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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 obtain geometric lower bounds for the low Steklov eigenvalues of finite-volume hyperbolic surfaces with geodesic boundary. The bounds we obtain depend on the length of a shortest multi-geodesic disconnecting the surfaces into connected…
In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…
We study the free boundary Euler equations in two spatial dimensions. We prove that if the boundary is sufficiently regular, then solutions of the free boundary fluid motion converge to solutions of the Euler equations in a fixed domain…
Various recent experiments hint at a geometry dependence of scaling relations in Rayleigh-B\'enard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is offered which can account for such dependences.…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
A single-column model is used to investigate regime transitions within the stable atmospheric boundary layer, focusing on the role of small-scale fluctuations in wind and temperature dynamics and of turbulence intermittency as triggers for…
In this note, we discuss a poorly known alternative boundary condition to the usual Neumann or `stress-free' boundary condition typically used to weaken boundary layers when diffusion is present but very small. These `diffusion-free'…
A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes. The momentum and enthalpy balance equations are derived…
This is a chapter of a forthcoming Lecture Notes in Mathematics "Modern Approaches to Discrete Curvature" edited by L. Najman and P. Romon. It provides a survey on geometric and spectral consequences of curvature bounds. The geometric…
Since the prediction of climate is mainly considered as a prediction of second kind, it is indispensable to assess the accuracy with which these boundary conditions can be determined so that we can find a reasonable answer, whether climate…
We propose a phenomenological yet very general model in a form of generalized complex Ginzburg-Landau equation to understand the dynamics of the quasi-periodic fluid instabilities (called edge-localized modes) in the boundary of toroidal…
Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study,…
Embedding fields provide a way of coupling a background structure to a theory while preserving diffeomorphism-invariance. Examples of such background structures include embedded submanifolds, such as branes; boundaries of local subregions,…
We show that the properties of Lagrangian mean curvature flow are a special case of a more general phenomenon, concerning couplings between geometric flows of the ambient space and of totally real submanifolds. Both flows are driven by…
Understanding how submerged vegetation modifies the water surface is crucial for modeling momentum exchange between shallow waters and the atmosphere. In particular, quantifying its impact on the equivalent aerodynamic roughness of the…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain…
We investigate a mechanism to manipulate wall-bounded flows whereby wave-like undulations of the wall topography drives the creation of bespoke longitudinal vortices. A resonant interaction between the ambient vorticity of the undisturbed…