An improved immersed finte element particle-in-cell method for plasma simulation

The particle-in-cell (PIC) method has been widely used for plasma simulation, because of its noise-reduction capability and moderate computational cost. The immersed finite element (IFE) method is efficient for solving interface problems on Cartesian meshes, which is desirable for PIC method. The combination of these two methods provides an effective tool for plasma simulation with complex interface/boundary. This paper introduces an improved IFE-PIC method that enhances the performance in both IFE and PIC aspects. For the electric field solver, we adopt the newly developed partially penalized IFE method with enhanced accuracy. For PIC implementation, we introduce a new interpolation technique to ensure the conservation of the charge. Numerical examples are provided to demonstrate the features of the improved IFE-PIC method

Predicting Crystal Structures with Data Mining of Quantum Calculations

Predicting and characterizing the crystal structure of materials is a key problem in materials research and development. It is typically addressed with highly accurate quantum mechanical computations on a small set of candidate structures, or with empirical rules that have been extracted from a large amount of experimental information, but have limited predictive power. In this letter, we transfer the concept of heuristic rule extraction to a large library of ab-initio calculated information, and demonstrate that this can be developed into a tool for crystal structure prediction.Comment: 4 pages, 3 pic

Self consistent kinetic simulations of SPT and HEMP thrusters including the near-field plume region

The Particle-in-Cell (PIC) method was used to study two different ion thruster concepts - Stationary Plasma Thrusters (SPT) and High Efficiency Multistage Plasma Thrusters (HEMP-T), in particular the plasma properties in the discharge chamber due to the different magnetic field configurations. Special attention was paid to the simulation of plasma particle fluxes on the thrusters channel surfaces. In both cases, PIC proved itself as a powerful tool, delivering important insight into the basic physics of the different thruster concepts. The simulations demonstrated that the new HEMP thruster concept allows for a high thermal efficiency due to both minimal energy dissipation and high acceleration efficiency. In the HEMP thruster the plasma contact to the wall is limited only to very small areas of the magnetic field cusps, which results in much smaller ion energy flux to the thruster channel surface as compared to SPT. The erosion yields for dielectric discharge channel walls of SPT and HEMP thrusters were calculated with the binary collision code SDTrimSP. For SPT, an erosion rate on the level of 1 mm of sputtered material per hour was observed. For HEMP, thruster simulations have shown that there is no erosion inside the dielectric discharge channel.Comment: 14 pages, 11 figures This work was presented at 21st International Conference on Numerical Simulation of Plasmas (ICNSP'09

The Convergence of Particle-in-Cell Schemes for Cosmological Dark Matter Simulations

Particle methods are a ubiquitous tool for solving the Vlasov-Poisson equation in comoving coordinates, which is used to model the gravitational evolution of dark matter in an expanding universe. However, these methods are known to produce poor results on idealized test problems, particularly at late times, after the particle trajectories have crossed. To investigate this, we have performed a series of one- and two-dimensional "Zel'dovich Pancake" calculations using the popular Particle-in-Cell (PIC) method. We find that PIC can indeed converge on these problems provided the following modifications are made. The first modification is to regularize the singular initial distribution function by introducing a small but finite artificial velocity dispersion. This process is analogous to artificial viscosity in compressible gas dynamics, and, as with artificial viscosity, the amount of regularization can be tailored so that its effect outside of a well-defined region - in this case, the high-density caustics - is small. The second modification is the introduction of a particle remapping procedure that periodically re-expresses the dark matter distribution function using a new set of particles. We describe a remapping algorithm that is third-order accurate and adaptive in phase space. This procedure prevents the accumulation of numerical errors in integrating the particle trajectories from growing large enough to significantly degrade the solution. Once both of these changes are made, PIC converges at second order on the Zel'dovich Pancake problem, even at late times, after many caustics have formed. Furthermore, the resulting scheme does not suffer from the unphysical, small-scale "clumping" phenomenon known to occur on the Pancake problem when the perturbation wave vector is not aligned with one of the Cartesian coordinate axes.Comment: 29 pages, 29 figures. Accepted for publication in ApJ. The revised version includes a discussion of energy conservation in the remapping procedure, as well as some interpretive differences in the Conclusions made in response to the referee report. Results themselves are unchange

Projekt for manufacturing of gears for Company Stab spol. s r. o.

Diplomová práca opisuje projekt na založenie novej divízie pre firmu ktorá sa zaoberá generálnymi opravami strojov. V prvej časti práce je rozoberaná teoretická časť o výrobnom procese ozubenia a ekonomická časť tejto práce. Hlávne časti práce sú analýza vyrábaných súčiastok, tvorba 3D modelov a výkresov vyrábaných súčastok a následná tvorba výrobných postupov. V ďalšej časti je rozoberaný návrh materiálov, strojov a nástrojov. V poslednej časti sú prevedené kalkulácie na výpočet celkových výrobných nákladov pre výrobu vybraných súčiastok.This Master Thesis describes the project to set up a new division for a company which is refurbishing machines. The first part of the thesis is a theoretical part about the manufacturing processes and the economical part of this thesis. The main parts of the thesis are parts analysis, making of 3D models and drawings of two selected parts and then making of process route sheets. Another part is consisting of material, machines and tools selection. In the last part are done calculations needed to calculate the total costs of the manufacturing process for selected parts

The Picard group of topological modular forms via descent theory

This paper starts with an exposition of descent-theoretic techniques in the study of Picard groups of $\mathbf{E}_{\infty}$-ring spectra, which naturally lead to the study of Picard spectra. We then develop tools for the efficient and explicit determination of differentials in the associated descent spectral sequences for the Picard spectra thus obtained. As a major application, we calculate the Picard groups of the periodic spectrum of topological modular forms $TMF$ and the non-periodic and non-connective $Tmf$. We find that $\mathrm{Pic} (TMF)$ is cyclic of order 576, generated by the suspension $\Sigma TMF$ (a result originally due to Hopkins), while $\mathrm{Pic}(Tmf) = \mathbb{Z}\oplus \mathbb{Z}/24$. In particular, we show that there exists an invertible $Tmf$-module which is not equivalent to a suspension of $Tmf$.Comment: 59 pages. Final version - to appear in Geometry and Topolog