79 citations · 638 across the 61 of their papers we have counts for
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On the numerical signature of blow-up in hydrodynamic equations
Erik Jansson, Klas Modin
The phenomenon of finite time blow-up in hydrodynamic partial differential equations is central in analysis and mathematical physics. While numerical studies have guided theoretica…
The Toda flow as a porous medium equation
Boris Khesin, Klas Modin
We describe the geometry of the incompressible porous medium (IPM) equation: we prove that it is a gradient dynamical system on the group of area-preserving diffeomorphisms and has…
An efficient geometric method for incompressible hydrodynamics on the sphere
Paolo Cifani, Milo Viviani, Klas Modin
We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hyd…
Casimir preserving spectrum of two-dimensional turbulence
Paolo Cifani, Milo Viviani, Erwin Luesink +2
We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mod…
Sub-Riemannian Landmark Matching and its interpretation as residual neural networks
Erik Jansson, Klas Modin
The problem of finding a time-dependent vector field which warps an initial set of points to a target set is common in shape analysis. It is an example of a problem in the diffeomo…
Shape analysis via gradient flows on diffeomorphism groups
Tracey Balehowsky, Carl-Joar Karlsson, Klas Modin
We study a gradient flow on Sobolev diffeomorphisms for the problem of image registration. The energy functional quantifies the effect of transforming a template to a target, while…