Provable first-order transitions for liquid crystal and lattice gauge models with continuous symmetries

We consider various sufficiently nonlinear sigma models for nematic liquid crystal ordering of RP^{N-1} type and of lattice gauge type with continous symmetries. We rigorously show that they exhibit a first-order transition in the temperature. The result holds in dimension 2 or more for the RP^{N-1} models and in dimension 3 or more for the lattice gauge models. In the two-dimensional case our results clarify and solve a recent controversy about the possibility of such transitions. For lattice gauge models our methods provide the first proof of a first-order transition in a model with a continuous gauge symmetry

Possible first order transition in the two-dimensional Ginzburg-Landau model induced by thermally fluctuating vortex cores

We study the two-dimensional Ginzburg-Landau model of a neutral superfluid in the vicinity of the vortex unbinding transition. The model is mapped onto an effective interacting vortex gas by a systematic perturbative elimination of all fluctuating degrees of freedom (amplitude {\em and} phase of the order parameter field) except the vortex positions. In the Coulomb gas descriptions derived previously in the literature, thermal amplitude fluctuations were neglected altogether. We argue that, if one includes the latter, the vortices still form a two- dimensional Coulomb gas, but the vortex fugacity can be substantially raised. Under the assumption that Minnhagen's generic phase diagram of the two- dimensional Coulomb gas is correct, our results then point to a first order transition rather than a Kosterlitz-Thouless transition, provided the Ginzburg-Landau correlation length is large enough in units of a microscopic cutoff length for fluctuations. The experimental relevance of these results is briefly discussed. [Submitted to J. Stat. Phys.]Comment: 36 pages, LaTeX, 6 figures upon request, UATP2-DB1-9

Density Functional for Anisotropic Fluids

We propose a density functional for anisotropic fluids of hard body particles. It interpolates between the well-established geometrically based Rosenfeld functional for hard spheres and the Onsager functional for elongated rods. We test the new approach by calculating the location of the the nematic-isotropic transition in systems of hard spherocylinders and hard ellipsoids. The results are compared with existing simulation data. Our functional predicts the location of the transition much more accurately than the Onsager functional, and almost as good as the theory by Parsons and Lee. We argue that it might be suited to study inhomogeneous systems.Comment: To appear in J. Physics: Condensed Matte

Entropy and Spin Susceptibility of s-wave Type-II Superconductors near Hc2H_{c2}

A theoretical study is performed on the entropy $S_{\rm s}$ and the spin susceptibility $\chi_{\rm s}$ near the upper critical field $H_{c2}$ of s-wave type-II superconductors with arbitrary impurity concentrations. The changes of these quantities through $H_{c2}$ may be expressed as $[S_{\rm s}(T,B)-S_{\rm s}(T,0)]/[S_{\rm n}(T)-S_{\rm s}(T,0)]=1-\alpha_{S}(1-B/H_{c2})\approx (B/H_{c2})^{\alpha_{S}}$, for example, where $B$ is the average flux density and $S_{\rm n}$ denotes entropy in the normal state. It is found that the slopes $\alpha_{S}$ and $\alpha_{\chi}$ at T=0 are identical, connected directly with the zero-energy density of states, and vary from 1.72 in the dirty limit to $0.5\sim 0.6$ in the clean limit. This mean-free-path dependence of $\alpha_{S}$ and $\alpha_{\chi}$ at T=0 is quantitatively the same as that of the slope $\alpha_{\rho}(T=0)$ for the flux-flow resistivity studied previously. The result suggests that $S_{\rm s}(B)$ and $\chi_{\rm s}(B)$ near T=0 are convex downward (upward) in the dirty (clean) limit, deviating substantially from the linear behavior $\propto B/H_{c2}$. The specific-heat jump at $H_{c2}$ also shows fairly large mean-free-path dependence.Comment: 8 pages, 5 figure

The Shapes of Flux Domains in the Intermediate State of Type-I Superconductors

In the intermediate state of a thin type-I superconductor magnetic flux penetrates in a disordered set of highly branched and fingered macroscopic domains. To understand these shapes, we study in detail a recently proposed "current-loop" (CL) model that models the intermediate state as a collection of tense current ribbons flowing along the superconducting-normal interfaces and subject to the constraint of global flux conservation. The validity of this model is tested through a detailed reanalysis of Landau's original conformal mapping treatment of the laminar state, in which the superconductor-normal interfaces are flared within the slab, and of a closely-related straight-lamina model. A simplified dynamical model is described that elucidates the nature of possible shape instabilities of flux stripes and stripe arrays, and numerical studies of the highly nonlinear regime of those instabilities demonstrate patterns like those seen experimentally. Of particular interest is the buckling instability commonly seen in the intermediate state. The free-boundary approach further allows for a calculation of the elastic properties of the laminar state, which closely resembles that of smectic liquid crystals. We suggest several new experiments to explore of flux domain shape instabilities, including an Eckhaus instability induced by changing the out-of-plane magnetic field, and an analog of the Helfrich-Hurault instability of smectics induced by an in-plane field.Comment: 23 pages, 22 bitmapped postscript figures, RevTex 3.0, submitted to Phys. Rev. B. Higher resolution figures may be obtained by contacting the author

Observations of the microphysical evolution of convective clouds in the southwest of the United Kingdom

