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Using the multi-point Pad\'e approach, we locate Lee-Yang edge singularities of the QCD pressure in the complex baryon chemical potential plane. These singularities are extracted from singularities in the net baryon-number density calculated in $N_f=2+1$ lattice QCD at physical quark mass and purely imaginary chemical potential. Taking an appropriate scaling ansatz in the vicinity of the conjectured QCD critical endpoint, we extrapolate the singularities on $N_\tau=6$ lattices to pure real baryon chemical potential to estimate the position of the critical endpoint (CEP). We find $T^{\rm CEP}=105^{+8}_{-18}$~ MeV and $\mu_B^{\rm CEP} = 422^{+80}_{-35}$~ MeV, which compares well with recent estimates in the literature. For the slope of the transition line at the critical point we find $-0.16(24)$., Comment: 10 pages, 7 figues

We discuss the scaling of the Yang-Lee singularity (YLs) and show how the universal scaling can be used to locate phase transitions in QCD. We describe two complementary methods to extract the location of the Yang-Lee singularity from lattice QCD data of the baryon-number density and higher order cumulants of the baryon number, obtained at imaginary chemical potential. The first method (multi-point Pad\'e resummation) is used to determine the Roberge-Weiss phase transition temperature. Our continuum extrapolated result is $T_{RW}=211.1\pm3.1$ MeV. The second method is based on the asymptotic behaviour of the Fourier coefficients of the baryon-number density. We discuss the derivation of a fitting function and demonstrate that the procedure can successfully locate the YLs in the Quark Meson model., Comment: 7 pages, 4figures, Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermilab, Batavia, Illinois, USA

Future gas turbine engines will operate at higher gas temperatures and consequentially hot-section components such as blades, vanes and combustors, will be subject to higher thermal radiation fluxes than today. Current thermal barrier coating materials are translucent over the spectral region of the heat flux so future coatings will also have to provide a barrier to thermal radiation. The effects of optical absorption and scattering properties of coating materials on the temperatures and heat fluxes through coatings are explored using a two-flux heat transfer model, and promising combinations are identified that reduce the coating-alloy interface temperatures. Lower interface temperatures occur for thickness normalized absorptions of $\overline{\kappa} L$ $>$1. The effect of both a narrow and a broad band spectrally selective absorbing Gd${_2}$Zr${_2}$O$_{7}$ based coating materials are then studied. These show that large values of the product of the normalized absorption length and the spectral width of the absorption are required to significantly decrease the radiative heat transport through a coating. The results emphasize the importance of enhancing the optical absorption of the next generation barrier materials as a strategy to increase gas turbine engine efficiency by decreasing compressor bleed air cooling requirements.

Python is a particularly appealing language to carry out data analysis, owing in part to its user-friendly character as well as its access to well maintained and powerful libraries like NumPy and SciPy. Still, for the purpose of analyzing data in a lattice QCD context, some desirable functionality is missing from these libraries. Moreover, scripting languages tend to be slower than compiled ones. To help address these points we present the AnalysisToolbox, a collection of Python modules to facilitate lattice QCD data analysis. Some highlighted features include general-purpose jackknife and bootstrap routines; modules for reading in and storing gauge configurations; a module to carry out hadron resonance gas model calculations; and convenience wrappers for SciPy integration, curve fitting, and splines. These features are sped up behind the scenes using parallelization and just-in-time compilation., Comment: 9 pages, 1 figure, presented at the 40th International Symposium on Lattice Field Theory

The rise of exascale supercomputers has fueled competition among GPU vendors, driving lattice QCD developers to write code that supports multiple APIs. Moreover, new developments in algorithms and physics research require frequent updates to existing software. These challenges have to be balanced against constantly changing personnel. At the same time, there is a wide range of applications for HISQ fermions in QCD studies. This situation encourages the development of software featuring a HISQ action that is flexible, high-performing, open source, easy to use, and easy to adapt. In this technical paper, we explain the design strategy, provide implementation details, list available algorithms and modules, and show key performance indicators for SIMULATeQCD, a simple multi-GPU lattice code for large-scale QCD calculations, mainly developed and used by the HotQCD collaboration. The code is publicly available on GitHub., Comment: 17 pages, 7 figures

We report updated results on the determination of Lee-Yang edge (LYE) singularities in $N_f = 2+1$ QCD using highly improved staggered quarks (HISQ) with physical masses on $N_\tau = 4, 6, 8$ lattices. The singularity structure of QCD in the complex $\mu_B$ plane is probed using conserved charges calculated at imaginary $\mu_B$. The location of the singularities is determined by studying the (uncancelled) poles of multi-point Pad\'e approximants. We show that close to the Roberge-Weiss (RW) transition, the location of the LYE singularities scales according to the $3$-$d$ $Z(2)$ universality class. By combining the new $N_\tau = 6$ data with the $N_\tau = 4$ data from our previous analysis we extract a rough estimate for the RW temperature in the continuum limit. We also discuss some preliminary results for the singularities close to the chiral phase transition obtained from simulations on $N_\tau = 6, 8$ lattices., Comment: 10 pages, 9 figures, Proceedings of the 39th International Symposium on Lattice Field Theory, 8-13 August 2022, Bonn, Germany

