Jacobus W. Portegies

A model for vortical plumes in rotating convection

Buoyant convection and the Coriolis force caused by the rotation of our Earth are important forces in the flows in the atmosphere and the oceans. A convenient model for such flows, although not fully compatible, is the rotating Rayleigh‐Benard setting: A horizontally infinite layer of fluid is vertically confined by solid walls rotating around a vertical axis, the bottom wall being at a higher temperature than the top wall. Although the lack of a top wall in the geophysical flows makes the model not directly applicable, the general behavior of the model flow shows considerable similarities to real flow in the atmosphere. Furthermore, in the atmosphere the tropopause can be regarded as a “top wall” to a certain extent. Especially for the large-scale flows in the atmosphere, the effect of the rotation is dominant. The Rossby number, the ratio between inertial and Coriolis forces, is rather small O0.1. A well-known theorem valid in rotation-dominated flows was formulated by Proudman 1 and experimentally proven by Taylor; 2 it is known as the Taylor‐Proudman theo

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic moving-boundary problem that models crystal dissolution and precipitation. In doing so we derive a new weak formulation for this moving-boundary problem and we show that this formulation is well-posed. In addition, we develop a new uniqueness technique based on the framework of gradient flows with respect to the Wasserstein metric. With this uniqueness technique, the Wasserstein framework becomes a complete well-posedness setting for this parabolic moving-boundary problem.

Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below

We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular, the limiting current is essentially unique, has multiplicity one, and mass equal to the Hausdorff measure. Moreover, the limit spaces satisfy a constancy theorem.

Efimov Trimers in a Harmonic Potential

We study the Efimov effect in a harmonic oscillator in the hyperspherical formulation, and show how a reduced model allows for a description that is a generalization of the Efimov effect in free space and leads to results that are easily interpreted. Three-particle states that resemble Efimov trimers for large scattering length, become more similar to independent particles in a harmonic trap when adiabatically decreasing the scattering length. In the transition region, Efimov physics may be observed, while the increased size of the bound states reduces decay into more deeply bound states. The model also allows for the study of non-universal Efimov trimers by including the effective range scattering parameter. While we find that in a certain regime the effective range parameter can take over the role of the three-body parameter, interestingly, we obtain a numerical relationship between these two parameters different from what was found in other models.

Continuity of nonlinear eigenvalues in \({{\mathrm{CD}}}(K,\infty )\) spaces with respect to measured Gromov–Hausdorff convergence

In this note we prove in the nonlinear setting of

Embeddings of Riemannian manifolds with heat kernels and eigenfunctions

{{\mathrm{CD}}}(K,\infty )

Semicontinuity of eigenvalues under intrinsic flat convergence

CD(K,∞) spaces the stability of the Krasnoselskii spectrum of the Laplace operator