Conformal Invariant Asymptotic Expansion Approach for Solving （3＋1）-Dimensional JM Equation

The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.

Impact of Rainfall Temporal Heterogeneity on Relationship between Curve Number and Rainfall Depth in the Zagros Mountain Region,Iran

The impact of temporal variation of rainfall on the relationship between rainfall and catchment response is investigated in a catchment with high temporally variable rainfalls and a high percentage of permeable soils in the southwest of Iran.Twenty-nine storm events are classified into two classes, High Temporal heterogeneous(HT) and Low Temporal heterogeneous(LT) events using the variogram technique and the storm events of each class are analyzed to detect the relationship between Curve Number(CN) and rainfall depth. It is found that there is not a similar correlation between CN values and rainfall depths for both temporally variable classes, and hence, two different responses can be observed in the catchment according to rainfall temporal heterogeneities. For HT events, a complacent behavior is detected in which the CNs decline as rainfall depth increases while a different response, violent behavior, is observed for LT events in which the CNs rise and asymptotically approach a constant value with increasing storm size. This considerable difference between CN-P relationships derived from the two temporally variable classes of rainfall is attributed to the provocation of different runoff generation mechanisms, infiltration-excess and saturation-excess caused by rainfall temporal heterogeneities. Moreover, the results support the validity of variogram technique to classify storm events into two LT and HT classes.

ASYMPTOTIC CONVERGENCE OF A GENERALIZED NON-NEWTONIAN FLUID WITH TRESCA BOUNDARY CONDITIONS

The goal of this article is to study the asymptotic analysis of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions.The yield stress and the constant viscosity are assumed to vary with respect to the thin layer parameterε.Firstly,the problem statement and variational formulation are formulated.We then obtained the existence and the uniqueness result of a weak solution and the estimates for the velocity field and the pressure independently of the parameterε.Finally,we give a specific Reynolds equation associated with variational inequalities and prove the uniqueness.

Analytical study of the interface in fibre-reinforced 2D composite material

Imperfect bonding between the constitutive components can greatly affect the properties of the composite structures.An asymptotic analysis of different types of imperfect interfaces arising in the problem of 2D fibrereinforced composite materials are proposed.The performed study is based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems.All solutions are obtained in a closed analytical form.The obtained results can be used for the calculation of pull-out and pushout tests,as well as for the investigation of the fracture of composite materials.

Asymptotic Analysis of a Bingham Fluid in a Thin Domain with Fourier and Tresca Boundary Conditions

In this paper we prove first the existence and uniqueness results for the weak solution,to the stationary equations for Bingham fluid in a three dimensional bounded domain with Fourier and Tresca boundary condition;then we study the asymptotic analysis when one dimension of the fluid domain tend to zero.The strong convergence of the velocity is proved,a specific Reynolds limit equation and the limit of Tresca free boundary conditions are obtained.