Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics

We use persistence modules and their corresponding barcodes to quantitatively distinguish between different fiberwise star-shaped domains in the cotangent bundle of a fixed manifold. The distance between two fiberwise star-shaped domains is measured by a nonlinear version of the classical Banach–Mazur distance, called symplectic Banach–Mazur distance and denoted by [Formula: see text] The relevant persistence modules come from filtered symplectic homology and are stable with respect to [Formula: see text] Our main focus is on the space of unit codisc bundles of orientable surfaces of positive genus, equipped with Riemannian metrics. We consider some questions about large-scale geometry of this space and in particular we give a construction of a quasi-isometric embedding of [Formula: see text] into this space for all [Formula: see text] On the other hand, in the case of domains in [Formula: see text], we can show that the corresponding metric space has infinite diameter. Finally, we discuss the existence of closed geodesics whose energies can be controlled.

Mid-altitude cusp dynamics and properties during the IMF By dominated intervals

<p>Observations inside the cusp can be used as distant monitoring of the large-scale geometry and properties of the magnetic reconnection at the magnetopause. The recent modelling and observations of the cusp and flux transfer events in the vicinity of the magnetopause show that the reconnection can occur along the X-line extended over many hours of magnetic local time (MLT), comprising sites of both component and anti-parallel reconnection scenarios. Such observations are in contradiction to the statistical DMSP studies showing that the cusp is rather limited in magnetic local time with an average size 2.5 hours of MLT. Moreover, some past observations indicate that the cusp is moving in response to the changes of the IMF By component, suggesting that the cusp is formed due to anti-parallel reconnection along the X-line limited in MLT.</p><p>In this presentation we analyse several events of the mid-altitude cusp observations during the Cluster campaign when the satellites cross the cusp mainly along the longitude in a string-of-pearls configuration during an Interplanetary Magnetic Field (IMF) configuration with a stable and dominant IMF By-component. During this particular Cluster orbit it was possible to define the dawn and dusk cusp boundaries and to study plasma parameters inside different parts of the cusp region. The observations will be discussed in terms of the cusp extension, cusp motion, and possible formation of the ‘double’ cusp structures. Finally, we will consider what these observations reveal about the large-scale reconnection geometry at the magnetopause.</p>

A Material Point Method for Glacier Calving

<p>Glaciers calving ice into the ocean is predicted to significantly contribute to sea-level rise and will thus influence future climate. Although numerous factors that induce glacier calving have been identified and studied, it is still extremely challenging to develop a unified and continuum computational framework that simulates ice fracture and glacier calving taking into account all important ingredients such as the interaction between ice and water, including buoyancy and melting, on complex and large scale geometry. This prevents scientists to precisely predict calving rates at the outlet of glaciers. Here, we propose to address this issue through numerical simulations of glacier calving based on the Material Point Method and finite strain elastoplasticity. A non-associative Cam-Clay model was developed to simulate the ice while the water is modeled as a nearly in-compressible fluid. First, simplified 2D simulations were performed to analyse the size of calved icebergs which were in good agreement with analytical solutions. The model reproduces not only the vertical glacier fracture observed in real calving events but also iceberg formation and tsunami-wave generation. Finally, 3D simulations of glacier calving were performed, taking into account opened crevasses on the top of the glacier. Although at a preliminary stage, and lacking experimental validation, we show the promise of our approach for modeling glacier calving, and more generally glacier and sea-ice dynamics.</p>

Experimental Approach for Printability Assessment: Toward a Practical Decision-Making Framework of Printability for Cementitious Materials

The objective of this paper is to propose a pre-experimental framework of printability pre-assessment of cementitious materials. This study firstly presents a general review of additive manufacturing in construction and then examines the main characteristic of the material formulation and printability properties based on extrusion technique. This framework comes with experimental tests to determine a qualitative printability index of mixtures. It uses mix-designs reported in the literature to define interval ratio of mixture design to be investigated in this study. The focus was put on two criteria that influence the formulation namely flowability and buildability. Two practiced based tests, mini slump and cone penetrometer, were used to draw the flowability and buildability dimensionless index. The results were analyzed by introducing an optimal printability coefficient and examining their time evolution. An optimal time of printing was determined Toptimal. Finally, a 3D mortar printing system and its operational process are presented. Then, based on the measurement, the optimal mixture is identified and printed in a large-scale geometry.

On the large-scale geometry of diffeomorphism groups of 1-manifolds

We apply the framework of Rosendal to study the large-scale geometry of the topological groups {\operatorname{Diff}_{+}^{k}(M^{1})} , consisting of orientation-preserving {C^{k}} -diffeomorphisms (for {1\leq k\leq\infty} ) of a compact 1-manifold {M^{1}} ( {=I} or {\mathbb{S}^{1}} ). We characterize the relative property (OB) in such groups: {A\subseteq\operatorname{Diff}_{+}^{k}(M^{1})} has property (OB) relative to {\operatorname{Diff}_{+}^{k}(M^{1})} if and only if {\sup_{f\in A}\sup_{x\in M^{1}}\lvert\log f^{\prime}(x)|<\infty} and {\sup_{f\in A}\sup_{x\in M^{1}}|f^{(j)}(x)|<\infty} for every integer j with {2\leq j\leq k} . We deduce that {\operatorname{Diff}_{+}^{k}(M^{1})} has the local property (OB), and consequently a well-defined non-trivial quasi-isometry class, if and only if {k<\infty} . We show that the groups {\operatorname{Diff}_{+}^{1}(I)} and {\operatorname{Diff}_{+}^{1}(\mathbb{S}^{1})} are quasi-isometric to the infinite-dimensional Banach space {C[0,1]} .

Asymptotic Dimension

This chapter considers the notion of asymptotic dimension. It first provides an overview of asymptotic dimension before explaining the asymptotic dimensions of free abelian and nonabelian groups, free groups, groups, integers, metric spaces, and products. It then looks at the large-scale geometry of a Cayley graph of a finitely generated group, along with the topological notion of dimension and the large-scale notion of dimension. It also analyzes three typical questions that are asked about asymptotic dimension before concluding with some other examples of groups where something is known about their asymptotic dimension, such as braid groups, Artin groups, surface groups, hyperbolic groups, Coxeter groups, Thompson's group, and wreath product. The discussion includes exercises and research projects.

Large-scale geometry of homeomorphism groups

Let $M$ be a compact manifold. We show that the identity component $\operatorname{Homeo}_{0}(M)$ of the group of self-homeomorphisms of $M$ has a well-defined quasi-isometry type, and study its large-scale geometry. Through examples, we relate this large-scale geometry to both the topology of $M$ and the dynamics of group actions on $M$. This gives a rich family of examples of non-locally compact groups to which one can apply the large-scale methods developed in previous work of the second author.