The COnvective Precipitation Experiment (COPE) was designed to investigate the origins of heavy convective precipitation over the southwestern UK, a region that experiences flash flooding due to heavy precipitation from slow-moving convective systems. In this study, the microphysical and dynamical characteristics of developing turrets during 4 days in July and August 2013 are analyzed. In situ cloud microphysical measurements from the University of Wyoming King Air and vertically pointing W-band radar measurements from Wyoming Cloud Radar are examined, together with data from the ground-based NXPol radar. The 4 days presented here cover a range of environmental conditions in terms of wind shear and instability, resulting in a similarly wide variability in observed ice crystal concentrations, both across days as well as between clouds on individual days. The highest concentration of ice was observed on the days in which there was an active warm-rain process supplying precipitation-sized liquid drops. The high ice concentrations observed ( > 100L−1) are consistent with the production of secondary ice particles through the Hallett–Mossop process. Turrets that ascended through remnant cloud layers above the 0°C level had higher ice particle concentrations, suggesting that entrainment of ice particles from older clouds or previous thermals may have acted to aid in the production of secondary ice through the Hallett–Mossop process. Other mechanisms such as the shattering of frozen drops may be more important for producing ice in more isolated clouds

Global Investments in Pandemic Preparedness and COVID-19: Development Assistance and Domestic Spending on Health Between 1990 and 2026

Background The COVID-19 pandemic highlighted gaps in health surveillance systems, disease prevention, and treatment globally. Among the many factors that might have led to these gaps is the issue of the financing of national health systems, especially in low-income and middle-income countries (LMICs), as well as a robust global system for pandemic preparedness. We aimed to provide a comparative assessment of global health spending at the onset of the pandemic; characterise the amount of development assistance for pandemic preparedness and response disbursed in the first 2 years of the COVID-19 pandemic; and examine expectations for future health spending and put into context the expected need for investment in pandemic preparedness. Methods In this analysis of global health spending between 1990 and 2021, and prediction from 2021 to 2026, we estimated four sources of health spending: development assistance for health (DAH), government spending, out-ofpocket spending, and prepaid private spending across 204 countries and territories. We used the Organisation for Economic Co-operation and Development (OECD)’s Creditor Reporting System (CRS) and the WHO Global Health Expenditure Database (GHED) to estimate spending. We estimated development assistance for general health, COVID-19 response, and pandemic preparedness and response using a keyword search. Health spending estimates were combined with estimates of resources needed for pandemic prevention and preparedness to analyse future health spending patterns, relative to need. Findings In 2019, at the onset of the COVID-19 pandemic, US$9·2 trillion (95$7·3 trillion (95% UI 7·2–7·4) in 2019; 293·7 times the $24·8 billion (95$43·1 billion in development assistance was provided to maintain or improve health. The pandemic led to an unprecedented increase in development assistance targeted towards health; in 2020 and 2021, $1·8 billion in DAH contributions was provided towards pandemic preparedness in LMICs, and$37·8 billion was provided for the health-related COVID-19 response. Although the support for pandemic preparedness is 12·2% of the recommended target by the High-Level Independent Panel (HLIP), the support provided for the healthrelated COVID-19 response is 252·2% of the recommended target. Additionally, projected spending estimates suggest that between 2022 and 2026, governments in 17 (95% UI 11–21) of the 137 LMICs will observe an increase in national government health spending equivalent to an addition of 1% of GDP, as recommended by the HLIP. Interpretation There was an unprecedented scale-up in DAH in 2020 and 2021. We have a unique opportunity at this time to sustain funding for crucial global health functions, including pandemic preparedness. However, historical patterns of underfunding of pandemic preparedness suggest that deliberate effort must be made to ensure funding is maintained

Pathologies of the large-N limit for RP^{N-1}, CP^{N-1}, QP^{N-1} and mixed isovector/isotensor sigma-models

We compute the phase diagram in the N\to\infty limit for lattice RP^{N-1}, CP^{N-1} and QP^{N-1} sigma-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=\infty limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N\to\infty. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component sigma-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.Comment: LaTeX, 88 pages, 33 figure

Secondary Ice Production : Current State of the Science and Recommendations for the Future

Measured ice crystal concentrations in natural clouds at modest supercooling (temperature ~>-10°C) are often orders of magnitude greater than the number concentration of primary ice nucleating particles. Therefore, it has long been proposed that a secondary ice production process must exist that is able to rapidly enhance the number concentration of the ice population following initial primary ice nucleation events. Secondary ice production is important for the prediction of ice crystal concentration and the subsequent evolution of some types of clouds, but the physical basis of the process is not understood and the production rates are not well constrained. In November 2015 an international workshop was held to discuss the current state of the science and future work to constrain and improve our understanding of secondary ice production processes. Examples and recommendations for in situ observations, remote sensing, laboratory investigations, and modeling approaches are presented.Peer reviewe

Codes of Fair Competition: The National Recovery Act, 1933-1935, and the Women’s Dress Manufacturing Industry

Controversial issues prevalent in today’s ready-to-wear apparel industry include the right of workers to join unions, the proliferation of sweatshops and sweatshop conditions, and design piracy. The idea of forming codes of conduct to establish criteria of ethical business practices is not new to the apparel industry. Indeed, the women’s dress manufacturing industry discussed and debated codes of fair competition under the New Deal Policies of the National Recovery Act (NRA) of 1933 to 1935. Primary sources for this study included governmental hearings in the establishment of the NRA Dress Code, The New York Times, Women’s Wear Daily, and the Journal of the Patent Office Society. The history of the NRA codes implemented in the U.S. women’s ready-to-wear apparel industry provides an important case study highlighting the difficulties and complexities of creating and achieving industry-wide standard practices through self-regulation. The failure of the NRA demonstrates that even with the joint cooperation of industry, labor, and consumer groups and the backing of the force of law, codes of fair competition proved impossible to enforce