Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean

A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.

Influence of Boundary Effect on Fracture of Concrete

The recently-developed boundary effect concept and the associated asymptotic model are used to analyze size-dependent fracture of concrete specimens.It is shown that the dependence of concrete fracture on specimen size,crack and/or ligament length is due to the same mechanism,i.e.the interactions between the crack tip fracture process zone and specimen's boundaries.By introducing an equivalent crack length ae,dimension dependent fracture becomes equivalent to fracture of a large plate with a small edge crack,and therefore,follows the same relationship of the 'net' nominal strength σn versus ae.As a result,the size dependent fracture can be predicted using the data measured on different types of specimens.To demonstrate the flexibility and effectiveness of the asymptotic boundary effect model,previously published results of three test series are analyzed.Excellent agreement has been found.Implications of the successful prediction are discussed.

Elasto-plastic analysis of crack in metallic foams

To determine the solutions of the well-known problem of a finite width strip with single edge crack,some results on elasto-plastic fracture analysis for metallic foams are reported.Meanwhile,in order to discuss and put an insight into the nonlinear fracture analysis,the Dugdale model for plastic deformation of this configuration for metallic foams is recommended and solved.Combining the asymptotic solution with the Dugdale model and elastic solution,the stress field in the plastic zone and the size of the plastic zone are expressed as analytical forms.Based on Williams expansion method,the estimate of the scale factor is also completed and analyzed.In view of these analytical solutions,the results show the scale factor is a useful parameter for the fracture theory of metallic foams.

Blast Waves in Multi-Component Medium with Thermal Relaxation

The mathematical models of relaxing media with a structure for describing nonlinear long-wave processes are explored. The wave processes in non-equilibrium heterogeneous media are studied in terms of the suggested asymptotic averaged model. On the microstructure level of the medium, the dynamical behavior is governed only by the laws of thermodynamics, while, on the macrolevel, the motion of the medium can be described by the wave-dynamical laws. It is proved rigorously that on the acoustic level, the propagation of long waves can be properly described only in terms of dispersive dissipative properties of the medium, and in this case, the dynamical behavior of the medium can be modeled by a homogeneous relaxing medium. At the same time, the dynamical behavior of the medium cannot be modeled by a homogeneous medium even for long waves, if they are nonlinear. For a finite-amplitude wave, the structure of medium produces nonlinear effects even if the individual components of the medium are described by a linear law. The heterogeneity of the structure of medium always introduces additional nonlinearity. It is shown that the solution of many problems for multi-component media with incompressible phases can be obtained through the known solution of a similar problem for a homogeneous compressible medium by means of the suggested transformation. It is not necessary to solve directly the problem for the medium with incompressible component, and it is sufficient just to transform the known solution of the similar problem for a homogeneous medium. The scope for the suggested transformation is demonstrated by the reference to the strong explosion state in a two-phase medium. The special attention is focused on the research of blast waves in multi-component media with thermal relaxation. The dependence of the shock damping parameters on the thermal relaxation time is analyzed in order to provide a deeper understanding of the damping of shock waves in such media and to determine their effectiveness as localizing media. This problem attracts the interest also in view of the practical possibility to estimate the efficiency of medium for damping the shock wave action. To find the nature of the relaxation interaction between the components of medium and to estimate the attenuation of shock waves generated by solid explosives, we have studied experimentally both the velocity field of shock waves and the pressure at front in an air foam. The comparison of experimental and theoretical investigations of the relaxation phenomena which accompany the propagation of shock waves in foam indicates that within the scope of relaxation hydrodynamics it is possible to explain the observed phenomena and estimate the efficiency of medium as localizer of the shock wave action.

Decay of Solutions to a Linear Viscous Asymptotic Model for Water Waves

The authors discuss a linear viscous asymptotic model for water waves and the decay rate of solutions towards the equilibrium.

Asymptotic behavior of solutions for some chemical reaction models

IN the process of forecasts, analyses and numerical treatments of the ground water resource, we often meet with various chemical reaction models. One type of them is three kinds of chemical substance M1, M2 and M3 which can react with each other to produce two new kinds of other chemical compounds: （M2）n （M1）m and （M3）r （M1）κ at the same time. Usually, these reactions are irreversible and they have the following forms:

THE ASYMPTOTIC VALIDITY OF THE F-TEST IN A TWO-STAGE LEAST SQUARES MODEL

The usual F--test has been used to test a general linear hypothesis for a two--stage least squaresmethod in a system of economic equations. However, we find that this F--test is actuallyasymptotically invalid. Some suggestions are given for testing a general linear hypothesis in thissituation.

Asymptotic behavior of solutions of defocusing integrable discrete nonlinear Schrodinger equation

We report our recent result about the long-time asymptotics for the defocusing integrable discrete nonlinear Schrodinger equation of Ablowitz- Ladik. The leading term is a sum of two terms that oscillate with decay of order t-1/2.