Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the cal...Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the calculation show that the period doubling bifurcation, quasi-periodic and chaotic motions may occur. In some typical parameter regions, the bifurcation diagrams, phase portrait, Poincaré maps and the frequency spectrums of the system are acquired with the numerical integration method. They demonstrate some motion state of the system. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. The analysis result of this paper provides the theoretical basis for qualitatively controlling the stable operating states of the rotors.展开更多
In this work, the stability of an endoreversible Curzon-Ahlbom engine is analyzed, using Van der Waals gas as a working substance and the corresponding efficiency for this engine working at temperatures withinthe maxi...In this work, the stability of an endoreversible Curzon-Ahlbom engine is analyzed, using Van der Waals gas as a working substance and the corresponding efficiency for this engine working at temperatures withinthe maximum ecological regime. By mean s of a local stability analysis we find that a critical point of an almost linear system is stable andanalytically expressed in eigenvalues. After an arbitrarily small perturbation, the system state exponentially decays to a critical point, with either of two characteristic relaxation times, which are a function of the thermal conductance （a）, heat capacity （C） and T=T2/T1. The behavior of relaxation times and solution of the systems are qualitatively shown by sketching its phase portrait, which results susceptible to operating regimes, i.e., the eigenvectors in the maximum ecological regime have a clockwise rotation with respect to the eigenvectors in the regime of maximumpower. Finally, it has to observe that afterto λvw = 1, approximation,ηVWE=4^-3ηC is obtained, where ηVWE is the Van der Waals efficiency atrnaximum ecological regime and r/c is Carnot＇s efficiency. Finally, it discussed the local stability and steady state of the energetic properties of the endoreversible engine.展开更多
By means of the continuous Glimm functional, a proof is given on the global existence of classical solutions to Cauchy problem for general first order quasilinear hyperbolic systems with small initial total variation.
For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the globa...For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.展开更多
The plane-wave expansion(PWE) method is employed to calculate the photonic band structures of metal/dielectric(M/D) periodic systems. We consider a one-dimensional(1D) M/D superlattice with a metal layer characterized...The plane-wave expansion(PWE) method is employed to calculate the photonic band structures of metal/dielectric(M/D) periodic systems. We consider a one-dimensional(1D) M/D superlattice with a metal layer characterized by a frequency-dependent dielectric function. To calculate the photonic band of such a system, we propose a new method and thus avoid solving the nonlinear eigenvalue equations. We obtained the frequency dispersions and the energy distributions of eigen-modes of 1D superlattices. This general method is applicable to calculate the photonic band of a broad class of physical systems, e.g. 2D and 3D M/D photonic crystals. For comparison, we present a simple introduction of the finite-difference(FD) method to calculate the same system, and the agreement turns out to be good. But the FD method cannot be applied to the TM modes of the M/D superlattice.展开更多
The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In partic...For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.展开更多
It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to fur...It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes place.LSQR for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov solver.However,there has not yet been an analogouslyelegant formula for residual norms.This paper derives such kind of formula.In addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.展开更多
In this work, we analyzed time-series and trends of the tropical belt edges and widths with three methods based on the tropopause using new global positioning system radio occultation(GPS RO) data from the Constellati...In this work, we analyzed time-series and trends of the tropical belt edges and widths with three methods based on the tropopause using new global positioning system radio occultation(GPS RO) data from the Constellation Observing System for Meteorology, Ionosphere, and Climate(COSMIC) mission for September 2006–February 2014. The results from the three methods agreed well with previous studies and new features were found. To avoid the El Ni?o Southern Oscillation(ENSO) and Quasi-Biennial Oscillation(QBO) influence, we applied a simple multiple linear regression model to the monthly anomalies to obtain the tropical belt edges and width trends. During the study, we found equatorward movements of the tropical belt edges on both hemispheres. The narrowing of the tropical belt mainly occurred in the Pacific Ocean. We also found that the deseasonalized monthly anomalies of the tropical belt width were closely related with the ENSO and QBO. The tropical belt at a height of 15 km was mostly closely related with the ENSO. The correlations between the QBO and the tropical belt were consistent for the three methods.展开更多
This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are i...This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata(ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.展开更多
文摘Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the calculation show that the period doubling bifurcation, quasi-periodic and chaotic motions may occur. In some typical parameter regions, the bifurcation diagrams, phase portrait, Poincaré maps and the frequency spectrums of the system are acquired with the numerical integration method. They demonstrate some motion state of the system. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. The analysis result of this paper provides the theoretical basis for qualitatively controlling the stable operating states of the rotors.
