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Full-Text Articles in Physical Sciences and Mathematics

Thermal Conductivity And Mechanical Properties Of Interlayer-Bonded Graphene Bilayers, Afnan Mostafa Nov 2023

Thermal Conductivity And Mechanical Properties Of Interlayer-Bonded Graphene Bilayers, Afnan Mostafa

Masters Theses

Graphene, an allotrope of carbon, has demonstrated exceptional mechanical, thermal, electronic, and optical properties. Complementary to such innate properties, structural modification through chemical functionalization or defect engineering can significantly enhance the properties and functionality of graphene and its derivatives. Hence, understanding structure-property relationships in graphene-based metamaterials has garnered much attention in recent years. In this thesis, we present molecular dynamics studies aimed at elucidating structure-property relationships that govern the thermomechanical response of interlayer-bonded graphene bilayers.

First, we present a systematic and thorough analysis of thermal transport in interlayer-bonded twisted bilayer graphene (IB-TBG). We find that the introduction of interlayer C-C …


Development Of Interatomic Potential Of High Entropy Diborides With Artificial Intelligence Approach To Simulate The Thermo-Mechanical Properties, Nur Aziz Octoviawan Jan 2023

Development Of Interatomic Potential Of High Entropy Diborides With Artificial Intelligence Approach To Simulate The Thermo-Mechanical Properties, Nur Aziz Octoviawan

MSU Graduate Theses

The interatomic potentials designed for binary/high entropy diborides and ultra-high temperature composites (UHTC) have been developed through the implementation of deep neural network (DNN) algorithms. These algorithms employed two different approaches and corresponding codes; 1) strictly local & invariant scalar-based descriptors as implemented in the DEEPMD code and 2) equivariant tensor-based descriptors as included in the ALLEGRO code. The samples for training and validation sets of the forces, energy, and virial data were obtained from the ab-initio molecular dynamics (AIMD) simulations and Density Functional Theory (DFT) calculations, including the simulation data from the ultra-high temperature region (> 2000K). The study …


Machine Learning Strategies For Potential Development In High-Entropy Driven Nickel-Based Superalloys, Marium Mostafiz Mou Jan 2023

Machine Learning Strategies For Potential Development In High-Entropy Driven Nickel-Based Superalloys, Marium Mostafiz Mou

MSU Graduate Theses

In this study, I developed Deep Learning interatomic potentials to model a multi-phase and multi-component system of Ni-based Superalloys. The system has up to three major phase constituents, namely Gamma, Gamma Prime, and Transition-metal rich Carbide. I utilized invariant scalar-based and/or equivariant, tensor-based neural network (NN) approach as implemented in DEEPMD, NEQUIP/ALLEGRO codes, respectively, and Moment Tensor Potential (MTP). For the training and validation sets, I employed the ab-initio molecular dynamics (AIMD) trajectory results and ground state DFT calculations, including the energy, force, and virial database from highly diverse compositions, temperatures, and pressures following a “High Entropy Strategy.” The Deep …


Classification Of Nuclear Pastas Through Alpha Shapes Model, Daniela Ramirez Chavez Dec 2022

Classification Of Nuclear Pastas Through Alpha Shapes Model, Daniela Ramirez Chavez

Open Access Theses & Dissertations

The nuclear pasta is important because is an astromaterial with incredible strength that may be a source for gravitational waves, which observe from the rotation of neutron stars. The characterization of the pasta is vital because the nuclear phases have transport properties - compressibility, neutrino opacity, thermal conductivity, and electrical conductivity - associated with their shape for which neutron stars may be sensitive. These properties could interpret observations of supernova neutrinos, magnetic field decay, and crust cooling of accreting neutron stars. Here, we study the nuclear pasta using alpha shapes to achieve a phase characterization with the Minkowski functionals (area, …


Turning Density Functional Theory Calculations Into Molecular Mechanics Simulations : Establishing The Fluctuating Density Model For Rna Nucleobases, Christopher A. Myers Dec 2022

Turning Density Functional Theory Calculations Into Molecular Mechanics Simulations : Establishing The Fluctuating Density Model For Rna Nucleobases, Christopher A. Myers

Legacy Theses & Dissertations (2009 - 2024)

