Multiparticle one-loop amplitudes and S-duality in closed superstring theory

Explicit expressions for one-loop five supergraviton scattering amplitudes in both type II superstring theories are determined by making use of the pure spinor formalism. The type IIB amplitude can be expressed in terms of a doubling of ten-dimensional super Yang--Mills tree amplitude, while the type IIA amplitude has additional pieces that cannot be expressed in that manner. We evaluate the coefficients of terms in the analytic part of the low energy expansion of the amplitude, which correspond to a series of terms in an effective action of the schematic form D^{2k}R^5 for 0\le k \le 5 (where R is the Riemann curvature). Comparison with earlier analyses of the tree amplitudes and of the four-particle one-loop amplitude leads to an interesting extension of the action of SL(2,Z) S-duality on the moduli-dependent coefficients in the type IIB theory. We also investigate closed-string five-particle amplitudes that violate conservation of the U(1) R-symmetry charge -- processes that are forbidden in supergravity. The coefficients of their low energy expansion are shown to agree with S-duality systematics. A less detailed analysis is also given of the six-point function, resulting in the vanishing of the analytic parts of the R^6 and D^4 R^6 interactions in the ten-dimensional effective action, but not in lower dimensions.Comment: 62 pages, Mathematica notebook on integral expansion included in submission. v2: minor modifications, references added, matches published versio

Magnetic trapping of buffer-gas cooled chromium atoms and prospects for the extension to paramagnetic molecules

We report the successful buffer-gas cooling and magnetic trapping of chromium atoms with densities exceeding $10^{12}$ atoms per cm$^{3}$ at a temperature of 350 mK for the trapped sample. The possibilities to extend the method to buffer-gas cool and magnetically trap molecules are discussed. To minimize the most important loss mechanism in magnetic trapping, molecules with a small spin-spin interaction and a large rotational constant are preferred. Both the CrH ($^6\Sigma^+$ ground state) and MnH ($^7\Sigma^+$) radicals appear to be suitable systems for future experiments.Comment: 9 pages, 4 Figure

Pion scattering in Wilson ChPT

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) a\Lambda_QCD^2 and (ii) a^2\Lambda_QCD^3. Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the O(a^2) terms the I=0 and I=2 scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a^2\ln M_{\pi}^2 are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.Comment: 20 pages, 4 figures. V3: Comments on finite size effects and the axial vector current added, one more reference. To be published in PR

Phase Transitions from Saddles of the Potential Energy Landscape

The relation between saddle points of the potential of a classical many-particle system and the analyticity properties of its thermodynamic functions is studied. For finite systems, each saddle point is found to cause a nonanalyticity in the Boltzmann entropy, and the functional form of this nonanalytic term is derived. For large systems, the order of the nonanalytic term increases unboundedly, leading to an increasing differentiability of the entropy. Analyzing the contribution of the saddle points to the density of states in the thermodynamic limit, our results provide an explanation of how, and under which circumstances, saddle points of the potential energy landscape may (or may not) be at the origin of a phase transition in the thermodynamic limit. As an application, the puzzling observations by Risau-Gusman et al. on topological signatures of the spherical model are elucidated.Comment: 5 pages, no figure

Development and testing of a risk indexing framework to determine field-scale critical source areas of faecal bacteria on grassland.

