Estimating the sea ice floe size distribution using satellite altimetry: Theory, climatology, and model comparison

In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are sparse - traditionally taken via a painstaking analysis of ice surface photography - and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power-law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this "power-law hypothesis". Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radar altimetric record, covering the period from 2010 to 2018, and incorporating 11 million individual floe samples, we produce the first pan-Arctic climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power-law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture

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

Geometric Exponents, SLE and Logarithmic Minimal Models

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic Loewner evolution (SLE_kappa), one can consider observables related to nonlocal degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working in the context of a loop gas with loop fugacity beta = -2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal dimensions of various geometric objects such as paths and the generalizations of cluster mass, cluster hull, external perimeter and red bonds. Specializing to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we argue that the geometric exponents are related to conformal dimensions found in the infinitely extended Kac tables of the logarithmic minimal models LM(p,p'). These theories describe lattice systems with nonlocal degrees of freedom. We present results for critical dense polymers LM(1,2), critical percolation LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising model LM(4,5) as well as LM(3,5). Our results are compared with rigourous results from SLE_kappa, with predictions from theoretical physics and with other numerical experiments. Throughout, we emphasize the relationships between SLE_kappa, geometric exponents and the conformal dimensions of the underlying CFTs.Comment: Added reference

Logarithmic two-point correlators in the Abelian sandpile model

We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\sigma_{1,1} \simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\sigma_{1,h} \simeq (c_h\log r + d_h)/r^4 + {\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients $c_h$ and $d_h$ (the latter are new).Comment: 28 page

The development and application of audit criteria for assessing knowledge exchange plans in health research grant applications.

Background: Research funders expect evidence of end user engagement and impact plans in research proposals. Drawing upon existing frameworks, we developed audit criteria to help researchers and their institutions assess the knowledge exchange plans of health research proposals. Findings: Criteria clustered around five themes: problem definition; involvement of research users; public and patient engagement; dissemination and implementation; and planning, management and evaluation of knowledge exchange. We applied these to a sample of grant applications from one research institution in the United Kingdom to demonstrate feasibility. Conclusion: Our criteria may be useful as a tool for researcher self-assessment and for research institutions to assess the quality of knowledge exchange plans and identify areas for systematic improvement

W-Extended Fusion Algebra of Critical Percolation

Two-dimensional critical percolation is the member LM(2,3) of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We consider the continuum scaling limit of this lattice model as a `rational' logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a lattice approach on a strip to study the fundamental fusion rules in this extended picture. We find that the representation content of the ensuing closed fusion algebra contains 26 W-indecomposable representations with 8 rank-1 representations, 14 rank-2 representations and 4 rank-3 representations. We identify these representations with suitable limits of Yang-Baxter integrable boundary conditions on the lattice and obtain their associated W-extended characters. The latter decompose as finite non-negative sums of W-irreducible characters of which 13 are required. Implementation of fusion on the lattice allows us to read off the fusion rules governing the fusion algebra of the 26 representations and to construct an explicit Cayley table. The closure of these representations among themselves under fusion is remarkable confirmation of the proposed extended symmetry.Comment: 30 page

Predicting plasticity in disordered solids from structural indicators

Amorphous solids lack long-range order. Therefore identifying structural defects -- akin to dislocations in crystalline solids -- that carry plastic flow in these systems remains a daunting challenge. By comparing many different structural indicators in computational models of glasses, under a variety of conditions we carefully assess which of these indicators are able to robustly identify the structural defects responsible for plastic flow in amorphous solids. We further demonstrate that the density of defects changes as a function of material preparation and strain in a manner that is highly correlated with the macroscopic material response. Our work represents an important step towards predicting how and when an amorphous solid will fail from its microscopic structure

Study of montelukast in children with sickle cell disease (SMILES): a study protocol for a randomised controlled trial

BACKGROUND: Young children with sickle cell anaemia (SCA) often have slowed processing speed associated with reduced brain white matter integrity, low oxygen saturation, and sleep-disordered breathing (SDB), related in part to enlarged adenoids and tonsils. Common treatments for SDB include adenotonsillectomy and nocturnal continuous positive airway pressure (CPAP), but adenotonsillectomy is an invasive surgical procedure, and CPAP is rarely well-tolerated. Further, there is no current consensus on the ability of these treatments to improve cognitive function. Several double-blind, randomised controlled trials (RCTs) have demonstrated the efficacy of montelukast, a safe, well-tolerated anti-inflammatory agent, as a treatment for airway obstruction and reducing adenoid size for children who do not have SCA. However, we do not yet know whether montelukast reduces adenoid size and improves cognition function in young children with SCA. METHODS: The Study of Montelukast In Children with Sickle Cell Disease (SMILES) is a 12-week multicentre, double-blind, RCT. SMILES aims to recruit 200 paediatric patients with SCA and SDB aged 3-7.99 years to assess the extent to which montelukast can improve cognitive function (i.e. processing speed) and sleep and reduce adenoidal size and white matter damage compared to placebo. Patients will be randomised to either montelukast or placebo for 12 weeks. The primary objective of the SMILES trial is to assess the effect of montelukast on processing speed in young children with SCA. At baseline and post-treatment, we will administer a cognitive evaluation; caregivers will complete questionnaires (e.g. sleep, pain) and measures of demographics. Laboratory values will be obtained from medical records collected as part of standard care. If a family agrees, patients will undergo brain MRIs for adenoid size and other structural and haemodynamic quantitative measures at baseline and post-treatment, and we will obtain overnight oximetry. DISCUSSION: Findings from this study will increase our understanding of whether montelukast is an effective treatment for young children with SCA. Using cognitive testing and MRI, the SMILES trial hopes to gain critical knowledge to help develop targeted interventions to improve the outcomes of young children with SCA. TRIAL REGISTRATION: ClinicalTrials.gov NCT04351698 . Registered on April 17, 2020. European Clinical Trials Database (EudraCT No. 2017-004539-36). Registered on May 19, 2020