Molecular mechanics (MD) simulations and density functional theory (DFT) have been the backbone of computational chemistry for decades. Due to its accuracy and computational feasibility, DFT has become the go-to method for theoretically predicting interaction energies, polarizability, and other electronic properties of small molecules at the quantum mechanical level. Although less fundamental than DFT, molecular mechanics (MM) algorithms have been just as influential in the fields of biology and chemistry, owing their success to the ability to compute measurable, macroscopic quantities for systems with tens of thousands to hundreds of thousands of atoms at a time. Nevertheless, MD simulations would …


Review Of Current Reactive Force Field Potentials For Use In Simulating The Atomic Layer Deposition Of Alumina On Aluminum, Devon T. Romine Jan 2022

Review Of Current Reactive Force Field Potentials For Use In Simulating The Atomic Layer Deposition Of Alumina On Aluminum, Devon T. Romine

MSU Graduate Theses

Alumina has recently garnered quite a bit of attention for use as a tunnel barrier in Josephson tunnel junctions. The quality of the metal oxide layer in the Josephson tunnel junction is a key factor in its effectiveness. To optimize the deposition method of alumina, we need a deep understanding of the large-scale surface interactions that cannot be reached using ab initio molecular dynamics. In this study, I have compared two existing reactive force field (ReaxFF) parameters to determine their abilities to model the atomic layer deposition (ALD) of alumina on an aluminum surface. ReaxFF molecular dynamics was chosen because …


Toward Improving Understanding Of The Structure And Biophysics Of Glycosaminoglycans, Elizabeth K. Whitmore Apr 2021

Toward Improving Understanding Of The Structure And Biophysics Of Glycosaminoglycans, Elizabeth K. Whitmore

Electronic Theses and Dissertations

Glycosaminoglycans (GAGs) are the linear carbohydrate components of proteoglycans (PGs) that mediate PG bioactivities, including signal transduction, tissue morphogenesis, and matrix assembly. To understand GAG function, it is important to understand GAG structure and biophysics at atomic resolution. This is a challenge for existing experimental and computational methods because GAGs are heterogeneous, conformationally complex, and polydisperse, containing up to 200 monosaccharides. Molecular dynamics (MD) simulations come close to overcoming this challenge but are only feasible for short GAG polymers. To address this problem, we developed an algorithm that applies conformations from unbiased all-atom explicit-solvent MD simulations of short GAG polymers …


Equations Of State For Warm Dense Carbon From Quantum Espresso, Derek J. Schauss Jan 2021

Equations Of State For Warm Dense Carbon From Quantum Espresso, Derek J. Schauss

Theses and Dissertations

Warm dense plasma is the matter that exists, roughly, in the range of 10,000 to 10,000,000 Kelvin and has solid-like densities, typically between 0.1 and 10 grams per centimeter. Warm dense fluids like hydrogen, helium, and carbon are believed to make up the interiors of many planets, white dwarfs, and other stars in our universe. The existence of warm dense matter (WDM) on Earth, however, is very rare, as it can only be created with high-energy sources like a nuclear explosion. In such an event, theoretical and computational models that accurately predict the response of certain materials are thus very …


Investigating Ice Nucleation At Negative Pressures Using Molecular Dynamics: A First Order Approximation Of The Dependence Of Ice Nucleation Rate On Pressure, Elise Rosky Jan 2021

Investigating Ice Nucleation At Negative Pressures Using Molecular Dynamics: A First Order Approximation Of The Dependence Of Ice Nucleation Rate On Pressure, Elise Rosky

Dissertations, Master's Theses and Master's Reports

Atmospheric scientists and climate modelers are faced with uncertainty around the process of ice production in clouds. While significant progress has been made in predicting homogeneous and heterogeneous ice nucleation rates as a function of temperature, recent experiments have shown that ice nucleation rates can be enhanced without decreasing temperature, through various mechanical agitations. One hypothesis for these findings is that mechanisms of stretching water and thereby inducing negative pressure in the liquid could lead to an increase in freezing rate. To better understand the viability of this concept, the effect of negative pressure on ice nucleation rates needs to …


Static And Dynamical Properties Of Multiferroics, Sayed Omid Sayedaghaee Dec 2020

