Quantitative Analysis of Insulator Degradation in a Single Layer Solenoid by Renormalization of the Transmission Parameter

In this paper, a novel method to quantitatively analyze insulator degradation in a single layer solenoid is proposed. The suggested method employs renormalization of scattering parameters to efficiently detect changes of permittivity in a degraded solenoid. Firstly, a transmission line model, including a locally degraded part in the insulator, was developed, and it was determined that the phase information of the transmission parameter was very informative to check the permittivity change in the transmission line. To check the workability of this idea in a solenoid, a 30-turn single-layer solenoid was designed and fabricated, and 51 degraded states for mimicking insulation deterioration in each turn were introduced by installing additional insulator rings, which increased local relative permittivity. The phase data of the measured transmission parameter turned out to be useful for quantifying changes of the insulator in the solenoid. To maximize the detectability, the measured scattering parameters were renormalized with different reference impedances, which was very useful for detecting degradation in the transmission parameter. In this paper, detailed procedures for quantitatively analyzing degradation of an insulator are proposed and we verify that the suggested renormalization technique is very promising for effectively evaluating the degradation of a solenoid.

Test of indestructibility of a nonsingular black hole

Classical singular black holes are known to obey the cosmic censorship conjecture, and therefore are indestructible until they get completely evaporated by the Hawking radiation phenomenon. However, a nonsingular quantum black hole may not be necessarily indestructible. To proceed in this test, we deduce the first law of thermodynamics for the renormalization technique based, quantum improved, nonsingular Kerr class black hole, and then the test is done by Wald’s method. It emerges that while the quantum improvement leads to an escape for black hole from complete evaporation, it also makes a spinning black hole well destructible against overspinning. Even though, in general, spinning quantum black holes appear quite destructible, in the regime of exceedingly low rate of allowed spin, slower the spin becomes, weaker happens to be the probability of black hole getting destroyed. In particular, the minimally energized black hole relic, which is of a Schwarzschild class, emerges absolutely indestructible. It has further been argued that the practical stable existence of “G-lumps” is improbable. In context of our formal work, we find a great scope for figuring out the quantum corrected differential version of “entropy-area law” for Kerr class black hole.

RESONANT AC CONDUCTING SPECTRA IN QUASIPERIODIC SYSTEMS

Based on the Kubo-Greenwood formula, a renormalization plus convolution method is developed to investigate the frequency-dependent electrical conductivity of quasiperiodic systems. This method combines the convolution theorem with the real-space renormalization technique which is able to address multidimensional systems with 1024 atoms. In this article, an analytical evaluation of the Kubo-Greenwood formula is presented for the ballistic ac conductivity in periodic chains. For quasiperiodic Fibonacci lattices connected to two semi-infinite periodic leads, the electrical conductivity, is calculated by using the renormalization method and the results show that at several frequencies, their ac conductivities could be larger than the ballistic ones. This fact might be related to the resonant scattering process in quasiperiodic systems. Finally, calculations made in segmented Fibonacci nanowires reveal that this improvement to the ballistic ac conductivity via quasiperiodicity is also present in multidimensional systems.

Trajectory-Tracking Scheme in Lagrangian Form for Solving Linear Advection Problems: Preliminary Tests

A Lagrangian linear advection scheme, which is called the trajectory-tracking scheme, is proposed in this paper. The continuous tracer field has been discretized as finite tracer parcels that are points moving with the velocity field. By using the inverse distance weighted interpolation, the density carried by parcels is mapped onto the fixed Eulerian mesh (e.g., regular latitude–longitude mesh on the sphere) where the result is rendered. A renormalization technique has been adopted to accomplish mass conservation on the grids. The major advantage of this scheme is the ability to preserve discontinuity very well. Several standard tests have been carried out, including 1D and 2D Cartesian cases, and 2D spherical cases. The results show that the spurious numerical diffusion has been eliminated, which is a potential merit for the atmospheric modeling.

RENORMALIZED HIGHER POWERS OF WHITE NOISE (RHPWN) AND CONFORMAL FIELD THEORY

The Virasoro–Zamolodchikov *-Lie algebra w∞ has been widely studied in string theory and in conformal field theory, motivated by the attempts of developing a satisfactory theory of quantization of gravity. The renormalized higher powers of quantum white noise (RHPWN) *-Lie algebra has been recently investigated in quantum probability, motivated by the attempts to develop a nonlinear generalization of stochastic and white noise analysis. We prove that, after introducing a new renormalization technique, the RHPWN Lie algebra includes a second quantization of the w∞ algebra. Arguments discussed at the end of this note suggest the conjecture that this inclusion is in fact an identification.

RENORMALIZED SQUARES OF BOSON FIELDS

The standard renormalization procedure consists of introducing a cutoff and then trying to remove it by some limiting procedure. In Ref. 2 a new renormalization technique was introduced based on the idea of renormalizing a closed set of commutation relations and then finding a nontrivial representation for them. In Ref. 5 it was proved that, in the case of quadratic fields the new renormalization procedure leads to quadratic field operator which is gamma distributed in the quadratic vacuum (as one would intuitively expect from the "square" of a white noise) and to Meixner or Pascal distributed Poisson fields. It is natural to ask if the same result can be obtained with the usual cutoff and take-limit procedure. In this paper we prove that the answer to this question is negative. More precisely, we show that, independently of the choice of the cutoff (cf. Sec. 7), if a quadratic field admits a limit in the sense of mixed moments, then this limit will be Gaussian distributed in the vacuum and consequently the associated Poisson fields will have a Poisson distribution.