TY - JOUR
AB - The goal of limiting global warming to 1.5 °C requires a drastic reduction in CO2 emissions across many sectors of the world economy. Batteries are vital to this endeavor, whether used in electric vehicles, to store renewable electricity, or in aviation. Present lithium-ion technologies are preparing the public for this inevitable change, but their maximum theoretical specific capacity presents a limitation. Their high cost is another concern for commercial viability. Metal–air batteries have the highest theoretical energy density of all possible secondary battery technologies and could yield step changes in energy storage, if their practical difficulties could be overcome. The scope of this review is to provide an objective, comprehensive, and authoritative assessment of the intensive work invested in nonaqueous rechargeable metal–air batteries over the past few years, which identified the key problems and guides directions to solve them. We focus primarily on the challenges and outlook for Li–O2 cells but include Na–O2, K–O2, and Mg–O2 cells for comparison. Our review highlights the interdisciplinary nature of this field that involves a combination of materials chemistry, electrochemistry, computation, microscopy, spectroscopy, and surface science. The mechanisms of O2 reduction and evolution are considered in the light of recent findings, along with developments in positive and negative electrodes, electrolytes, electrocatalysis on surfaces and in solution, and the degradative effect of singlet oxygen, which is typically formed in Li–O2 cells.
AU - Kwak, WJ
AU - Sharon, D
AU - Xia, C
AU - Kim, H
AU - Johnson, LR
AU - Bruce, PG
AU - Nazar, LF
AU - Sun, YK
AU - Frimer, AA
AU - Noked, M
AU - Freunberger, Stefan Alexander
AU - Aurbach, D
ID - 7985
IS - 14
JF - Chemical Reviews
SN - 0009-2665
TI - Lithium-oxygen batteries and related systems: Potential, status, and future
VL - 120
ER -
TY - CONF
AB - We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.
AU - Patakova, Zuzana
ID - 7989
SN - 18688969
T2 - 36th International Symposium on Computational Geometry
TI - Bounding radon number via Betti numbers
VL - 164
ER -
TY - CONF
AB - Given a finite point set P in general position in the plane, a full triangulation is a maximal straight-line embedded plane graph on P. A partial triangulation on P is a full triangulation of some subset P' of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge, removes a non-extreme point of degree 3, or adds a point in P ⧵ P' as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The goal of this paper is to investigate the structure of this graph, with emphasis on its connectivity. For sets P of n points in general position, we show that the bistellar flip graph is (n-3)-connected, thereby answering, for sets in general position, an open questions raised in a book (by De Loera, Rambau, and Santos) and a survey (by Lee and Santos) on triangulations. This matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points and projecting the lower convex hull), where (n-3)-connectivity has been known since the late 1980s through the secondary polytope (Gelfand, Kapranov, Zelevinsky) and Balinski’s Theorem. Our methods also yield the following results (see the full version [Wagner and Welzl, 2020]): (i) The bistellar flip graph can be covered by graphs of polytopes of dimension n-3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n-3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations are regular iff the trivial subdivision has height n-3 in the partial order of partial subdivisions. (iv) There are arbitrarily large sets P with non-regular partial triangulations, while every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular partial triangulations (answering a question by F. Santos in the unexpected direction).
AU - Wagner, Uli
AU - Welzl, Emo
ID - 7990
SN - 18688969
T2 - 36th International Symposium on Computational Geometry
TI - Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips)
VL - 164
ER -
TY - CONF
AB - We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between "grid peeling" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.
AU - Avvakumov, Sergey
AU - Nivasch, Gabriel
ID - 7991
SN - 18688969
T2 - 36th International Symposium on Computational Geometry
TI - Homotopic curve shortening and the affine curve-shortening flow
VL - 164
ER -
TY - CONF
AB - Let K be a convex body in ℝⁿ (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K ∩ h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p₀ is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n ≥ 2, there are always at least three distinct barycentric cuts through the point p₀ ∈ K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p₀ are guaranteed if n ≥ 3.
AU - Patakova, Zuzana
AU - Tancer, Martin
AU - Wagner, Uli
ID - 7992
SN - 18688969
T2 - 36th International Symposium on Computational Geometry
TI - Barycentric cuts through a convex body
VL - 164
ER -