Nonlinear sigma Model Treatment of Quantum Antiferromagnets in a Magnetic Field

We present a theoretical analysis of the properties of low-dimensional quantum antiferromagnets in applied magnetic fields. In a nonlinear sigma model description, we use a spin stiffness analysis, a 1/N expansion, and a renormalization group approach to describe the broken-symmetry regimes of finite magnetization, and, in cases of most interest, a low-field regime where symmetry is restored by quantum fluctuations. We compute the magnetization, critical fields, spin correlation functions, and decay exponents accessible by nuclear magnetic resonance experiments. The model is relevant to many systems exhibiting Haldane physics, and provides good agreement with data for the two-chain spin ladder compound CuHpCl.Comment: 14 pages, 6 figures, full paper to accompany cond-mat/980415

Undermining and Strengthening Social Networks through Network Modification

Social networks have well documented effects at the individual and aggregate level. Consequently it is often useful to understand how an attempt to influence a network will change its structure and consequently achieve other goals. We develop a framework for network modification that allows for arbitrary objective functions, types of modification (e.g. edge weight addition, edge weight removal, node removal, and covariate value change), and recovery mechanisms (i.e. how a network responds to interventions). The framework outlined in this paper helps both to situate the existing work on network interventions but also opens up many new possibilities for intervening in networks. In particular use two case studies to highlight the potential impact of empirically calibrating the objective function and network recovery mechanisms as well as showing how interventions beyond node removal can be optimised. First, we simulate an optimal removal of nodes from the Noordin terrorist network in order to reduce the expected number of attacks (based on empirically predicting the terrorist collaboration network from multiple types of network ties). Second, we simulate optimally strengthening ties within entrepreneurial ecosystems in six developing countries. In both cases we estimate ERGM models to simulate how a network will endogenously evolve after intervention

Effects of self-consistent rest-ultraviolet colours in semi-empirical galaxy formation models

Connecting the observed rest-ultraviolet (UV) luminosities of high-$z$ galaxies to their intrinsic luminosities (and thus star formation rates) requires correcting for the presence of dust. We bypass a common dust-correction approach that uses empirical relationships between infrared (IR) emission and UV colours, and instead augment a semi-empirical model for galaxy formation with a simple -- but self-consistent -- dust model and use it to jointly fit high-$z$ rest-UV luminosity functions (LFs) and colour-magnitude relations ($M_{\mathrm{UV}}$-$\beta$). In doing so, we find that UV colours evolve with redshift (at fixed UV magnitude), as suggested by observations, even in cases without underlying evolution in dust production, destruction, absorption, or geometry. The observed evolution in our model arises due to the reduction in the mean stellar age and rise in specific star formation rates with increasing $z$. The UV extinction, $A_{\mathrm{UV}}$, evolves similarly with redshift, though we find a systematically shallower relation between $A_{\mathrm{UV}}$ and $M_{\mathrm{UV}}$ than that predicted by IRX-$\beta$ relationships derived from $z \sim 3$ galaxy samples. Finally, assuming that high $1600 \r{A}$ transmission ($\gtrsim 0.6$) is a reliable LAE indicator, modest scatter in the effective dust surface density of galaxies can explain the evolution both in $M_{\mathrm{UV}}$-$\beta$ and LAE fractions. These predictions are readily testable by deep surveys with the James Webb Space Telescope.Comment: 14+4 pages, 11+5 figures, accepted for publication in MNRA

Climate and Land-Use Controls on Surface Water Diversions in the Central Valley, California

California’s Central Valley (CV) is one of the most productive agricultural regions in the world, enabled by the conjunctive use of surface water and groundwater. We investigated variations in the CV’s managed surface water diversions relative to climate variability. Using a historical record (1979−2010) of diversions from 531 sites, we found diversions are largest in the wetter Sacramento basin to the north, but most variable in the drier Tulare basin to the south. A rotated empirical orthogonal function (REOF) analysis finds 72% of the variance of diversions is captured by the first three REOFs. The leading REOF (35% of variance) exhibited strong positive loadings in the Tulare basin, and the corresponding principal component time-series (RPC1) was strongly correlated (ρ > 0.9) with contemporaneous hydrologic variability. This pattern indicates larger than average diversions in the south, with neutral or slightly less than average diversions to the north during wet years, with the opposite true for dry years. The second and third REOFs (20% and 17% of variance, respectively), were strongest in the Sacramento basin and San Francisco Bay−Delta. RPC2 and RPC3 were associated with variations in agricultural- and municipal-bound diversions, respectively. RPC2 and RPC3 were also moderately correlated with 7-year cumulative precipitation based on lagged correlation analysis, indicating that diversions in the north and central portions of the CV respond to longer-term hydrologic variations. The results illustrate a dichotomy of regimes wherein diversions in the more arid Tulare are governed by year-to-year hydrologic variability, while those in wetter northern basins reflect land-use patterns and low-frequency hydrologic variations