Static And Dynamical Properties Of Multiferroics, Sayed Omid Sayedaghaee

Graduate Theses and Dissertations

Since the silicon industrial revolution in the 1950s, a lot of effort was dedicated to the research and development activities focused on material and solid-state sciences. As a result, several cutting-edge technologies are emerging including the applications of functional materials in the design and enhancement of novel devices such as sensors, highly capable data storage media, actuators, transducers, and several other types of electronic tools. In the last two decades, a class of functional materials known as multiferroics has captured significant attention because of providing a huge potential for new designs due to possessing multiple ferroic order parameters at the …


The Journey Of A Single Polymer Chain To A Nanopore, Navid Afrasiabian Apr 2020

The Journey Of A Single Polymer Chain To A Nanopore, Navid Afrasiabian

Electronic Thesis and Dissertation Repository

Single chain translocation has been eagerly studied for more than two decades due to its importance in biological processes and also, providing a better understanding of polymer dynamics. Polymer translocation can be divided into three stages of reaching the pore, entering the pore and passing through it. We study the delivery of the chain from the bulk to the entrance, which is called the capture process, for a single chain driven by hydrodynamic flow. Our molecular dynamics-lattice Boltzmann simulations show that the converging flow around the nanopore not only facilitates the process of finding the pore but also deforms the …


Development Of Embedded Atom Method Interatomic Potentials For Ge-Sn-Si Ternary And Constituent Binary Alloys For Modeling Material Crystallization, Sudip Acharya Jan 2020

Development Of Embedded Atom Method Interatomic Potentials For Ge-Sn-Si Ternary And Constituent Binary Alloys For Modeling Material Crystallization, Sudip Acharya

Browse all Theses and Dissertations

Group IV elements based nanoelectronics devices (mainly Si and Ge based devices) have been developed and improved over a long period of time and are the most influencing materials of semiconductor electronics, but due to their indirect bandgap their use in optoelectronics is limited. Alternatively, new Group IV alloys comprised of Ge, Si, and Sn semiconductor materials have emerged as attractive options for various electronic and optoelectronic applications. The binary and ternary alloys provide strain and energy bandgap engineering by controlling element content, a route for realizing direct-transition semiconductors, improvement in interface and defect properties, and a reduction of the …


Amyloid Proteins And Fibrils Stability, Farbod Mahmoudinobar Dec 2019

Amyloid Proteins And Fibrils Stability, Farbod Mahmoudinobar

Dissertations

Compared to globular proteins that have a stable native structure, intrinsically disordered peptides (IDP) sample an ensemble of structures without folding into a native conformation.One example of IDP is the amyloid-beta(Abeta) protein which is the main constituent of senile plaques in the brain of Alzheimer's patients.Understanding the process by which IDPs undergo structural changes to form oligomers that eventually aggregate into senile plaques/amyloid fibrils may significantly advance the development of novel therapeutic methods to treat neurodegenerative diseases, for which there is no cure to date. This dissertation has two main objectives. The first one is to investigate and identify structural …


Study Of Amorphous Boron Carbide And Hydrogenated Boron Carbide Materials Using Molecular Dynamics And Hybrid Reverse Monte Carlo, Rajan Khadka Dec 2019

Study Of Amorphous Boron Carbide And Hydrogenated Boron Carbide Materials Using Molecular Dynamics And Hybrid Reverse Monte Carlo, Rajan Khadka

MSU Graduate Theses

We present a computational study of amorphous boron carbide (a-BxC) models using Molecular Dynamics (MD) studied with Stillinger-Weber (SW) and ReaxFF potential. The atomic structure factor (S(Q)), radial distribution function (RDF) and bond lengths comparison with other experimental and ab initio models shows that a random arrangement of icosahedra (B12, B11C) interconnected by chains (CCC, CBC) are present in a-BxC. Afterward, Hybrid Reverse Monte Carlo (HRMC) technique is used to recreate a-BxC structures. The existing SW potential parameters of Boron are optimized for the α-rhombohedral (Icosahedral B12 …


Computational Investigation Of The Interactions Between Bioactive Compounds And Biological Assemblies, Tye D. Martin Jul 2019

Computational Investigation Of The Interactions Between Bioactive Compounds And Biological Assemblies, Tye D. Martin

