Magnetohydrodynamic With Embedded Particle-In-Cell Simulation of the Geospace Environment Modeling Dayside Kinetic Processes Challenge Event

We use the magnetohydrodynamic (MHD) with embedded particle-in-cell model (MHD-EPIC) to study the Geospace Environment Modeling (GEM) dayside kinetic processes challenge event at 01:50-03:00 UT on 18 November 2015, when the magnetosphere was driven by a steady southward interplanetary magnetic field (IMF). In the MHD-EPIC simulation, the dayside magnetopause is covered by a PIC code so that the dayside reconnection is properly handled. We compare the magnetic fields and the plasma profiles of the magnetopause crossing with the MMS3 spacecraft observations. Most variables match the observations well in the magnetosphere, in the magnetosheath, and also during the current sheet crossing. The MHD-EPIC simulation produces flux ropes, and we demonstrate that some magnetic field and plasma features observed by the MMS3 spacecraft can be reproduced by a flux rope crossing event. We use an algorithm to automatically identify the reconnection sites from the simulation results. It turns out that there are usually multiple X-lines at the magnetopause. By tracing the locations of the X-lines, we find that the typical moving speed of the X-line endpoints is about 70 km/s, which is higher than but still comparable with the ground-based observations

Fully kinetic numerical modeling of a plasma thruster

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2001.Includes bibliographical references (p. 372-375).A Hall effect plasma thruster with conductive acceleration channel walls was numerically modeled using 2D3V Particle-in-Cell (PIC) and Monte-Carlo Collision (MCC) methodolo- gies. Electron, ion, and neutral dynamics were treated kinetically on the electron time scale to study transport, instabilities, and the electron energy distribution function. Axisymmet- ric R-Z coordinates were used with a non-orthogonal variable mesh to account for important small-scale plasma structures and a complex physical geometry. Electric field and sheath structures were treated self-consistently. Conductive channel walls were allowed to float electrically. The simulation included, via MCC, elastic and inelastic electron-neutral colli- sions, ion-neutral scattering and charge exchange collisions, and Coulomb collisions. The latter were also treated through a Langevin (stochastic) differential equation for the particle trajectories in velocity space. Ion-electron recombination was modeled at the boundaries, and neutrals were recycled into the flow. The cathode was modeled indirectly by inject- ing electrons at a rate which preserved quasineutrality. Anomalous diffusion was included through an equivalent scattering frequency. Free space permittivity was increased to allow a coarser grid and longer time-step. A method for changing the ion to electron mass ratio and retrieving physical results was developed and used throughout. Results were compared with theory, experiments. Gradients and anisotropy in electron temperature were observed. Non-Maxwellian electron energy distribution functions were observed. The thruster was numerically redesigned; substantial performance benefits were predicted.by James Joseph Szabo, Jr.Ph.D

Isogeometric Analysis for Electromagnetism

The combination of numerical analysis with the scanning technology has been seeing increased use in many research areas. There is an emerging need for high-fidelity geometric modeling and meshing for practical applications. The Isogeometric Analysis (IGA) is a comprehensive computational framework, which integrates geometric modeling and meshing with analysis. Different from other existing numerical methods, the IGA can generate analysis ready models without loss of geometrical accuracy. In IGA, the continuity and the quality of a solution can be conveniently controlled and refined. These features enable IGA to integrate modeling, analysis, and design in a unified framework, the root idea of IGA. The IGA for electromagmetics is studied here for steady and transient electromagnetics as well as electromagnetic scattering. The solution procedure and the associated Matlab codes are developed to simulate the electromagnetic radiation on a biological tissues. The scattered and the total electrical fields are computed over the complex geometry of a brain section with realistic material properties. A perfectly matched layer (PML) is developed to model the far field boundary condition. The IGA platform developed here offers a reliable simulation within an accurate representation of the geometry. The results of this research can be used both in evaluating the potential health and safety risks of electromagnetic radiations and in optimizing the design of radiating devices used in non-invasive diagnostics and therapies

Numerical Boundary Condition Procedures

Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Emission properties of radiative chiral nematic liquid crystals

In this work, we calculate the density of photon states (DOS) of the normal modes in dye-doped chiral nematic liquid crystal (LC) cells in the presence of various loss mechanisms. Losses and gain are incorporated into the transmission characteristics through the introduction of a small imaginary part in the dielectric constant perpendicular and along the director, for which we assume no frequency dispersion. Theoretical results are presented on the DOS in the region of the photonic band gap for a range of values of the loss coefficient and different values of the optical anisotropy. The obtained values of the DOS at the photonic band gap edges predict a reversal of the dominant modes in the structure. Our results are found to be in good agreement with the experimentally obtained excitation thresholds in chiral nematic LC lasers. The behaviour of the DOS is also discussed for amplifying LC cells providing an additional insight to the lasing mechanism of these structures. We subsequently investigate the spontaneous emission properties, under the assumption that the electronic transition frequency is close to the photonic edge mode of the structure (resonance). We take into account the transition broadening and the decay of electromagnetic field modes supported by the so-called 'mirror-less' cavity. We employ the Jaynes-Cummings Hamiltonian to describe the electron interaction with the electromagnetic field, focusing on the mode with the diffracting polarization in the chiral nematic layer. As known in these structures, the density of photon states, calculated via the Wigner method, has distinct peaks on either side of the photonic band gap, which manifests itself as a considerable modification of the emission spectrum. We demonstrate that, near resonance, there are notable differences between the behaviour of the density of states and the spontaneous emission profile of these structures. In addition, we examine in some detail the case of the logarithmic peak exhibited in the density of states in 2D photonic structures and obtain analytic relations for the Lamb shift and the broadening of the atomic transition in the emission spectrum. The dynamical behaviour of the atom-field system is described by a system of two first order differential equations, solved using the Green's function method and the Fourier transform. The emission spectra are then calculated and compared with experimental data. Finally, we detail a new technique for the pumping of dye lasers which requires no moving parts or flushing mechanisms and is applicable to both solid state and liquid based devices. A reconfigurable hologram is used to control the position of incidence of a pump beam onto a dye laser and significant increases in device lifetimes are achieved. The technique is also applied to wavelength tune a dye laser. This offers access to higher repetition rates and larger average output powers. With higher repetition rate pump lasers it is feasible that the approach could allow such organic lasers to reach operating frequencies on the order of MHz. The unique nature of the adaptive pumping method also allows precise control of the spatial wave-front and configuration of the pumping wave which allows greater versatility and functionality to be realised. It is possible to envisage that novel pump beam profiles that optimise propagation through the medium could also be demonstrated

Annual Research Briefs: 1995

This report contains the 1995 annual progress reports of the Research Fellows and students of the Center for Turbulence Research (CTR). In 1995 CTR continued its concentration on the development and application of large-eddy simulation to complex flows, development of novel modeling concepts for engineering computations in the Reynolds averaged framework, and turbulent combustion. In large-eddy simulation, a number of numerical and experimental issues have surfaced which are being addressed. The first group of reports in this volume are on large-eddy simulation. A key finding in this area was the revelation of possibly significant numerical errors that may overwhelm the effects of the subgrid-scale model. We also commissioned a new experiment to support the LES validation studies. The remaining articles in this report are concerned with Reynolds averaged modeling, studies of turbulence physics and flow generated sound, combustion, and simulation techniques. Fundamental studies of turbulent combustion using direct numerical simulations which started at CTR will continue to be emphasized. These studies and their counterparts carried out during the summer programs have had a noticeable impact on combustion research world wide