This is a writeup of lectures delivered at the Asian Pacific Introductory School on Superstring and Related Topics in Beijing(2006)and an expanded version of these lectures given at the Third Summer School on Strings,...This is a writeup of lectures delivered at the Asian Pacific Introductory School on Superstring and Related Topics in Beijing(2006)and an expanded version of these lectures given at the Third Summer School on Strings,Fields and Holography in Nanjing(2023).It aims to provide both a historical and pedagogical account of developments in finding 1/2 Bogomol?nyi–Prasad–Sommerfield(BPS)extended string solitons during the early stage of the so-called second string revolution,before which these objects were thought to be unrelated to strings.Nonsupersymmetric solutions related to brane/anti brane systems or non-BPS systems are also discussed.展开更多
Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-represent...Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-representation is either a string representation or a band representation by using the coefficient quivers.It is worth noting that for a given band and a positive integer,there exists a unique band representation up to isomorphism.展开更多
In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue...In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.展开更多
During drilling operations,cyclic loading is exerted on the wellbore wall by the vibrations of the drill string.This loading could lead to rock fatigue,which in turn might result in wellbore failure.In this study,a nu...During drilling operations,cyclic loading is exerted on the wellbore wall by the vibrations of the drill string.This loading could lead to rock fatigue,which in turn might result in wellbore failure.In this study,a numerical model is developed to simulate the effects of repeated loading on rock fatigue and failure.The simulation is based on an elasto-plastic constitutive model coupled with a damage mechanics approach,which allows us to examine the wellbore instability due to drill string vibrations.The model is verified with the existing data in the literature related to experiments on impact of a steel ball against a curved wall.The findings indicate that cyclic loading increases the development of plastic strain around the wellbore significantly compared to static conditions,promoting rock fatigue.Furthermore,the cyclic loading expands the radius of the yielded zone substantially,a critical factor for maintaining wellbore integrity.The proposed model can be used to evaluate the wellbore stability under repetitive loading caused by the drill string action.展开更多
A new phenomenological model(axionic QCD string)is constructed to study the topological issues of the QCD vacuum and hadron structure.It provides an alternative way of tackling the Strong CP problem,which is different...A new phenomenological model(axionic QCD string)is constructed to study the topological issues of the QCD vacuum and hadron structure.It provides an alternative way of tackling the Strong CP problem,which is different from the traditional Peccei–Quinn approach.Neither new particle nor extra symmetry is introduced,and the role of the Peccei–Quinn axion is played by a quasiparticle arising from the phase of the quark condensate,dubbed as axionic excitation.The derivative of this excitation field is decomposed into a regular part and a singular part,and the latter contains vorticity from the string configuration.A hidden gauge symmetry is revealed in this decomposition and vorticity is represented by an emergent gauge field associated with anomalies.These components,together with the anomaly-inflow mechanism,complete the effective Lagrangian description for the axionic QCD string.展开更多
In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the...In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes(QNMs)and shadow cast.To do this,we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins:massless scalar field,electromagnetic field and gravitational field.Then,using the sixth-order Wentzel-Kramers-Brillouin approximation,we examine QNMs of the BH disturbed by the three fields and derive quasinormal frequencies.The changes in QNM versus the core density parameter and the cloud string parameter for three disturbances are explored.We also investigate how the core density and the cloud string parameter affect the photon sphere and shadow radius.Interestingly,the study shows that the influence of Dehnen-type DM and cloud strings increases both the photon sphere and the shadow radius.Finally,we employ observational data from Sgr A^(*) and M87^(*) to set limitations on the BH parameters.展开更多
The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of dril...The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.展开更多
