The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example of bulk-boundary correspondence. We show that the chiral edge modes are not strictly ...tied to the Chern numbers defined by a non-Hermitian Bloch Hamiltonian. This breakdown of conventional bulk-boundary correspondence stems from the non-Bloch-wave behavior of eigenstates (non-Hermitian skin effect), which generates pronounced deviations of phase diagrams from the Bloch theory. We introduce non-Bloch Chern numbers that faithfully predict the numbers of chiral edge modes. The theory is backed up by the open-boundary energy spectra, dynamics, and phase diagram of representative lattice models. Our results highlight a unique feature of non-Hermitian bands and suggest a non-Bloch framework to characterize their topology.
The FactSage computer package consists of a series of information, calculation and manipulation modules that enable one to access and manipulate compound and solution databases. With the various ...modules running under Microsoft Windows® one can perform a wide variety of thermochemical calculations and generate tables, graphs and figures of interest to chemical and physical metallurgists, chemical engineers, corrosion engineers, inorganic chemists, geochemists, ceramists, electrochemists, environmentalists, etc. This paper presents a summary of the developments in the FactSage thermochemical software and databases during the last six years. Particular emphasis is placed on the new databases and developments in calculating and manipulating phase diagrams.
This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements ...in static equilibrium. It is intended to support the collaborative work of structural engineers and architects from the conceptual phase of the design process. Several procedures for the construction of a vector-based 3D force diagram for any given 3D form diagram with an underlying planar or non-planar graph are identified and described. In the non-planar case, the proposed procedures rely on the preliminary topological planarization of the graph by cutting the crossing edges and reconnecting them to one or more newly inserted auxiliary vertices. Resulting planar graphs can be then used as a base for the assembly of 3D force diagrams, without altering the static equilibrium of the structure. An implementation of the proposed framework to real design scenarios is presented through two case studies. These examples demonstrate the benefits of bi-directional manipulations of form and force diagrams in the structural design process.
In earlier papers we introduced a representation of isotopy classes of compact surfaces embedded in the three-sphere S3 by so called rectangular diagrams. The formalism proved useful for comparing ...Legendrian knots. The aim of this paper is to prove a Reidemeister type theorem for rectangular diagrams of surfaces.
Abstract
We have recently shown that the ∼2 Gyr old Large Magellanic Cloud star cluster NGC 1978 hosts multiple populations in terms of star-to-star abundance variations in N/Fe. These can be seen as ...a splitting or spread in the subgiant and red giant branches (SGB and RGB) when certain photometric filter combinations are used. Because of its relative youth, NGC 1978 can be used to place stringent limits on whether multiple bursts of star formation have taken place within the cluster, as predicted by some models for the origin of multiple populations. We carry out two distinct analyses to test whether multiple star formation epochs have occurred within NGC 1978. First, we use ultraviolet colour--magnitude diagrams (CMDs) to select stars from the first and second population along the SGB, and then compare their positions in optical CMDs, where the morphology is dominantly controlled by age as opposed to multiple population effects. We find that the two populations are indistinguishable, with age differences of 1 ± 20 Myr between them. This is in tension with predictions from the asymptotic giant branch scenario for the origin of multiple populations. Second, we estimate the broadness of the main-sequence turn-off (MSTO) of NGC 1978 and we report that it is consistent with the observational errors. We find an upper limit of ∼65 Myr on the age spread in the MSTO of NGC 1978. This finding is in conflict with the age spread scenario as origin of the extended MSTO in intermediate-age clusters, while it fully supports predictions from the stellar rotation model.
Unified modelling language (UML) is a visual modelling language, which has gained popularity among software practitioners. In a model-driven software development environment, the existing UML tools ...mainly support automatic generation of structural code from UML class diagrams. However, the code generation from UML diagrams such as statechart, activity, collaboration and sequence diagrams (SDs) are not supported by most UML tools and also have scarcely been reported in the literatures. This work proposes an approach to automatic generation of code from UML 2.x SDs of use cases. From the XML metadata interchange (XMI) representation of an SD of a use case, the authors construct a graph model called sequence integration graph (SIG). The SIG encapsulates information related to messages, control flow and method scope of interactions. These information are then used to generate code. The proposed approach has been tested using a number of real-life application systems and the results substantiate the efficacy of the approach to synthesise the code for controller classes. The authors observe that approximately 48% of the total lines of code within controller class methods can be generated with the proposed approach. The proposed approach can be easily extended to other behavioural UML models such as interaction-overview diagrams, communication diagrams and activity diagrams.
Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair ...at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.
We construct an injection from the set of r-fans of Dyck paths (resp. vacillating tableaux) of length n into the set of chord diagrams on n that intertwines promotion and rotation. This is done in ...two different ways, namely as fillings of promotion matrices and in terms of Fomin growth diagrams. Our analysis uses the fact that r-fans of Dyck paths and vacillating tableaux can be viewed as highest weight elements of weight zero in crystals of type Br and Cr, respectively, which in turn can be analyzed using virtual crystals. On the level of Fomin growth diagrams, the virtualization process corresponds to the Roby–Krattenthaler blow up construction. One of the motivations for finding rotation invariant diagrammatic bases such as chord diagrams is the cyclic sieving phenomenon. Indeed, we give a cyclic sieving phenomenon on r-fans of Dyck paths and vacillating tableaux using the promotion action.
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