Vertex Sequences in Graphs

We consider a variety of types of vertex sequences, which are defined in terms of a requirement that the next vertex in the sequence must meet. For example, let S = (v1, v2, …, vk ) be a sequence of distinct vertices in a graph G such that every vertex vi in S dominates at least one vertex in V that is not dominated by any of the vertices preceding it in the sequence S. Such a sequence of maximal length is called a dominating sequence since the set {v1, v2, …, vk } must be a dominating set of G. In this paper we survey the literature on dominating and other related sequences, and propose for future study several new types of vertex sequences, which suggest the beginning of a theory of vertex sequences in graphs

Numerical modelling of additive manufacturing process for stainless steel tension testing samples

Nowadays additive manufacturing (AM) technologies including 3D printing grow rapidly and they are expected to replace conventional subtractive manufacturing technologies to some extents. During a selective laser melting (SLM) process as one of popular AM technologies for metals, large amount of heats is required to melt metal powders, and this leads to distortions and/or shrinkages of additively manufactured parts. It is useful to predict the 3D printed parts to control unwanted distortions and shrinkages before their 3D printing. This study develops a two-phase numerical modelling and simulation process of AM process for 17-4PH stainless steel and it considers the importance of post-processing and the need for calibration to achieve a high-quality printing at the end. By using this proposed AM modelling and simulation process, optimal process parameters, material properties, and topology can be obtained to ensure a part 3D printed successfully

Stellar iron core collapse in {3+1} general relativity and the gravitational wave signature of core-collapse supernovae

I perform and analyse the first ever calculations of rotating stellar iron core collapse in {3+1} general relativity that start out with presupernova models from stellar evolutionary calculations and include a microphysical finite-temperature nuclear equation of state, an approximate scheme for electron capture during collapse and neutrino pressure effects. Based on the results of these calculations, I obtain the to-date most realistic estimates for the gravitational wave signal from collapse, bounce and the early postbounce phase of core collapse supernovae.thesi

Accretion and Ejection in Resistive GR-MHD

In this thesis, the accretion and ejection processes from a black hole accretion system is investigated by means of resistive general relativistic magnetohydrodynamic simulations. As a supplement to the results from prior research with non-relativistic simulations, my results confirm that the winds and outflows originated from thin accretion disks can also be observed in general relativistic simulations. In the first part, the execution of the implementation of resistivity, namely magnetic diffusivity, into the existing non-resistive general relativistic magnetohydrodynamic code HARM is illustrated. The test simulations of the new code {\HAR} include the comparison with analytical solution of the diffusion equation and a classic shock tube test. {\HAR} shows reliable performances in these tests. In the second part, {\HAR} is applied to investigate the evolution of magnetized tori. The results show that the existence of resistivity leads to inefficient accretions of matter from tori onto black holes by weakening the magnetorotational instability inside the tori. An indication for a critical magnetic diffusivity in this simulation setup is found beyond which no magnetorotational instability develops in the linear regime. In the third part, as the main purpose of this PhD project, {\HAR} is used to perform simulations of magnetically diffusive thin accretion disks that are threaded by a large-scale poloidal magnetic field around non-rotating and rotating black holes. These long-term simulations last 3000 code time units, which are about 195 rotation periods at the disk inner boundary, correspondingly. Their computational domains extend from black hole horizon to 80 Schwarzschild radii. Outflows driven from the accretion disk are clearly seen. These outflows have the typical radial velocity of 0.1 speed of light. In my analyses, I argue that these outflows are driven by the magnetic pressure gradient from the toroidal magnetic field generated by the rotation of the disk. The small ratios of the poloidal field strengths to the toroidal field strengths suggest the interpretation of the outflows as ``tower jet," rather than centrifugally driven winds (Blandford-Payne effect). Furthermore, I find direct evidence of the growths of magnetorotational instabilities inside the accretion disks, which are suppressed by the increasing levels of magnetic diffusivity. This suppression leads to inefficient accretion and ejection processes of the accretion system. Finally, the influences of rotating black holes on the accretion systems are explored. The results show an suppression effect on the black hole spin on the accretion and ejection processes in the system. The tangled field lines within the ergosphere induced by the black hole rotation produce magnetic pressure that pushes against the accreting matter from the disk. In the simulations with large spin parameters, energy extraction from the black hole (Blandford-Znajek effect) is observed, which is, nevertheless, $\sim 10^{2}$ times smaller than the energy production from the disk outflow

Geometric partial differential equations: Surface and bulk processes

The workshop brought together experts representing a wide range of topics in geometric partial differential equations ranging from analyis over numerical simulation to real-life applications. The main themes of the conference were the analysis of curvature energies, new developments in pdes on surfaces and the treatment of coupled bulk/surface problems

NASA Tech Briefs, August 1994

Topics covered include: Computer Hardware; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences; Books and Reports

Modeling of directional solidification of multicrystalline silicon in a traveling magnetic field

Melt flow plays an important role in directional solidification of multicrystalline silicon influencing the temperature field and the crystallization interface as well as the transport of impurities. This work investigates the potential of a traveling magnetic field (TMF) for an active control of the melt flow. A system of 3D numerical models was developed and adapted based on open-source software for calculations of Lorentz force, melt flow, and related phenomena. Isothermal and non-isothermal model experiments with a square GaInSn melt were used to validate the numerical models by direct velocity measurements. Several new 3D flow structures of turbulent TMF flows were observed for different melt heights. Further numerical parameter studies carried out for silicon melts showed that already a weak TMF-induced Lorentz force can stir impurities near to the complete mixing limit. Simultaneously, the deformed temperature field leads to an increase of the deflection of crystallization interface, which may exhibit a distinct asymmetry. The numerical results of this work were implemented in a research-scale silicon crystallization furnace. Scaling laws for various phenomena were derived allowing a limited transfer of the results to the industrial scale