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\leftline{\bf Technical Review} 

\leftline{Pat Q.\ Student}

\leftline{AME 538}

\leftline{16 September 2000}

\bigskip
In their recent article,
 Dahm, et al.\hspace{-2mm}
\footnote{Dahm, W.\ J.\ A., Tryggvason, G., and Zhuang, M.,
 1996,
 ``Integral Method Solution of Time-Dependent Strained Diffusion-Reaction
 Layers with Multistep Kinetics,''
 {\em SIAM Journal of Applied Mathematics}, Vol.\ 56, No.\ 4,
 pp.\ 1039-1059.}
 describe a novel and efficient method for...  
 The physical problem of interest is ....  The problem has application
 in the fields of....
 A key model equation in this study is the reaction kinetics equation

 \begin{equation}
 {\partial c_i \over \partial t} + {\bf u} \cdot \nabla c_i
 -{1 \over \rho} \nabla \cdot \rho D_i \nabla c_i 
 = \sum_{j=1}^r \nu_{ij} w_j.
 \end{equation}
 In this equation $t$ represents time, $c_i$ the molar concentration of the species $i$, 
 $\bf u$ the velocity vector, $\rho$ the density, $D_i$ the diffusivity of species
 $i$, $\nu_{ij}$ the matrix of stoichiometric coefficients, and $w_j$ the reaction
 rate of the $j$th reaction. 
 
 The typical method
 of solving this problem is to.....In many cases this is deficient because....
 Hence a new method is proposed which....
 The method is applied to a set of test problems.  It is seen that....
 The authors summarize their major conclusions as follows....

 The article is generally well written....
 A small deficiency is seen in that...
 Nevertheless the strength of 
 this paper is its clarity in.....and novelty in.....Those who are interested
 in problems in the related fields of.... would find this paper to be useful.

\bigskip
{\bf Notes} 
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