Interaction of oblique dark solitons in two-dimensional supersonic nonlinear Schr\"odinger flow

We investigate the collision of two oblique dark solitons in the two dimensional supersonic nonlinear Schr\"odinger flow past two impenetrable obstacles. We numerically show that this collision is very similar to the dark soliton collisions in the one dimensional case. We observe that it is practically elastic and we measure the shifts of the solitons positions after their interaction

Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analogue of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed suffciently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x-coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half-planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear "ship wave" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles

Virtual design and dynamical simulation of flexible cables, hoses, and wires

Computer simulation can provide significant help to solve practical problems concerning the optimal design and the dynamical behavior of flexible cables, hoses, and wires in vehicles and on production equipment like robots. Typical questions are the ideal cable's length, its minimal bending radius, possible collision to surrounding parts, and designed space. To solve these problems, we developed a non-linear beam model, which accounts for large global deformations of the cable. It is based on Cosserat's geometrically exact theory of rods and is able to represent extension, shearing, bending and torsion of the cable. With our innovative approach, one can optimize the cables design and their assembly positions in real time and with high accuracy. One can also consider a variety of material types and cross-sections profiles. Our implementation allows one to import CAD files and rigid body motions as well as the analysis of the local stress distribution within the cable volume. Important questions like finding the optimal length or the ideal assembly positions can be efficiently answered. Material and the necessary physical space can be already reduced during the design process, without the need of costly tests with hardware prototypes. We present relevant industrial examples of applicability our approach. Finally, we introduce a dynamical viscoelastic version our model, which is suitable for fast and accurate dynamical simulation of multi-body systems (MBS)