Tootfinder

This https://arxiv.org/abs/2410.03475 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Noncommutative metric geometry of quantum circle bundles
In this paper we investigate quantum circle bundles from the point of view of compact quantum metric spaces. The raw input data is a circle action on a unital $C^*$-algebra together with a quantum metric of spectral geometric origin on the fixed point algebra. Under a few extra conditions on the spectral subspaces we show that the spectral geometric data on the base algebra can be lifted to the total algebra. Notably, the lifted spectral geometry is independent of the choice of frames and is pe…

This https://arxiv.org/abs/2502.13067 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Spectral geometry of the curl operator on smoothly bounded domains
We show that the spectrum of the curl operator on a generic smoothly bounded domain in three-dimensional Euclidean space consists of simple eigenvalues. The main new ingredient in our proof is a formula for the variation of curl eigenvalues under a perturbation of the domain, reminiscent of Hadamard's formula for the variation of Laplace eigenvalues under Dirichlet boundary conditions. As another application of this variational formula, we simplify the derivation of a well-known necessary condi…

This https://arxiv.org/abs/2411.04869 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Modelling of the atomic lines' emission of fast moving pulsar nebulae
Bow shocks generated by pulsars moving through weakly ionized interstellar medium (ISM) produce emission dominated by non-equilibrium atomic transitions. These bow shocks are primarily observed as H$_α$ nebulae. We developed a package, named Shu, that calculates non-LTE intensity maps in more than 150 spectral lines, taking into account geometrical properties of the pulsars' motion and lines of sight. We argue here that atomic (CI, NI, OI) and ionic (SII, NII, OIII, NeIV) transitions can be us…

On the geometric $k$-colored crossing number of $K_n$
Benedikt Hahn, Bettina Klinz, Birgit Vogtenhuber
https://arxiv.org/abs/2505.18014 https://

On the geometric $k$-colored crossing number of $K_n$
We study the \emph{geometric $k$-colored crossing number} of complete graphs $\overline{\overline{\text{cr}}}_k(K_n)$, which is the smallest number of monochromatic crossings in any $k$-edge colored straight-line drawing of $K_n$. We substantially improve asymptotic upper bounds on $\overline{\overline{\text{cr}}}_k(K_n)$ for $k=2,\ldots, 10$ by developing a procedure for general $k$ that derives $k$-edge colored drawings of $K_n$ for arbitrarily large $n$ from initial drawings with a low num…

This https://arxiv.org/abs/2505.15750 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Localising invariants in derived bornological geometry
We study several categories of analytic stacks relative to the category of bornological modules over a Banach ring. When the underlying Banach ring is a nonarchimedean valued field, this category contains derived rigid analytic spaces as a full subcategory. When the underlying field is the complex numbers, it contains the category of derived complex analytic spaces. In the second part of the paper, we consider localising invariants of rigid categories associated to bornological algebras. The ma…

Viscoelasticity of biomimetic scale beams from trapped complex fluids
Pranta Rahman Sarkar, Outi Tammisola, Ranajay Ghosh
https://arxiv.org/abs/2505.21760 …

Viscoelasticity of biomimetic scale beams from trapped complex fluids
We investigate the nonlinear viscoelastic behavior of a biomimetic scale-covered beam in which shear-dependent complex fluids are trapped between overlapping scales under bending loads. These fluids mimic biological mucus and slime layers commonly enveloping the skins found in nature. An energy-based analytical model is developed to quantify the interplay between substrate elasticity, scale geometry, and fluid rheology at multiple length scales. Constant strain rate and oscillatory bending are …

This https://arxiv.org/abs/2310.04052 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spectral metrics on quantum projective spaces
We show that the noncommutative differential geometry of quantum projective spaces is compatible with Rieffel's theory of compact quantum metric spaces. This amounts to a detailed investigation of the Connes metric coming from the unital spectral triple introduced by D'Andrea and Dabrowski. In particular, we establish that the Connes metric metrizes the weak-* topology on the state space of quantum projective space. This generalizes previous work by the second author and Aguilar regarding spect…

This https://arxiv.org/abs/2012.13515 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Boundaries of $\varepsilon$-neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature
We study the geometry, topological properties and smoothness of the boundaries of closed $\varepsilon$-neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \varepsilon \}$ of compact planar sets $E \subset \mathbb{R}^2$. We develop a novel technique for analysing the boundary, and use this to obtain a classification of singularities (i.e.~non-smooth points) on $\partial E_\varepsilon$ into eight categories. We show that the set of singularities is either countab…

This https://arxiv.org/abs/2505.12876 has been replaced.
initial toot: https://mastoxiv.page/@ar…

What Price Fiber Bundle Substantivalism? On How to Avoid Holes in Fibers
On a mathematically foundational level, our most successful physical theories (gauge field theories and general-relativistic theories) are formulated in a framework based on the differential geometry of connections on principal bundles. After reviewing the essentials of this framework, we articulate the generalized hole and point-coincidence arguments, examining how they weight on a substantivalist position towards bundle spaces. This question, then, is considered in light of the Dressing Field…

Solar-cycle Variability of Composite Geometry in the Solar Wind Turbulence
Zhan Fa, H. -Q. He
https://arxiv.org/abs/2505.12870 https://

Solar-cycle Variability of Composite Geometry in the Solar Wind Turbulence
The composite geometry and spectral anisotropy of the solar wind turbulence are very important topics in the investigations of solar wind. In this work, we use the magnetic field and plasma data from Wind spacecraft measured during 1995 January to 2023 December, which covers more than two solar cycles, to systematically investigate these subjects in the context of solar-cycle variability. The so-called spectrum ratio test and spectrum anisotropy test are employed to determine the three-dimensio…