Introduction of non-uniformity through linearization of the system governing turbulent, mixing of a scalar quantity in a 2-d mixing layer

The introduction of mathematical non-uniformity in the formulation of the turbulent mixing of a scalar quantity (mass, temperature, etc.) for a 2-d, free shear flow using Goertler's [ZAMM 22 (1942) 244] perturbation argument is discussed. Approximate, i.e. thin shear layer self-similar forms for mass, momentum and the scalar quantity are derived, and then linearized using Goertler's method. Though successful for the mean velocity field, the regular expansion yields inconsistent solutions for the transport of a scalar. Sources of the non-uniformity are identified using appropriate numerical methods for both non-linear and linear formulations. A consistent result is obtained by rescaling the independent variable and equation system and identifying dominant behavior. The results of this corrected formulation are shown to be consistent with the relationships obtained by the author using an approximate matched asymptotic expansion procedure.     

The enhancement of the mixing of a 2D supersonic mixing layer

Numerical simulations have been performed for a 2D supersonic mixing layer with two different types of excitation, namely the introduction of a T-S wave at the inlet and the enforcement of the inflow speed on the low speed side to have periodic stream-wise undulations. The results showed that both ways were effective when the convective Mach numberMc was less than 1, but the latter was more effective than the former. Systematic computations have also been done to analyze the effect of different parameters on mixing.     

Method for enhancing the mixing of a compressible mixing layer

Numerical simulations have been done for a compressible mixing layer, in which the inflow speed on the low speed side was made to have periodic undulations, so as to see if this method could enhance the mixing effect of the layer. Systematic computations for a 2-D compressible mixing layer with Mach numberM _e = 0.6 have been done, and the results showed that the proposed method was indeed effective in enhancing the mixing.     

Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model

Summary In this paper we obtain asymptotic expansions for the distribution function and the density function of a linear combination of the MLE in a GMANOVA model, and for the density function of the MLE itself. We also obtain certain error bounds for the asymptotic expansions.     

Existence of shocklets in a two-dimensional supersonic mixing layer and its influence on the flow structure

The spatial evolution of a T-S wave and its subharmonic wave, introduced at the inlet in a 2-D supersonic mixing layer, was investigated by using DNS. The relationship between the amplitude of the disturbance wave and the strength of the shocklet caused by the disturbance was investigated. We analyzed the shape of the disturbance velocity profile on both sides of the shocklet, and found that the existence of shocklet affected appreciably the disturbance velocity. The effects on the high speed side and low speed side of the mixing layer were found to be different     

Direct numerical simulation of transition and turbulence in compressible mixing layer

The three-dimensional compressible Navier-Stokes equations are approximated by a fifth order upwind compact and a sixth order symmetrical compact difference relations combined with three-stage Ronge-Kutta method. The computed results are presented for convective Mach numberMc = 0.8 andRe = 200 with initial data which have equal and opposite oblique waves. From the computed results we can see the variation of coherent structures with time integration and full process of instability, formation of A -vortices, double horseshoe vortices and mushroom structures. The large structures break into small and smaller vortex structures. Finally, the movement of small structure becomes dominant, and flow field turns into turbulence. It is noted that production of small vortex structures is combined with turning of symmetrical structures to unsymmetrical ones. It is shown in the present computation that the flow field turns into turbulence directly from initial instability and there is not vortex pairing in process of transition. It means that for large convective Mach number the transition mechanism for compressible mixing layer differs from that in incompressible mixing layer.     

An effective asymptotic method in the axisymmetric frictionless contact problem for an elastic layer of finite thickness

A brief review of asymptotic methods to deal with frictionless unilateral contact problems for an elastic layer of finite thickness is presented. Under the assumption that the contact radius is small with respect to the layer thickness, an effective asymptotic method is suggested for solving the unilateral contact problem with a priori unknown contact radius. A specific feature of the method is that the construction of an asymptotic approximation is reduced to a linear algebraic system with respect to integral characteristics (polymoments) of the contact pressure. As an example, the sixth‐order asymptotic model has been written out. Copyright © 2015 John Wiley & Sons, Ltd.     

Second order asymptotic comparison of estimators of a common parameter in the double exponential case

Summary The problem to estimate a common parameter for the pooled sample from the double exponential distributions is discussed in the presence of nuisance parameters. The maximum likelihood estimator, a weighted median, a weighted mean and others are asymptotically compared up to the second order, i.e. the ordern ^−1/2 with the asymptotic expansions of their distributions. University of Electro-communications     

Error estimate in a finite volume approximation of the partial asymptotic domain decomposition

The method of asymptotic partial domain decomposition has been proposed for partial differential equations set in rod structures, depending on a small parameter. It reduces the dimension of the problem (or simplifies it in another way) in the main part of the domain keeping the initial formulation in the remaining part and prescribing the asymptotically precise conditions on the interface. This paper is devoted to the finite volume implementation of the method of asymptotic partial domain decomposition. We consider a model problem in a thin domain (its thickness is a small parameter). We obtain an error estimate, expressed in terms of the small parameter and the step of the mesh. Copyright © 2013 John Wiley & Sons, Ltd.     

An asymptotic approach for a semi‐Markovian inventory model of type (s,S)

In this study, we constructed a stochastic process (X(t)) that expresses a semi‐Markovian inventory model of type (s, S) and it is shown that this process is ergodic under some weak conditions. Moreover, we obtained exact and asymptotic expressions for the n^th order moments (n = 1,2,3, … ) of ergodic distribution of the process X(t), as S ? s → ∞ . Finally, we tested how close the obtained approximation formulas are to the exact expressions. Copyright © 2012 John Wiley & Sons, Ltd.     

An asymptotic formula for the moments of the Minkowski question mark function in the interval [0, 1]

In this paper, we prove an asymptotic formula for the moments of the Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that a certain variation of a Laplace method is applicable in this problem, and hence the task reduces to a number of technical calculations. Dedicated to Antanas Laurinčikas on the occasion of his 60th birthday     

Solvability,asymptotic analysis and regularity results for a mixed type interaction problem of acoustic waves and piezoelectric structures

In the paper, we investigate the mixed type transmission problem arising in the model of fluid–solid acoustic interaction when a piezoceramic elastic body (Ω⁺) is embedded in an unbounded fluid domain (Ω^?). The corresponding physical process is described by the boundary‐transmission problem for second‐order partial differential equations. In particular, in the bounded domain Ω⁺, we have a 4×4 dimensional matrix strongly elliptic second‐order partial differential equation, while in the unbounded complement domain Ω^?, we have a scalar Helmholtz equation describing acoustic wave propagation. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations based on the Wiener–Hopf factorization method, the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces. We derive asymptotic expansion of solutions, and on the basis of asymptotic analysis, we establish optimal Hölder smoothness results for solutions. Copyright © 2017 John Wiley & Sons, Ltd.