11 jul., 2025 - Palabras de Escritores | #PDE - #vida #life #literaverso #mastodon #fediverse.

New paper by #ModConFlex researcher Zhuo Xu on the robustness of a fluid-particle interaction system.

"A distinctive feature, not yet considered in the ISS literature, is that our system involves a free boundary. More precisely, the fluid is described by the viscous Burgers equation, and the motion of the particle obeys Newton second law. ... The proof is based on the construction of a Lyapunov functional derived from a special test function."

https://arxiv.org/abs/2505.08393

#PDE

#MSCA
#HorizonEU

I'm wondering: #physics makes a lot of use of #periodic functions, in particular it is very useful to solve space-dependent equations in representative volumes with #periodicBoundaryConditions.

However I've only seen it done with periodicity along orthogonal directions, aligned with a Cartesian frame.

Do you know of work, e.g. #PDE resolution, in nonrectangular #periodicDomains? E.g., in a #tiled hexagon? (but with a sufficiently generic setting, not exploiting regular hexagon symmetries) Even better if the periodicity parameters themselves are among the unknowns.

(Maybe I'm completely missing something obvious there, I'm in my first steps towards defining what I want - any random thought on the topic highly welcome!)

#tiling people?

I have arrived, and given my talk, at the tri-section #MAA meeting
#PDE #MathConference

Can anyone recommend a writeup on 1st order linear PDEs which is not written for engineering majors, but for working mathematicians? #PDE #math

So I found https://github.com/tracel-ai/cubecl which allows #gpgpu in #rust. Already using it to calculate some determinants for triangulations. Wondering if it can be leveraged to build a numeric #pde solver

Effects of OpenCL-Based Parallelization Methods on Explicit Numerical Methods to Solve the Heat Equation

#OpenCL #PDE #Performance #Physics

https://hgpu.org/?p=29451

Surprisingly many nonlinear partial differential equations of real interest have closed-form solutions: https://johndcook.com/blog/2024/04/25/closed-form-pde/

Just found this little helper for #neovim, #lazyvim that lets you manage your node dependencies from within your editor.
I have already seen this in VSCode but never missed it until I installed it in my #pde

https://github.com/vuki656/package-info.nvim

We've been working on a massive riddle tying together #self-organization, #carbonate #diagenesis, reactive transport, #paleoclimate and #Milankovich cycles, and very stiff PDE systems.

If you've missed the poster at #egu24, you can still find it attached to the abstract in the conference program (https://meetingorganizer.copernicus.org/EGU24/EGU24-16400.html) and on Zenodo https://zenodo.org/records/10943274 If you're into numerical methods, tricky PDEs or other aspects of #modeling, please see if you have any advice to us #solvers #PDE

LINEAR TRANSPORT EQUATION
The linear transport equation (LTE) models the variation of the concentration of a substance flowing at constant speed and direction. It's one of the simplest partial differential equations (PDEs) and one of the few that admits an analytic solution.

Given \(\mathbf{c}\in\mathbb{R}^n\) and \(g:\mathbb{R}^n\to\mathbb{R}\), the following Cauchy problem models a substance flowing at constant speed in the direction \(\mathbf{c}\).
\[\begin{cases}
u_t+\mathbf{c}\cdot\nabla u=0,\ \mathbf{x}\in\mathbb{R}^n,\ t\in\mathbb{R}\\
u(\mathbf{x},0)=g(\mathbf{x}),\ \mathbf{x}\in\mathbb{R}^n
\end{cases}\]
If \(g\) is continuously differentiable, then \(\exists u:\mathbb{R}^n\times\mathbb{R}\to\mathbb{R}\) solution of the Cauchy problem, and it is given by
\[u(\mathbf{x},t)=g(\mathbf{x}-\mathbf{c}t)\]

VisualPDE: an interactive, lightning-fast browser-based solver for models in #physics, #chemistry, or #biology. #PDE https://visualpde.com/

Congratulations to my colleague and co-author Yuan Zhang on receiving a research award from our College of Science at #PurdueFortWayne
https://photos.app.goo.gl/dj2PjHaMgkGx77XN7
#NSFfunded #math #ComplexAnalysis #PDE

'Neural Q-learning for solving PDEs', by Samuel N. Cohen, Deqing Jiang, Justin Sirignano.

http://jmlr.org/papers/v24/22-1075.html

#pdes #pde #nonlinear

`The fast multipole method (FMM), introduced by Rokhlin Jr. and Greengard has been said to be one of the top ten #algorithms of the 20th century. The FMM algorithm reduces the complexity of matrix-vector multiplication involving a certain type of dense #matrix which can arise out of many #physical #systems.`

https://en.wikipedia.org/wiki/Fast_multipole_method

Ginger Consumption May Mitigate Neutrophil Dysfunction
TOPLINE:
Blood samples from healthy adults show an inhibition of neutrophil extracellular trap formation (NET) after 1 week of daily ginger supplements.
https://www.medscape.com/viewarticle/996737?src=rss #ginger #supplement #neutrophil dysfunction #inhibition #PDE

FElupe - A Python package for Finite Element Analysis, Version 7.8.0 is available on PyPI. Now with mesh-generators for the elementary shapes line, rectangle, cube, triangle and circle.

https://github.com/adtzlr/felupe

This is the best IDE in the world! Why? Because I configured that. I updated this repository a lot, and it's so much better than before.
I will make realize of that, as soon as possible.
Check this out
#code #neovim #nvim #fox_ide #ide #pde #programming #program #vscode #github #hack #hacker
https://github.com/Mr-Fox-h/fox-ide

Interesting ...

Combining Physics-Informed Neural Networks (PINNs) w. Classical Numerical Methods
https://old.reddit.com/r/MachineLearning/comments/15u8wky/r_combining_physicsinformed_neural_networks_pinns

* 2 papers try to reconcile/harmonize classical methods (finite difference) w. PINN

https://northboot.xyz/search?q=Neural+operators

Neural Operator: https://zongyi-li.github.io/neural-operator
Neural Operator: Learning Maps Between Function Spaces: https://arxiv.org/abs/2108.08481
Physics-Informed Deep Neural Operator Networks: https://arxiv.org/abs/2207.05748