Pinning of interfaces in a random medium with zero mean

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

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.

• Jezik: Angleški jezik
• Ključne besede: Quenched Edwards–Wilkinson model, phase boundaries, pinning, random environment, viscosity super-solutions
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FGG - Fakulteta za gradbeništvo in geodezijo
• Leto izida: 2021
• Št. strani: Str. 305-321
• Številčenje: Vol. 23, iss. 3
• PID: 20.500.12556/RUL-135491
• UDK: 51
• ISSN pri članku: 1463-9963
• DOI: 10.4171/IFB/455
• COBISS.SI-ID: 92464899
• Datum objave v RUL: 16.03.2022

Gradivo je del revije

• Naslov: Interfaces and free boundaries
• Skrajšan naslov: Interfaces free bound.
• Založnik: Oxford University Press, EMS Publishing House
• ISSN: 1463-9963
• COBISS.SI-ID: 512083993

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: matematika, gradbeništvo, Edwards-Wilkinsonov model, meje faz, vkleščenost, slučajno okolje, super-rešitve v viskoznem smislu