end, we generalize a laminar water hammer equation of Wang et al. （J. Hydrodynamics, B2, 51, 1995） to include arbitrary initial condition and variable viscosity, and obtain its solution by Green＇s function method. The pre- dicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and, by adjusting the eddy viscosity coefficient, experimentally measured turbulent flow data. Optimal WH control principle is thereby constructed and demonstrated.
基金supported by the National Natural Science Foundation of China(11571132,12301542)the Natural Science Foundation of Hubei(2022CFB725)the Natural Science Foundation of Yichang(A23-2-027)。
文摘We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.
基金support from the National Natural Science Foundation of China(21073168,21290193)The National Basic Research Program of China(2011CB808501)is acknowledged
文摘We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution.The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory(TDDFT).The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown.It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency.The computational cost for a TDDFT excited-state Hessian calculation is only 2–3 times as that for the DFT ground-state Hessian calculation.With the low computational complexity of the developed analytical approaches,it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies,vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission,and resonance Raman spectroscopies for medium-to large-sized systems.
基金Project supported by the State Key Development Program for Basic Research of China(Grant No.2006CB806000)the Open Fund of the State Key Laboratory of High Field Laser Physics(Shanghai Institute of Optics and Fine Mechanics),Higher Educational Science and Technology Program of Shandong Province(Grant No.J09LA13)
文摘On the level of the time-dependent hybrid density functional theory, the one- and two-photon absorption properties of a series of symmetric 4-bis{2-[4-（2-aryl） phenyl]vinyl）-2,5-bisdialkoxybenzenes are studied respectively utilizing the analytic response theory and the few-state model methods. The calculated results show that the planarity of the geometrical structure plays a great role in enhancing the linear and nonlinear optical abilities of the molecule. However the effect of the length of the chain linked to the π-centre on the optical property is very little. For the investigated compounds, the A-π-A type charge-transfer molecules display more superior one- and two-photon absorption characteristics than the D-π-D type ones. Furthermore, the two-photon absorption results by use of few-state model are generally consistent with those by analytic response theory, demonstrating the reliability of the few-state model for evaluating the two-photon absorption cross section. The numerical simulations are in good agreement in tendency with the available experimental measurements.
基金Project supported by the State Key Development Program for Basic Research of China(Grant No.2006CB806000)the Open Fund of the State Key Laboratory of High Field Laser Physics(Shanghai Institute of Optics and Fine Mechanics)Natural Science Foundation of Shandong Province of China(Grant No.Z2007A02)
文摘This paper has theoretically designed a series of aggregate polymers on the basis of several para-nitroaniline monomers by hydrogen-bond interactions. At the level of time-dependent hybrid density functional theory, it has optimized their geometrical structures and studied their two-photon absorption （TPA） properties by using analytical response theory. The calculated results exhibit that the aggregation effects not only bring out the conaiderable red shift of the excited energies but also greatly enhance the TPA intensities of the aggregate polymers in comparison with the para-nitroaniline monomer. The aggregate configurations also have an important influence on the TPA abilities of the polymers; the trimer has the largest TPA cross section. The electron transitions between the molecular orbits involving the strong TPA excitations of the trimer are depicted to illuminate the relationship between the intermolecular charge transfer and the TPA property.
基金supported by the National Natural Science Foundation of China (Grant No. 10974121)the Open Fund of the State Key Laboratory of High Field Laser Physics (Shanghai Institute of Optics and Fine Mechanics)Higher Educational Science and Technology Program of Shandong Province, China (Grant No. J09LA13)
文摘The linear and nonlinear optical properties of two metalloporphyrin complexes formed by the complementary coordination of central zinc or magnesium ions to the ligand 5, 10, 15-tri-（p-tolyl）-20-phenylethynylporphyrin are theo- retically investigated by using the analytic response theory at the density functional theory level. The results indicate that the studied complexes present more symmetric geometry structures than the ligand. The charge-transfer states of the two complexes in the lower energy region are all almost degenerate but those of the ligand are well separated. The ratio of the two-photon absorption cross sections of the ligand, zinc-porphyrin and magnesium-porphyrin com- plexes is 1.0：1.5：1.8, demonstrating that the two-photon absorption capability can be greatly increased when the ligand is coordinated with a metal ion. Moreover, several physical micro-mechanisms including electron transitions and in- tramolecular charge-transfer processes are discussed to explore the differences in optical property between the ligand and two complexes.
文摘We provide analytical solutions to the problems of a circular bending of a beam in plane strain and the torsion of a non-circular cross-section beam, the beams obeying a second-gradient elasticity law proposed by the author, following a previous suggestion of delrlsola et al. （2009）. The motivation was to find benchmark analytical solutions that can serve to grasp the physical foundations of second gradient elasticity laws for heterogeneous materials. The analytical solution of the circular beam problem presents the additional advantage to establish some nice properties on the unknown second gradient elastic moduli introduced by Enakoutsa （2014） model and the classical elasticity constants for both incompressible and compressible heterogeneous elastic materials. A framework to find the elastic moduli of the new model is also proposed.
