The Periodic Table in Flatland

The $D$-dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in $D$ dimensions. This rule together with an {\it Aufbau Prinzip} is applied to produce a $D$-dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of an Hamiltonian, invariant under the $q$-deformed algebra $U_q($so$(D))$, that breaks down the SO($D+1$) dynamical symmetry of the hydrogen atom in $D$ dimensions. The $D=2$ case (Flatland) is investigated with some details. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values $q=0.8$ and $q=1$, respectively, of the deformation parameter $q$.Comment: 18 pages, Latex File, to be published in Int. J. Quantum Che

Mean-Field-Theory for Polymers in Mixed Solvents Thermodynamic and Structural Properties

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the pure mixed solvent is near criticality, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymer-solvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes a phase transition from a swollen state to an unperturbed state or even take a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein-Zernike series expansion.Comment: accepted in Macromol. Theory Simu

A q-deformed Aufbau Prinzip

A building principle working for both atoms and monoatomic ions is proposed in this Letter. This principle relies on the q-deformed chain SO(4) > G where G = SO(3)_q

Climate Change Impacts Can Be Differentially Perceived Across Time Scales: A Study Among the Tuareg of the Algerian Sahara

Unidad de excelencia María de Maeztu CEX2019-000940-MAs an Indigenous community of Algeria and the broader Sahel, the Tuareg hold unique ecological knowledge, which might contribute to broader models of place-based climate change impacts. Between January and April 2019, we carried out semi-structured interviews (N = 23) and focus group discussions (N = 3) in five villages of the province of Illizi, Algeria, to document the local Tuareg community's timeline and ecological calendar, both of which are instruments used to understand place-based reports of climate change impacts. The livelihoods of the Tuareg of Illizi are finely tuned to climate variability as reflected in changes reported in the cadence of events in their ecological calendar (marked by cyclical climatic and religious events). Participants reported rain and temperature irregularities and severe drought events, which have impacted their pastoral and semi-pastoral livelihoods. These reports are aligned with scientifically measured climate observations and predictions. Paradoxically, although participants recall with detail the climatic disasters that happened in the region over the last century, the Tuareg do not explicitly report decadal trends in the frequency of extreme events. The differential perception of climate change impacts across scales can have important implications for undertaking climate change adaptation measures