Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,ca...Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.展开更多
This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the me...This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.展开更多
We claim that the linking of a shrinking prior universe to our own via a wormhole bridge solution of about ten to the minus forty four power seconds permits the formation of a short-term quintessence scalar field. Sym...We claim that the linking of a shrinking prior universe to our own via a wormhole bridge solution of about ten to the minus forty four power seconds permits the formation of a short-term quintessence scalar field. Symmetries allow for creating high-frequency gravitational waves at the onset of inflation, which has consequences in our present cosmological era. This instantaneous energy transfer between prior to present universes permits relic graviton production which we claim is a viable candidate for future propulsion technologies in space craft design. The Big Bang started as the passage of thermal energy from an existing universe into ours resulting in another Big Bang, and helps us understand how a graviton burst can occur in the first place.展开更多
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourie...This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.展开更多
We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a...We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.展开更多
We have recently published a series of papers on a theory we call collision space-time, that seems to unify gravity and quantum mechanics. In this theory, mass and energy are redefined. We have not so far demonstrated...We have recently published a series of papers on a theory we call collision space-time, that seems to unify gravity and quantum mechanics. In this theory, mass and energy are redefined. We have not so far demonstrated how to make it compatible with electric properties such as charge and the Coulomb force. The aim of this paper is to show how electric properties can be reformulated to make it consistent with collision space-time. It is shown that we need to incorporate the Planck scale into the electric constants to do so. This is also fully possible from a practical point of view, as it has recently been shown how to measure the Planck length independent of other constants and without the need for dimensional analysis.展开更多
The conditions for the emergence of the non-Hermitian skin effect, as a unique physical response of non-Hermitian systems, have now become one of the hot research topics. In this paper, we study the novel physical res...The conditions for the emergence of the non-Hermitian skin effect, as a unique physical response of non-Hermitian systems, have now become one of the hot research topics. In this paper, we study the novel physical responses of nonHermitian systems with anomalous time-reversal symmetry, in both one dimension and two dimensions. Specifically, we focus on whether the systems will exhibit a non-Hermitian skin effect. We employ the theory of generalized Brillouin zone and also numerical methods to show that the anomalous time-reversal symmetry can prevent the skin effect in onedimensional non-Hermitian systems, but is unable to exert the same effectiveness in two-dimensional cases.展开更多
Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traver...Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.展开更多
In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived...In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.展开更多
In further discussion on the Maxwell-Lorentz equations in Dirac’s symmetrisation, I introduce the concept of magnetic monopole as an “act of electric current” in the 2<sup>nd</sup> equation (i.e. the an...In further discussion on the Maxwell-Lorentz equations in Dirac’s symmetrisation, I introduce the concept of magnetic monopole as an “act of electric current” in the 2<sup>nd</sup> equation (i.e. the analog of the “act of movement” in Classical Mechanics), I postulate a “magnetic displacement current” and a “magnetomotive force” in the 3<sup>rd</sup> and 4<sup>th</sup> equations, respectively (i.e. the analogs of the “electric displacement current” and of the “electromotive force” in the 4<sup>th</sup> and 3<sup>rd</sup> equations, respectively). As a consequence, I propose a generalised vision of the Electromagnetism in which inhomogeneous, microscopic, and relativistically linked equations describe the static and the oscillatory phenomena. Then, in the frame of Relativity, I propose analog microscopic equations to study the Gravitation and the Space-Time in terms of static and oscillatory phenomena: the static equations show the sources of newly defined vector fields (the generalised mass density as the source of the generalised mass field, the generalised time density as the source of the generalised space field, respectively), whereas the oscillatory equations describe the propagation of the gravitational waves and of the spatiotemporal waves, respectively. In other words, I propose to unify Electromagnetism, Gravitation, and Space-Time in terms of microscopic Maxwell-Lorentz-like equations in Dirac’s symmetrisation, where the unifying trait is c. Finally, using the concepts of the proposed generalised Electromagnetism, I discuss the conservation in Electromagnetism and the interaction between matter and electromagnetic waves.展开更多
Flat supersymmetric space-time (x, θ) has been discussed under assumption that the Fermi variables are symplectic vectors only. We have abandoned the traditional assumption, that it must be the spinor representation ...Flat supersymmetric space-time (x, θ) has been discussed under assumption that the Fermi variables are symplectic vectors only. We have abandoned the traditional assumption, that it must be the spinor representation of Lorentz group, which makes in the usual theory of supersymmetry.The even and odd generators of the ortho-symplectic group OS_p(414) have been calculated concretely in its dyads representation.New superfields, Lagrangian and the action integral, different from the usual theory, have been introduced in this flat case.展开更多
Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presen...Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented. The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.展开更多
In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients ...In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.展开更多
The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for t...The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then these results are generalized to the constrained Birkhoff system. One example is presented to illustrate these results.展开更多
This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of m...This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.展开更多
In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTR...In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...展开更多
This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton act...This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.展开更多
In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian ...In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian is also given by means of the obtained constant of motion. By discussing the Lie symmetry for this classical system, this paper obtains the general expression of the conserved quantity, It is shown that the conserved quantity is the same as the constant of motion in essence,展开更多
By using MTS815 rock mechanics test system,a series of acoustic emission(AE) location experiments were performed under unloading confining pressure,increasing the axial stress.The AE space-time evolution regularities ...By using MTS815 rock mechanics test system,a series of acoustic emission(AE) location experiments were performed under unloading confining pressure,increasing the axial stress.The AE space-time evolution regularities and energy releasing characteristics during deformation and failure process of coal of different loading rates are compared,the influence mechanism of loading rates on the microscopic crack evolution were studied,combining the AE characteristics and the macroscopic failure modes of the specimens,and the precursory characteristics of coal failure were also analyzed quantitatively.The results indicate that as the loading rate is higher,the AE activity and the main fracture will begin earlier.The destruction of coal body is mainly the function of shear strain at lower loading rate and tension strain at higher rate,and will transform from brittleness to ductility at critical velocities.When the deformation of the coal is mainly plasticity,the amplitude of the AE ringing counting rate increases largely and the AE energy curves appear an obvious ''step'',which can be defined as the first failure precursor point.Statics of AE information shows that the strongest AE activity begins when the axial stress level was 92-98%,which can be defined as the other failure precursor point.As the loading rate is smaller,the coal more easily reaches the latter precursor point after the first one,so attention should be aroused to prevent dynamic disaster in coal mining when the AE activity reaches the first precursor point.展开更多
基金supported by the National Natural Science Foundation of China (No.61971412)。
文摘Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.
文摘This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.
文摘We claim that the linking of a shrinking prior universe to our own via a wormhole bridge solution of about ten to the minus forty four power seconds permits the formation of a short-term quintessence scalar field. Symmetries allow for creating high-frequency gravitational waves at the onset of inflation, which has consequences in our present cosmological era. This instantaneous energy transfer between prior to present universes permits relic graviton production which we claim is a viable candidate for future propulsion technologies in space craft design. The Big Bang started as the passage of thermal energy from an existing universe into ours resulting in another Big Bang, and helps us understand how a graviton burst can occur in the first place.
基金supported by the Deanship of Scientific Research at King Khalid University,Saudi Arabia (R.G.P.1/207/43)。
文摘This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.
基金supported by the National Natural Science Foun-dation of China(NSFC)Basic Science Center Program for“Multiscale Problems in Nonlinear Mechanics”(Grant No.11988102).
文摘We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.
文摘We have recently published a series of papers on a theory we call collision space-time, that seems to unify gravity and quantum mechanics. In this theory, mass and energy are redefined. We have not so far demonstrated how to make it compatible with electric properties such as charge and the Coulomb force. The aim of this paper is to show how electric properties can be reformulated to make it consistent with collision space-time. It is shown that we need to incorporate the Planck scale into the electric constants to do so. This is also fully possible from a practical point of view, as it has recently been shown how to measure the Planck length independent of other constants and without the need for dimensional analysis.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12304201)。
文摘The conditions for the emergence of the non-Hermitian skin effect, as a unique physical response of non-Hermitian systems, have now become one of the hot research topics. In this paper, we study the novel physical responses of nonHermitian systems with anomalous time-reversal symmetry, in both one dimension and two dimensions. Specifically, we focus on whether the systems will exhibit a non-Hermitian skin effect. We employ the theory of generalized Brillouin zone and also numerical methods to show that the anomalous time-reversal symmetry can prevent the skin effect in onedimensional non-Hermitian systems, but is unable to exert the same effectiveness in two-dimensional cases.
