Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence

Main mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence are presented and discussed. The underlying fact is that there does not exist the absolute zero fluid-volume. Therefore, the physical object corresponding to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-particle corresponds to the uniform monad, while the nonuniform fluid-particle to the nonuniform monad. There are two kinds of the differentiations, one is based on the absolute point, and the other based on the monad. The former is adopted in the Navier-Stokes equations, and the latter in the fundamental equations presented in this paper for the nonstandard analysis theory of turbulence. The continuity of fluid is elucidated by virtue of the concepts of the fluid-particle and fluid-particle at a lower level. Furthermore, the characters of the continuity in two cases, i.e. in the standard and nonstandard analyses, are presented in this paper. And the difference in discretization between the Navier-Stokes equations and the fundamental equations given herein is also pointed out.

Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.

Nonlinearity analysis of piezoelectric micromachined ultrasonic transducers based on couple stress theory

This paper studies the static deformation behavior of a piezoelectric micromachined ultrasonic transducer （PMUT） actuated by a strong external electric field. The transducer membrane consists of a piezoelectric layer, a passive layer and two electrode layers. The nonlinearities of the piezoelectric layer caused by electrostriction under a strong electric field are analyzed. Because the thickness of the transducer membrane is on the microscale, the size dependence of the deformation behavior is evaluated using the couple stress theory. The results show that the optimal ratio of the top electrode diameter and the membrane diameter is around 0.674. It is also found that this optimal value does not depend on any other parameters if the thicknesses of the two electrodes are negligible compared with those of the piezo- electric and passive layers. In addition, the nonlinearities of the piezoelectric layer will become stronger along with the increase of the electric field, which means that softening of the membrane stiffness occurs when a strong external electric field is applied. Meanwhile, the optimal thickness ratio for the passive layer and the piezoelectric layer is not equal to 1.0 which is usually adopted by previous researchers. Because there exists size dependence of membrane deforma-tion, the optimal value of this thickness ratio needs to be greater than 1.0 on the microscale.

THE RATIONALISM THEORY AND ITS FINITE ELEMENT ANALYSIS METHOD OF SHELL STRUCTURES

In this paper, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.

Impact of failure mode and effects analysis-based emergency management on the effectiveness of craniocerebral injury treatment

BACKGROUND Craniocerebral injuries encompass brain injuries,skull fractures,cranial soft tissue injuries,and similar injuries.Recently,the incidence of craniocerebral injuries has increased dramatically due to the increased numbers of traffic accidents and aerial work injuries,threatening the physical and mental health of patients.AIM To investigate the impact of failure modes and effects analysis(FMEA)-based emergency management on craniocerebral injury treatment effectiveness.METHODS Eighty-four patients with craniocerebral injuries,treated at our hospital from November 2019 to March 2021,were selected and assigned,using the random number table method,to study(n=42)and control(n=42)groups.Patients in the control group received conventional management while those in the study group received FMEA theory-based emergency management,based on the control group.Pre-and post-interventions,details regarding the emergency situation;levels of inflammatory stress indicators[Interleukin-6(IL-6),C-reactive protein(CRP),and procalcitonin(PCT)];incidence of complications;prognoses;and satisfaction regarding patient care were evaluated for both groups.RESULTS For the study group,the assessed parameters[pre-hospital emergency response time(9.13±2.37 min),time to receive a consultation(2.39±0.44 min),time needed to report imaging findings(1.15±4.44 min),and test reporting time(32.19±6.23 min)]were shorter than those for the control group(12.78±4.06 min,3.58±0.71 min,33.49±5.51 min,50.41±11.45 min,respectively;P<0.05).Pre-intervention serum levels of IL-6(78.71±27.59 pg/mL),CRP(19.80±6.77 mg/L),and PCT(3.66±1.82 ng/mL)in the study group patients were not significantly different from those in the control group patients(81.31±32.11 pg/mL,21.29±8.02 mg/L,and 3.95±2.11 ng/mL respectively;P>0.05);post-intervention serum indicator levels were lower in both groups than pre-intervention levels.Further,serum levels of IL-6(17.35±5.33 pg/mL),CRP(2.27±0.56 mg/L),and PCT(0.22±0.07 ng/mL)were lower in the study group than in the control group(30.15±12.38 pg/mL,3.13±0.77 mg/L,0.38±0.12 ng/mL,respectively;P<0.05).The complication rate observed in the study group(9.52%)was lower than that in the control group(26.19%,P<0.05).The prognoses for the study group patients were better than those for the control patients(P<0.05).Patient care satisfaction was higher in the study group(95.24%)than in the control group(78.57%,P<0.05).CONCLUSION FMEA-based craniocerebral injury management effectively shortens the time spent on emergency care,reduces inflammatory stress and complication risk levels,and helps improve patient prognoses,while achieving high patient care satisfaction levels.

