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Title:  Development of large scale tightbinding methods, and application to electron transfer in symmetric dielectric barrier discharges (DBDS) 
Author(s):  Ghale, Purnima 
Director of Research:  Johnson, Harley T 
Doctoral Committee Chair(s):  Johnson, Harley T 
Doctoral Committee Member(s):  Ertekin, Elif; Schleife, Andre; Stephani, Kelly 
Department / Program:  Mechanical Sci & Engineering 
Discipline:  Mechanical Engineering 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  tightbinding
electronic structure LandauZener dynamics timedependence under AC voltage device physics, dielectric barrier discharges graph theory asynchronous programming density matrix calculations hysteresis 
Abstract:  Extending the size of electronic structure simulations is an ongoing effort at various levels of electronic structure theory. In tightbinding and density functional theory, the most expensive part of the computation is obtaining the density matrix, which traditionally scales cubically with the number of atoms. Tightbinding is a semiempirical electronic structure method that is the least expensive among methods capable of resolving charge, energies and electronic wavefunctions at the atomistic level. While linearly scaling algorithms have been developed previously, the focus was on using localization or sparsity of the density matrix to obtain linear scaling. The disadvantage of this approach is that localization and sparsity are dependent on the basisset choice, which is generally unknown apriori. Furthermore, calculations often also rely on matrixmatrix multiplication, which are harder to optimize over distributed nodes. Thus, we present a linearly scaling method that relies on sampling the density matrix via matrixvector multiplication, by combining polynomial expansion and polynomial purification methods that are wellknown in the tightbinding literature, allowing us to simulate multimillion atom systems on a large memory node on the campus cluster, as well as demonstrations of larger systems and faster, more accurate, simulations on the BlueWaters supercomputer. Next, we investigate the underlying microscopic mechanism for electron transfer in symmetric dielectric barrier discharge plasma generators (DBDs). DBDs are useful in a wide variety of applications where the plasma generated is used for materials processing, combustion, and flow control. Our interest is in determining the rate of electron emission from dielectrics under AC voltage. While phenomenological models have existed, a microscopic electronicstructure based model to compute and predict the rate of electron transfer from dielectric surfaces had not been presented so far. We propose that electron transfer between the dielectric and gaseous regions under AC voltage, is a particular case of the LandauZener avoided levelcrossing model, where electron transfer occurs between localized states due to timedependent resonance. We first show that the temporal profile of currentvoltage obtained from this model are consistent with experimental observations, and then go on to numerically compute the rates of electron transfer under a parametric sweep of AC voltages and frequencies. The dataset produced will be useful as boundary conditions in numerical plasma simulations as DBD devices are miniaturized and surface effects become more important  previously, these values were experimentally inferred after plasma generation. Finally, motivated by the numerical results obtained from simulations of electron transfer within DBDs, we investigate how ratedependent chargevoltage hysteresis might occur in closed finite systems driven at finite frequencies. While a lot of work has been done to characterize dissipation due to coupling to a bath, here we investigate how coherent unitary quantum dynamics give rise to dissipation and ratedependent hysteresis in finite systems. We show irreversibility of closed quantum mechanical systems under finite driving near an avoided levelcrossing, accompanied by representative simulations of spinmagnetic field hysteresis in spinsystems, chargevoltage hysteresis in a 50atom finite flake of graphene, and chargevoltage hysteresis in a dielectricgasdielectric system driven at an AC frequency of 20 MHz. 
Issue Date:  20200505 
Type:  Thesis 
URI:  http://hdl.handle.net/2142/107878 
Rights Information:  Copyright 2020 Purnima Ghale 
Date Available in IDEALS:  20200826 
Date Deposited:  202005 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois