Tootfinder

Non-augmented velocity-vorticity-pressure formulation for the Navier--Stokes--Brinkman--Forchheimer problem
Santiago Badia, Carsten Carstensen, Alberto F. Martin, Ricardo Ruiz-Baier, Segundo Villa-Fuentes
https://arxiv.org/abs/2506.10533

Non-augmented velocity-vorticity-pressure formulation for the Navier--Stokes--Brinkman--Forchheimer problem
The flow of incompressible fluid in highly permeable porous media in vorticity - velocity - Bernoulli pressure form leads to a double saddle-point problem in the Navier--Stokes--Brinkman--Forchheimer equations. The paper establishes, for small sources, the existence of solutions on the continuous and discrete level of lowest-order piecewise divergence-free Crouzeix--Raviart finite elements. The vorticity employs a vector version of the pressure space with normal and tangential velocity jump pen…

Analysis of Atomic Charge State and Atomic Number for VAMOS Magnetic Spectrometer using Deep Neural Networks and Fractionally Labelled Events
M. Rejmund, A. Lemasson
https://arxiv.org/abs/2507.07109

Analysis of Atomic Charge State and Atomic Number for VAMOS++ Magnetic Spectrometer using Deep Neural Networks and Fractionally Labelled Events
The VAMOS++ magnetic spectrometer is a multi-parametric system that integrates ion optical magnetic elements with a multi-detector stack. The magnetic elements, along with the tracking and timing detectors and the trajectory reconstruction method, provide the analysis of the magnetic rigidity, the trajectory length between the beam interaction point and the focal plane of the spectrometer, and the related velocity and mass-over-charge ratio. The segmented ionization chamber provides the energy …

Generic infinite generation, fixed-point-poor representations and compact-element abundance in disconnected Lie groups
Alexandru Chirvasitu
https://arxiv.org/abs/2507.04065

Generic infinite generation, fixed-point-poor representations and compact-element abundance in disconnected Lie groups
The semidirect product $\mathbb{G}=\mathbb{L}\rtimes \mathbb{K}$ attached to a compact-group action on a connected, simply-connected solvable Lie group has a dense set of compact elements precisely when the $s\in \mathbb{K}$ operating on $\mathbb{L}$ fixed-point-freely constitute a dense set. This (along with a number of alternative equivalent characterizations) extends the Wu's analogous result for connected Lie $\mathbb{K}$, and also provides ample supplies of examples of almost-connected Lie…

“Inclusion is GOOD!”
(I posed with this great sign at the Indivisible CLT social gathering tonight at Starlight on 22nd)
https://indivisibleclt.org
https://starlighton…

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PINN-DG: Residual neural network methods trained with Finite Elements
Georgios Grekas, Charalambos G. Makridakis, Tristan Pryer
https://arxiv.org/abs/2507.03521

PINN-DG: Residual neural network methods trained with Finite Elements
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical techniques such as finite elements and finite differences. In this paper, we introduce a new class of Physics-Informed Neural Networks (PINNs) trained using discontinuous Galerkin finite element methods. Unlike standard collocation-based PINNs that rely on pointwise g…

#Blakes7 Series D, Episode 01 - Rescue
SLAVE: Yes, Master.
DORIAN: Analyze exterior disturbance.
SLAVE: It is an earthquake, Master.
AVON: Cause?
[Slave does not answer. Avon points his gun at Dorian.]
DORIAN: Cause?

Blakes7Bot | Search
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Counting Reciprocal Hyperbolic Elements in Hecke Groups
Ara Basmajian, Blanca Marmolejo, Robert Suzzi Valli
https://arxiv.org/abs/2505.21365 https://

Counting Reciprocal Hyperbolic Elements in Hecke Groups
A reciprocal geodesic on a (2,k, $\infty$) Hecke surface is a geodesic loop based at an even order cone point p traversing its path an even number of times. Associated to each reciprocal geodesic is the conjugacy class of a hyperbolic element in the (2,k,$\infty$) Hecke group whose axis passes through a cone point that projects to p. Such an element is called a reciprocal hyperbolic element based at p. In this paper, we determine the asymptotic growth rate and limiting constant (in terms of w…

Series B, Episode 05 - Pressure Point
JENNA: It's over an hour since our last contact.
CALLY: It can't be a communicator fault.
JENNA: Not on all four bracelets, no.
CALLY: What do you think has happened?
JENNA: They've run into trouble.
https://blake.torpidity.net/m/205/407

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

Pointwise-relatively-compact subgroups and trivial-weight-free representations
Alexandru Chirvasitu
https://arxiv.org/abs/2506.18861 https://

Pointwise-relatively-compact subgroups and trivial-weight-free representations
A pointwise-elliptic subset of a topological group is one whose elements all generate relatively-compact subgroups. A connected locally compact group has a dense pointwise-elliptic subgroup if and only if it is an extension by a compact normal subgroup of a semidirect product $\mathbb{L}\rtimes \mathbb{K}$ with connected, simply-connected Lie $\mathbb{L}$, compact Lie $\mathbb{K}$, with the commutator subgroup $\mathbb{K}'$ acting on the Lie algebra $Lie(\mathbb{L})$ with no trivial weights. Th…

A $\mathcal{CR}$-rotated $Q_1$ nonconforming finite element method for Stokes interface problems on local anisotropic fitted mixed meshes
Geng Chenchen, Hua Wang, Fengren Zou
https://arxiv.org/abs/2507.02741

A $\mathcal{CR}$-rotated $Q_1$ nonconforming finite element method for Stokes interface problems on local anisotropic fitted mixed meshes
We propose a new nonconforming finite element method for solving Stokes interface problems. The method is constructed on local anisotropic mixed meshes, which are generated by fitting the interface through simple connection of intersection points on an interface-unfitted background mesh, as introduced in \cite{Hu2021optimal}. For triangular elements, we employ the standard $\mathcal{CR}$ element; for quadrilateral elements, a new rotated $Q_1$-type element is used. We prove that this rotated $Q…