Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

Behaviour of Gaseous Chlorine and Alkali Metals During Biomass Thermal Utilisation

The behaviour of gaseous chlorine and alkali metals of three sorts of biomass (Danish straw, Swedish wood, and sewage sludge) in combustion or gasification is investigated by the chemical equilibrium calculating tool. The ranges of temperature, air-to-fuel ratio, and pressure are varied widely in the calculations (T=400-1800 K, gimel=0-1.8, and P=0.1-2.0 MPa). Results show that the air excess coefficient only has less significant influence on the release of gaseous chlorine and potassium or sodium during combustion. However, in biomass gasification, the influence of the air excess coefficient is very significant. Increasing air excess coefficient enhances the release of HCl(g), KOH(g), or NaOH(g) as well as it reduces the formation of KCl(g), NaCl(g), K(g), or Na(g). In biomass combustion or straw and sludge gasification, increasing pressure enhances the release of HCl(g) and reduces the amount of KCI(g), NaCl(g), KCI(g), or NaOH(g) at high temperatures. However, during wood gasification, the pressure enhances the formation of KOH(g) and KCI(g) and reduces the release of K(g) and HCl(g) at high temperatures. During wood and sewage sludge pyrolysis, nitrogen addition enhances the formation of KCN(g) and NaCN(g) and reduces the release of K(g) and Na(g). Kaolin addition in straw combustion may enhance the formation of potassium aluminosilicate in ash and significantly reduces the release of KCl(g) and KOH(g) and increases the formation of HCl(g).

A Variational Approach to the Burridge-Knopoff Equation

A variational principle is obtained for the Burridge-Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation.

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method.

A family of interesting exact solutions of the sine-Gordon equation

By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

Dynamic constitutive equation of GFRP obtained by Lagrange experiment

The note presents a method of constructing dynamic constitutive equations of material by means of Lagrange experiment and analysis. Tests were carried out by a light gas gun and the stress history profiles were recorded on multiple Lagrange positions. The dynamic constitutive equations were deduced from the regression of a series of data which was obtained by Lagrange analysis based upon recorded multiple stress histories. Here constitutive equations of glass fibre reinforced phenolic resin composite(GFRP) in uniaxil strain state under dynamic loading are given. The proposed equations of the material agree well with experimental results.

A generalized wave action conservative equation for the dissipative dynamical system in the nearshore region

To describe the various complex mechanisms of the dissipative dynamical system between waves, currents, and bottoms in the nearshore region that induce typically the wave motion on large-scale variation of ambient currents, a generalized wave action equation for the dissipative dynamical system in the nearshore region is developed by using the mean-flow equations based on the Navier-Stokes equations of viscous fluid, thus raising two new concepts: the vertical velocity wave action and the dissipative wave action, extending the classical concept, wave action, from the ideal averaged flow conservative system into the real averaged flow dissipative system (that is, the generalized conservative system). It will have more applications.

A Semi-Empirical Equation of Penetration Depth on Concrete Target Impacted by Ogive-Nose Projectiles

In this paper, the penetration process of ogive-nose projectiles into the semi-infinite concrete target is investigated by the dimensional analysis method and FEM simulation. With the dimensional analysis, main non-dimensional parameters which control the penetration depth are obtained with some reasonable hypothesis. Then, a new semi-empirical equation is present based on the original work of Forrestal et al., has only two non-dimensional combined variables with definite physical meanings. To verify this equation, prediction results are compared with experiments in a wide variation region of velocity. Then, a commercial FEM code, LS-DYNA, is used to simulate the complex penetration process, that also show the novel semi-empirical equation is reasonable for determining the penetration depth in a concrete target.

Cauchy singular integral equation method for transient antiplane dynamic problems

In this paper, by use of the boundary integral equation method and the techniques of Green basic solution and singularity analysis, the dynamic problem of antiplane is investigated. The problem is reduced to solving a Cauchy singular integral equation in Laplace transform space. This equation is strictly proved to be equivalent to the dual integral equations obtained by Sih [Mechanics of Fracture, Vol. 4. Noordhoff, Leyden (1977)]. On this basis, the dynamic influence between two parallel cracks is also investigated. By use of the high precision numerical method for the singular integral equation and Laplace numerical inversion, the dynamic stress intensity factors of several typical problems are calculated in this paper. The related numerical results are compared to be consistent with those of Sih. It shows that the method of this paper is successful and can be used to solve more complicated problems. Copyright (C) 1996 Elsevier Science Ltd