We introduce an orthogonal body-fitted grid generation technique, and employ a high-order finite difference method to simulate the acoustic wave under the orthogonal curvilinear coordinate system. Compared with the rectangular grid, the orthogonal body-fitted grid can describe the rugged topography more accurately and eliminate the false scattering waves caused by ladder-like mesh effectively. ...

In literature, Extended Object Tracking (EOT) algorithms developed for autonomous driving predominantly provide obstacles state estimation in cartesian coordinates the Vehicle Reference Frame. However, many scenarios, representation road-aligned curvilinear is preferred when implementing subsystems like cruise control, lane-keeping assist, platooning, etc. This paper proposes a Gaussian Mixture...

1. Everything is number 2. Ancient Astronomy 3. Optics and statics 4. The middle ages and the renaissance 5. Mechanics of motion 6. Newtonian mechanics 7. Early differential equations 8. The Brachistochrone 9. Early methods of solutionLinear differential equations 10 Newton’s second law as a differential equationThe method of perturbations 11. The vibrating stringPartial differential equations ...

We present an analytical derivation of a 3D conformal perfectly matched layer (PML's) for mesh termination in general orthogonal curvilinear coordinates. The derivation is based on the analytic continuation to complex space of the normal coordinate to the mesh termination. The resultant elds in the complex space do not obey the Maxwell's equations. However, it is demonstrated that through simpl...

A set of pseudorotation coordinates is proposed for characterizing the puckering of the furanose ring. These are defined from the curvilinear displacements of the C1' and C4' atoms from the planar conformation. The present coordinates have some practical advantages over the ones currently used.