On the enumeration of finite LL-algebras

We use Constraint Satisfaction Methods to construct and enumerate finite $L$-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang-Baxter equation. There are 377322225 isomorphism classes of $L$-algebras of size eight. The database constructed suggest the existence of bijections between certain classes of $L$-algebras and well-known combinatorial objects. On the one hand, we prove that Bell numbers enumerate isomorphism classes of finite linear $L$-algebras. On the other hand, we also prove that finite regular $L$-algebras are in bijective correspondence with infinite-dimensional Young diagrams.Comment: 17 pages, 3 tables, 2 figures. Postprint versio

Formation of Nanopillar Arrays in Ultrathin Viscous Films: The Critical Role of Thermocapillary Stresses

Experiments by several groups during the past decade have shown that a molten polymer nanofilm subject to a large transverse thermal gradient undergoes spontaneous formation of periodic nanopillar arrays. The prevailing explanation is that coherent reflections of acoustic phonons within the film cause a periodic modulation of the radiation pressure which enhances pillar growth. By exploring a deformational instability of particular relevance to nanofilms, we demonstrate that thermocapillary forces play a crucial role in the formation process. Analytic and numerical predictions show good agreement with the pillar spacings obtained in experiment. Simulations of the interface equation further determine the rate of pillar growth of importance to technological applications.Comment: 5 pages, 4 figure

Politics, Voice, and Just Transition: Who has a Say in Climate Change Decision Making, and Who Does Not

The city of Bristol, UK, set out to pursue a just transition to climate change in 2020. This paper explores what happened next. We set out to study how just transition is unfolding politically on the ground, focusing on procedural justice. Over the course of a year, we conducted interviews and observations to study decision making at three levels – public sector, private sector and civil society. We found that not only is it difficult to define what just transition means, even for experts, but that the process of deciding how to pursue such a transition is highly exclusionary, especially to women and ethnic minorities. We therefore argue there is an urgency to revise decision-making procedures and ensure that there is ample opportunity to feed into decision-making processes by those who are typically excluded. Inclusive decision making must be embedded into the process of just transition from the beginning and throughout its implementation – it is not a step that can be ‘ticked off’ and then abandoned, but rather an ongoing process that must be consistently returned to. Finally, we conclude that cities have the unique opportunity to pilot bottom-up participatory approaches and to feed into the process of how a just transition might be pursued at the global level – for example, through their participation in the United Nations Framework for the Convention on Climate Change (UNFCCC) Conference of the Parties (COP) processes

Technical note: Lithium isotopes in dolostone as a palaeo-environmental proxy - an experimental approach

Lithium (Li) isotopes in marine carbonates have considerable potential as a proxy to constrain past changes in silicate weathering fluxes and improve our understanding of Earth\u27s climate. To date the majority of Li isotope studies on marine carbonates have focussed on calcium carbonates. The determination of the Li isotope fractionation between dolomite and a dolomitizing fluid would allow us to extend investigations to deep times (i.e. Precambrian) when dolostones were the most abundant marine carbonate archives. Dolostones often contain a significant proportion of detrital silicate material, which dominates the Li budget; thus, pretreatment needs to be designed so that only the isotope composition of the carbonate-associated Li is measured. This study aims to serve two main goals: (1) to determine the Li isotope fractionation between Ca-Mg carbonates and solution, and (2) to develop a method for leaching the carbonate-associated Li out of dolostone while not affecting the Li contained within the detrital portion of the rock. We synthesized Ca-Mg carbonates at high temperatures (150 to 220 ∘C) and measured the Li isotope composition (δ7Li) of the precipitated solids and their respective reactive solutions. The relationship of the Li isotope fractionation factor with temperature was obtained ..

Constraints on the preservation of proxy data in carbonate archives – lessons from a marine limestone to marble transect, Latemar, Italy

This work evaluates an exceptionally complex natural laboratory, the Middle Triassic Latemar isolated platform in the northern Italian Dolomite Mountains and explores spatial and temporal gradients in processes and products related to contact metamorphism, dolomitization and dedolomitization of marine limestones. The relation between petrographic change and re-equilibration of geochemical proxy data is evaluated from the perspective of carbonate-archive research. Hydrothermal dolomitization of the limestone units is triggered by dykes and associated hydrothermal fluids radiating from the nearby Predazzo Intrusion. Detailed petrography, fluid inclusion analysis, δ13C and δ18O data and 87Sr/86Sr isotope ratios shed light on the extreme textural and geochemical complexity. Metamorphic and diagenetic patterns include: (i) peak-metamorphic and retrograde-metamorphic phases including three dolomite marbles, two dedolomite marbles, brucite, magnesium silicates and late-stage meteoric/vadose cement at the contact aureole; (ii) four spatially defined episodes of dolomitization, authigenic quartz, low magnesium calcite and late-stage meteoric cement at the Latemar isolated platform; and (iii) kilometre-scale gradients in δ13C values from the contact aureole towards the platform interior. Results shown here are relevant for two reasons: first, the spatial analysis of alteration products ranging from high-grade metamorphic overprint of marbles at temperatures of 700˚C in the contact aureole to moderately altered limestones in the platform interior at temperatures 20 km. Second, under rock-buffered conditions, and irrespective of metamorphic to diagenetic fluid-rock interactions, both marbles, and low-temperature hydrothermal dolomites have conservative marine δ13C and δ18O values. The fact that metamorphism and hydrothermal dolomitization of precursor limestones and early diagenetic dolostones did not per se reset environmental proxy data is of interest for those concerned with carbonate archive research in Earth’s deep time

Laser modulated optical reflectance of thin semiconductor films on glass

Semiconductor films, deposited by reactive magnetron sputtering on glass substrates have been analyzed with the help of laser-modulated optical reflectance. The results are discussed with respect to the thermal and charge carrier transport properties. Semiconductor properties have been identified both for micro-crystalline and amorphous film

Ballistic nanofriction

Sliding parts in nanosystems such as Nano ElectroMechanical Systems (NEMS) and nanomotors, increasingly involve large speeds, and rotations as well as translations of the moving surfaces; yet, the physics of high speed nanoscale friction is so far unexplored. Here, by simulating the motion of drifting and of kicked Au clusters on graphite - a workhorse system of experimental relevance -- we demonstrate and characterize a novel "ballistic" friction regime at high speed, separate from drift at low speed. The temperature dependence of the cluster slip distance and time, measuring friction, is opposite in these two regimes, consistent with theory. Crucial to both regimes is the interplay of rotations and translations, shown to be correlated in slow drift but anticorrelated in fast sliding. Despite these differences, we find the velocity dependence of ballistic friction to be, like drift, viscous

Missing 2k_F Response for Composite Fermions in Phonon Drag

The response of composite Fermions to large wavevector scattering has been studied through phonon drag measurements. While the response retains qualitative features of the electron system at zero magnetic field, notable discrepancies develop as the system is varied from a half-filled Landau level by changing density or field. These deviations, which appear to be inconsistent with the current picture of composite Fermions, are absent if half-filling is maintained while changing density. There remains, however, a clear deviation from the temperature dependence anticipated for 2k_F scattering.Comment: 4 pages, 3 figures. Submitted to Phys. Rev. Let