Future development programs

A company program was planned which has a main drive to develop those emission reduction concepts that have the promise of earliest success. These programs were proposed in an attempt to enhance existing engine systems, exploiting their potential for emission reduction as far as is compatible with retaining the well established features in them that are well understood and in current production. The intended programs identified in the area of new concepts were: (1) upgrading the TCM fuel system, (2) evaluation of accelerator pump, (3) reduced cooling requirement, and (4) variable spark timing

Lime and Water

Stor

Low Regularity Ray Tracing for Wave Equations with Gaussian beams

We prove observability estimates for oscillatory Cauchy data modulo a small kernel for $n$-dimensional wave equations with space and time dependent $C^2$ and $C^{1,1}$ coefficients using Gaussian beams. We assume the domains and observability regions are in $\mathbb{R}^n$, and the GCC applies. This work generalizes previous observability estimates to higher dimensions and time dependent coefficients. The construction for the Gaussian beamlets solving $C^{1,1}$ wave equations represents an improvement and simplification over Waters (2011).Comment: this version shortens and changes the previous construction and contains an extension to space time dependent coefficient

Unique Determination of Sound Speeds for Coupled Systems of Semi-linear Wave Equations

We consider coupled systems of semi-linear wave equations with different sound speeds on a finite time interval $[0,T]$ and a bounded Lipschitz domain $\Omega$ in $\mathbb{R}^3$, with boundary $\partial\Omega$. We show the coupled systems are well posed for variable coefficient sounds speeds and short times. Under the assumption of small initial data, we prove the source to solutions map on $[0,T]\times\partial\Omega$ associated with the nonlinear problem is sufficient to determine the source-to-solution map for the linear problem. We can then reconstruct the sound speeds in $\Omega$ for the coupled nonlinear wave equations under certain geometric assumptions. In the case of the full source to solution map in $\Omega\times[0,T]$ this reconstruction could also be accomplished under fewer geometric assumptions.Comment: minor update