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1. Birth–death dynamics for sampling: global convergence, approximations and their asymptotics

   https://doi.org/10.1088/1361-6544/acf988  

   Lu, Yulong; Slepčev, Dejan; Wang, Lihan (September 2023, Nonlinearity)

   Abstract Motivated by the challenge of sampling Gibbs measures with nonconvex potentials, we study a continuum birth–death dynamics. We improve results in previous works (Liuet al2023Appl. Math. Optim.8748; Luet al2019 arXiv:1905.09863) and provide weaker hypotheses under which the probability density of the birth–death governed by Kullback–Leibler divergence or byχ²divergence converge exponentially fast to the Gibbs equilibrium measure, with a universal rate that is independent of the potential barrier. To build a practical numerical sampler based on the pure birth–death dynamics, we consider an interacting particle system, which is inspired by the gradient flow structure and the classical Fokker–Planck equation and relies on kernel-based approximations of the measure. Using the technique of Γ-convergence of gradient flows, we show that on the torus, smooth and bounded positive solutions of the kernelised dynamics converge on finite time intervals, to the pure birth–death dynamics as the kernel bandwidth shrinks to zero. Moreover we provide quantitative estimates on the bias of minimisers of the energy corresponding to the kernelised dynamics. Finally we prove the long-time asymptotic results on the convergence of the asymptotic states of the kernelised dynamics towards the Gibbs measure. 

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2. Scaling laws and exact results in turbulence ^*

   https://doi.org/10.1088/1361-6544/ad6057  

   Novack, Matthew (July 2024, Nonlinearity)

   Abstract In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000Nonlinearity13249–55) and Eyink (2003Nonlinearity16137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s $\frac{4}{5}$, $\frac{4}{3}$, $\frac{4}{15}$laws. We apply these computations to improve a recent result of Hofmanovaet al(2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruèet al(2023Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giriet al(2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws. 

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3. OrbitN: A Symplectic Integrator for Planetary Systems Dominated by a Central Mass—Insight into Long-term Solar System Chaos

   https://doi.org/10.3847/1538-3881/acd63b  

   Zeebe, Richard E. (June 2023, The Astronomical Journal)

   Abstract Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds at or close to machine precision (∼10⁻¹⁶, double-precision arithmetic); otherwise, numerical chaos may dominate over physical chaos. Currently, the speed/accuracy demands are usually only met by symplectic integrators. For example, the most up-to-date long-term astronomical solutions for the solar system in the past (widely used in, e.g., astrochronology and high-precision geological dating) have been obtained using symplectic integrators. However, the source codes of these integrators are unavailable. Here I present the symplectic integratororbitN(lean version 1.0) with the primary goal of generating accurate and reproducible long-term orbital solutions for near-Keplerian planetary systems (here the solar system) with a dominant massM₀. Among other features,orbitN-1.0includesM₀’s quadrupole moment, a lunar contribution, and post-Newtonian corrections (1PN) due toM₀(fast symplectic implementation). To reduce numerical round-off errors, Kahan compensated summation was implemented. I useorbitNto provide insight into the effect of various processes on the long-term chaos in the solar system. Notably, 1PN corrections have the opposite effect on chaoticity/stability on a 100 Myr versus Gyr timescale. For the current application,orbitNis about as fast as or faster (factor 1.15–2.6) than comparable integrators, depending on hardware.¹¹The orbitN source code (C) is available athttp://github.com/rezeebe/orbitN. 

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4. Synthetic Gaia DR3 Surveys from the FIRE Cosmological Simulations of Milky Way-mass Galaxies

   https://doi.org/10.3847/1538-4357/ad35ba  

   Nguyen, Tri; Ou, Xiaowei; Panithanpaisal, Nondh; Shipp, Nora; Necib, Lina; Sanderson, Robyn; Wetzel, Andrew (April 2024, The Astrophysical Journal)

   Abstract The third data release (DR3) of Gaia has provided a fivefold increase in the number of radial velocity measurements of stars, as well as a stark improvement in parallax and proper motion measurements. To help with studies that seek to test models and interpret Gaia DR3, we present nine Gaia synthetic surveys, based on three solar positions in three Milky Way-mass galaxies of theLattesuite of theFire-2 cosmological simulations. These synthetic surveys match the selection function, radial velocity measurements, and photometry of Gaia DR3, adapting the code baseAnanke, previously used to match the Gaia DR2 release by Sanderson et al. The synthetic surveys are publicly available and can be found athttp://ananke.hub.yt/. Similarly to the previous release ofAnanke, these surveys are based on cosmological simulations and thus are able to model nonequilibrium dynamical effects, making them a useful tool in testing and interpreting Gaia DR3. 

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5. The Farmer: A Reproducible Profile-fitting Photometry Package for Deep Galaxy Surveys

   https://doi.org/10.3847/1538-4365/acf850  

   Weaver, J R; Zalesky, L; Kokorev, V; McPartland, C_J R; Chartab, N; Gould, K_M L; Shuntov, M; Davidzon, I; Faisst, A; Stickley, N; et al (November 2023, The Astrophysical Journal Supplement Series)

   Abstract While space-borne optical and near-infrared facilities have succeeded in delivering a precise and spatially resolved picture of our Universe, their small survey area is known to underrepresent the true diversity of galaxy populations. Ground-based surveys have reached comparable depths but at lower spatial resolution, resulting in source confusion that hampers accurate photometry extractions. What once was limited to the infrared regime has now begun to challenge ground-based ultradeep surveys, affecting detection and photometry alike. Failing to address these challenges will mean forfeiting a representative view into the distant Universe. We introduceThe Farmer: an automated, reproducible profile-fitting photometry package that pairs a library of smooth parametric models fromThe Tractorwith a decision tree that determines the best-fit model in concert with neighboring sources. Photometry is measured by fitting the models on other bands leaving brightness free to vary. The resulting photometric measurements are naturally total, and no aperture corrections are required. Supporting diagnostics (e.g.,χ²) enable measurement validation. As fitting models is relatively time intensive,The Farmeris built with high-performance computing routines. We benchmarkThe Farmeron a set of realistic COSMOS-like images and find accurate photometry, number counts, and galaxy shapes.The Farmeris already being utilized to produce catalogs for several large-area deep extragalactic surveys where it has been shown to tackle some of the most challenging optical and near-infrared data available, with the promise of extending to other ultradeep surveys expected in the near future.The Farmeris available to download from GitHub (https://github.com/astroweaver/the_farmer) and Zenodo (https://doi.org/10.5281/zenodo.8205817). 

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