Publications related to Directed mean curvature flow in noisy environment

The Allen-Cahn equation with generic initial datum

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

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory

Johan Comparat, Jean-Paul Richard Kneib, Amélie Tamone, Anand Stéphane Raichoor, Andrei Variu, Cheng Zhao, Yuting Wang, Zheng Zheng

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Ly alpha forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of ...

American Physical Society2021

Standard model meets gravity: Electroweak symmetry breaking and inflation

Mikhail Chapochnikov, Andrey Shkerin, Sebastian Zell

We propose a model for combining the Standard Model (SM) with gravity. It relies on a nonminimal coupling of the Higgs field to the Ricci scalar and on the Palatini formulation of gravity. Without introducing any new degrees of freedom in addition to those ...

American Physical Society2021

Tribological Approach to the Watch Movements

Valentine Agnès Madeleine Magnin

Mechanical watches are complex and sensitive systems that have to maintain a faultless precision over their lifetime. However, this precision can be altered by disturbances occurring during the functioning time, such as friction, lubricant drying, or wear, ...

EPFL2020

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 Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

Out-of-plane instability of thin reinforced concrete walls under seismic loading

Angelica Rosso

Out of plane instability of reinforced concrete walls is a failure mechanism observed rather recently following the earthquakes in Chile (2010) and New Zealand (2011). Global out of plane instability is a phenomenon that may occur in thin walls, subjected ...

EPFL2018

Numerical Modelling of Two-Phase Flow with Moving Boundary Fitted Meshes

Erik Gros

In this thesis, a computational approach is used to study two-phase flow including phase change by direct numerical simulation. This approach follows the interface with an adaptive moving mesh. The incompressible Navier-Stokes equations are solved, in tw ...

EPFL2018

Gaussian Curvature as an Identifier of Shell Rigidity

Davit Harutyunyan

In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shell for zero or periodic Dirichlet, Neumann, and Robin type boundary conditions. ...

Springer Verlag2017

Axially equilibrated displacement-based beam element for simulating the cyclic inelastic behaviour of RC members

Katrin Beyer, João Saraiva Esteves Pacheco de Almeida, Danilo Tarquini

Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits since they directly relate to damage and are the ...

2017

Isogeometric Analysis for High Order Geometric Partial Differential Equations with Applications

Andrea Bartezzaghi

In this thesis, we consider the numerical approximation of high order geometric Partial Differential Equations (PDEs). We first consider high order PDEs defined on surfaces in the 3D space that are represented by single-patch tensor product NURBS. Then, we ...

EPFL2017

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

Preconditioned Low-Rank Riemannian Optimization For Linear Systems With Tensor Product Structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

Siam Publications2016

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

Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound

Daniele Valtorta

We complete the picture of sharp eigenvalue estimates for the -Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator when the Ricci curvature is bounded from below by a negative constant. We ...

Springer Verlag2014

The connectivity at infinity of a manifold and Sobolev inequalities

Marc Troyanov

The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an L-q,L-p-Sobolev inequality (2

Elsevier2014

Coupled equations for Kahler metrics and Yang-Mills connections

Mario Garcia Fernandez

We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler metric and Hermite-Yang-Mi ...

Geometry & Topology Publications2013

Phase-field modeling of micropore formation in a solidifying alloy

Hossein Meidani

This thesis is focused on the study of the morphology of micropores formed during solidification of metallic alloys. Micropores constrained to form in well-developed dendritic solid network adopt complex non-spherical shapes. Previous studies using X-ray t ...

EPFL2013