The main purpose of this paper is two-fold： （i） to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 （2011）, pp....The main purpose of this paper is two-fold： （i） to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 （2011）, pp. 2014-2047]; （ii） to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58 （2004）, pp. 719-731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.展开更多
Rank-1 attractors play a vital role in biological systems and the circuit systems.In this paper,we consider a periodically kicked Chua model with two delays in a circuit system.We first analyze the local stability of ...Rank-1 attractors play a vital role in biological systems and the circuit systems.In this paper,we consider a periodically kicked Chua model with two delays in a circuit system.We first analyze the local stability of the equilibria of the Chua system and obtain the existence conditions of supercritical Hopf bifurcations.Then,we derive some explicit formulas about Hopf bifurcation,which could help us find the form of Hopf bifurcation and the stability of bifurcating period solutions through the Hassards method.Also,we show that rank-1 chaos occurs when the Chua model with two delays undergoes a supercritical Hopf bifurcation and encounters a periodic kick,which shows the effect of two delays on the circuit system.Finally,we illustrate the theoretical analysis by simulations and try to explain the mechanism of delay in our system.展开更多
In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudo...In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudoclassical theory that applies only in the neighborhoods of the lowest two quantum resonances, the proposed theory is applicable in the neighborhoods of all quantum resonances in principle by considering the quantum effect of the free rotation at a quantum resonance. In particular, it is confirmed by simulations that the quantum wavepacket dynamics can be successfully forecasted based on the generalized pseudoclassical dynamics, offering an intriguing example where it is feasible to bridge the dynamics in the deep quantum regime to the classical dynamics. The application of the generalized pseudoclassical theory to the PT-symmetric kicked rotor is also discussed.展开更多
We theoretically study the transition dynamics of a two-component Bose-Einstein condensate driven by a train of weak δ-shaped laser pulses. We find that the atomic system can experience peculiar resonant transition e...We theoretically study the transition dynamics of a two-component Bose-Einstein condensate driven by a train of weak δ-shaped laser pulses. We find that the atomic system can experience peculiar resonant transition even under weak optical excitations and derive the resonance condition by the perturbation method. Employing this mechanism, we propose a scheme to obtain an atomic ensemble with desired odd/even atom number and also a scheme to prepare a nonclassical state of the many-body system with fixed atom number.展开更多
基金supported by the Research Council of Norway under grant number 197739/V30("DMPL")supported by A/S Norske Shell
文摘The main purpose of this paper is two-fold： （i） to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 （2011）, pp. 2014-2047]; （ii） to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58 （2004）, pp. 719-731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.
基金supported by the National Natural Science Foundation of China(Grant Nos.11772291 and 12002297)Youth Talent Support Project of Henan,China(Grant No.2020HYTP012)+1 种基金Basic Research Project of Universities in Henan Province,China(Grant No.21zx009)Program for Science&Technology Innovation Talents in Universities of Henan Province,China(Grant No.22HASTIT018)。
文摘Rank-1 attractors play a vital role in biological systems and the circuit systems.In this paper,we consider a periodically kicked Chua model with two delays in a circuit system.We first analyze the local stability of the equilibria of the Chua system and obtain the existence conditions of supercritical Hopf bifurcations.Then,we derive some explicit formulas about Hopf bifurcation,which could help us find the form of Hopf bifurcation and the stability of bifurcating period solutions through the Hassards method.Also,we show that rank-1 chaos occurs when the Chua model with two delays undergoes a supercritical Hopf bifurcation and encounters a periodic kick,which shows the effect of two delays on the circuit system.Finally,we illustrate the theoretical analysis by simulations and try to explain the mechanism of delay in our system.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12075198, 12247106, and 12247101)。
文摘In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudoclassical theory that applies only in the neighborhoods of the lowest two quantum resonances, the proposed theory is applicable in the neighborhoods of all quantum resonances in principle by considering the quantum effect of the free rotation at a quantum resonance. In particular, it is confirmed by simulations that the quantum wavepacket dynamics can be successfully forecasted based on the generalized pseudoclassical dynamics, offering an intriguing example where it is feasible to bridge the dynamics in the deep quantum regime to the classical dynamics. The application of the generalized pseudoclassical theory to the PT-symmetric kicked rotor is also discussed.
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFA0301504)the National Natural Science Foundation of China(Grant Nos.61835013 and 11774362)
文摘We theoretically study the transition dynamics of a two-component Bose-Einstein condensate driven by a train of weak δ-shaped laser pulses. We find that the atomic system can experience peculiar resonant transition even under weak optical excitations and derive the resonance condition by the perturbation method. Employing this mechanism, we propose a scheme to obtain an atomic ensemble with desired odd/even atom number and also a scheme to prepare a nonclassical state of the many-body system with fixed atom number.
