Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal

Weyl points (WPs) are isolated degeneracies carrying quantized topological charges, and are therefore robust against Hermitian perturbations. WPs are predicted to spread to the Weyl exceptional rings (WERs) in the presence of non-Hermiticity. Here, we use a one-dimensional (1D) Aubry-Andre-Harper (AAH) model to construct a Weyl semimetal in a 3D parameter space comprised of one reciprocal dimension and two synthetic dimensions. The inclusion of non-Hermiticity in the form of gain and loss produces a WER. The topology of the WER is characterized by both its topological charge and non-Hermitian winding numbers. The WER is experimentally observed in a 1D phononic crystal with the non-Hermiticity introduced by active acoustic components. In addition, Fermi arcs are observed to survive the presence of non-Hermitian effect. We envision our findings to pave the way for studying the high-dimensional non-Hermitian topological physics in acoustics.Comment: 14 pages, 5 figure

Adjacency Graphs of Polyhedral Surfaces

We study whether a given graph can be realized as an adjacency graph of the polygonal cells of a polyhedral surface in $\mathbb{R}^3$. We show that every graph is realizable as a polyhedral surface with arbitrary polygonal cells, and that this is not true if we require the cells to be convex. In particular, if the given graph contains $K_5$, $K_{5,81}$, or any nonplanar $3$-tree as a subgraph, no such realization exists. On the other hand, all planar graphs, $K_{4,4}$, and $K_{3,5}$ can be realized with convex cells. The same holds for any subdivision of any graph where each edge is subdivided at least once, and, by a result from McMullen et al. (1983), for any hypercube. Our results have implications on the maximum density of graphs describing polyhedral surfaces with convex cells: The realizability of hypercubes shows that the maximum number of edges over all realizable $n$-vertex graphs is in $\Omega(n \log n)$. From the non-realizability of $K_{5,81}$, we obtain that any realizable $n$-vertex graph has $O(n^{9/5})$ edges. As such, these graphs can be considerably denser than planar graphs, but not arbitrarily dense.Comment: To appear in Proc. SoCG 202

Contribution of Ex-Situ and In-Situ X-ray Grazing Incidence Scattering Techniques to the Understanding of Quantum Dot Self-Assembly:A Review

Quantum dots are under intense research, given their amazing properties which favor their use in electronics, optoelectronics, energy, medicine and other important applications. For many of these technological applications, quantum dots are used in their ordered self-assembled form, called superlattice. Understanding the mechanism of formation of the superlattices is crucial to designing quantum dots devices with desired properties. Here we review some of the most important findings about the formation of such superlattices that have been derived using grazing incidence scattering techniques (grazing incidence small and wide angle X-ray scattering (GISAXS/GIWAXS)). Acquisition of these structural information is essential to developing some of the most important underlying theories in the field

Unitals in projective planes revisited

This thesis revisits the topic of unitals in finite projective planes. A unital U in a projective plane of order q2 is a set of q3 + 1 points, such that every line meets U in one or q + 1 points. Unitals are an important class of point-set in finite projective planes, whose combinatorial and algebraic properties have been the subject of considerable study. In this work, we summarise, revise, and extend contemporary research on unitals. Chapter 1 covers the necessary prerequisites to study unitals and related objects in finite geometry. In Chapter 2, we focus on Buekenhout-Tits unitals and answer some open problems regarding their equivalence, stabilisers and feet. The results presented in Chapter 2 are also available in a preprint paper [22]. Following this, Chapter 3 summarises recent results on Buekenhout- Metz unitals, and presents a small result on the intersection of ovoidal-Buekenhout-Metz unitals and Buekenhout-Metz unitals. Chapter 4 highlights Kestenband arcs and their relationship to Hermitian unitals, and makes explicit a proof of their equivalence. Finally in Chapter 5, we review our understanding of Figueroa planes. Beyond describing ovals and unitals in Figueroa planes, we also suggest generalisations of their constructions to semi-ovals

On hierarchical hyperbolicity of cubical groups

Let X be a proper CAT(0) cube complex admitting a proper cocompact action by a group G. We give three conditions on the action, any one of which ensures that X has a factor system in the sense of [BHS14]. We also prove that one of these conditions is necessary. This combines with results of Behrstock--Hagen--Sisto to show that $G$ is a hierarchically hyperbolic group; this partially answers questions raised by those authors. Under any of these conditions, our results also affirm a conjecture of BehrstockHagen on boundaries of cube complexes, which implies that X cannot contain a convex staircase. The conditions on the action are all strictly weaker than virtual cospecialness, and we are not aware of a cocompactly cubulated group that does not satisfy at least one of the conditions.Comment: Minor changes in response to referee report. Streamlined the proof of Lemma 5.2, and added an examples of non-rotational action

Picturing Number in the Central Middle Ages.

