Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions
arXiv:2205.07355 · doi:10.1088/1742-5468/ad4af9
Abstract
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to growth rule, and compare the estimated values with the previous numerical and experimental results. For the (2+1)-dimensional case, we perform extensive simulations on pinning-depinning transitions in these { discrete models with quenched disorder}. For full comparisons in the physically relevant spatial dimensions, we also perform numerically two distinct universality classes, including the quenched Edwards-Wilkinson (QEW), and the quenched Kardar-Parisi-Zhang (QKPZ) equations with and without external driving forces. The critical exponents of these {systems in the presence of quenched disorder} are numerically estimated. Our results show that the critical exponents satisfy scaling relations well, and these two discrete elastic-string models do not fall into the existing universality classes. In order to visually comparisons of these {discrete systems with quenched disorder} in the (2+1)-dimensional cases, we present surface morphologies with various external driving forces during the saturated time regimes. The relationships between surface morphologies, scaling exponents and correlation length are also revealed.
References in corpus (32)
- Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
- Statistical Models of Fracture
- The one-dimensional KPZ equation: an exact solution and its universality
- Inhomogeneity of charge density wave order and quenched disorder in a high Tc superconductor
- Generic Dynamic Scaling in Kinetic Roughening
- Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
- Two-dimensional melting under quenched disorder
- Origin of the roughness exponent in elastic strings at the depinning threshold
- Width distribution of contact lines on a disordered substrate
- Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
- Effective toughness of heterogeneous brittle materials
- Non-steady relaxation and critical exponents at the depinning transition
- Inter-event correlations from avalanches hiding below the detection threshold
- Numerical Approaches on Driven Elastic Interfaces in Random Media
- Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
- Short time relaxation of a driven elastic string in a random medium
- From microstructural features to effective toughness in disordered brittle solids
- Depinning exponents of the driven long-range elastic string
- The depinning transition in presence of disorder: a toy model
- Functional renormalization group for anisotropic depinning and relation to branching processes
- Skyrmion relaxation dynamics in the presence of quenched disorder
- Observation of strongly heterogeneous dynamics at the depinning transition in a colloidal glass
- Interface Scaling in the Contact Process
- Domain growth and aging scaling in coarsening disordered systems
- Dynamics of edge current in a linearly quenched Haldane model
- Universal scaling of the velocity field in crack front propagation
- Static properties of 2D spin-ice as a sixteen-vertex model
- Pinning time statistics for vortex lines in disordered environments
- Interface Depinning in the Absence of External Driving Force
- Depinning in the quenched Kardar-Parisi-Zhang class I: Mappings, simulations and algorithm
- Critical Scaling and Aging near the Flux Line Depinning Transition
- The role of the non-linearity in controlling the surface roughness in the one-dimensional Kardar--Parisi--Zhang growth process