Biomedical Engineering ETDs

Small, biologically active molecules with unique properties and applications are potential solutions to a wide range of threats to global health including infectious agents and neurodegenerative disease. Experimental studies on a class of oligomeric p-phenylene ethynylenes (OPEs) have shown potential both as bioactive antimicrobials and fluorescent sensing agents for tracking amyloid-β (Aβ) aggregates found in Alzheimer’s Disease (AD). A second type of small molecule with potential applications in AD therapy, curcumin, has been found to interfere with Aβ fibril growth. Curcumin also attenuates Aβ-membrane interactions and Aβ toxicity. Our goal has been to use computational techniques to better understand the …


Predicting The Mechanical Properties Of Nanocomposites Reinforced With 1-D, 2-D And 3-D Nanomaterials, Scott Edward Muller May 2019

Predicting The Mechanical Properties Of Nanocomposites Reinforced With 1-D, 2-D And 3-D Nanomaterials, Scott Edward Muller

Graduate Theses and Dissertations

Materials with features at the nanoscale can provide unique mechanical properties and increased functionality when included as part of a nanocomposite. This dissertation utilizes computational methods at multiple scales, including molecular dynamics (MD) and density functional theory (DFT), and the coupled atomistic and discrete dislocation multiscale method (CADD), to predict the mechanical properties of nanocomposites possessing nanomaterials that are either 1-D (carbyne chains), 2-D (graphene sheets), or 3-D (Al/amorphous-Si core-shell nanorod).

The MD method is used to model Ni-graphene nanocomposites. The strength of a Ni-graphene nanocomposite is found to improve by increasing the gap between the graphene sheet and a …


Direct Polymer Grafting As A Method Of Maintaining The Mechanical Properties Of Cellulose Nanocrystals In The Presence Of Moisture, Mary Elizabeth Breen-Lyles Jan 2019

Direct Polymer Grafting As A Method Of Maintaining The Mechanical Properties Of Cellulose Nanocrystals In The Presence Of Moisture, Mary Elizabeth Breen-Lyles

Graduate Research Theses & Dissertations

Cellulose nanocrystals (CNCs) are a distinctive nanomaterial derived from cellulose, the most abundant natural polymer on Earth, and the primary reinforcing structural component of cellulose fibrils found within the plant cell wall. These nanocrystals exhibit mechanical properties comparable to synthetic aramid fibers but are advantageous as they are biodegradable, renewable, and can be produced sustainably as they are predominantly extracted from naturally occurring cellulosic materials. These qualities make it a sustainable, highly renewable and environmentally friendly material to be used in place of synthetic materials in a variety of applications. With their high surface area to volume ratio, low level …


Structure And Thermodynamics Of Polyglutamine Peptides And Amyloid Fibrils Via Metadynamics And Molecular Dynamics Simulations, Riley Workman Aug 2018

Structure And Thermodynamics Of Polyglutamine Peptides And Amyloid Fibrils Via Metadynamics And Molecular Dynamics Simulations, Riley Workman

Electronic Theses and Dissertations

Aggregation of polyglutamine (polyQ)-rich polypeptides in neurons is a marker for nine neurodegenerative diseases. The molecular process responsible for the formation of polyQ fibrils is not well understood and represents a growing area of study. To enable development of treatments that could interfere with aggregation of polyQ peptides, it is crucial to understand the molecular mechanisms by which polyQ peptides aggregate into fibrils. Many experimental techniques have been employed to probe polyQ aggregation, however, observations from these studies have not lead to a unified understanding of the properties of these systems, instead yielding competing, fragmented theories of polyQ aggregation. This …


Transport Of Water And Ions Through Single-Walled Armchair Carbon Nanotubes: A Molecular Dynamics Study, Michelle Patricia Aranha Dec 2017

Transport Of Water And Ions Through Single-Walled Armchair Carbon Nanotubes: A Molecular Dynamics Study, Michelle Patricia Aranha

Doctoral Dissertations

The narrow hydrophobic interior of a carbon nanotube (CNT) poses a barrier to the transport of water and ions, and yet, unexpectedly, numerous experimental and simulation studies have confirmed fast water transport rates comparable to those seen in biological aquaporin channels. These outstanding features of high water permeability and high solute rejection of even dissolved ions that would typically require a lot of energy for separation in commercial processes makes carbon nanotubes an exciting candidate for desalination membranes. Extending ion exclusion beyond simple mechanical sieving by the inclusion of electrostatics via added functionality to the nanotube bears promise to not …


Characterization Of Hydrophobic Interactions Of Polymers With Water And Phospholipid Membranes Using Molecular Dynamics Simulations, Mihaela Drenscko Sep 2017

