In this paper we analyse some classical laws in physics from the viewpoint of systems science and find out some doubtful points, and revise them by the use of the known method in systems science. In the end a general ...In this paper we analyse some classical laws in physics from the viewpoint of systems science and find out some doubtful points, and revise them by the use of the known method in systems science. In the end a general methodology based on system identification for studying dynamic relationship between various causes and effects is given.展开更多
Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and giv...Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.展开更多
We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce t...We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner–Nordstr¨om geometry.展开更多
In 1937, Paul Dirac proposed Large Number Hypothesis and Hypothesis of Variable Gravitational Constant, and later added notion of Continuous Creation of Matter in the World. Hypersphere World-Universe Model (WUM) foll...In 1937, Paul Dirac proposed Large Number Hypothesis and Hypothesis of Variable Gravitational Constant, and later added notion of Continuous Creation of Matter in the World. Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing different mechanism of Matter creation. In this paper, we show that WUM is a natural continuation of Classical Physics. WUM is proposed as an alternative to prevailing Big Bang Model (BBM) that relies on General Relativity. WUM and BBM are principally different Models: 1) Instead of Initial Singularity with infinite energy density and extremely rapid expansion of spacetime (Inflation) in BBM;in WUM, there was Fluctuation (4D Nucleus of World with extrapolated radius equal to basic size unit of a) in Eternal Universe with finite extrapolated energy density (~10<sup>4</sup> less than nuclear density) and finite expansion of Nucleus in Its fourth spatial dimension with speed c that is gravitodynamic constant;2) Instead of alleged practically Infinite Homogeneous and Isotropic Universe around Initial Singularity in BBM;in WUM, 3D Finite Boundless World (Hypersphere of 4D Nucleus) presents Patchwork Quilt of various Luminous Superclusters (≧10<sup>3</sup>), which emerged in different places of World at different Cosmological times. Medium of World, consisting of protons, electrons, photons, neutrinos, and dark matter particles, is Homogeneous and Isotropic. Distribution of Macroobjects is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous. Most direct observational evidence of validity of WUM are: 1) Microwave Background Radiation and Intergalactic Plasma speak in favor of existence of Medium;2) Laniakea Supercluster with binding mass ~10<sup>17</sup>M<sub>⊙</sub> is home to Milky Way (MW) and ~10<sup>5</sup> other nearby galaxies, which did not start their movement from Initial Singularity;3) MW is gravitationally bounded with Virgo Supercluster (VS) and has Orbital Angular Momentum that far exceeds its rotational angular momentum;4) Mass-t展开更多
This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation the...This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supp展开更多
It is proposed a representation of the basic laws (i.e. the zeroth, first, second and third laws) in thermodynamics for quantum systems in the pure and mixed ensembles, respectively. We show that the basic laws are re...It is proposed a representation of the basic laws (i.e. the zeroth, first, second and third laws) in thermodynamics for quantum systems in the pure and mixed ensembles, respectively. We show that the basic laws are represented by parameters that specify respective quantum states. The parameters are the elements of the thermodynamic state space Mθand the state space Mϑof the mixed ensemble for quantum systems. The introduction of such parameters is based on a probabilistic nature of quantum theory. Consistency between quantum theory and classical thermodynamics is preserved throughout the formulation for the representation of the thermodynamical laws in quantum systems (quantum thermodynamics). The present theory gives the mathematical foundations of quantum thermodynamics.展开更多
文摘In this paper we analyse some classical laws in physics from the viewpoint of systems science and find out some doubtful points, and revise them by the use of the known method in systems science. In the end a general methodology based on system identification for studying dynamic relationship between various causes and effects is given.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx 16
文摘Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.
文摘We are going to prove that the Monopole and the Coulomb fields are duals within the unifying structure provided by the Reissner–Nordstr¨om spacetime. This is accomplished when noticing that in order to produce the tetrad that locally and covariantly diagonalizes the stress-energy tensor, both the Monopole and the Coulomb fields are necessary in the construction. Without any of them it would be impossible to express the tetrad vectors that locally and covariantly diagonalize the stress-energy tensor. Then, both electromagnetic fields are an integral part of the same structure, the Reissner–Nordstr¨om geometry.
文摘In 1937, Paul Dirac proposed Large Number Hypothesis and Hypothesis of Variable Gravitational Constant, and later added notion of Continuous Creation of Matter in the World. Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing different mechanism of Matter creation. In this paper, we show that WUM is a natural continuation of Classical Physics. WUM is proposed as an alternative to prevailing Big Bang Model (BBM) that relies on General Relativity. WUM and BBM are principally different Models: 1) Instead of Initial Singularity with infinite energy density and extremely rapid expansion of spacetime (Inflation) in BBM;in WUM, there was Fluctuation (4D Nucleus of World with extrapolated radius equal to basic size unit of a) in Eternal Universe with finite extrapolated energy density (~10<sup>4</sup> less than nuclear density) and finite expansion of Nucleus in Its fourth spatial dimension with speed c that is gravitodynamic constant;2) Instead of alleged practically Infinite Homogeneous and Isotropic Universe around Initial Singularity in BBM;in WUM, 3D Finite Boundless World (Hypersphere of 4D Nucleus) presents Patchwork Quilt of various Luminous Superclusters (≧10<sup>3</sup>), which emerged in different places of World at different Cosmological times. Medium of World, consisting of protons, electrons, photons, neutrinos, and dark matter particles, is Homogeneous and Isotropic. Distribution of Macroobjects is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous. Most direct observational evidence of validity of WUM are: 1) Microwave Background Radiation and Intergalactic Plasma speak in favor of existence of Medium;2) Laniakea Supercluster with binding mass ~10<sup>17</sup>M<sub>⊙</sub> is home to Milky Way (MW) and ~10<sup>5</sup> other nearby galaxies, which did not start their movement from Initial Singularity;3) MW is gravitationally bounded with Virgo Supercluster (VS) and has Orbital Angular Momentum that far exceeds its rotational angular momentum;4) Mass-t
文摘This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supp
文摘It is proposed a representation of the basic laws (i.e. the zeroth, first, second and third laws) in thermodynamics for quantum systems in the pure and mixed ensembles, respectively. We show that the basic laws are represented by parameters that specify respective quantum states. The parameters are the elements of the thermodynamic state space Mθand the state space Mϑof the mixed ensemble for quantum systems. The introduction of such parameters is based on a probabilistic nature of quantum theory. Consistency between quantum theory and classical thermodynamics is preserved throughout the formulation for the representation of the thermodynamical laws in quantum systems (quantum thermodynamics). The present theory gives the mathematical foundations of quantum thermodynamics.
