Quantum oscillations between weakly coupled Bose–Einstein condensates: Evolution in a non-degenerate double well

In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.

Effects of phase difference between instability modes on boundary-layer transition

Phase effect on the modal interaction of flow instabilities is investigated for laminar-to-turbulent transition in a flat-plate boundary-layer flow. Primary and secondary three-dimensional (3-D) oblique waves at various initial phase differences between these two instability modes. Three numerical methods are used for a systematic approach for the entire transition process, i.e. before the onset of transition well into fully turbulent flow. Floquet analysis predicts the subharmonic resonance where a subharmonic mode locally resonates for a given basic flow composed of the steady laminar flow and the fundamental mode. Because Floquet analysis is limited to the resonating subharmonic mode, nonlinear parabolised stability equation analysis (PSE) is conducted with various phase shifts of the subharmonic mode with respect to the given fundamental mode. The application of PSE offers insights on the modal interaction affected by the phase difference up to the weakly nonlinear stage of transition. Large-eddy simulation (LES) is conducted for a complete transition to turbulent boundary layer because PSE becomes prohibitively expensive in the late nonlinear stage of transition. The modulation of the subharmonic resonance with the initial phase difference leads to a significant delay in the transition location up to $\Delta Re_{x, tr} \simeq 4\times 10^5$ as predicted by the current LES. Effects of the initial phase difference on the spatial evolution of the modal shape of the subharmonic mode are further investigated. The mechanism of the phase evolution is discussed, based on current numerical results and relevant literature data.

Measurement of Microvibration by Using Dual-Cavity Fiber Fabry-Perot Interferometer for Structural Health Monitoring

Extensive researches have recently been performed to study structural integrity using structural vibration data measured by in-structure sensors. A fiber optic sensor is one of candidates for the in-structure sensors because it is low in cost, light in weight, small in size, resistant to EM interference, long in service life, and so forth. Especially, an interferometric fiber optic sensor is very useful to measure vibrations with high resolution and accuracy. In this paper, a dual-cavity fiber Fabry-Perot interferometer was proposed with a phase-compensating algorithm for measuring micro-vibration. The interferometer has structurally two arbitrary cavities; therefore the initial phase difference between two sinusoidal signals induced from the interferometer was also arbitrary. In order to do signal processing including an arc-tangent method, a random value of the initial phase difference is automatically adjusted to the exact 90 degrees in the phase-compensating algorithm part. For the verification of the performance of the interferometer, a simple vibration-test was performed to measure micro-vibration caused by piezoelectric transducer (PZT). As an experimental result, the interferometer attached on the PZT successfully measured the 50 Hz-vibration of which the absolute displacement oscillated between −424 nm and +424 nm.

Coupled Bending-Torsional Vibration Analysis of Rotor System with Two Asymmetric Disks

The dynamic equations derived based on the actual rotor system with two asymmetric disks. In the analysis, the eccentric, rubbing fault characteristics and internal damping effects is considered, and all the analysis is established based on nonlinear oil film force model and coupled bending-torsional differential equations. The Rugge-Kutta method is used to solve numerical model, the torsional displacement response, torsion angle and Poincare map are obtained. The results show torsion amplitudes with initial phase difference π / 2 is larger than initial phase difference of π and 0. In order to eliminate the rigid rolling component the relative torsional angle must be considered.

The Flowing and Heat Transfer Models of Turbulent Flow in Rolling Motion

The flowing and heat transfer characteristics of turbulent flow in tubes in rolling motion are investigated theoretically. The flowing and heat transfer models of turbulent flow in rolling motion are established. The correlations of frictional resistance coefficient and Nusselt number are derived. The results are also validated with experiments. The effects of several parameters on Nusselt number are investigated. The oscillating amplitude of Nusselt number is in direct ratio with Prandtl number and rolling frequency approximately. The more the flowing velocity is, the less the effect of rolling motion on the flow is. The variation of initial phase difference between Nusselt number and rolling motion with rolling frequency is very limited.