Classification of Links Up to 0-Solvability

The $n$-solvable filtration of the $m$-component smooth (string) link concordance group, $$\dots \subset \mathcal{F}^m_{n+1} \subset \mathcal{F}^m_{n.5} \subset \mathcal{F}^m_n \dots \subset \mathcal{F}^m_1 \subset \mathcal{F}^m_{0.5} \subset \mathcal{F}^m_0 \subset \mathcal{F}^m_{-0.5} \subset \mathcal{C}^m,$$ as defined by Cochran, Orr, and Teichner, is a tool for studying smooth knot and link concordance that yields important results in low-dimensional topology. The focus of this paper is to give a characterization of the set of 0-solvable links. We introduce a new equivalence relation on links called 0-solve equivalence and establish both an algebraic and a geometric classification of $\mathbb{L}_0^m$, the set of links up to 0-solve equivalence. We show that $\mathbb{L}_0^m$ has a group structure isomorphic to the quotient $\mathcal{F}_{-0.5}/\mathcal{F}_0$ of concordance classes of string links and classify this group, showing that $$\mathbb{L}_0^m \cong \mathcal{F}_{-0.5}^m/\mathcal{F}_0^m \cong \mathbb{Z}_2^m \oplus \mathbb{Z}^{m \choose 3} \oplus \mathbb{Z}_2^{m \choose 2}.$$ Finally, using results of Conant, Schneiderman, and Teichner, we show that 0-solvable links are precisely the links that bound class 2 gropes and support order 2 Whitney towers in the 4-ball.Comment: 34 page

Documenting numerical experiments in support of the Coupled Model Intercomparison Project Phase 6 (CMIP6)

Numerical simulation, and in particular simulation of the earth system, relies on contributions from diverse communities, from those who develop models to those involved in devising, executing, and analysing numerical experiments. Often these people work in different institutions and may be working with significant separation in time (particularly analysts, who may be working on data produced years earlier), and they typically communicate via published information (whether journal papers, technical notes, or websites). The complexity of the models, experiments, and methodologies, along with the diversity (and sometimes inexact nature) of information sources, can easily lead to misinterpretation of what was actually intended or done. In this paper we introduce a taxonomy of terms for more clearly defining numerical experiments, put it in the context of previous work on experimental ontologies, and describe how we have used it to document the experiments of the sixth phase for the Coupled Model Intercomparison Project (CMIP6). We describe how, through iteration with a range of CMIP6 stakeholders, we rationalized multiple sources of information and improved the clarity of experimental definitions. We demonstrate how this process has added value to CMIP6 itself by (a) helping those devising experiments to be clear about their goals and their implementation, (b) making it easier for those executing experiments to know what is intended, (c) exposing interrelationships between experiments, and (d) making it clearer for third parties (data users) to understand the CMIP6 experiments. We conclude with some lessons learnt and how these may be applied to future CMIP phases as well as other modelling campaigns

Composition and luminescence studies of InGaN epilayers grown at different hydrogen flow rates

Indium gallium nitride (In(x)Ga(1-x)N) is a technologically important material for many optoelectronic devices, including LEDs and solar cells, but it remains a challenge to incorporate high levels of InN into the alloy while maintaining sample quality. A series of InGaN epilayers was grown with different hydrogen flow rates (0-200 sccm) and growth temperatures (680-750 °C) to obtain various InN fractions and bright emission in the range 390-480 nm. These 160-nm thick epilayers were characterized through several compositional techniques (wavelength dispersive x-ray spectroscopy, x-ray diffraction, Rutherford backscattering spectrometry) and cathodoluminescence hyperspectral imaging. The compositional analysis with the different techniques shows good agreement when taking into account compositional gradients evidenced in these layers. The addition of small amounts of hydrogen to the gas flow at lower growth temperatures is shown to maintain a high surface quality and luminescence homogeneity. This allowed InN fractions of up to ~16% to be incorporated with minimal peak energy variations over a mapped area while keeping a high material quality

Stochastic models which separate fractal dimension and Hurst effect

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal dimension, a measure of roughness, and Hurst coefficient, a measure of long-memory dependence. This letter introduces simple stochastic models which allow for any combination of fractal dimension and Hurst exponent. We synthesize images from these models, with arbitrary fractal properties and power-law correlations, and propose a test for self-similarity.Comment: 8 pages, 2 figure