提出通过String Kernel方法把负实例语法数据库中的负实例转化成核矩阵,再用Kernel Principal Component Analysis(KPCA)对转换的核矩阵进行特征提取,进而可将原始负实例数据库按照这些特征分成多个容量较小的特征表。通过构造负实例特...提出通过String Kernel方法把负实例语法数据库中的负实例转化成核矩阵,再用Kernel Principal Component Analysis(KPCA)对转换的核矩阵进行特征提取,进而可将原始负实例数据库按照这些特征分成多个容量较小的特征表。通过构造负实例特征索引表设计了一个分类器,待检查的句子通过此分类器被分配到某个负实例特征表里进行匹配搜索,而此特征表的特征属性数和记录数要远远小于原始负实例数据库中的相应数目,从而大大提高了检查的速度,同时不影响语法检查的精度。通过比较测试,可看出提出的方法在保证语法检查精确度的同时有更快的速度。展开更多
This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation...This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.展开更多
Insulator becomes wet partially or completely, and the pollution layer on itbecomes conductive, when collecting pollutants for an extended period during dew, light rain, mist,fog or snow melting. Heavy rain is a compl...Insulator becomes wet partially or completely, and the pollution layer on itbecomes conductive, when collecting pollutants for an extended period during dew, light rain, mist,fog or snow melting. Heavy rain is a complicated factor that it may wash away the pollution layerwithout initiating other stages of breakdown or it may bridge the gaps between sheds to promoteflashover. The insulator with a conducting pollution layer being energized, can cause a surfaceleakage current to flow (also temperature-rise). As the surface conductivity is non-uniform, theconducting pollution layer becomes broken by dry bands (at spots of high current density),interrupting the flow of leakage current. Voltage across insulator gets concentrated across drybands, and causes high electric stress and breakdown (dry band arcing). If the resistance of theinsulator surface is sufficiently low, the dry band arcs can be propagated to bridge the terminalscausing flashover. The present paper concerns the evaluation of the temperature distribution alongthe surface of an energized artificially polluted insulator string.展开更多
This paper proposes cooperative adaptive control schemes for a train platoon to improve efficient utility and guarantee string stability. The control schemes are developed based on a bidirectional strategy, i.e., the ...This paper proposes cooperative adaptive control schemes for a train platoon to improve efficient utility and guarantee string stability. The control schemes are developed based on a bidirectional strategy, i.e., the information of proximal（preceding and following） trains is used in the controller design. Based on available proximal information（prox-info） of location, speed, and acceleration, a direct adaptive control is designed to maintain the tracking interval at the minimum safe distance. Based on available prox-info of location, an observer-based adaptive control is designed to achieve the same target, which alleviates the requirements of equipped sensors to measure prox-info of speed and acceleration. The developed schemes are capable of on-line estimating of the unknown system parameters and stabilizing the closed-loop system, the string stability of train platoon is guaranteed on the basis of Lyapunov stability theorem. Numerical simulation results are presented to verify the effectiveness of the proposed control laws.展开更多
Background: Birds produce alarm calls to convey information about threats. Some Passerine alarm calls consist of several note strings, but few studies have examined their function. Previous studies have shown that Jap...Background: Birds produce alarm calls to convey information about threats. Some Passerine alarm calls consist of several note strings, but few studies have examined their function. Previous studies have shown that Japanese Tits(Parus minor) can alter the calling rate and number and combination of notes in response to predators. We previously found the combinations of note types in Japanese Tit alarm calls to be significantly different in response to the Sparrowhawk(Accipiter nisus) and Common Cuckoo(Cuculus canorus).Methods: Through playback experiments, we tested whether the note strings in Japanese Tit alarm calls to the Common Cuckoo have different functions in conveying information. The note strings of selected alarm calls were divided into the categories of C and D, and different calls were then constructed separately based on the two note string categories. Original alarm calls(C–D), C calls and D calls were played back to male Japanese Tits during the incubation period.Results: Male Japanese Tits had a significantly stronger response to C calls than to C–D calls, and they showed a significantly stronger response to both C and C–D calls than to D calls, suggesting that Japanese Tits discriminated between the C and D calls.Conclusions: Our study demonstrated that the C-and D-category note strings of Japanese Tit alarm calls to the Common Cuckoo have different functions, which supports the previous finding that different note strings in an alarm call can provide different information to receivers. However, the exact meanings of these note strings are not yet known, and further investigation is therefore required.展开更多
