A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

Strategic Interaction and Trade Policymaking: Formal Analysis and Simulation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73499/1/j.1467-9701.2006.00797.x.pd

Smouldering Combustion Treatment of Soils and Granular Activated Carbon Contaminated with Per- and Polyfluoroalkyl Substances

Per- and polyfluoroalkyl substances (PFAS) are emerging contaminants, ubiquitous in the environment, and are challenging to remediate. Self-sustaining Treatment for Active Remediation (STAR) destroys organic contaminants embedded in porous media using smouldering combustion. Self-sustaining smouldering conditions allow the reaction to propagate through the contaminated media without external energy. This study explored STAR as a remediation option for PFAS-impacted granular activated carbon (GAC) and PFAS-contaminated soil. Three smouldering mixtures were used (i) PFAS-spiked GAC and sand, (ii) PFAS-spiked soil and GAC, (iii) PFAS-contaminated field site soil and GAC. Smouldering temperatures were greater than 900˚C, destroying the GAC. Post-treatment PFAS concentrations of the sand, soil, and ash were near or below detection limits (0.5 μg/kg). Analysis of emissions demonstrated hydrogen fluoride and shorter-chain PFAS were produced suggesting PFAS had been mineralized and altered during smouldering. Results suggest STAR is an effective remediation technique for PFAS-impacted soils and PFAS-saturated GAC

Refined conformal spectra in the dimer model

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu-Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c=-2.Comment: 44 page

Parent-to-parent advice: What can we learn by listening to parents of deaf children

Parent-to-parent support is an important component of early hearing detection and intervention (EHDI) programs for deaf and hard of hearing (DHH) children. In this study, we asked parents of DHH children what advice they would give to new parents in their situation. Seventy-one hearing parents of DDH children living in Canada, Switzerland, France, and Belgium participated in interviews that included the following question: “What advice you would give to parents who just learned that their child is deaf?”. We performed a thematic analysis and developed three overarching themes, revolving around the importance of trust, the need for reassurance, and finally, the quest for help. The findings allow to better understand how parental expertise can be used to improve early intervention services for DHH children

Group-size-mediated habitat selection and group fusion-fission dynamics of bison under predation risk

For gregarious animals the cost-benefit trade-offs that drive habitat selection may vary dynamically with group size, which plays an important role in foraging and predator avoidance strategies. We examined how habitat selection by bison (Bison bison) varied as a function of group size and interpreted these patterns by testing whether habitat selection was more strongly driven by the competing demands of forage intake vs. predator avoidance behavior. We developed an analytical framework that integrated group size into resource selection functions (RSFs). These group-size-dependent RSFs were based on a matched casecontrol design and were estimated using conditional logistic regression (mixed and populationaveraged models). Fitting RSF models to bison revealed that bison groups responded to multiple aspects of landscape heterogeneity and that selection varied seasonally and as a function of group size. For example, roads were selected in summer, but not in winter. Bison groups avoided areas of high snow water equivalent in winter. They selected areas composed of a large proportion of meadow area within a 700-m radius, and within those areas, bison selected meadows. Importantly, the strength of selection for meadows varied as a function of group size, with stronger selection being observed in larger groups. Hence the bison-habitat relationship depended in part on the dynamics of group formation and division. Group formation was most likely in meadows. In contrast, risk of group fission increased when bison moved into the forest and was higher during the time of day when movements are generally longer and more variable among individuals. We also found that stronger selection for meadows by large rather than small bison groups was caused by longer residence time in individual meadows by larger groups and that departure from meadows appears unlikely to result from a depression in food intake rate. These group-size-dependent patterns were consistent with the hypothesis that avoidance of predation risk is the strongest driver of habitat selection

Impacts of an Ammonia Leak on the Cabin Atmosphere of the International Space Station

Toxic chemical release into the cabin atmosphere is one of the three major emergency scenarios identified on the International Space Station (ISS). The release of anhydrous ammonia, the coolant used in the U.S. On-orbit Segment (USOS) External Active Thermal Control Subsystem (EATCS), into the ISS cabin atmosphere is one of the most serious toxic chemical release cases identified on board ISS. The USOS Thermal Control System (TCS) includes an Internal Thermal Control Subsystem (ITCS) water loop and an EATCS ammonia loop that transfer heat at the interface heat exchanger (IFHX). Failure modes exist that could cause a breach within the IFHX. This breach would result in high pressure ammonia from the EATCS flowing into the lower pressure ITCS water loop. As the pressure builds in the ITCS loop, it is likely that the gas trap, which has the lowest maximum design pressure within the ITCS, would burst and cause ammonia to enter the ISS atmosphere. It is crucial to first characterize the release of ammonia into the ISS atmosphere in order to develop methods to properly mitigate the environmental risk. This paper will document the methods used to characterize an ammonia leak into the ISS cabin atmosphere. A mathematical model of the leak was first developed in order to define the flow of ammonia into the ISS cabin atmosphere based on a series of IFHX rupture cases. Computational Fluid Dynamics (CFD) methods were then used to model the dispersion of the ammonia throughout the ISS cabin and determine localized effects and ventilation effects on the dispersion of ammonia. Lastly, the capabilities of the current on-orbit systems to remove ammonia were reviewed and scrubbing rates of the ISS systems were defined based on the ammonia release models. With this full characterization of the release of ammonia from the USOS TCS, an appropriate mitigation strategy that includes crew and system emergency response procedures, personal protection equipment use, and atmosphere monitoring and scrubbing hardware can be established