856 research outputs found
Gevrey Smoothing Effect for Solutions of the Non-Cutoff Boltzmann Equation in Maxwellian Molecules Case
In this paper we study the Gevrey regularity for the weak solutions to the
Cauchy problem of the non-cutoff spatially homogeneous Botlzmann equation for
the Maxwellian molecules model with the singularity exponent . We
establish that any weak solution belongs to the Gevrey spaces for any positive
time.Comment: 35 page
Phase-locked scroll waves defy turbulence induced by negative filament tension
Scroll waves in a three-dimensional media may develop into turbulence due to negative tension of the filament. Such negative tension-induced instability of scrollwaves has been observed in the Belousov-Zhabotinsky reaction systems. Here we propose a method to restabilize scroll wave turbulence caused by negative tension in three-dimensional chemical excitable media using a circularly polarized (rotating) external field. The stabilization mechanism is analyzed in terms of phase-locking caused by the external field, which makes the effective filament tension positive. The phase-locked scrollwaves that have positive tension and higher frequency defy the turbulence and finally restore order. A linear theory for the change of filament tension caused by a generic rotating external field is presented and its predictions closely agree with numerical simulations
Online Bearing Remaining Useful Life Prediction Based on a Novel Degradation Indicator and Convolutional Neural Networks
In industrial applications, nearly half the failures of motors are caused by
the degradation of rolling element bearings (REBs). Therefore, accurately
estimating the remaining useful life (RUL) for REBs are of crucial importance
to ensure the reliability and safety of mechanical systems. To tackle this
challenge, model-based approaches are often limited by the complexity of
mathematical modeling. Conventional data-driven approaches, on the other hand,
require massive efforts to extract the degradation features and construct
health index. In this paper, a novel online data-driven framework is proposed
to exploit the adoption of deep convolutional neural networks (CNN) in
predicting the RUL of bearings. More concretely, the raw vibrations of training
bearings are first processed using the Hilbert-Huang transform (HHT) and a
novel nonlinear degradation indicator is constructed as the label for learning.
The CNN is then employed to identify the hidden pattern between the extracted
degradation indicator and the vibration of training bearings, which makes it
possible to estimate the degradation of the test bearings automatically.
Finally, testing bearings' RULs are predicted by using a -support
vector regression model. The superior performance of the proposed RUL
estimation framework, compared with the state-of-the-art approaches, is
demonstrated through the experimental results. The generality of the proposed
CNN model is also validated by transferring to bearings undergoing different
operating conditions
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