Geometry of Maslov cycles

We introduce the notion of induced Maslov cycle, which describes and unifies geometrical and topological invariants of many apparently unrelated situations, from real algebraic geometry to sub-Riemannian geometry

The Sphaleron Rate in SU(N) Gauge Theory

The sphaleron rate is defined as the diffusion constant for topological number NCS = int g^2 F Fdual/32 pi^2. It establishes the rate of equilibration of axial light quark number in QCD and is of interest both in electroweak baryogenesis and possibly in heavy ion collisions. We calculate the weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most sensible extrapolation towards intermediate coupling which we can. We also study the behavior of the sphaleron rate at weak coupling at large Nc.Comment: 18 pages with 3 figure

Analysis, Prevalence & Impact of Microplastics in Freshwater and Estuarine Environments Evidence Review 2 What are the sources of the microplastics found in freshwater environments?

This Rapid Evidence Assessment used the systematic review procedure to assess the current evidence available on the sources of the microplastics found in freshwater and estuarine environments. To fully comprehend the prevalence of microplastics in freshwater and estuarine environments, it is important to understand which sources contribute to the microplastics present and the relative importance of those sources. Furthermore, we need to understand the influence of any physical and biologically-mediated processes that affect the concentrations, characteristics and profile of the microplastic particles present, so that their influence can be taken into account when interpreting the microplastics present in terms of contributing sources. A review was conducted of literature, including grey literature, which reported evidence of the sources of the microplastics found in freshwater and estuarine environments. The factors influencing the transport and modification of microplastics in freshwater and estuarine environments were also considered, noting in particular those that alter the profile of microplastics thus obscuring identification of sources. Publications released prior to April 2019 were included in this review. Evidence was acquired according to a predefined set of questions, compiled into a database containing full details of the source and its relevance to the project questions, and the evidence analysed, taking into account reporting biases in the literature, to produce a digestible summary of the evidence base available to answer the main project question and sub-questions, namely, What are the sources of microplastics reported to have been found in freshwater and estuarine environments? a) Are these primary (i.e. manufactured) or secondary (i.e. degradation products) microplastics? b) Within studies reporting the predominant types of microplastics found, is there a link identified to local land use or industry? c) How are microplastics transported and modified in the freshwater and estuarine environments? d) Are microplastics from different sources prevalent in different matrices of the aquatic environment (biota, water, or sediment)

Evidence Reviews on Analysis, Prevalence & Impact of Microplastics in Freshwater and Estuarine Environments Evidence Review 3 What is/are the impact(s) of microplastics on freshwater and estuarine biota?

This Rapid Evidence Assessment used the systematic review procedure to assess the current evidence available on the impact of microplastics on freshwater and estuarine biota. It is important to understand what consequences microplastics may cause in the environment. Furthermore, we need to understand which types of microplastics cause impacts and at what concentrations. A review was conducted of the primary literature, including grey literature, which reported evidence of the impact of microplastics on freshwater and estuarine biota. A particular focus were those publications which reported evidence on the extent to which microplastics influence the behaviour, feeding, growth, reproduction and survival of freshwater and estuarine biota, and any thresholds at which impacts occurred. Publications released prior to April 2019 were included in this review. Evidence was acquired according to a predefined set of questions, compiled into a database containing full details of the source and its relevance to the project questions, and the evidence analysed, taking into account reporting biases in the literature, to produce a digestible summary of the evidence base available to answer the main project question and sub-questions, namely, What is/are the impact(s) of microplastics on freshwater and estuarine biota? a) To what extent do microplastics influence the feeding, growth, reproduction and survival of freshwater and estuarine biota? Do we know trigger levels or threshold values for microplastic impacts on biota? b) Are any differences between different taxonomic groups observed? c) Are results from laboratory studies relevant to microplastics at environmentally relevant field concentrations? d) Are any adverse impacts attributable to the particles or to adsorbed chemicals/microbes on the particles? e) Is there evidence to suggest impacts on populations of aquatic organisms

Kerr-CFT From Black-Hole Thermodynamics

We analyze the near-horizon limit of a general black hole with two commuting killing vector fields in the limit of zero temperature. We use black hole thermodynamics methods to relate asymptotic charges of the complete spacetime to those obtained in the near-horizon limit. We then show that some diffeomorphisms do alter asymptotic charges of the full spacetime, even though they are defined in the near horizon limit and, therefore, count black hole states. We show that these conditions are essentially the same as considered in the Kerr/CFT corresponcence. From the algebra constructed from these diffeomorphisms, one can extract its central charge and then obtain the black hole entropy by use of Cardy's formula.Comment: 19 pages, JHEP3, no figures. V2: References added, small typos fixe

On the geometry of the set of symmetric matrices with repeated eigenvalues

We investigate some geometric properties of the real algebraic variety \u394 of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection with the sphere and prove a Eckart\u2013Young\u2013Mirsky-type theorem for the distance function from a generic matrix to points in \u394. We exhibit connections of our study to real algebraic geometry (computing the Euclidean distance degree of \u394) and random matrix theory

Stability boundary approximation of periodic dynamics

We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2 degrees of freedom (DOF) we derive general approximate stability conditions. We study domains of stability with the use of fourth order approximations of monodromy matrix on example of inverted position of a pendulum with vertically oscillating pivot. Addition of small damping shifts the stability boundaries upwards, thus resulting to both stabilization and destabilization effects.Comment: 9 pages, 2 figure

The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory

We determine a next-to-leading order result for the correlator of the shear stress operator in high-temperature Yang-Mills theory. The computation is performed via an ultraviolet expansion, valid in the limit of small distances or large momenta, and the result is used for writing operator product expansions for the Euclidean momentum and coordinate space correlators as well as for the Minkowskian spectral density. In addition, our results enable us to confirm and refine a shear sum rule originally derived by Romatschke, Son and Meyer.Comment: 16 pages, 2 figures. v2: small clarifications, one reference added, published versio