This paper draws on lessons from a UK case study in the management of diffuse microbial pollution from grassland farm systems in the Taw catchment, south west England. We report on the development and preliminary testing of a field-scale faecal indicator organism risk indexing tool (FIORIT). This tool aims to prioritise those fields most vulnerable in terms of their risk of contributing FIOs to water. FIORIT risk indices were related to recorded microbial water quality parameters (faecal coliforms [FC] and intestinal enterococci [IE]) to provide a concurrent on-farm evaluation of the tool. There was a significant upward trend in Log[FC] and Log[IE] values with FIORIT risk score classification (r2 =0.87 and 0.70, respectively and P<0.01 for both FIOs). The FIORIT was then applied to 162 representative grassland fields through different seasons for ten farms in the case study catchment to determine the distribution of on-farm spatial and temporal risk. The high risk fields made up only a small proportion (1%, 2%, 2% and 3% for winter, spring, summer and autumn, respectively) of the total number of fields assessed (and less than 10% of the total area), but the likelihood of the hydrological connection of high FIO source areas to receiving watercourses makes them a priority for mitigation efforts. The FIORIT provides a preliminary and evolving mechanism through which we can combine risk assessment with risk communication to end-users and provides a framework for prioritising future empirical research. Continued testing of FIORIT across different geographical areas under both low and high flow conditions is now needed to initiate its long term development into a robust indexing tool

Phase transitions induced by saddle points of vanishing curvature

Based on the study of saddle points of the potential energy landscapes of generic classical many-particle systems, we present a necessary criterion for the occurrence of a thermodynamic phase transition. Remarkably, this criterion imposes conditions on microscopic properties, namely curvatures at the saddle points of the potential, and links them to the macroscopic phenomenon of a phase transition. We apply our result to two exactly solvable models, corroborating that the criterion derived is not only valid, but also sharp and useful: For both models studied, the criterion excludes the occurrence of a phase transition for all values of the potential energy but the transition energy. This result adds a geometrical ingredient to an established topological condition for the occurrence of a phase transition, thereby providing an answer to the long standing question of which topology changes in configuration space can induce a phase transition.Comment: 5 page

Cuyahoga Greenways: A Community-Driven, Data-Enriched Initiative to Implement a Regional Greenway Vision

Cleveland and surrounding Cuyahoga County is undergoing a gradual transformation. A highly urbanized region in America’s rust belt, it has experienced decades of declining population and sprawling development. Presently however, the region has shown signs of economic and social improvement as it recovers from years of stagnation and disinvestment. Accompanying this rebound is an increased awareness to the region’s fluctuating socioeconomic conditions and residual challenges to improving mobility. Moreover, there is a desire to ensure that change is sustainable and leads to equitable outcomes for all segments of the community. Greenways, most notably the county-wide Emerald Necklace, have long been a staple and signature asset of Cuyahoga County. However, the needs of the population are diversifying, particularly regarding mobility and how people access jobs, parks, cultural resources, public services, and commercial centers. Being such, non-motorized travel -- a rising trend for a broad spectrum of the populace -- has become a key component in the region’s renewal as it grapples with constricted transit, geographic inequality, and an existing Greenway network whose benefits do not fully reach all sectors of the population. Cuyahoga Greenways is a county-wide initiative to envision, plan, and implement over 800-miles of greenways and urban trails throughout the region. Unlike conventional approaches to building nonmotorized facilities, like bike lanes, that may only serve a segment of the population, Cuyahoga Greenways seeks to build an interconnected, non-motorized transportation network that is safe and welcoming for people of all ages and all abilities. This initiative, which featured input from 29 regional agencies and 43 participating communities, developed a vision, framework plan, and implementation tools for making the new greenway framework a reality. The planning process was community-driven and data-enriched, empowering local leaders and stakeholders with the knowledge necessary to make informed decisions and craft a plan that benefits the community both economically and socially. A cornerstone of the process was a robust public engagement program with over 20 community-wide events. Leveraging both traditional and digital tools, a rigorous spatial analysis of over 300 corridor opportunities was completed. The resulting analysis, coupled with the community’s involvement, allowed stakeholders to identify and prioritize actionable greenway proposals that provide the biggest return to the community while dispensing more equitable outcomes. With the greenway framework plan in place, community leadership has shown a willingness to more effectively collaborate across jurisdictions, leveraging resources to implement projects. The Cuyahoga Greenways initiative exemplifies a regionally coordinated and evidence-based process to improve equity, mobility, and expand the benefits of greenways to all neighborhoods in Northeast Ohio