文摘In this work, the stability of an endoreversible Curzon-Ahlbom engine is analyzed, using Van der Waals gas as a working substance and the corresponding efficiency for this engine working at temperatures withinthe maximum ecological regime. By mean s of a local stability analysis we find that a critical point of an almost linear system is stable andanalytically expressed in eigenvalues. After an arbitrarily small perturbation, the system state exponentially decays to a critical point, with either of two characteristic relaxation times, which are a function of the thermal conductance （a）, heat capacity （C） and T=T2/T1. The behavior of relaxation times and solution of the systems are qualitatively shown by sketching its phase portrait, which results susceptible to operating regimes, i.e., the eigenvectors in the maximum ecological regime have a clockwise rotation with respect to the eigenvectors in the regime of maximumpower. Finally, it has to observe that afterto λvw = 1, approximation,ηVWE=4^-3ηC is obtained, where ηVWE is the Van der Waals efficiency atrnaximum ecological regime and r/c is Carnot＇s efficiency. Finally, it discussed the local stability and steady state of the energetic properties of the endoreversible engine.
文摘By means of the continuous Glimm functional, a proof is given on the global existence of classical solutions to Cauchy problem for general first order quasilinear hyperbolic systems with small initial total variation.
基金supported by the Fudan University Creative Student Cultivation Program in Key Disciplinary Areas (No. EHH1411208)
文摘For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H 2 classical solution to the Cauchy problem with small initial data is obtained.
基金supported by the special funds for the National Basic Research Program of China(Grant No.069c031001)the National Natural Science Foundation of China(Grant No.60521001).
文摘The plane-wave expansion(PWE) method is employed to calculate the photonic band structures of metal/dielectric(M/D) periodic systems. We consider a one-dimensional(1D) M/D superlattice with a metal layer characterized by a frequency-dependent dielectric function. To calculate the photonic band of such a system, we propose a new method and thus avoid solving the nonlinear eigenvalue equations. We obtained the frequency dispersions and the energy distributions of eigen-modes of 1D superlattices. This general method is applicable to calculate the photonic band of a broad class of physical systems, e.g. 2D and 3D M/D photonic crystals. For comparison, we present a simple introduction of the finite-difference(FD) method to calculate the same system, and the agreement turns out to be good. But the FD method cannot be applied to the TM modes of the M/D superlattice.
文摘The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.
文摘For first-order quasilinear hyperbolic systems with zero eigenvaiues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.
基金supported in part by the National Science Foundation of China under Grant No. 10771116the Doctoral Program of the Ministry of Education under Grant No. 20060003003
文摘It is well-known that many Krylov solvers for linear systems,eigenvalue problems,andsingular value decomposition problems have very simple and elegant formulas for residual norms.Theseformulas not only allow us to further understand the methods theoretically but also can be usedas cheap stopping criteria without forming approximate solutions and residuals at each step beforeconvergence takes place.LSQR for large sparse linear least squares problems is based on the Lanczosbidiagonalization process and is a Krylov solver.However,there has not yet been an analogouslyelegant formula for residual norms.This paper derives such kind of formula.In addition,the authorgets some other properties of LSQR and its mathematically equivalent CGLS.
基金supported by the National Natural Science Foundation of China(Grant No.41374036)the National Key Basic Research Program of China(Grant No.2013CB733301)+1 种基金the Funds for Innovative Research Groups of the National Natural Science Foundation of China(Grant No.41021061)the Fundamental Research Funds for the Central Universities
文摘In this work, we analyzed time-series and trends of the tropical belt edges and widths with three methods based on the tropopause using new global positioning system radio occultation(GPS RO) data from the Constellation Observing System for Meteorology, Ionosphere, and Climate(COSMIC) mission for September 2006–February 2014. The results from the three methods agreed well with previous studies and new features were found. To avoid the El Ni?o Southern Oscillation(ENSO) and Quasi-Biennial Oscillation(QBO) influence, we applied a simple multiple linear regression model to the monthly anomalies to obtain the tropical belt edges and width trends. During the study, we found equatorward movements of the tropical belt edges on both hemispheres. The narrowing of the tropical belt mainly occurred in the Pacific Ocean. We also found that the deseasonalized monthly anomalies of the tropical belt width were closely related with the ENSO and QBO. The tropical belt at a height of 15 km was mostly closely related with the ENSO. The correlations between the QBO and the tropical belt were consistent for the three methods.
基金supported by the National Natural Science Foundation of China under Grant Nos.61473189,61374176,61203142 and 61203073a Doctoral Program of High Education of China under Grant No.20110073120027partly by the Excellent Young Technology Innovation Foundation of Hebei University of Technology under Grant No.2012005
文摘This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata(ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.
