Related papers: Artificial eigenmodes in truncated flow domains
In this paper, we study the forced mean curvature flows and the prescribed mean curvature equations of both graphs and level-sets with capillary-type boundary conditions on a $C^3$ bounded domain, which is not necessarily convex. We prove a…
The purpose of this paper is to explore the asymptotics of the eigenvalue spectrum of the Laplacian on 2 dimensional spaces of constant curvature, giving strong experimental evidence for a conjecture of the second author…
We study the half-plane problem for the elastic wave equation subject to a free surface boundary condition, with particular emphasis on almost incompressible materials. A normal mode analysis is developed to estimate the solution in terms…
We study asymptotically slowly varying perturbations of the AdS black brane in Einstein's gravity with a negative cosmological constant. We allow both the induced metric and the Brown-York stress tensor at a given radial cut-off slice to…
Effects of truncation in self-similar continuous unitary transformations (S-CUT) are estimated rigorously. We find a formal description via an inhomogeneous flow equation. In this way, we are able to quantify truncation errors within the…
The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude, and the low-amplitude oblique traveling modes with the same…
The extreme heat fluxes characteristic of hypersonic flows significantly limit the flight envelope of hypersonic vehicles. The role of hydrodynamic instability and the onset of laminar to turbulent boundary layer transition is of notable…
Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking…
Large-eddy simulations of the atmospheric boundary layer are often performed using pseudo-spectral methods, which adopt a fringe-region approach to introduce inflow boundary conditions. However, we notice that a standard fringe-region…
Direct numerical simulations are carried out to investigate the flow features responsible for secondary tones arising in trailing-edge noise at moderate Reynolds numbers. Simulations are performed for a NACA 0012 airfoil at freestream Mach…
This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…
In this paper, we study an eigenvalue problem with piecewise constant coefficients on thin domains with Neumann boundary condition, and we analyze the asymptotic behavior of each eigenvalue as the domain degenerates into a certain…
The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…
We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide $\Pi_{l}^{\varepsilon}$ obtained from a straight unit strip by a low box-shaped perturbation of size $2l\times\varepsilon,$ where $\varepsilon>0$ is…
We study a heretofore ignored class of spiral patterns for oscillatory media as characterized by the complex Landau-Ginzburg model. These spirals emerge from modulating the growth rate as a function of $r$, thereby turning off the…
Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes…
Resonances, isolated eigenvalues of a transfer operator acting on suitably chosen Banach spaces, play a fundamental role in understanding the statistical properties of chaotic dynamical systems. In this paper, we introduce a pseudospectral…
The bulk boundary correspondence, one of the most significant features of topological matter, theoretically connects the existence of edge modes at the boundary with topological invariants of the bulk spectral bands. However, it remains…
The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including L\'evy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which…
A bypass transition scenario in a wind-stress driven aqueous flow is analysed using a temporally developing boundary layer model with accelerating surface drift velocity. The parameters of the model are selected to mimic a wave-tank…