Tootfinder

Fourth-order Adaptive Mesh Refinement both in space and in time for incompressible Navier-Stokes equations with Dirichlet boundary conditions
Shubo Zhao, Qinghai Zhang
https://arxiv.org/abs/2506.02663

Fourth-order Adaptive Mesh Refinement both in space and in time for incompressible Navier-Stokes equations with Dirichlet boundary conditions
We present a fourth-order projection method with adaptive mesh refinement (AMR) for numerically solving the incompressible Navier-Stokes equations (INSE) with subcycling in time. Our method features (i) a reformulation of INSE so that the velocity divergence decays exponentially on the coarsest level, (ii) a derivation of coarse-fine interface conditions that preserves the decay of velocity divergence on any refinement level of the AMR hierarchy, (iii) an approximation of the coarse-fine interf…

Refining Yoneda Lemma under Finiteness Constrains and Applications
Antonio Ceres, Cristina Costoya, Antonio Viruel
https://arxiv.org/abs/2506.01501 https:/…

Refining Yoneda Lemma under Finiteness Constrains and Applications
Classical Yoneda Lemma asserts that the isomorphism type of an object $a$ in a category $C$ is determined by the natural type of the set-valued functor $Hom_C(a,-)$. Here we show that if finiteness hypothesis are assumed to hold in $C$, then the isomorphism type of an object $a$ in $C$ is determined by the integer-valued function $|Hom_C(a,-)|$ on objects in $C$. We present applications of this result to the isomorphism problem in Group, Graph, and Ring Theory.

A novel stratified sampler with unbalanced refinement for network reliability assessment
Jianpeng Chan, Iason Papaioannou, Daniel Straub
https://arxiv.org/abs/2506.01044

A novel stratified sampler with unbalanced refinement for network reliability assessment
We investigate stratified sampling in the context of network reliability assessment. We propose an unbalanced stratum refinement procedure, which operates on a partition of network components into clusters and the number of failed components within each cluster. The size of each refined stratum and the associated conditional failure probability, collectively termed failure signatures, can be calculated and estimated using the conditional Bernoulli model. The estimator is further improved by det…

Spin refinement of moduli spaces of residueless meromorphic differentials and the BKP hierarchy
David Klompenhouwer, Stijn Velstra
https://arxiv.org/abs/2506.02540

Spin refinement of moduli spaces of residueless meromorphic differentials and the BKP hierarchy
We consider strata of curves carrying a residueless meromorphic differential inducing a spin structure on the curve. The cohomology classes of the closures of these strata, weighted by the parity of the spin structures, form a partial cohomological field theory (CohFT) of infinite rank. After applying the DR hierarchy construction to this partial CohFT and reducing to differentials with two zeros and arbitrarily many poles, we show that the resulting system of evolutionary PDEs coincides with t…

An efficient GPU-accelerated adaptive mesh refinement framework for high-fidelity compressible reactive flows modeling
Yuqi Wang, Yadong Zeng, Ralf Deiterding, Jianhan Liang
https://arxiv.org/abs/2506.02602

An efficient GPU-accelerated adaptive mesh refinement framework for high-fidelity compressible reactive flows modeling
This paper presents a heterogeneous adaptive mesh refinement (AMR) framework for efficient simulation of moderately stiff reactive problems. This framework features an elaborate subcycling-in-time algorithm along with a specialized refluxing algorithm, all unified in a highly parallel codebase. We have also developed a low-storage variant of explicit chemical integrators by optimizing the register usage of GPU, achieving respectively 6x and 3x times speedups as compared to the implicit and stan…

This https://arxiv.org/abs/2410.15630 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A bijective proof of Andrews' refinement of the Alladi-Schur theorem
In this paper, I will bijectively prove Andrews' refinement of the Alladi-Schur theorem. I will also use the framework of my bijection to reproduce and give a bijective account of Andrews' recursive relations for the Alladi-Schur polynomials.

A refinement of the Lorentz local field expression with impact on the Clausius-Mossotti and Lorentz-Lorenz models
Jeroen van Duivenbode, Anne-Jans Faber
https://arxiv.org/abs/2506.01993

A refinement of the Lorentz local field expression with impact on the Clausius-Mossotti and Lorentz-Lorenz models
In the 19th century Mossotti and Clausius formulated an expression that relates electrical permittivity of a dielectric to the product of molecular polarizability and number density. Lorenz and Lorentz extended the use of that expression to also cover the dielectric s refractive index. These expressions successfully predict the change of the dielectric s permittivity and refractive index as a function of a wide range of its number density, using the consideration that molecular polarizability s…

#Blakes7 Series B, Episode 13 - Star One
DURKIM: She can't be, it's unmanned. The systems are automatic.
SERVALAN: A group of scientists and technicians elected to spend the rest of their lives refining, checking and guarding the systems.

Blakes7Bot | Search
Companion site to the Blakes7Bot Twitter, Mastodon, and Bluesky accounts. Automated lines of Blakes 7 dialog. Includes a script search facility.

This https://arxiv.org/abs/2501.05311 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Adaptive refinement for eigenvalue problems based on an associated source problem
We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinement is driven by the solution of a single source problem -- the so-called landscape problem for the operator -- instead of refining based on the computed eigenpairs. Some theoretical justification for the approach is provided, and extensive empirical results indicate that it can provide an attractive alternative to st…

This https://arxiv.org/abs/2205.12953 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces
We prove a blow-up formula for the generating series of virtual $χ_y$-genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological $χ_y$-genera of Göttsche. Our formula is a refinement of one by Vafa-Witten relating to S-duality. We prove the formula simultaneously in the setting of Gieseker stable sheaves on polarised surfaces and also in the setting of framed sheaves on $\mathbb{P}^2$. The proof is based on the blow-up algorithm of N…