Characterization Of Hydrophobic Interactions Of Polymers With Water And Phospholipid Membranes Using Molecular Dynamics Simulations, Mihaela Drenscko

Dissertations, Theses, and Capstone Projects

Polymers and lipid membranes are both essential soft materials. The structure and hydrophobicity/hydrophilicity of polymers, as well as the solvent they are embedded in, ultimately determines their size and shape. Understating the variation of shape of the polymer as well as its interactions with model biological membranes can assist in understanding the biocompatibility of the polymer itself. Computer simulations, in particular molecular dynamics, can aid in characterization of the interaction of polymers with solvent, as well as polymers with model membranes. In this thesis, molecular dynamics serve to describe polymer interactions with a solvent (water) and with a lipid membrane. …


Molecular Mechanisms Of Protein Thermal Stability, Lucas Sawle Jan 2016

Molecular Mechanisms Of Protein Thermal Stability, Lucas Sawle

Electronic Theses and Dissertations

Organisms that thrive under extreme conditions, such as high salt concentration, low pH, or high temperature, provide an opportunity to investigate the molecular and cellular strategies these organisms have adapted to survive in their harsh environments. Thermophilic proteins, those extracted from organisms that live at high temperature, maintain their structure and function at much higher temperatures compared to their mesophilic counterparts, found in organisms that live near room temperature. Thermophilic and mesophilic homolog protein pairs have identical functionality, and show a high degree of structural and sequential similarity, but differ significantly in their response to high temperature. Addressing the principles …


The Interaction Mechanisms Of A Screw Dislocation With A Defective Coherent Twin Boundary In Copper, Qiongjiali Fang Jan 2015

The Interaction Mechanisms Of A Screw Dislocation With A Defective Coherent Twin Boundary In Copper, Qiongjiali Fang

Graduate College Dissertations and Theses

Σ3{111} coherent twin boundary (CTB) in face-centered-cubic (FCC) metals and alloys have been regarded as an efficient way to simultaneously increase strength and ductility at the nanoscale. Extensive study of dislocation-CTB interaction has been carried out by a combination of computer simulations, experiments and continuum theory. Most of them, however, are based on the perfect CTB assumption. A recent study [Wang YM, Sansoz F, LaGrange T, et al. Defective twin boundaries in nanotwinned metals. Nat Mater. 2013;12(8):697-702.] has revealed the existence of intrinsic kink-like defects in CTBs of nanotwinned copper through nanodiffraction mapping technique, and has confirmed the effect of …


Application Of Computational Molecular Biophysics To Problems In Bacterial Chemotaxis, Davi Ortega May 2013

Application Of Computational Molecular Biophysics To Problems In Bacterial Chemotaxis, Davi Ortega

Doctoral Dissertations

The combination of physics, biology, chemistry, and computer science constitutes the promising field of computational molecular biophysics. This field studies the molecular properties of DNA, protein lipids and biomolecules using computational methods. For this dissertation, I approached four problems involving the chemotaxis pathway, the set of proteins that function as the navigation system of bacteria and lower eukaryotes.

In the first chapter, I used a special-purpose machine for molecular dynamics simulations, Anton, to simulate the signaling domain of the chemoreceptor in different signaling states for a total of 6 microseconds. Among other findings, this study provides enough evidence to propose …


Organic Photovoltaics: A Charge Transfer Perspective In The Study Of Donor-Acceptor Systems, Marco Olguin Jan 2013

Organic Photovoltaics: A Charge Transfer Perspective In The Study Of Donor-Acceptor Systems, Marco Olguin

Open Access Theses & Dissertations

The present research involves the study of donor-acceptor (D/A) dyad complexes from a charge transfer energy perspective. The aim is to provide insight and predictive understanding into the charge transfer processes of the molecular-level components in donor-acceptor based organic solar cells using computational methods to describe photochemical processes at the quantum mechanical level within the Density Functional Theory (DFT) approximation. Predictive understanding is anchored in reproducing experimental results, wherein the present work a perturbative excited-state DFT method is described in detail and shown to give Charge Transfer (CT) energies in excellent agreement with benchmark experimental data. With an accurate excited …


Study Of Local Structure, Stress And Dynamics In Disordered Materials Using Ab-Initio And Molecular Dynamics Simulation, Madhusudan Ojha Aug 2012

