Thermal roughening of {001} surfaces

Within the framework of a solid-on-solid model that incorporates nearest- (epsilon) and next-nearest-neighbor (delta) interactions we have determined the free energy of the high-symmetry steps on a (001) surface of a cubic crystal. We have found a simple expression that allows one to determine the thermal roughening temperature TR of a (001) surface (2e¿(epsilon/2+delta)/kbTR¿e¿(epsilon+2delta)/kbTR+2e¿(epsilon+delta)/kbTR=1). In a more refined analysis we have explicitly included step-edge overhangs. This results in a slightly lower thermal roughening temperature. Our results are also applicable to the two-dimensional Ising spin system

Finite type invariants and fatgraphs

We define an invariant $\nabla_G(M)$ of pairs M,G, where M is a 3-manifold obtained by surgery on some framed link in the cylinder $S\times I$, S is a connected surface with at least one boundary component, and G is a fatgraph spine of S. In effect, $\nabla_G$ is the composition with the $\iota_n$ maps of Le-Murakami-Ohtsuki of the link invariant of Andersen-Mattes-Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., $\nabla_G$ establishes an isomorphism from an appropriate vector space $\bar{H}$ of homology cylinders to a certain algebra of Jacobi diagrams. Via composition $\nabla_{G'}\circ\nabla_G^{-1}$ for any pair of fatgraph spines G,G' of S, we derive a representation of the Ptolemy groupoid, i.e., the combinatorial model for the fundamental path groupoid of Teichmuller space, as a group of automorphisms of this algebra. The space $\bar{H}$ comes equipped with a geometrically natural product induced by stacking cylinders on top of one another and furthermore supports related operations which arise by gluing a homology handlebody to one end of a cylinder or to another homology handlebody. We compute how $\nabla_G$ interacts with all three operations explicitly in terms of natural products on Jacobi diagrams and certain diagrammatic constants. Our main result gives an explicit extension of the LMO invariant of 3-manifolds to the Ptolemy groupoid in terms of these operations, and this groupoid extension nearly fits the paradigm of a TQFT. We finally re-derive the Morita-Penner cocycle representing the first Johnson homomorphism using a variant/generalization of $\nabla_G$.Comment: 39 page

Surface bubble nucleation phase space

Recent research has revealed several different techniques for nanoscopic gas nucleation on submerged surfaces, with findings seemingly in contradiction with each other. In response to this, we have systematically investigated the occurrence of surface nanobubbles on a hydrophobised silicon substrate for various different liquid temperatures and gas concentrations, which we controlled independently. We found that nanobubbles occupy a distinct region of this phase space, occurring for gas concentrations of approximately 100-110%. Below the nanobubble phase we did not detect any gaseous formations on the substrate, whereas micropancakes (micron wide, nanometer high gaseous domains) were found at higher temperatures and gas concentrations. We moreover find that supersaturation of dissolved gases is not a requirement for nucleation of bubbles.Comment: 4 pages, 4 figure

Phase diagram of the random field Ising model on the Bethe lattice

The phase diagram of the random field Ising model on the Bethe lattice with a symmetric dichotomous random field is closely investigated with respect to the transition between the ferromagnetic and paramagnetic regime. Refining arguments of Bleher, Ruiz and Zagrebnov [J. Stat. Phys. 93, 33 (1998)] an exact upper bound for the existence of a unique paramagnetic phase is found which considerably improves the earlier results. Several numerical estimates of transition lines between a ferromagnetic and a paramagnetic regime are presented. The obtained results do not coincide with a lower bound for the onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If the latter one proves correct this would hint to a region of coexistence of stable ferromagnetic phases and a stable paramagnetic phase.Comment: Article has been condensed and reorganized; Figs 3,5,6 merged; Fig 4 omitted; Some discussion added at end of Sec. III; 9 pages, 5 figs, RevTeX4, AMSTe

Stationary Properties of a Randomly Driven Ising Ferromagnet

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. Analytic results for the stationary state are presented in mean-field approximation, exhibiting a novel type of first order phase transition related to dynamic freezing. Monte Carlo simulations performed on a quadratic lattice indicate that many features of the mean field theory may survive the presence of fluctuations.Comment: 5 pages in RevTex format, 7 eps/ps figures, send comments to "mailto:[email protected]", submitted to PR

Exploring Set-Theoretic Practices of Youth Engagement in Connective Journalism: What We Lose in School-Mathematical Descriptions

Analyzing youth video submissions regarding COVID-19 to KQED’s ‘Let’s Talk About the Election’ website, we explore the mathematics these youth engaged in through their submissions without creating any explicit connection to school mathematical concepts or standards. Our focus is the students’ construction of sets (e.g. sets of nurses, doctors, American workers), as a means of creating connection with voters and other media authors through Marchi and Clark’s (2021) construct of connective journalism. We observe these youth constructing sets of varying sizes and reflecting on how these sets are contextualized within a larger political dialogue. We also attempt to rewrite part of one student composition using school mathematical symbolic logic, reviewing what in the student’s message is no longer present in the school mathematical analogue and why. We conclude by encouraging practitioners to explore with their students other instances in which they can challenge numerical or school mathematical symbolic writing as a superior means of communicating ideas

Greenhouse gas emissions in the agricultural phase of wine production in the Maremma rural district (Tuscany, Italy).

In recent years, there has been an increasing interest from retailers, industries and environmental associations in estimating the life cycle of greenhouse gases emitted in the atmosphere from everyday products and services, also known as carbon footprint (CF). Life cycle assessment (LCA) is the most common methodology used to evaluate the environmental impact of a product. This approach was largely used in many industrial sectors and was also recently applied to quantify the environmental impact of the agri-food chain. Within agri-food products, wine is one of the most analysed, both for its importance in economic production and in the world distribution market. The present study is a part of the Carbon Label Project carried out in the wine production chain in the Maremma rural district (Tuscany, Italy). The project assessed the greenhouse gas (GHG) emissions from wine production for labelling purposes. Here, we evaluated the environmental performances of four high quality wines for carbon labelling. The international standards ISO 14040, ISO 14044, and the Product Category Rules (PCR) Wine from Fresh Grapes (except sparkling wine) and Grape Must for the Environmental Product Declaration (EPD) certification, specifically for Climate Declaration, were used in order to carry out our analyses. The functional unit (FU) used here was one 0.75 L bottle of wine. The system boundaries were set from the vineyard planting to the distribution and waste disposal. The global warming potential (GWP) of four investigated wines was found to lie between 0.6 and 1.3 kg CO2-eq./bottle, showing a value comparable with literature. With all the four wines analysed, the agricultural phase covered, on average, 22% of the total GWP/bottle, while the main impact was in the production of the glass bottle. The results showed that the vineyard-planting phase has a significant impact on the wine CF, thus it has to be considered in the life cycle, while in literature it is frequently omitted. On the contrary, the pre-production phase did not present a relevant impact. The use of nitrogen fertilisers, the grapes’ yield and N2O emissions were the parameters that mostly affected the carbon footprint in the agricultural phase, as underlined by the sensitivity analysis