Helical Mode Absolute Statistical Equilibrium of Ideal Three-Dimensional Hall Magnetohydrodynamics

Using the Fourier helical decomposition, we obtain the absolute statistical equilibrium spectra of left- and right-handed helical modes in the incompressible ideal Hall magnetohydrodynamics (MHD). It is shown that the left-handed helical modes play a major role on the spectral transfer properties of turbulence when the generalized helicity and magnetic helicity are both positive. In contrast, the right-handed helical modes will play a major role when both are negative. Furthermore, we also find that if the generalized helicity and magnetic helicity have opposite signs, the tendency of equilibrium spectra to condense at the large or small wave numbers will be presented in different helical sectors. This indicates that the generalized helicity dominates the forward cascade and the magnetic helicity dominates the inverse cascade properties of the Hall MHD turbulence.

Standards of Classical Architecture Criticism: Between Mathematics and Philosophy

Criticism is an intellectual process that primarily searches for beauty aspects in the works of art,including architecture.This article explores the mathematical and philosophical principles of classical architectural criticism.It is hypothesized that design criteria during the Classic period were clear and specific.The research presents theories of classical art that focus on the process of beauty interpretation.It also assesses the mathematical evaluation of architectural art and beauty through“The Golden Ratio”and“The Fibonacci Sequence.”Classical philosophy,and its perception of beauty,is discussed as an essential basis in any artistic critical activity.The research asserts that the science of aesthetics is both objective and subjective,which explains the difference in aesthetic evaluation across eras.Objectivity stems from conditions of proportionality that must be met for an architectural art to be aesthetically judged as beautiful.Subjectivity lies in the time and place of the architectural work,whereby tendencies,tastes,and needs related to the human and geographical environment can affect the standards of beauty.This makes the evaluation of beauty in classical architecture a delicate and complex process in which many aspects must be considered to have an objective,fair,and correct judgment.

Similarity evaluation of stratum anti-drilling ability and a new method of drill bit selection

Considering the stratum anti-drilling ability,drill bit working conditions,drill bit application effect and drill bit economic benefits,the similarity of stratum anti-drilling ability was evaluated by grey relational analysis theory to screen out candidate drill bits with reference values.A new comprehensive performance evaluation model of drill bit was established by constructing the absolute ideal solution,changing the relative distance measurement method,and introducing entropy weight to work out the closeness between the candidate drill bits and ideal drill bits and select the reasonable drill bit.Through the construction of absolute ideal solution,improvement of relative distance measurement method and introduction of entropy weight,the inherent defects of TOPSIS decision analysis method,such as non-absolute order,reverse order and unreasonable weight setting,can be overcome.Simple in calculation and easy to understand,the new bit selection method has good adaptability to drill bit selection using dynamic change drill bit database.Field application has proved that the drill bits selected by the new drill bit selection method had significant increase in average rate of penetration,low wear rate,and good compatibility with the drilled formations in actual drilling.This new method of drill bit selection can be used as a technical means to select drill bits with high efficiency,long life and good economics in oilfields.

An Improved Prediction Model of Vortex Shedding Noise from Blades of Fans

The main source of the noise of an axial flow fan is the fluctuating pressure field on blade surfaces caused by the shedding of vortices at the trailing edge of blades.An analytical model to predict the vortex shedding noise generated at the trailing edge of blades of axial flow fans was proposed by Lee in 1993.In this model,for mathematical convenience,an idealized vortex street is considered.However,the agreement between the analytical results and the experimental data needs to be improved because of the simplification about the Karman vortex street in the wake of blade.In the present study,a modified model is proposed based on the prediction model by Lee.The boundary layer theory is used to analyze and calculate the boundary layer development on both the pressure and the suction sides of blades.Considering the effect of boundary layer separation on the location of noise source,the predicted overall sound pressure level compares favorably with the experimental data of an axial fan.In the calculation of A-weighted sound pressure level(La),considering the effect of static pressure on radiate energy,the predicted broadband noise with the modified model compares favorably with the experimental data of a multiblade centrifugal fan.