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Under a longitudinal rescaling of coordinates x 0,3 → λ x 0,3 , λ ≪ 1, the classical QCD action simplifies dramatically. This is the high-energy limit, as λ ∼ s −1/2 , where s is the center-of-mass energy squared of a hadronic collision. We find the quantum corrections to the rescaled action at one loop, in particular finding the anomalous powers of λ in this action, with λ < 1. The method is an integration over high-momentum components of the gauge field. This is a Wilsonian renormalization procedure, and counterterms are needed to make the sharp-momentum cut-off gauge invariant. Our result for the quantum action is found, assuming | ln λ | ≪ 1, which is essential for the validity of perturbation theory. If λ is sufficiently small (so that | ln λ | ≫ 1), then the perturbative renormalization group breaks down. This is due to uncontrollable fluctuations of the longitudinal chromomagnetic field.

Based on the social and economic development, environmental protection needs, industrial policies and other smart energy systems have brought a new round of great changes compared with the traditional energy structure. Now the development of information technology provides a strong technical support for the transformation and upgrading of traditional energy to smart energy. This paper combines cloud computing, big data, artificial intelligence, blockchain and other emerging technologies to enable the traditional energy system, a smart energy system architecture based on cloud computing platform is proposed, which connects the bottom layer to the top layer of the energy system, and realizes the comprehensive integration of physical energy flow, information flow and value flow of smart energy.

The sonic drill mainly utilizes a sonic vibrator to initiate standing wave resonance of the drill string to achieve high-speed drilling. However, the explicit function relation between the lumped mass and modal frequency could not be revealed. Precisely controlling the sonic vibrator frequency to maintain the standing wave resonance of the drill string is difficult. In this study, the one-dimensional wave theory is employed to establish the longitudinal vibration differential equations of the sonic drill string with vibrator mass. The modal frequency equation of the sonic drill string with an inertial boundary is obtained via the method of separation of variables. The explicit expression of the modal frequency with respect to the vibrator mass and system structure parameters is calculated by mathematical analysis. Moreover, the influence of the large vibrator mass on the dynamic characteristics of the drill string is revealed during drilling of a shallow hole. This can precisely track the vibration control frequency of the sonic drill during shallow hole drilling, while maintaining the standing wave resonance of the drill string coupled with the sonic vibrator. Thus the efficiency of sonic drilling is improved.

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