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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."

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?

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 (meetingorganizer.copernicus.or) and on Zenodo 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
\[u(\mathbf{x},t)=g(\mathbf{x}-\mathbf{c}t)\]

`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.`

en.wikipedia.org/wiki/Fast_mul

en.wikipedia.orgFast multipole method - Wikipedia