Study Of Local Structure, Stress And Dynamics In Disordered Materials Using Ab-Initio And Molecular Dynamics Simulation, Madhusudan Ojha

Doctoral Dissertations

Understanding the atomic structure and dynamics in structurally disordered systems has been a long-standing and most challenging problem in physics and material science. To begin with, it is difficult to describe disorder quantitatively and to differentiate the degree of disorder from one system to another. The majorities of experimental and theoretical approaches to the study of disordered systems are either transferred directly from the study of crystals or address the problem in the macroscopic scale where the atomic origin of behavior is obscured. First principle atomic level stresses and dynamic pair distribution functions described in this dissertation represent attempts to …


Dynamical Properties Of Ferroelectric Perovskites (Ba,Sr)Tio3 And Pb(Zr,Ti)O3 Systems From First Principles, Jeevaka Weerasinghe Aug 2012

Dynamical Properties Of Ferroelectric Perovskites (Ba,Sr)Tio3 And Pb(Zr,Ti)O3 Systems From First Principles, Jeevaka Weerasinghe

Graduate Theses and Dissertations

A first-principles-based effective Hamiltonian scheme which incorporates coupling between ferroelectric (FE) and antiferrodistortive (AFD) motions is applied to Pb(Zr,Ti)O3 alloys. It validates the existence of two modes of E symmetry (rather than the single E(1TO) soft mode) in the 50-75 cm-1 range for temperatures smaller than 200 K and for compositions falling within the Rhombohedral R3c phase. Coupling between long-range-ordered FE and AFD motions is shown to be the cause of the additional mode and more insight into its nature is provided. This scheme is further used to reveal a field-induced anticrossing involving FE and AFD degrees of …


Agent-Based Modeling Of Emergency Building Evacuation, Vi Q. Ha May 2012

Agent-Based Modeling Of Emergency Building Evacuation, Vi Q. Ha

Master's Theses

Panic during emergency building evacuation can cause crowd stampede, resulting in serious injuries and casualties. Agent-based methods have been successfully employed to investigate the collective human behavior during emergency evacuation in cases where the configurational space is extremely simple - usually one rectangular room - but not in evacuations of multi-room or multi-floor buildings. This implies that the effect of the complexity of building architecture on the collective behavior of the agents during evacuation has not been fully investigated. Here, we employ a system of self-moving particles whose motion is governed by the social-force model to investigate the effect of …


Parallel Fast Multipole Method For Molecular Dynamics, Reid G. Ormseth Jun 2007

Parallel Fast Multipole Method For Molecular Dynamics, Reid G. Ormseth

Theses and Dissertations

We report on a parallel version of the Fast Multipole Method (FMM) implemented in the classical molecular dynamics code, NAMD (Not Another Molecular Dynamics program). This novel implementation of FMM aims to minimize interprocessor communication through the modification of the FMM grid to match the hybrid force and spatial decomposition scheme already present in NAMD. This new implementation has the benefit of replacing all-to-all communications broadcasts with direct communications between nearest neighbors. This results in a significant reduction in the amount of communication compared to earlier attempts to integrate FMM into common molecular dynamics programs. The early performance of FMM …


Molecular Dynamics Simulations Of Amphiphilic Molecules, Roger L. Mcmullen Jr. Jan 2005

Molecular Dynamics Simulations Of Amphiphilic Molecules, Roger L. Mcmullen Jr.

Seton Hall University Dissertations and Theses (ETDs)

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A Rapidly-Converging Alternative To Source Iteration For Solving The Discrete Ordinates Radiation Transport Equations In Slab Geometry, Nicholas J. Wager Mar 2004

A Rapidly-Converging Alternative To Source Iteration For Solving The Discrete Ordinates Radiation Transport Equations In Slab Geometry, Nicholas J. Wager

Theses and Dissertations

I present a numerical technique to solve the time independent Boltzmann Transport Equation for the transport of neutrons and photons. The technique efficiently solves the discrete ordinates equations with a new iteration scheme. I call this new scheme the angle space distribution iteration method because it combines a non-linear, high angular-resolution flux approximation within individual spatial cells with a coarse angular-resolution flux approximation that couples all cells in a spatial mesh. This shown to be an efficient alternative to source iteration. The new method is implemented using the step characteristic and exponential characteristic spatial quadrature schemes. The latter was introduced …