A new approach is presented to explore the singularity structure of lattice QCD in the complex chemical potential plane. Our method can be seen as a combination of the Taylor expansion and analytic continuation approaches. Its novelty lies in using rational (Pad\'e) approximants for studying Lee-Yang edge singularities. We present a calculation of the cumulants of the net-baryon number as a function of a purely imaginary baryon number chemical potential, obtained with highly improved staggered quarks at temporal lattice extent of $N_\tau=4,6$. We construct various rational function approximations of the lattice data and determine their poles (and roots) in the complex plane. We compare the position of the closest pole to the theoretically expected position of the Lee-Yang edge singularity. At high temperature, we find scaling that is in accordance with the expected power law behavior of the Roberge-Weiss transition while a different behavior is found for $T\lesssim 170$ MeV., Comment: 6 pages, 3 figures, presented at the 29th international conference on ultrarelativistic nucleus-nucleus collisions, April 4-10, 2022, Krac\'ow, Poland

We introduce a number of techniques in quantitative convergent-beam electron diffraction under development by our group and discuss the basis for measuring interatomic electrostatic potentials (and therefore also electron densities), localised at sub-nanometre scales, with sufficient accuracy and precision to map chemical bonds in and around nanostructures in nanostructured materials. This has never been possible as experimental measurements of bonding have always been restricted to homogeneous single-phased crystals., Comment: 11 pages, 4 figures

We present $\texttt{SIMULATeQCD}$, HotQCD's software for performing lattice QCD calculations on GPUs. Started in late 2017 and intended as a full replacement of the previous single GPU lattice QCD code used by the HotQCD collaboration, our software has been developed into an extensive framework for lattice QCD calculations distributed on multiple GPUs over many compute nodes. The code is built on C++, CUDA, and MPI and leverages modern C++ language features to provide high-level data structures, objects, and algorithms that allow users to express lattice QCD calculations in an intuitive way without sacrificing performance. Implemented algorithms range from gradient flow, correlator measurements, and mixed precision conjugate gradient solvers all the way to full HISQ gauge field configuration generation using RHMC. After successful deployment in large-scale computing projects, we want to share the result of our efforts with the lattice QCD community by making it publicly available. In these proceedings, we will present some of the key features of our code, demonstrate its ease of use, and show benchmarks of performance critical kernels on state-of-the-art supercomputers., Comment: 7 pages, 3 figures, presented at the 38th International Symposium on Lattice Field Theory

The Polyakov loop expectation value $\langle P\rangle$ is an order parameter of the deconfinement transition in the heavy quark mass regime, whereas its sensitivity to the deconfinement of light, dynamical quarks is not apparent. From the perspective of an effective Lagrangian in the vicinity of the chiral transition, the Polyakov loop, $P$, is an energy-like observable, and $\langle P\rangle$ should hence scale like the energy density. Using $N_f=2+1$ HISQ configurations at finite lattice spacing, we show that near the chiral transition temperature, the scaling behavior of $\langle P\rangle$ and the heavy quark free energy $F_q$ is consistent with energy-like observables in the 3-$d$, O($N$) universality class. We extend this analysis to other Polyakov loop observables, including the response of the heavy quark free energy, $F_q$, to the baryon chemical potential, which is expected to scale like a specific heat., Comment: 10 pages, 3 figures, presented at the 38th International Symposium on Lattice Field Theory

Data Science advances in sports commonly involve "big data", i.e., large sport-related data sets. However, such big data sets are not always available, necessitating specialized models that apply to relatively few observations. One important area of sport-science research that features small data sets is the study of recovery from exercise. In this area, models are typically fitted to data collected from exhaustive exercise test protocols, which athletes can perform only a few times. Recent findings highlight that established recovery such as the so-called work-balance models are too simple to adequately fit observed trends in the data. Therefore, we investigated a hydraulic model that requires the same few data points as work-balance models to be applied, but promises to predict recovery dynamics more accurately. To compare the hydraulic model to established work-balance models, we retrospectively applied them to data compiled from published studies. In total, one hydraulic model and three work-balance models were compared on data extracted from five studies. The hydraulic model outperformed established work-balance models on all defined metrics, even those that penalize models featuring higher numbers of parameters. These results incentivize further investigation of the hydraulic model as a new alternative to established performance models of energy recovery., Comment: 26 pages, 9 figures, 6 tables, this manuscript has been submitted and is currently under review