More Like this

1. Mach limits in analytic spaces on exterior domains

   https://doi.org/10.3934/dcds.2022027  

   Jang, Juhi; Kukavica, Igor; Li, Linfeng (January 2022, Discrete and Continuous Dynamical Systems)

   We address the Mach limit problem for the Euler equations in an exterior domain with an analytic boundary. We first prove the existence of tangential analytic vector fields for the exterior domain with constant analyticity radii and introduce an analytic norm in which we distinguish derivatives taken from different directions. Then we prove the uniform boundedness of the solutions in the analytic space on a time interval independent of the Mach number, and Mach limit holds in the analytic norm. The results extend more generally to Gevrey initial data with convergence in a Gevrey norm. 

   more » « less
2. Dead Science: Most Resources Linked in Biomedical Articles Disappear in Eight Years

   https://doi.org/10.1007/978-3-030-15742-5_16  

   Zeng, Tong; Shema, Alain; Acuna, Daniel E (October 2020, iConference 2019, LNCS 11420)

   Scientific progress critically depends on disseminating analytic pipelines and datasets that make results reproducible and replicable. Increasingly, researchers make resources available for wider reuse and embed links to them in their published manuscripts. Previous research has shown that these resources become unavailable over time but the extent and causes of this problem in open access publications has not been explored well. By using 1.9 million articles from PubMed Open Access, we estimate that half of all resources become unavailable after 8 years. We find that the number of times a resource has been used, the international (int) and organization (org) domain suffixes, and the number of affiliations are positively related to resources being available. In contrast, we found that the length of the URL, Indian (in), European Union (eu), and Chinese (cn) domain suffixes, and abstract length are negatively related to resources being available. Our results contribute to our understanding of resource sharing in science and provide some guidance to solve resource decay. 

   more » « less
3. Uniform bounds of families of analytic semigroups and Lyapunov Linear Stability of planar fronts

   https://doi.org/10.1002/mana.202300273  

   Latushkin, Yuri; Pogan, Alin (July 2024, Mathematische Nachrichten)

   Abstract We study families of analytic semigroups, acting on a Banach space, and depending on a parameter, and give sufficient conditions for existence of uniform with respect to the parameter norm bounds using spectral properties of the respective semigroup generators. In particular, we use estimates of the resolvent operators of the generators along vertical segments to estimate the growth/decay rate of the norm for the family of analytic semigroups. These results are applied to prove the Lyapunov linear stability of planar traveling waves of systems of reaction–diffusion equations, and the bidomain equation, important in electrophysiology. 

   more » « less
4. Nonequilibrium steady-state dynamics of Markov processes on graphs

   https://doi.org/10.21468/SciPostPhys.19.2.045  

   Crotti, Stefano; Barthel, Thomas; Braunstein, Alfredo (August 2025, SciPost Physics)

   We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite matrix products. For homogeneous ensembles on regular graphs, the distribution is parametrized by a single d×d×r^2 tensor, where r is the number of states per variable, and d is the matrix-product bond dimension. While the method becomes exact in the large-d limit, it typically provides highly accurate results even for small bond dimensions d. The d^2r^2 parameters are determined by solving a fixed point equation, for which we provide an efficient belief-propagation procedure. We apply this approach to a variety of models, including Ising-Glauber dynamics with symmetric and asymmetric couplings, as well as the SIS model. Even for small d, the results are compatible with Monte Carlo estimates and accurately reproduce known exact solutions. The method provides access to precise temporal correlations, which, in some regimes, would be virtually impossible to estimate by sampling. 

   more » « less
5. On finite energy monopoles on $$C x \Sigma$$.

   Wang, Donghao (July 2019, ArXiv.org)

   Let $$X=\mathbb{C}\times\Sigma$$ be the product of the complex plane and a compact Riemann surface. We establish a classification theorem of solutions to the Seiberg-Witten equation on $$X$$ with finite analytic energy. The spin bundle $$S^+\to X$$ splits as $$L^+\oplus L^-$$. When $$2-2g\leq c_1(S^+)[\Sigma]<0$$, the moduli space is in bijection with the moduli space of pairs $$((L^+,\bar{\partial}), f)$$ where $$(L^+,\bar{\partial})$$ is a holomorphic structure on $L^+$ and $$f: \mathbb{C}\to H^0(\Sigma, L^+,\bar{\partial})$$ is a polynomial map. Moreover, the solution has analytic energy $$-4\pi^2d\cdot c_1(S^+)[\Sigma]$$ if $$f$$ has degree $$d$$. When $$c_1(S^+)=0$$, all solutions are reducible and the moduli space is the space of flat connections on $$\bigwedge^2 S^+$$. We also estimate the decay rate at infinity for these solutions. 

   more » « less