An analysis of collective damage for short fatigue cracks based on equilibrium of crack numerical density

Collective damage of short fatigue cracks was analyzed in the light of equilibrium of crack numerical density. With the estimation of crack growth rate and crack nucleation rate, the solution of the equilibrium equation was studied to reveal the distinct feature of saturation distribution for crack numerical density. The critical time that characterized the transition of short and long-crack regimes was estimated, in which the influences of grain size and grain-boundary obstacle effect were investigated. Furthermore, the total number of cracks and the first order of damage moment were discussed.

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations (CDEs) is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.

Analysis of Instabilities in Non-Equilibrium Plasmas

Plasma instabilities with charged particle production processes in non-equilibrium plasma are analysed. A criterion on plasma instabilities is deduced by 6rst-order perturbation theory. The relationship between plasma instabilities and certain factors (degree of non-equilibrium in Plasma, the electron attachment rate coefficient and electron temperature) are described.

A non-equilibrium sediment transport model for rill erosion

Sediment transport in rill flows exhibits the characteristics of non-equilibrium transport, and the sediment transport rate of rill flow gradually recovers along the flow direction by erosion. By employing the concept of partial equilibrium sediment transport from open channel hydraulics, a dynamic model of rill erosion on hillslopes was developed. In the model, a parameter, called the restoration coefficient of sediment transport capacity, was used to express the recovery process of sediment transport rate, which was analysed by dimensional analysis and determined from laboratory experimental data. The values of soil loss simulated by the model were in agreement with observed values. The model results showed that the length and gradient of the hillslope and rainfall intensity had different influences on rill erosion. Copyright (c) 2006 John Wiley & Sons, Ltd.

Equilibrium of isolated magnetostatic flux structure

Two-dimensional magnetostatic models of flux structure confined in stratified atmosphere are discussed in the present paper. The magnetic field in the flux structure is assumed to be force-free at the first step. Numerical solutions for this nonlinear free boundary problem are obtained by finite element method. Results show clearly the relation between the inside fields and outside pressure, especially the influence of atmospheric pressure distribution on the flux structure.

Magnetohydrodynamics equilibrium of a self-confined elliptic plasma ball

A variational principle is applied to the problem of magnetohydrodynamics (MHD) equilibrium of a self-contained elliptical plasma ball, such as elliptical ball lightning. The principle is appropriate for an approximate solution of partial differential equations with arbitrary boundary shape. The method reduces the partial differential equation to a series of ordinary differential equations and is especially valuable for treating boundaries with nonlinear deformations. The calculations conclude that the pressure distribution and the poloidal current are more uniform in an oblate self-confined plasma ball than that of an elongated plasma ball. The ellipticity of the plasma ball is obviously restricted by its internal pressure, magnetic field, and ambient pressure. Qualitative evidence is presented for the absence of sighting of elongated ball lightning.

The induction plasma chemical reactor: Part I. Equilibrium model

A mathematical model is presented for the numerical simulation of the flow, temperature, and concentration fields in an rf plasma chemical reactor. The simulation is performed assuming chemical equilibrium. The extent of validity of this assumption is discussed. The system considered is the reaction of SiCl4 and NH3 for the production of Si3N4.

Magnetostatic equilibrium of isolated magnetic-flux tube

In the present paper, an isolated axisymmetric flux tube is discussed for slender magnetic configuration. The magnetostatic model and the stratified atmospheric model are applied, respectively, to the regions inside and outside the flux tube. The problem is described mathematically by the nonlinear partial differential equations under the nonlinear boundary condition at the free boundary of flux tube. According to the approximation of a small expansive angle, the solutions of series expressions are obtained formally. The model of polytropic plasma is discussed in detail especially. The results show the distributions of thermodynamic quantities and magnetic field extending from the high β region to the low β region, and the flux tube may be either divergent or convergent according to the pressure difference outside and inside the flux tube.