To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string,the method of multiple scales is applied directly to the nonlinear partial differentia...To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string,the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string.To derive the governing equation,Newton's second law,Lagrangean strain,and Kelvin's model are respectively used to account the dynamical relation,geometric nonlinearity and the viscoelasticity of the string material. Based on the solvability condition of eliminating the secular terms,closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance.The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance.Some numerical examples are presented to show the effects of the mean transport speed,the amplitude and the frequency of speed variation.展开更多
The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly provide enlightenment on ...The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly provide enlightenment on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied. In this paper, we first give five microparameters to describe the individual molecular string （MS） relaxation based on the dynamical Hamiltonian of the MS model, and then simulate the images of individual MS ensemble, and at the same time calculate the parameters of the equilibrium state. The results show that the main molecular orientation flipping image in liquids （including supercooled liquid） is similar to the random walk. In addition, two pairs of the parameters are equal, and one can be ignored compared with the other. This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of the general Glauber type, and the computer simulation time of interaction MS relaxation. Moreover, the conclusion is of reference significance for solving and simulating the multi-state MS model.展开更多
基金the support by grants from the NNSF of China with Grant Nos.12275264 and 12247103。
文摘This is a writeup of lectures delivered at the Asian Pacific Introductory School on Superstring and Related Topics in Beijing(2006)and an expanded version of these lectures given at the Third Summer School on Strings,Fields and Holography in Nanjing(2023).It aims to provide both a historical and pedagogical account of developments in finding 1/2 Bogomol?nyi–Prasad–Sommerfield(BPS)extended string solitons during the early stage of the so-called second string revolution,before which these objects were thought to be unrelated to strings.Nonsupersymmetric solutions related to brane/anti brane systems or non-BPS systems are also discussed.
文摘Let F_(1)be the virtual field consisting of one element and(Q,I)a string pair.In this paper,we study the representations of string pairs over the virtual field F_(1).It is proved that an indecomposable F_(1)-representation is either a string representation or a band representation by using the coefficient quivers.It is worth noting that for a given band and a positive integer,there exists a unique band representation up to isomorphism.
文摘In this paper, in Section 1, we have described some equations and theorems concerning the Lebesgue integral and the Lebesgue measure. In Section 2, we have described the possible mathematical applications, of Lebesgue integration, in some equations concerning various sectors of Chern-Simons theory and Yang-Mills gauge theory, precisely the two dimensional quantum Yang-Mills theory. In conclusion, in Section 3, we have described also the possible mathematical connections with some sectors of String Theory and Number Theory, principally with some equations concerning the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings, some Ramanujan’s identities concerning π and the zeta strings.
基金funded by the Research council of Norway,Equinor and Sekal with NFR(Grant No.308826).
文摘During drilling operations,cyclic loading is exerted on the wellbore wall by the vibrations of the drill string.This loading could lead to rock fatigue,which in turn might result in wellbore failure.In this study,a numerical model is developed to simulate the effects of repeated loading on rock fatigue and failure.The simulation is based on an elasto-plastic constitutive model coupled with a damage mechanics approach,which allows us to examine the wellbore instability due to drill string vibrations.The model is verified with the existing data in the literature related to experiments on impact of a steel ball against a curved wall.The findings indicate that cyclic loading increases the development of plastic strain around the wellbore significantly compared to static conditions,promoting rock fatigue.Furthermore,the cyclic loading expands the radius of the yielded zone substantially,a critical factor for maintaining wellbore integrity.The proposed model can be used to evaluate the wellbore stability under repetitive loading caused by the drill string action.
