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Concept

Curve-shortening flow

Related publications (10)

The Allen-Cahn equation with generic initial datum

Martin Hairer

We consider the Allen-Cahn equation ?(t)u - ?u = u - u(3) with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets o ...

SPRINGER HEIDELBERG2023

Directed mean curvature flow in noisy environment

Martin Hairer

We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole-Hopf solution of the KPZ equati ...

Wiley2023

Effects of aquifer geometry on seawater intrusion in annulus segment island aquifers

David Andrew Barry, Zhaoyang Luo

Seawater intrusion in island aquifers was considered analytically, specifically for annulus segment aquifers (ASAs), i.e., aquifers that (in plan) have the shape of an annulus segment. Based on the Ghijben–Herzberg and hillslope-storage Boussinesq equation ...

2021

Robustness via curvature regularization, and vice versa

Pascal Frossard, Alhussein Fawzi, Seyed Mohsen Moosavi Dezfooli

State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the ...

IEEE2019

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Isogeometric Analysis of geometric partial differential equations

Alfio Quarteroni, Luca Dede', Andrea Bartezzaghi

We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2L2-gradient flow. We a ...

Elsevier2016

Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

Joachim Krieger, Roland Donninger, Willie Wai Yeung Wong

We study time-like hypersurfaces with vanishing mean curvature in the (3+1) dimensional Minkowski space, which are the hyperbolic counterparts to minimal embeddings of Riemannian manifolds. The catenoid is a stationary solution of the associated Cauchy pro ...

Duke Univ Press2015

On stability of the catenoid under vanishing mean curvature flow on Minkowski space

Joachim Krieger

We establish basic local existence as well as a stability result concerning small perturbations of the Catenoid minimal surface in R-3 under hyperbolic vanishing mean curvature flow. ...

International Press2012

An experimental study on main flow, secondary flow and turbulence in open-channel bends with emphasis on their interaction with the outer-bank geometry

This research focus on the influence of bank inclination and roughness on the near-bank flow patterns which is relevant for bank protection, bank erosion and design of stable river configuration. Foregoing studies have been carried out mostly in rectangula ...

EPFL2008

Particle migration in a concentrated suspension flowing between rotating parallel plates: Investigation of diffusion flux coefficients

Etienne Pierre Lemaire

This paper reports an experimental and numerical study conducted to investigate the behavior of macroscopic monomodal concentrated suspensions (40%) undergoing a creeping torsional flow between two rotating plates. An experimental technique based on the de ...

2005