基金Supported by the National Natural Science Foundation of China
文摘Is it possible that the current cosmic accelerating expansion will turn into a decelerating one？ Can this transition be realized by some viable theoretical model that is consistent with the standard Big Bang cosmology？ We study a class of phenomeno- logical models with a transient acceleration, based on a dynamical dark energy with a very general form of equation of state Pde = αPde -- βpdem. It mimics the cosmolog- ical constant αde → const for a small scale factor a, and behaves as a barotropic gas with pde → α-3（α＋1） with α 〉 0 for large a. The cosmic evolution of four models in the class has been examined in detail, and all yield a smooth transient acceleration. Depending on the specific model, the future universe may be dominated by either dark energy or by matter. In two models, the dynamical dark energy can be explicitly real- ized by a scalar field with an analytical potential V（O）. Moreover, a statistical analysis shows that the models can be as robust as ACDM in confronting the observational data of Type Ia supernovae, cosmic microwave background （CMB） and baryon acoustic os- cillation. As improvements over previous studies, our models overcome the problem of over-abundance of dark energy during early eras, and satisfy the constraints on dark energy from WMAP observations of CMB.
基金supported by Vietnam National Foundation for Science and Technology Development (103.01-2023.16)。
文摘General one-loop formulas for loop-induced processes gg/γγ → Φ_(i)Φ_(j) with Φ_(i)Φ_(j)= hh, hH, HH are presented in this paper. The analytic expressions evaluated in this study are valid for a class of Higgs Extensions of the Standard Model, e.g., Inert Doublet Higgs, Two Higgs Doublet, Zee-Babu, and Triplet Higgs Models. Analytic expressions for one-loop form factors are expressesd in terms of the basic scalar one-loop two-, three-, and fourpoint functions following the output format of the packages LoopTools and Collier. Hence, physical results can be evaluated numerically using one of these packages. The analytic results are tested using several checks such as the ultraviolet finiteness and infrared finiteness of the one-loop amplitudes. Furthermore, the amplitudes obey the ward identity due to massless gauge bosons in the initial states. This identity is also verified numerically. Regarding applications, we present the phenomenological results for the investigated processes in the Zee-Babu model as a typical example. In particular, production cross-sections for the processes γγ → hh are scanned over the parameter space of the Zee-Babu Model.
文摘The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself.
基金supported by Hong Kong RGC Grant GRF 16308219 and Hong Kong RGC Grant ECS 26304920supported by the National Key R and D Program of China 2020YFA0713100+4 种基金National Natural Science Foundation of China Grant 12125106Innovation Program for Quantum Science and Technology 2021ZD0302904Anhui Initiative in Quantum Information Technologies Grant AHY150200Research supported in part by NSFC Grant 11922113National Key Research and Development Program of China 2021YFA1000700.
文摘Given integers m and f,let Sn(m,f)be the set consisting of all integers e such that every n-vertex graph with e edges contains an m-vertex induced subgraph with f edges,and let σ(m,f)=lim sup_(n→∞)|S_(n)(m,f)|/(_(2)^(n)).As a natural extension of an extremal problem of Erdös,this was investigated by Erd˝os,Füredi,Rothschild and Sós 20 years ago.Their main result indicates that integers in S_(n)(m,f)are rare for most pairs(m,f),though they also found infinitely many pairs(m,f)whose σ(m,f)is a fixed positive constant.Here we aim to provide some improvements on this study.Our first result shows that σ(m,f)≤1/2 holds for all but finitely many pairs(m,f)and the constant 1/2 cannot be improved.This answers a question of Erdös et al.Our second result considers infinitely many pairs(m,f)of special forms,whose exact values of σ(m,f)were conjectured by Erdös et al.We partially solve this conjecture(only leaving two open cases)by making progress on some constructions which are related to number theory.Our proofs are based on the research of Erdös et al.and involve different arguments in number theory.We also discuss some related problems.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.20473034 and 20573048)the Open Project Program of the Key Laboratory of Industrial Biotechnology,Ministry of Education of China(Grant No.KLIB-KF200504).
文摘The iterative method in functional analysis is applied to looking for asolution of the Poisson-Boltzmann equation in order to describe the problems of the distribution ofthe potentials in the electric double layer(EDL)inside the water pool for a cylindrical inversemicelle.Potentials as a function of the position of a particular point in EDL are computed,whichdisplay a quantitative agreement with those from earlier calculation of Debye and Huckel in the caseof low potentials.But it is also shown that in the higher-potential range the iterativecalculations can give more accurate results.These results indicate the utility of this functionalanalysis technique in the description of the properties of EDL for a cylindrical inverse micelle.
