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We study two relaxation problems in the class of partially dissipative hyperbolic systems: the compressible Euler system and the compressible Euler-Maxwell system. In classical Sobolev spaces, we derive a global convergence rate of…
We design and analyse an energy stable, structure preserving, well-balanced and asymptotic preserving (AP) scheme for the barotropic Euler system with gravity in the anelastic limit. The key to energy stability is the introduction of…
We study a system of particles in the interval $[0,\epsilon^{-1}] \cap \mathbb Z$, $\epsilon^{-1}$ a positive integer. The particles move as symmetric independent random walks (with reflections at the endpoints); simultaneously new…
In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler…
We use dynamic light scattering and computer simulations to study equilibrium dynamics and dynamic heterogeneity in concentrated suspensions of colloidal hard spheres. Our study covers an unprecedented density range and spans seven decades…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler…
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic…
In symmetric gravitating systems experiencing rapid mass loss, particle orbits change almost instantaneously, which can lead to the development of a sharply contoured density profile, including singular caustics for collisionless systems.…
Pauli's exclusion principle forces fermions to occupy distinct quantum states, creating a filled region of momentum space at low temperature, the Fermi sea, whose topology governs the system's response to perturbations and the nature of its…
Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces…
We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the energy surface is identified with a Reeb flow on the tight…
There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are…
We employ small-angle X-ray and dynamic light scattering to investigate the microscopic structure and dynamics of dense suspensions of ultra-low crosslinked (ULC) poly(N-isopropylacrylamide) (PNIPAM) microgels. By probing the supercooled…
Fix a bounded, analytic, and simply connected domain $\Omega\subset\mathbb{R}^2.$ We show that all analytic steady states of the Euler equations with stream function $\psi$ are either radial or solve a semi-linear elliptic equation of the…
We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in…
For expectation functions on metric spaces, we provide sufficient conditions for epi-convergence under varying probability measures and integrands, and examine applications in the area of sieve estimators, mollifier smoothing,…
This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…
We prove that the divergence-free component of the compressible Euler equations with solid-wall boundary condition converges strongly towards the incompressible Euler equations at the same order as the Mach number. General initial data are…
The confinement of elementary excitations induces distinctive features in the non-equilibrium quench dynamics. One of the most remarkable is the suppression of entanglement entropy which in several instances turns out to oscillate rather…