Possible pair-graphene structures govern the thermodynamic properties of arbitrarily stacked few-layer graphene

The thermodynamic properties of few-layer graphene arbitrarily stacked on LiNbO3 crystal were characterized by measuring the parameters of a surface acoustic wave as it passed through the graphene/LiNbO3 interface. The parameters considered included the propagation velocity, frequency, and attenuation. Mono-, bi-, tri-, tetra-, and penta-layer graphene samples were prepared by transferring individual graphene layers onto LiNbO3 crystal surfaces at room temperature. Intra-layer lattice deformation was observed in all five samples. Further inter-layer lattice deformation was confirmed in samples with odd numbers of layers. The inter-layer lattice deformation caused stick–slip friction at the graphene/LiNbO3 interface near the temperature at which the layers were stacked. The thermal expansion coefficient of the deformed few-layer graphene transitioned from positive to negative as the number of layers increased. To explain the experimental results, we proposed a few-layer graphene even–odd layer number stacking order effect. A stable pair-graphene structure formed preferentially in the few-layer graphene. In even-layer graphene, the pair-graphene structure formed directly on the LiNbO3 substrate. Contrasting phenomena were noted with odd-layer graphene. Single-layer graphene was bound to the substrate after the stable pair-graphene structure was formed. The pair-graphene structure affected the stacking order and inter-layer lattice deformation of few-layer graphene substantially.

The KSBA compactification of the moduli space of $$D_{1,6}$$-polarized Enriques surfaces

We describe a compactification by stable pairs (also known as KSBA compactification) of the 4-dimensional family of Enriques surfaces which arise as the $${\mathbb {Z}}_2^2$$ Z 2 2 -covers of the blow up of $${\mathbb {P}}^2$$ P 2 at three general points branched along a configuration of three pairs of lines. Up to a finite group action, we show that this compactification is isomorphic to the toric variety associated to the secondary polytope of the unit cube. We relate the KSBA compactification considered to the Baily–Borel compactification of the same family of Enriques surfaces. Part of the KSBA boundary has a toroidal behavior, another part is isomorphic to the Baily–Borel compactification, and what remains is a mixture of these two. We relate the stable pair compactification studied here with Looijenga’s semitoric compactifications.

Stable Pair Invariants of Local Calabi–Yau 4-folds

In 2008, Klemm–Pandharipande defined Gopakumar–Vafa type invariants of a Calabi–Yau 4-folds $X$ using Gromov–Witten theory. Recently, Cao–Maulik–Toda proposed a conjectural description of these invariants in terms of stable pair theory. When $X$ is the total space of the sum of two line bundles over a surface $S$, and all stable pairs are scheme theoretically supported on the zero section, we express stable pair invariants in terms of intersection numbers on Hilbert schemes of points on $S$. As an application, we obtain new verifications of the Cao–Maulik–Toda conjectures for low-degree curve classes and find connections to Carlsson–Okounkov numbers. Some of our verifications involve genus zero Gopakumar–Vafa type invariants recently determined in the context of the log-local principle by Bousseau–Brini–van Garrel. Finally, using the vertex formalism, we provide a few more verifications of the Cao–Maulik–Toda conjectures when thickened curves contribute and also for the case of local $\mathbb{P}^3$.

Observations on a presumed bilateral gynandromorph Black Redstart Phoenicurus ochruros paired with a male

A supposed bilateral gynandromorph Black Redstart Phoenicurus ochruros in northwestern Switzerland formed a pair with a phenotypically classical male, but apparently was not breeding. The bird was documented before and after moult, when all replaced feathers were again of the same sex type. It was also recorded singing, the song being typical for the species. This is the second recorded case of a bilateral gynandromorph Black Redstart, one of only a handful cases where wild bilateral gynandromorph birds have been observed throughout the breeding season, and the first unequivocal documentation of a presumed bilateral gynandromorph bird forming a stable pair with a typical male.

Adult sex ratio and social status predict mating and parenting strategies in Northern Ireland

Evidence from animal species indicates that a male-biased adult sex ratio (ASR) can lead to higher levels of male parental investment and that there is heterogeneity in behavioural responses to mate scarcity depending on mate value. In humans, however, there is little consistent evidence of the effect of the ASR on pair-bond stability and parental investment and even less of how it varies by an individual's mate value. In this paper we use detailed census data from Northern Ireland to test the association between the ASR and pair-bond stability and parental investment by social status (education and social class) as a proxy for mate value. We find evidence that female, but not male, cohabitation is associated with the ASR. In female-biased areas women with low education are less likely to be in a stable pair-bond than highly educated women, but in male-biased areas women with the lowest education are as likely to be in a stable pair-bond as their most highly educated peers. For both sexes risk of separation is greater at female-biased sex ratios. Lastly, our data show a weak relationship between parental investment and the ASR that depends on social class. We discuss these results in the light of recent reformulations of parental investment theory. This article is part of the themed issue ‘Adult sex ratios and reproductive decisions: a critical re-examination of sex differences in human and animal societies’.