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We propose a class of electrical circuits for extremely wideband ͑EWB͒ signal shaping. A one-dimensional, nonlinear, nonuniform transmission line is proposed for narrow pulse generation. A two-dimensional transmission lattice is proposed for EWB signal combining. Model equations for the circuits are derived. Theoretical and numerical solutions of the model equations are presented, showing that the circuits can be used for the desired application. The procedure by which the circuits are designed exemplifies a modern, mathematical design methodology for EWB circuits.

Abstract. This paper extends the derivation of the Lagrangian averaged Euler (LAE-α) equations to the case of barotropic compressible flows. The aim of Lagrangian averaging is to regularize the compressible Euler equations by adding dispersion instead of artificial viscosity. Along the way, the derivation of the isotropic and anisotropic LAE-α equations is simplified and clarified.The derivation in this paper involves averaging over a tube of trajectories η ǫ centered around a given Lagrangian flow η. With this tube framework, the Lagrangian averaged Euler (LAE-α) equations are derived by following a simple procedure: start with a given action, Taylor expand in terms of small-scale fluid fluctuations ξ, truncate, average, and then model those terms that are nonlinear functions of ξ. Closure of the equations is provided through the use of flow rules, which prescribe the evolution of the fluctuations along the mean flow.