基金supported by the Natural Science Foundation of Fujian Province(Grant No.2022J011130)the Research Starting Grant from Minjiang University(Grant No.30804317)。
文摘A new phenomenological model(axionic QCD string)is constructed to study the topological issues of the QCD vacuum and hadron structure.It provides an alternative way of tackling the Strong CP problem,which is different from the traditional Peccei–Quinn approach.Neither new particle nor extra symmetry is introduced,and the role of the Peccei–Quinn axion is played by a quasiparticle arising from the phase of the quark condensate,dubbed as axionic excitation.The derivative of this excitation field is decomposed into a regular part and a singular part,and the latter contains vorticity from the string configuration.A hidden gauge symmetry is revealed in this decomposition and vorticity is represented by an emergent gauge field associated with anomalies.These components,together with the anomaly-inflow mechanism,complete the effective Lagrangian description for the axionic QCD string.
基金supported by the National Natural Science Foundation of China under Grant No.11675143the National Key Research and Development Program of China under Grant No.2020YFC2201503。
文摘In this paper we consider a static spherically symmetric black hole(BH)embedded in a Dehnen-(1,4,0)-type dark matter(DM)halo in the presence of a cloud string.We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes(QNMs)and shadow cast.To do this,we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins:massless scalar field,electromagnetic field and gravitational field.Then,using the sixth-order Wentzel-Kramers-Brillouin approximation,we examine QNMs of the BH disturbed by the three fields and derive quasinormal frequencies.The changes in QNM versus the core density parameter and the cloud string parameter for three disturbances are explored.We also investigate how the core density and the cloud string parameter affect the photon sphere and shadow radius.Interestingly,the study shows that the influence of Dehnen-type DM and cloud strings increases both the photon sphere and the shadow radius.Finally,we employ observational data from Sgr A^(*) and M87^(*) to set limitations on the BH parameters.
基金supported by the National Natural Science Foundation of China(52174003,52374008).
文摘The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.
文摘提出通过String Kernel方法把负实例语法数据库中的负实例转化成核矩阵,再用Kernel Principal Component Analysis(KPCA)对转换的核矩阵进行特征提取,进而可将原始负实例数据库按照这些特征分成多个容量较小的特征表。通过构造负实例特征索引表设计了一个分类器,待检查的句子通过此分类器被分配到某个负实例特征表里进行匹配搜索,而此特征表的特征属性数和记录数要远远小于原始负实例数据库中的相应数目,从而大大提高了检查的速度,同时不影响语法检查的精度。通过比较测试,可看出提出的方法在保证语法检查精确度的同时有更快的速度。
文摘This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.
文摘Insulator becomes wet partially or completely, and the pollution layer on itbecomes conductive, when collecting pollutants for an extended period during dew, light rain, mist,fog or snow melting. Heavy rain is a complicated factor that it may wash away the pollution layerwithout initiating other stages of breakdown or it may bridge the gaps between sheds to promoteflashover. The insulator with a conducting pollution layer being energized, can cause a surfaceleakage current to flow (also temperature-rise). As the surface conductivity is non-uniform, theconducting pollution layer becomes broken by dry bands (at spots of high current density),interrupting the flow of leakage current. Voltage across insulator gets concentrated across drybands, and causes high electric stress and breakdown (dry band arcing). If the resistance of theinsulator surface is sufficiently low, the dry band arcs can be propagated to bridge the terminalscausing flashover. The present paper concerns the evaluation of the temperature distribution alongthe surface of an energized artificially polluted insulator string.