基金Project supported by the Heilongjiang Province Natural Science Foundation Joint Guidance Project,China (Grant No.LH2020F022)the Fundamental Research Funds for the Central Universities,China (Grant No.3072022CF0801)。
文摘Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.
文摘In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.
文摘In further discussion on the Maxwell-Lorentz equations in Dirac’s symmetrisation, I introduce the concept of magnetic monopole as an “act of electric current” in the 2<sup>nd</sup> equation (i.e. the analog of the “act of movement” in Classical Mechanics), I postulate a “magnetic displacement current” and a “magnetomotive force” in the 3<sup>rd</sup> and 4<sup>th</sup> equations, respectively (i.e. the analogs of the “electric displacement current” and of the “electromotive force” in the 4<sup>th</sup> and 3<sup>rd</sup> equations, respectively). As a consequence, I propose a generalised vision of the Electromagnetism in which inhomogeneous, microscopic, and relativistically linked equations describe the static and the oscillatory phenomena. Then, in the frame of Relativity, I propose analog microscopic equations to study the Gravitation and the Space-Time in terms of static and oscillatory phenomena: the static equations show the sources of newly defined vector fields (the generalised mass density as the source of the generalised mass field, the generalised time density as the source of the generalised space field, respectively), whereas the oscillatory equations describe the propagation of the gravitational waves and of the spatiotemporal waves, respectively. In other words, I propose to unify Electromagnetism, Gravitation, and Space-Time in terms of microscopic Maxwell-Lorentz-like equations in Dirac’s symmetrisation, where the unifying trait is c. Finally, using the concepts of the proposed generalised Electromagnetism, I discuss the conservation in Electromagnetism and the interaction between matter and electromagnetic waves.
文摘Flat supersymmetric space-time (x, θ) has been discussed under assumption that the Fermi variables are symplectic vectors only. We have abandoned the traditional assumption, that it must be the spinor representation of Lorentz group, which makes in the usual theory of supersymmetry.The even and odd generators of the ortho-symplectic group OS_p(414) have been calculated concretely in its dyads representation.New superfields, Lagrangian and the action integral, different from the usual theory, have been introduced in this flat case.
基金Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant No 0311010900).
文摘Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented. The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.
文摘In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.
基金The project supported by the National Natural Science Foundation(19972010)the Doctoral Program Foundation of Institution of Higher Education of Chinathe Natural Science Foundation of Henan Province
文摘The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then these results are generalized to the constrained Birkhoff system. One example is presented to illustrate these results.
基金supported by the National Natural Science Foundation of China (Grant No. 10372053)
文摘This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.
基金Supported by the National Natural Science Foundation of China (10771185 and 10871200)
文摘In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10672143 and 60575055)the Natural Science Foundation of Henan Province, China (Grant No 0511022200)
文摘This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.
文摘In this paper, a constant of motion of charged particle motion in homogeneous electromagnetic field is derived from Newton's equations and the characteristics of partial differential equation, the related Lagrangian is also given by means of the obtained constant of motion. By discussing the Lie symmetry for this classical system, this paper obtains the general expression of the conserved quantity, It is shown that the conserved quantity is the same as the constant of motion in essence,
文摘By using MTS815 rock mechanics test system,a series of acoustic emission(AE) location experiments were performed under unloading confining pressure,increasing the axial stress.The AE space-time evolution regularities and energy releasing characteristics during deformation and failure process of coal of different loading rates are compared,the influence mechanism of loading rates on the microscopic crack evolution were studied,combining the AE characteristics and the macroscopic failure modes of the specimens,and the precursory characteristics of coal failure were also analyzed quantitatively.The results indicate that as the loading rate is higher,the AE activity and the main fracture will begin earlier.The destruction of coal body is mainly the function of shear strain at lower loading rate and tension strain at higher rate,and will transform from brittleness to ductility at critical velocities.When the deformation of the coal is mainly plasticity,the amplitude of the AE ringing counting rate increases largely and the AE energy curves appear an obvious ''step'',which can be defined as the first failure precursor point.Statics of AE information shows that the strongest AE activity begins when the axial stress level was 92-98%,which can be defined as the other failure precursor point.As the loading rate is smaller,the coal more easily reaches the latter precursor point after the first one,so attention should be aroused to prevent dynamic disaster in coal mining when the AE activity reaches the first precursor point.