\def\figdir{Fig}
\def\bx{ {\bf x}     }
\def\w{ \omega      }
\def\ri{ {\rm i}     }
\def\rd{ {\rm d}     }
\def\di{ \partial    }
\def\t{ \tau        }
\def\g{ \gamma      }
\def\U{ {\cal U}     }
\def\S{ {\cal S}     }
\def\R{ {\cal R}     }
\def\I{ {\cal I}     }
\def\kt{ k_\tau      }
\def\kg{ k_\gamma    }
\def\aj{ \frac{\AA}{J} }
\def\ja{ \frac{J}{\AA} }
\def\dit{ \frac{\partial}{\partial \tau} }
\def\dig{ \frac{\partial}{\partial \gamma} }
\def\dikt{ \frac{\partial}{\partial k_{\tau}} }
\def\dikg{ \frac{\partial}{\partial k_{\gamma}} }
\def\dpdy{ \frac{\partial \phi}{\partial y_j} }
\def\dpdylm{ \frac{\partial \phi}{\partial y_m} }
\def\dydx{ \frac{\partial y_j}{\partial x_i} }
\def\dydxlm{ \frac{\partial y_m}{\partial x_l} }
\def\dir{ \delta}
\def\ti1{ \tau^t}
\def\gi1{ \gamma^{g-1}}
\def\dpdx{ \frac{\partial \phi}{\partial x}}
\def\dpdz{ \frac{\partial \phi}{\partial z}}
\def\ci{\cal i}
\def\kkt0{k_{\tau0}}

