Topological Designs

We give an exponential upper and a quadratic lower bound on the number of pairwise non-isotopic simple closed curves can be placed on a closed surface of genus g such that any two of the curves intersects at most once. Although the gap is large, both bounds are the best known for large genus. In genus one and two, we solve the problem exactly. Our methods generalize to variants in which the allowed number of pairwise intersections is odd, even, or bounded, and to surfaces with boundary components.Comment: 14 p., 4 Figures. To appear in Geometriae Dedicat

Rigidity percolation by next-nearest-neighbor bonds on generic and regular isostatic lattices

Theoretical Physic

Integrating Positive and Clinical Psychology: Viewing Human Functioning as Continua from Positive to Negative Can Benefit Clinical Assessment, Interventions and Understandings of Resilience

In this review we argue in favour of further integration between the disciplines of positive and clinical psychology. We argue that most of the constructs studied by both positive and clinical psychology exist on continua ranging from positive to negative (e.g., gratitude to ingratitude, anxiety to calmness) and so it is meaningless to speak of one or other field studying the “positive” or the “negative”. However, we highlight historical and cultural factors which have led positive and clinical psychologies to focus on different constructs; thus the difference between the fields is more due to the constructs of study rather than their being inherently “positive” or “negative”. We argue that there is much benefit to clinical psychology of considering positive psychology constructs because; (a) constructs studied by positive psychology researchers can independently predict wellbeing when accounting for traditional clinical factors, both cross-sectionally and prospectively, (2) the constructs studied by positive psychologists can interact with risk factors to predict outcomes, thereby conferring resilience, (3) interventions that aim to increase movement towards the positive pole of well-being can be used encourage movement away from the negative pole, either in isolation or alongside traditional clinical interventions, and (4) research from positive psychology can support clinical psychology as it seeks to adapt therapies developed in Western nations to other cultures

Reactive Uptake of an Isoprene-Derived Epoxydiol to Submicron Aerosol Particles

The reactive uptake of isoprene-derived epoxydiols (IEPOX) is thought to be a significant source of atmospheric secondary organic aerosol (SOA). However, the IEPOX reaction probability (γIEPOX) and its dependence upon particle composition remain poorly constrained. We report measurements of γIEPOX for trans-β-IEPOX, the predominant IEPOX isomer, on submicron particles as a function of composition, acidity, and relative humidity (RH). Particle acidity had the strongest effect. γIEPOX is more than 500 times greater on ammonium bisulfate (γ ∼ 0.05) than on ammonium sulfate (γ ≤ 1 × 10–4). We could accurately predict γIEPOX using an acid-catalyzed, epoxide ring-opening mechanism and a high Henry’s law coefficient (1.7 × 108 M/atm). Suppression of γIEPOX was observed on particles containing both ammonium bisulfate and poly­(ethylene glycol) (PEG-300), likely due to diffusion and solubility limitations within a PEG-300 coating, suggesting that IEPOX uptake could be self-limiting. Using the measured uptake kinetics, the predicted atmospheric lifetime of IEPOX is a few hours in the presence of highly acidic particles (pH 3). This work highlights the importance of aerosol acidity for accurately predicting the fate of IEPOX and anthropogenically influenced biogenic SOA formation

Reactive Uptake of an Isoprene-Derived Epoxydiol to Submicron Aerosol Particles

The reactive uptake of isoprene-derived epoxydiols (IEPOX) is thought to be a significant source of atmospheric secondary organic aerosol (SOA). However, the IEPOX reaction probability (γ_IEPOX) and its dependence upon particle composition remain poorly constrained. We report measurements of γ_IEPOX for <i>trans</i>-β-IEPOX, the predominant IEPOX isomer, on submicron particles as a function of composition, acidity, and relative humidity (RH). Particle acidity had the strongest effect. γ_IEPOX is more than 500 times greater on ammonium bisulfate (γ ∼ 0.05) than on ammonium sulfate (γ ≤ 1 × 10^–4). We could accurately predict γ_IEPOX using an acid-catalyzed, epoxide ring-opening mechanism and a high Henry’s law coefficient (1.7 × 10⁸ M/atm). Suppression of γ_IEPOX was observed on particles containing both ammonium bisulfate and poly­(ethylene glycol) (PEG-300), likely due to diffusion and solubility limitations within a PEG-300 coating, suggesting that IEPOX uptake could be self-limiting. Using the measured uptake kinetics, the predicted atmospheric lifetime of IEPOX is a few hours in the presence of highly acidic particles (pH < 0) but is greater than 25 h on less acidic particles (pH > 3). This work highlights the importance of aerosol acidity for accurately predicting the fate of IEPOX and anthropogenically influenced biogenic SOA formation