Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar

Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this we developed a code called DNGR (Double Negative Gravitational Renderer) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering. This paper has four purposes: (i) To describe DNGR for physicists and CGI practitioners . (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie \emph{Interstellar}, were generated with DNGR. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting.Comment: 46 pages, 17 figure

Numerical Simulation of Hot Accretion Flows (III): Revisiting wind properties using trajectory approach

Previous MHD simulations have shown that wind must exist in black hole hot accretion flows. In this paper, we continue our study by investigating the detailed properties of wind, such as mass flux and poloidal speed, and the mechanism of wind production. For this aim, we make use of a three dimensional GRMHD simulation of hot accretion flows around a Schwarzschild black hole. The simulation is designed so that the magnetic flux is not accumulated significantly around the black hole. To distinguish real wind from turbulent outflows, we track the trajectories of the virtual Largrangian particles from simulation data. We find two types of real outflows, i.e., a quasi-relativistic jet close to the axis and a sub-relativistic wind subtending a much larger solid angle. Most of the wind originates from the surface layer of the accretion flow. The poloidal wind speed almost remains constant once they are produced, but the flux-weighted wind speed roughly follows $v_{\rm p, wind}(r)\approx 0.25 v_k(r)$. The mass flux of jet is much lower but the speed is much higher, $v_{\rm p,jet}\sim (0.3-0.4) c$. Consequently, both the energy and momentum fluxes of the wind are much larger than those of the jet. We find that the wind is produced and accelerated primarily by the combination of centrifugal force and magnetic pressure gradient, while the jet is mainly accelerated by magnetic pressure gradient. Finally, we find that the wind production efficiency $\epsilon_{\rm wind}\equiv\dot{E}_{\rm wind}/\dot{M}_{\rm BH}c^2\sim 1/1000$, in good agreement with the value required from large-scale galaxy simulations with AGN feedback.Comment: 13 pages, 13 figures; submitted to Ap

On the role of extensional rheology and Deborah number on the neck-in phenomenon during flat film casting

In this work, viscoelastic, isothermal extrusion film casting simulations have been performed utilizing a 1D membrane model and the viscoelastic modified Leonov model as the constitutive equation in order to elucidate the role of planar to uniaxial extensional viscosity ratio, extensional strain hardening and Deborah number on the neck-in phenomenon. Based on the performed theoretical parametric study, it has been found that neck-in can be correlated to all the above mentioned variables via a simple dimensionless analytical equation. This correlation can provide detailed view into the complicated relationship between polymer melt rheology, die design, process conditions and undesirable neck-in phenomenon. Obtained results have been validated against literature experimental data for different polyethylene melts and processing conditions. © 2017 Elsevier Ltd16-05886S, GACR, Grantová Agentura České RepublikyGrant Agency of the Czech Republic [16-05886S

Structure and pressure drop of real and virtual metal wire meshes

An efficient mathematical model to virtually generate woven metal wire meshes is presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional images of real meshes, which are produced via computer tomography. Virtual structures are generated for three types of metal wire meshes using only easy to measure parameters. For these geometries the velocity-dependent pressure drop is simulated and compared with measurements performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of the measurements. The generation of the structures and the numerical simulations were done at GKD using the Fraunhofer GeoDict software

Advances and trends in plastic forming technologies for welded tubes

AbstractWith the implementation of environmental protection, sustainable development and conservation-oriented policies, components and parts of thin-walled welded tubes have gained increasing application in the aircraft and automotive industries because of their advantages: easily achieving forming and manufacturing process at low cost and in a short time. The current research on welded tube plastic forming is mainly concentrated on tube internal high-pressure forming, tube bending forming, and tube spinning forming. The focuses are on the material properties and characterization of welded tubes, finite element modeling for welded tube forming, and inhomogeneous deformation behavior and the mechanism and rules of deformation coordination in welded tube plastic forming. This paper summarizes the research progress in welded tube plastic forming from these aspects. Finally, with a focus on the urgent demand of the aviation, aerospace and automotive industries for high-strength and light-weight tubes, this paper discusses the development trends and challenges in the theory and technology of welded tube plastic forming in the future. Among them, laser tailor-welded technology will find application in the manufacture of high-strength steel tubes. Tube-end forming technology, such as tube flaring and flanging technology, will expand its application in welded tubes. Therefore, future studies will focus on the FE modeling regarding how to consider effects of welding on residual stresses, welding distortions and microstructure, the inhomogeneous deformation and coordination mechanism of the plastic forming process of tailor-welded tubes, and some end-forming processes of welded tubes, and more comprehensive research on the forming mechanism and limit of welded tubes

Analysis and modelling of a rotary forming process for cast aluminum alloy A356

Spinning of a common aluminum automotive casting alloy A356 (Al-7Si-0.3 Mg) at elevated temperatures has been investigated experimentally with a novel industrial-scale apparatus. This has permitted the implementation of a fully coupled thermomechanical finite element model aimed at quantifying the processing history (stress, strain, strain-rate and temperature) and predicting the final geometry. The geometric predictions of this model have been compared directly to the geometry of the workpieces obtained experimentally. This study is novel in regards to both the size and shape of the component as well as the constitutive material representation employed. The model predictions are in reasonable agreement with experimental results for small deformations, but errors increase for large deformation conditions. The model has also enabled the characterization of the mechanical state which leads to a common spinning defect. Suggestions for improving the accuracy and robustness of the model to provide a predictive tool for industry are discussed