Numeracy was as highly valued as literacy in the schools of Latin-speaking Europe around the year 1000, and the skills inculcated by masters, engendering specific modes of seeing and imagining, had demonstrable impact on contemporary visual culture. The trivium—grammar, rhetoric, and dialectic—continued to be taught as the foundation of learning, but the quadrivium, the four disciplines of number—arithmetic, geometry, astronomy, and music—received new emphasis. Two of the era’s greatest intellects, Gerbert of Aurillac (Pope Sylvester II; c.940–1003) and Abbo of Fleury (c.944–1004), gained renown for their mathematical prowess and charismatic teaching. They educated a generation of Europe's powerful elites—including Emperor Otto III—and a host of anonymous clerics, monks, and priests. In the closed economy of the central middle ages, these men were also the primary patrons, makers, and viewers of objects. Works of the time, like the Pericope Book of Henry II, reveal new qualities when examined through the lens of number. This project is located at the cathedral school of Reims and the monastery school of Saint-Benoît-sur-Loire (Fleury)—where Gerbert and Abbo were masters, epicenters of a pan-European network of exchange linking monastic, episcopal, and lay institutions. Numeric knowledge was drawn from late antique and early medieval tracts by such figures as Boethius, Calcidius, Macrobius, Martianus Capella, Cassiodorus, Isidore of Seville, and Bede. Manuscript copies of these works produced and used at Reims and Fleury c.1000 give evidence of active engagement with their content, visual as well as verbal. Diagrammatic images earlier devised to explicate numeric concepts were now adapted and artfully elaborated for classroom use. This is evident in important introductions to the quadrivial disciplines prepared by Abbo (Explanatio in Calculo Victorii), Abbo’s student Byrhtferth of Ramsey (Enchiridion), and Gerbert (Isagoge geometriae). Accompanying images to these tracts are witness to contemporary notions of materiality, sight, and the limits of representation. Students of arithmetic became freshly attuned to placement and order. Computistic study developed an active, agile, and "curious" eye, while the practice of geometry exercised the intellectual eye, sharpening it, according to Gerbert, "for contemplating spiritual things and truths."PHDHistory of ArtUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/116774/1/mcnameme_1.pd

The Earth: Plasma Sources, Losses, and Transport Processes

This paper reviews the state of knowledge concerning the source of magnetospheric plasma at Earth. Source of plasma, its acceleration and transport throughout the system, its consequences on system dynamics, and its loss are all discussed. Both observational and modeling advances since the last time this subject was covered in detail (Hultqvist et al., Magnetospheric Plasma Sources and Losses, 1999) are addressed

Probing and harnessing photonic Fermi arc surface states using light-matter interactions

Fermi arcs, i.e., surface states connecting topologically distinct Weyl points, represent a paradigmatic manifestation of the topological aspects of Weyl physics. We investigate a light-matter interface based on the photonic counterpart of these states and prove that it can lead to phenomena with no analog in other setups. First, we show how to image the Fermi arcs by studying the spontaneous decay of one or many emitters coupled to the system's border. Second, we demonstrate that, exploiting the negative refraction of these modes, the Fermi arc surface states can act as a robust quantum link, enabling, e.g., the occurrence of perfect quantum state transfer between the considered emitters or the formation of highly entangled states. In addition to their fundamental interest, our findings evidence the potential offered by the photonic Fermi arc light-matter interfaces for the design of more robust quantum technologiesI.G.-E. acknowledges financial support from the Spanish Ministry for Science, Innovation, and Universities through FPU grant AP-2018-02748. A.G.-T. acknowledges financial support from the Proyecto Sinérgico CAM 2020 Y2020/TCS-6545 (NanoQuCo-CM), from the CSIC Interdisciplinary Thematic Platform (PTI) Quantum Technologies (PTI-QTEP+), from Spanish project PID2021-127968NB-I00 and the project TED2021-130552B-C22 funded by MCIN/AEI/ 10.13039/ 501100011033/FEDER, UE, and MCIN/AEI/ 10.13039/501100011033, respectively, and the support from a 2022 Leonardo Grant for Researchers and Cultural Creators, BBVA. J.B.-A. and J.M. acknowledge financial support from the Spanish Ministry for Science, Innovation, and Universities through grants RTI2018-098452-B-I00 (MCIU/AEI/FEDER,UE) and MDM-2014-0377 (María de Maeztu programme for Units of Excellence in R&

1-Safe Petri nets and special cube complexes: equivalence and applications

Nielsen, Plotkin, and Winskel (1981) proved that every 1-safe Petri net $N$ unfolds into an event structure $\mathcal{E}_N$. By a result of Thiagarajan (1996 and 2002), these unfoldings are exactly the trace regular event structures. Thiagarajan (1996 and 2002) conjectured that regular event structures correspond exactly to trace regular event structures. In a recent paper (Chalopin and Chepoi, 2017, 2018), we disproved this conjecture, based on the striking bijection between domains of event structures, median graphs, and CAT(0) cube complexes. On the other hand, in Chalopin and Chepoi (2018) we proved that Thiagarajan's conjecture is true for regular event structures whose domains are principal filters of universal covers of (virtually) finite special cube complexes. In the current paper, we prove the converse: to any finite 1-safe Petri net $N$ one can associate a finite special cube complex ${X}_N$ such that the domain of the event structure $\mathcal{E}_N$ (obtained as the unfolding of $N$) is a principal filter of the universal cover $\widetilde{X}_N$ of $X_N$. This establishes a bijection between 1-safe Petri nets and finite special cube complexes and provides a combinatorial characterization of trace regular event structures. Using this bijection and techniques from graph theory and geometry (MSO theory of graphs, bounded treewidth, and bounded hyperbolicity) we disprove yet another conjecture by Thiagarajan (from the paper with S. Yang from 2014) that the monadic second order logic of a 1-safe Petri net is decidable if and only if its unfolding is grid-free. Our counterexample is the trace regular event structure $\mathcal{\dot E}_Z$ which arises from a virtually special square complex $\dot Z$. The domain of $\mathcal{\dot E}_Z$ is grid-free (because it is hyperbolic), but the MSO theory of the event structure $\mathcal{\dot E}_Z$ is undecidable