GNC Architecture Design for ARES Simulation. Revision 3.0

The purpose of this document is to describe the GNC architecture and associated interfaces for all ARES simulations. Establishing a common architecture facilitates development across the ARES simulations and provides an efficient mechanism for creating an end-to-end simulation capability. In general, the GNC architecture is the frame work in which all GNC development takes place, including sensor and effector models. All GNC software applications have a standard location within the architecture making integration easier and, thus more efficient

Node-to-segment and node-to-surface interface finite elements for fracture mechanics

The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets (in 3D) belonging to the opposite crack faces and enforce the cohesive traction-separation relation. In the present work we propose a novel type of interface element for fracture mechanics sharing some analogies with the node-to-segment (in 2D) and with the node-to-surface (in 3D) contact elements. The displacement gap of a node belonging to the finite element discretization of one crack face with respect to its projected point on the opposite face is used to determine the cohesive tractions, the residual vector and its consistent linearization for an implicit solution scheme. The following advantages with respect to classical interface finite elements are demonstrated: (i) non-matching finite element discretizations of the opposite crack faces is possible; (ii) easy modelling of cohesive cracks with non-propagating crack tips; (iii) the internal rotational equilibrium of the interface element is assured. Detailed examples are provided to show the usefulness of the proposed approach in nonlinear fracture mechanics problems.Comment: 37 pages, 17 figure

Coherent transport of armchair graphene constrictions

The coherent transport properties of armchair graphene nanoconstrictions(GNC) are studied using tight-binding approach and Green's function method. We find a non-bonding state at zero Fermi energy which results in a zero conductance valley, when a single vacancy locates at $y=3n\pm 1$ of a perfect metallic armchair graphene nanoribbon(aGNR). However, the non-bonding state doesn't exist when a vacancy locates at y=3n, and the conductance behavior of lowest conducting channel will not be affected by the vacancy. For the square-shaped armchair GNC consisting of three metallic aGNR segments, resonant tunneling behavior is observed in the single channel energy region. We find that the presence of localized edge state locating at the zigzag boundary can affect the resonant tunneling severely. A simplified one dimensional model is put forward at last, which explains the resonant tunneling behavior of armchair GNC very well.Comment: 6 pages, 11 figure

Conductance quantization in graphene nanoconstrictions with mesoscopically smooth but atomically stepped boundaries

We present the results of million atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ~0.5*2e2/h as in recent experiments [Tombros et al., Nature Physics 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/h occur even for strongly non-adiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also show that conductance plateaus near 0.5*2e2/h can occur as a result of electron backscattering at stepped edges even in the absence of electron-electron interactions.Comment: 5 pages, 4 figure

The Hilbert series of U/SU SQCD and Toeplitz Determinants

We present a new technique for computing Hilbert series of N=1 supersymmetric QCD in four dimensions with unitary and special unitary gauge groups. We show that the Hilbert series of this theory can be written in terms of determinants of Toeplitz matrices. Applying related theorems from random matrix theory, we compute a number of exact Hilbert series as well as asymptotic formulae for large numbers of colours and flavours -- many of which have not been derived before.Comment: 49 pages, 6 figures. Version 2: references adde

Large Graph Analysis in the GMine System

Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed in an interactive environment, where human expertise can guide the process. For large graphs, though, there are some challenges: the excessive processing requirements are prohibitive, and drawing hundred-thousand nodes results in cluttered images hard to comprehend. To cope with these problems, we propose an innovative framework suited for any kind of tree-like graph visual design. GMine integrates (a) a representation for graphs organized as hierarchies of partitions - the concepts of SuperGraph and Graph-Tree; and (b) a graph summarization methodology - CEPS. Our graph representation deals with the problem of tracing the connection aspects of a graph hierarchy with sub linear complexity, allowing one to grasp the neighborhood of a single node or of a group of nodes in a single click. As a proof of concept, the visual environment of GMine is instantiated as a system in which large graphs can be investigated globally and locally