Magnetohydrodynamic equilibrium of plasma ball lightning

Thin foil observations using transmission electron microscopy reveal that the density of dislocations within the band is extremely high and the tangled arrangement of dislocations tends to align along the length of the shear band. The grains in the band were also elongated along the shear band and clearly exhibited a crystallographic nature.

Non-axisymmetric magnetostatic equilibrium with strong twisted component of magnetic field

The perturbation theory is applied further to the discussion of the equilibrium properties of a sunspot-like magnetic field with a strong twisted component. The basic state reduces to the usual one discussed extensively for the axisymmetric magnetostatic equilibrium with twisted component of magnetic field, and the perturbed state is described by two coupled equations. As the magnetic force-line is twisted, there is a magnetic tension in the azimuthal direction. In this case, the perturbed total pressure is no longer independent of the azimuthal variable θ, and the magnetic field in the dark penumbal fibril may be either stronger or weaker relatively.

The magnetohydrostatic equilibrium of horizontal prominence of torus configuration

There are several examples of horizontal ringlike prominences in the observations of Ha monochromatic image of the sun. In the present paper the statie equilibrium of the plasma loop is discussed. The analytic solutions to magnetic field and density are obtained for the axisymmetrie case under the closed boundary condition. Results show the great influence of the gravity and different force-free factors on the configurations of magnetic surfaces and the distributions of thermodynamical quantities for the prominence.

Universal equilibrium range of turbulence

An attempt is made to determine the form of F(x), the dimensionless function of universal nature which occurs in the energy spectrum for the universal equilibrium range of fully developed turbulence, by the method of statistical mechanics without introducing any parameter of semiempirical nature. Then, the validity of the variational approach to the closure problem of turbulence theory is tested by applying it to the study of the universal equilbrium range of turbulence.

Static equilibrium of horizontal ring prominence

In 1980 the Beijing Observatory had successively observed sevesal rare completely closed ring prominences whose ring plane was approximately parallel to the solar surface with a characteristic life about 1—2 days. In this paper we discuss the static equilibrium of this kind of horizontal ring plasma under the simultaneous actions of magnetic force, gravity and pressure gradients. Assuming ring plasma with axisymmetry and rectangular plasma cross-section and adopting closed magnetic field boundary condition from the basic equations we obtain the exact zero order general solutions for magnetic field (force-free field) and density (pressure). We further obtain an eigen-solution for the zero order magnetic field and density as well as the first order magnetic field, thus giving a kind of the possible distribution of magnetic field and density for the horizontal closed ring prominence. The closed magnetic structure of ring prominence as presented in this paper, has no link with the force lines of the outside corona magnetic field. This is helpful to explain the great temperature difference between prominenee and corona.

The Propagation Characteristics of Microwave in a Non-Equilibrium Plasma Layer

The influence of non-equilibrium plasma layer pressure and thickness on the transmission of microwave is considered when the incidence of wave is at an arbitrary angle. The plasma is cold, weakly ionized, and steady-state. It is assumed that it is a layered media with a kind of distribution of electron number density and the microwave is a plane wave. The results show that the pressure of plasma affects the absorption of microwave deeply, and the thickness relatively weakly in a non-equilibrium plasma slab.

Chemical equilibrium analysis and CFD simulation of coal combustion and NOx formation

A full two-fluid model of reacting gas-particle flows with an algebraic unified second-order moment (AUSM) turbulence-chemistry model is used to simulate Beijing coal combustion and NOx formation. The sub-models are the k-epsilon-kp two-phase turbulence model, the EBU-Arrhenius volatile and CO combustion model, the six-flux radiation model, coal devolatilization model and char combustion model. The blocking effect on NOx formation is discussed. In addition, the chemical equilibrium analysis is used to predict NOx concentration at different temperature. Results of CID simulation and chemical equilibrium analysis show that, optimizing air dynamic parameters can delay the NOx formation and decrease NOx emission, but it is effective only in a restricted range. In order to decrease NOx emission near to zero, the re-burning or other chemical methods must be used.