Stability Analysis on Speed Control System of Autonomous Underwater Vehicle

The stability of the motion control system is one of the decisive factors of the control quality for Autonomous Underwater Vehicle（AUV）.The divergence of control,which the unstable system may be brought about,is fatal to the operation of AUV.The stability analysis of the PD and S-surface speed controllers based on the Lyapunov＇s direct method is proposed in this paper.After decoupling the six degree-of-freedom（DOF）motions of the AUV,the axial dynamic behavior is discussed and the condition is deduced,in which the parameters selection within stability domain can guarantee the system asymptotically stable.The experimental results in a tank and on the sea have successfully verified the algorithm reliability,which can be served as a good reference for analyzing other AUV nonlinear control systems.

A case study of blasting vibration attenuation based on wave component characteristics

A typical blasting vibration wave is a composite wave,and its attenuation law is affected by the type of dominant wave component.The purpose of the present study is to establish an attenuation equation of the peak particle velocity(PPV),taking into account the attenuation characteristics of P-,S-and R-waves in the blasting vibration wave.Field blasting tests were carried out as a case to specifically apply the proposed equation.In view of the fact that the discrete properties of rock mass will inevitably cause the uncertainty of blasting vibration,we also carried out a probability analysis of PPV uncertainty,and introduced the concept of reliability to evaluate blasting vibration.The results showed that the established attenuation equation had a higher prediction accuracy,and can be considered as a promising equation implemented on more complex sites.The adopted uncertainty analysis method can comprehensively take account of the attenuation law of blasting vibration measured on site and discrete properties of rock masses.The obtained distribution of the PPV uncertainty factor can quantitatively evaluate the reliability of blasting vibration,which is a powerful and necessary supplement to the PPV attenuation equation.

Nonequilibrium free energy and information flow of a double quantum-dot system with Coulomb coupling

We build a double quantum-dot system with Coulomb coupling and aim at studying connections among the entropy production,free energy,and information flow.By utilizing concepts in stochastic thermodynamics and graph theory analysis,Clausius and nonequilibrium free energy inequalities are built to interpret local second law of thermodynamics for subsystems.A fundamental set of cycle fluxes and affinities is identified to decompose two inequalities by using Schnakenberg's network theory.Results show that the thermodynamic irreversibility has energy-related and information-related contributions.A global cycle associated with the feedback-induced information flow would pump electrons against the bias voltage,which implements a Maxwell demon.

Failure mechanism of large-diameter shield tunnels and its effects on ground surface settlements

A new technique for the analysis of the three-dimensional collapse failure mechanism and the ground surface settlements for the large-diameter shield tunnels were presented.The technique is based on a velocity field model using more different truncated solid conical blocks to clarify the multiblock failure mechanism.Furthermore,the shape of blocks between the failure surface and the tunnel face was considered as an entire circle,and the supporting pressure was assumed as non-uniform distribution on the tunnel face and increased with the tunnel embedded depth.The ground surface settlements and failure mechanism above large-diameter shield tunnels were also investigated under different supporting pressures by the finite difference method.

2D-and 3D-QSBR Studies on the Relationship between Structure and Biodegradability of Phthalates

Nine phthalates were calculated at the B3LYP/6-311G＊＊ level using DFT method. The corresponding linear relationship equations （R2 were 0.853 and 0.936 respectively） for the biodegradation rate （Kb） and half-life time （h/2） of biodegradation were obtained with the structural parameters as theoretical descriptors. Furthermore, CoMFA method was also applied to establish 3D models which revealed the fields influencing these properties. The relationship between the properties and the structure was obtained. The correlation coefficients of the models were 0.992 and 0.999, respectively. Analyses of 2D and 3D models demonstrated that the molecular volume was an important factor affecting the biodegradability of these compounds.

Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length: Functional Theoretical Approach

With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities cointide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeψ〈〈kT is introduced.

NOTICE

1. The Journal Analysis in Theory and Applications （ abbr. ATA used to be Approximation Theory and its Applications in 1984-2002） publishes original papers in the following fields：

The Single Valley Character of Level Degree Function

Strict proof has been given to single valley character of level degree function by use of convex analysis theory, which provides reliable theoretical basis for the optimization of the data processing with respect to level degree. As circle degree and cylindrical degree have the same mathematical structures, their single valley character can be proved by the same method.

NOTICE

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NOTICE

1. The Journal Analysis in Theory and Applications （ abbr. ATA used to be Approximation Theory and its Applications in 1984-2002） publishes original papers in the following fields：