Modern Physics Letters B

This paper is dedicated to investigating the asymptotic synchronization of delayed Lur’e systems via non-fragile aperiodic sampled-data control. Two different kinds of gain fluctuations are taken into consideration. A time-dependent two-sided looped functional is proposed, which makes efficient use of the obtainable information not only of the whole sampling intervals, but also of the nonlinear functions of the considered systems. A criterion on global asymptotic stability is derived by means of the constructed looped functional and using the free-weighting matrix approach. Then, a non-fragile aperiodic sampled-data controller, which allows both additive and multiplicative gain fluctuations, is designed to ensure the asymptotic synchronization based on solutions of a set of linear matrix inequities. Finally, an example with simulations is presented, which shows that the designed controller allows a larger sampling period in comparison with the existing results.

The derivations of the most probable distribution are not self-consistent in most statistical physics textbooks since the Stirling’s approximation adopted in the derivations is not valid for systems with very few particles. Any improvement by taking more higher terms of the Stirling series is insufficient due to erroneous divergence for small number. In this paper, we derive the equilibrium distribution by extrapolating the factorial function by the gamma function so that the Stirling’s approximation or the Stirling formula is avoided. For the ideal Bose system in a one-dimensional harmonic trap, we find that the equilibrium distribution given by this paper coincide with the rigorous result perfectly even for very small system size.

In this paper, we have developed a combined magnetic field system to explore an alternative technical route for the generation of Bose–Einstein condensates containing numerous atoms on an atom chip. The system is characterized by the fact that the quadrupole magnetic field required by the magneto-optic trap is generated by U-shaped current-carrying wires combined with bias magnetic fields, whereas the quadrupole magnetic field adopted for the magnetic trap is generated by anti-Helmholtz coils. By fine-tuning the bias magnetic fields, the collection of atoms in the mirror MOT and the loading of the quadrupole magnetic trap can be optimized. The initial number of ${}^{87}$Rb atoms in the magnetic trap is approximately $1\times 10^8$, and the lifetime of the atoms is over 30 s. This scheme can facilitate the chip-surface design and is suitable for the precise manipulation of Bose–Einstein condensates near the chip surface.

In the case of high pressure, the size of the multistage pump axial force sometimes reaches hundreds of tons, the seriousness of the problem generated by excessive axial force has surpassed the efficiency, wear and other factors, and has become a decisive factor in the stable operation of multistage pumps. In this paper, the 11-stage double-case multistage pump is taken as the research object. On the basis of studying the clearance internal flow mechanism, according to the pressure difference equation of axial motion of clearance fluid, the main factors affecting the balance force of the balance drum are analyzed, and a new type of balance drum — “double helical balance drum” is proposed, which is compared with the smooth balance drum in the hydraulic performance and axial force performance. The research shows that with the increase of the axial displacement of the balance clearance, the pressure drop between the clearances decreases linearly. Compared with the smooth balance drum, the pressure drop at the inlet and outlet of the helical balance drum is 1.30 times that of the smooth balance drum under the design flow rate condition, the mean velocity, mean velocity curl and velocity coefficient of the double helical balance drum increase, indicating that adding double helix can increase the dynamic pressure ratio of clearance fluid. In addition, the test results show that the head and efficiency of the double helical balance drum of multistage pump is increased by 0.76% and 1.1%, respectively, compared with the smooth balance drum, and the vibration amplitude of the front and rear bearing is reduced by 3.36%, 0.76% and 1.75% on average along the axial, radial and tangential direction. In addition, the temperature of the front and rear bearing is reduced by 3.1% and 8.7%, respectively, indicating that the double helical balance drum can effectively improve the hydraulic performance and axial force performance of the multistage pump at design operating point. The results of the study can provide reference for the long-cycle stable operation of multistage pumps and the optimization of balance drum design.

The role of dissipation with respect to a microscopic superposition of quantum states is investigated by means of master equations. This has implications for the study of the emergence of classicality from the quantum level. In particular, it illustrates why it is difficult to observe a macroscopic quantum state. The role of the environment is assumed by the measuring apparatus. A pure state is reduced to a mixture in the pointer basis of the system by means of the interaction with the apparatus. It is the intention that this type of analysis will have applications to experiments which are designed to better understand the environmental-assisted invariance formulation of quantum mechanics.