基金Project supported by the Beijing Jiaotong University Research Program,China(Grant No.RCS2014ZT18)the Fundamental Research Funds for Central Universities,China(Grant No.2015JBZ007)the National Natural Science Foundation of China(Grant Nos.61233001,61322307,and 61304196)
文摘This paper proposes cooperative adaptive control schemes for a train platoon to improve efficient utility and guarantee string stability. The control schemes are developed based on a bidirectional strategy, i.e., the information of proximal（preceding and following） trains is used in the controller design. Based on available proximal information（prox-info） of location, speed, and acceleration, a direct adaptive control is designed to maintain the tracking interval at the minimum safe distance. Based on available prox-info of location, an observer-based adaptive control is designed to achieve the same target, which alleviates the requirements of equipped sensors to measure prox-info of speed and acceleration. The developed schemes are capable of on-line estimating of the unknown system parameters and stabilizing the closed-loop system, the string stability of train platoon is guaranteed on the basis of Lyapunov stability theorem. Numerical simulation results are presented to verify the effectiveness of the proposed control laws.
基金supported by the National Natural Science Foundation of China(31272331 and 31470458 to HW,31472013 and 31772453 to WL)the Fundamental Research Funds for the Central Universities(2412016KJ043)the Open Project Program of Jilin Provincial Key Laboratory of Animal Resource Conservation and Utilization(130028685)
文摘Background: Birds produce alarm calls to convey information about threats. Some Passerine alarm calls consist of several note strings, but few studies have examined their function. Previous studies have shown that Japanese Tits(Parus minor) can alter the calling rate and number and combination of notes in response to predators. We previously found the combinations of note types in Japanese Tit alarm calls to be significantly different in response to the Sparrowhawk(Accipiter nisus) and Common Cuckoo(Cuculus canorus).Methods: Through playback experiments, we tested whether the note strings in Japanese Tit alarm calls to the Common Cuckoo have different functions in conveying information. The note strings of selected alarm calls were divided into the categories of C and D, and different calls were then constructed separately based on the two note string categories. Original alarm calls(C–D), C calls and D calls were played back to male Japanese Tits during the incubation period.Results: Male Japanese Tits had a significantly stronger response to C calls than to C–D calls, and they showed a significantly stronger response to both C and C–D calls than to D calls, suggesting that Japanese Tits discriminated between the C and D calls.Conclusions: Our study demonstrated that the C-and D-category note strings of Japanese Tit alarm calls to the Common Cuckoo have different functions, which supports the previous finding that different note strings in an alarm call can provide different information to receivers. However, the exact meanings of these note strings are not yet known, and further investigation is therefore required.
基金The project supported by the National Natural Science Foundation of China (10172056)
文摘To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string,the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string.To derive the governing equation,Newton's second law,Lagrangean strain,and Kelvin's model are respectively used to account the dynamical relation,geometric nonlinearity and the viscoelasticity of the string material. Based on the solvability condition of eliminating the secular terms,closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance.The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance.Some numerical examples are presented to show the effects of the mean transport speed,the amplitude and the frequency of speed variation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10774064 and 30860076)the National Basic Research Program of China (Grant No. 2012CB821503)the Natural Science Foundations of Xinjiang Uygur Autonomous Region,China (Grant Nos. 200821104 and 200821184)
文摘The relaxation dynamics of liquids is one of the fundamental problems in liquid physics, and it is also one of the key issues to understand the glass transition mechanism. It will undoubtedly provide enlightenment on understanding and calculating the relaxation dynamics if the molecular orientation flipping images and relevant microparameters of liquids are studied. In this paper, we first give five microparameters to describe the individual molecular string （MS） relaxation based on the dynamical Hamiltonian of the MS model, and then simulate the images of individual MS ensemble, and at the same time calculate the parameters of the equilibrium state. The results show that the main molecular orientation flipping image in liquids （including supercooled liquid） is similar to the random walk. In addition, two pairs of the parameters are equal, and one can be ignored compared with the other. This conclusion will effectively reduce the difficulties in calculating the individual MS relaxation based on the single-molecule orientation flipping rate of the general Glauber type, and the computer simulation time of interaction MS relaxation. Moreover, the conclusion is of reference significance for solving and simulating the multi-state MS model.
