Pinning of interfaces in a random medium with zero mean

Dondl, Patrick W. (author), Jesenko, Martin (author), Scheutzow, Michael (author)

We consider two related models for the propagation of a curvature sensitive interface in a time independent random medium. In both cases we suppose that the medium contains obstacles that act on the propagation of the interface with an inhibitory or an acceleratory force. We show that the interface remains bounded for all times even when a small constant external driving force is applied. This phenomenon has already been known when only inhibitory obstacles are present. In this work we extend this result to the case of – for example – a random medium of random zero mean forcing. The first model we study is discrete with a random forcing on each lattice site. In this case we construct a supersolution employing a local path optimization procedure. In the second, continuous, model we consider a random heterogenous medium consisting of localized small obstacles of random sign. To construct a stationary supersolution here, we need to pass through sufficiently many blocking obstacles while avoiding any obstacles of the other sign. This is done by employing a custom percolation argument.

• Language: English
• Keywords: Quenched Edwards–Wilkinson model, phase boundaries, pinning, random environment, viscosity super-solutions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Year: 2021
• Number of pages: Str. 305-321
• Numbering: Vol. 23, iss. 3
• PID: 20.500.12556/RUL-135491
• UDC: 51
• ISSN on article: 1463-9963
• DOI: 10.4171/IFB/455
• COBISS.SI-ID: 92464899
• Publication date in RUL: 16.03.2022

Record is a part of a journal

• Title: Interfaces and free boundaries
• Shortened title: Interfaces free bound.
• Publisher: Oxford University Press, EMS Publishing House
• ISSN: 1463-9963
• COBISS.SI-ID: 512083993

Secondary language

• Language: Slovenian
• Keywords: matematika, gradbeništvo, Edwards-Wilkinsonov model, meje faz, vkleščenost, slučajno okolje, super-rešitve v viskoznem smislu