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We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…

Analysis of PDEs · Mathematics 2025-01-28 Vinh Nguyen , Keith Promislow , Brian Wetton

The effect of geometry in the statistics of \textit{nonlinear} universality classes for interface growth has been widely investigated in recent years and it is well known to yield a split of them into subclasses. In this work, we…

Statistical Mechanics · Physics 2019-10-16 I. S. S. Carrasco , T. J. Oliveira

The universality of intermittency in hydrodynamic turbulence is considered based on a recent model for the velocity gradient tensor evolution. Three possible versions of the model are investigated differing in the assumed correlation…

Fluid Dynamics · Physics 2007-05-23 Laurent Chevillard , Charles Meneveau

We further study the interfaces arising in a situation of inhomogeneity. More precisely, we identify a characteristic length for the gradient percolation model, that enables us to tighten previous estimates established for it. This allows…

Probability · Mathematics 2009-07-10 Pierre Nolin

The response of spatially extended systems to a force leading their steady state out of equilibrium is strongly affected by the presence of disorder. We focus on the mean velocity induced by a constant force applied on one-dimensional…

Understanding possible universal properties for systems far from equilibrium is much less developed than for their equilibrium counterparts and poses a major challenge to present day statistical physics. The study of aging properties, and…

Statistical Mechanics · Physics 2017-03-22 Jacopo De Nardis , Pierre Le Doussal , Kazumasa A. Takeuchi

Frictional interfaces are abundant in natural and manmade systems and their dynamics still pose challenges of fundamental and technological importance. A recent extensive compilation of multiple-source experimental data has revealed that…

Materials Science · Physics 2015-01-20 Yohai Bar-Sinai , Robert Spatschek , Efim A. Brener , Eran Bouchbinder

Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards…

Materials Science · Physics 2025-07-08 Oğuz Umut Salman , Alphonse Finel , Lev Truskinovsky

We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely…

Statistical Mechanics · Physics 2023-10-06 Rahul Chhimpa , Avinash Chand Yadav

A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $\xi \sim \exp\left(A…

Condensed Matter · Physics 2009-10-28 E. D. Moore , R. B. Stinchcombe , S. L. A. de Queiroz

This paper concerns the asymmetric transport associated with a low-energy interface Dirac model of graphene-type materials subject to external magnetic and electric fields. We show that the relevant physical observable, an interface…

Mathematical Physics · Physics 2024-05-22 Solomon Quinn , Guillaume Bal

We report experimental evidences of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists on a random modulation of the gap spacing…

Disordered Systems and Neural Networks · Physics 2016-08-16 Jordi Soriano , Jordi Ortín , A. Hernández-Machado

A theoretical model is proposed to explain the roughness characteristics of an ice surface grown from a gravity and wind-driven supercooled water film flowing over an inclined plane. The effects of the water supply rate, plane slope and air…

Fluid Dynamics · Physics 2015-03-19 K. Ueno , M. Farzaneh

We review in these notes some dynamical properties of interfaces in random media submitted to an external force. We focuss in particular to the response to a very small force (so called creep motion) and discuss various theoretical aspects…

Disordered Systems and Neural Networks · Physics 2009-11-11 T. Giamarchi , A. B. Kolton , A. Rosso

For sedimenting colloidal hard spheres, the propagation and broadening of the crystal-fluid interface is studied by Brownian dynamics computer simulations of an initially homogeneous sample. Two different types of interface broadenings are…

Soft Condensed Matter · Physics 2015-05-28 Elshad Allahyarov , Hartmut Löwen

The Edwards-Wilkinson (EW) growth of $1+1$ interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a…

Statistical Mechanics · Physics 2021-05-20 N. Valizadeh , M. Samadpour , H. Hamzehpour , M. N. Najafi

We present an introduction to modern theories of interfacial fluctuations and the associated interfacial parameters: surface tension and surface stiffness, as well as their interpretation within the capillary wave model. Transfer matrix…

Condensed Matter · Physics 2014-10-13 Vladimir Privman

Turbulence is omnipresent in Nature and technology, governing the transport of heat, mass, and momentum on multiple scales. For real-world applications of wall-bounded turbulence, the underlying surfaces are virtually always rough; yet…

Inspired by the chemical etching processes, where experiments show that growth rates depending on the local environment might play a fundamental role in determining the properties of the etched surfaces, we study here a model for kinetic…

Statistical Mechanics · Physics 2007-05-23 Raffaele Cafiero

We consider an interface above an attractive hard wall in the complete wetting regime, and submitted to the action of an external increasing, convex potential, and study its delocalization as the intensity of this potential vanishes. Our…

Probability · Mathematics 2011-08-25 Yvan Velenik