The Allen-Cahn equation with generic initial datum

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.

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 ...

We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased Spatial Whittle l ...

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 ...

Motivation: Large-scale kinetic models are an invaluable tool to understand the dynamic and adaptive responses of biological systems. The development and application of these models have been limited by the availability of computational tools to build and ...

The flow of a thin film coating the underside of an inclined substrate is studied. We measure experimentally spatial growth rates and compare them to the linear stability analysis of a flat film modelled by the lubrication equation. When forced by a statio ...

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 ...

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 ...

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.

...

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 ...

The dependence of curvature-induced secondary flow on the curvature ratio H/R (H is the average flow depth and R is the centreline radius of curvature), the Froude number Fr, and the dimensionless roughness coefficient Cf was systematically investigated in ...

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 ...

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 ...

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. ...

Realistic models of particle physics include many scalar fields. These fields generically have nonminimal couplings to the Ricci curvature scalar, either as part of a generalized Einstein theory or as necessary counterterms for renormalization in curved ba ...

In this paper we define a scale-space for cortical mean curvature maps on the sphere, that offers a hierarchical representation of the brain cortical structures, useful in multi-scale registration and analysis algorithms. A spherical feature map is obtaine ...

We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit viable metastable vacua with spontaneously broken supersymmetry and realistic cosmological constant. To do so, we impose that on the vacuum th ...

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 ...

The Allen-Cahn equation with generic initial datum

Chattez avec Graph Search

Directed mean curvature flow in noisy environment

The Debiased Spatial Whittle likelihood

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

Symbolic kinetic models in python (SKiMpy): intuitive modeling of large-scale biological kinetic models

Instability of a thin viscous film flowing under an inclined substrate: steady patterns

Robustness via curvature regularization, and vice versa

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

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

Isogeometric Analysis of geometric partial differential equations

A parametrical study on secondary flow in sharp open-channel bends: experiments and theoretical modelling

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

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

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

Primordial perturbations from multifield inflation with nonminimal couplings

A Scale-Space of Cortical Feature Maps

Metastable supergravity vacua with F and D supersymmetry breaking

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