منابع مشابه
Slow crossover to Kardar-Parisi-Zhang scaling.
The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that associated with the KPZ equation. A feature common to these studies is the presence of holes (bubbles and overhangs) in the bulk and an interface that is smeared out....
متن کاملA Modified Kardar–parisi–zhang Model
A one dimensional stochastic differential equation of the form dX = AXdt+ 1 2 (−A) ∂ξ[((−A)X)]dt+ ∂ξdW (t), X(0) = x is considered, where A = 1 2∂ 2 ξ . The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar–Parisi–Zhang model. For α 6= 0, this equation conserves two important properties of the Kardar–Parisi–Zhang model: it contains a quadratic...
متن کامل1/f power spectrum in the Kardar-Parisi-Zhang universality class
The power spectrum of interface fluctuations in the (1 + 1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class is studied both experimentally and numerically. The 1/f-type spectrum is found and characterized through a set of “critical exponents” for the power spectrum. The recently formulated “aging WienerKhinchin theorem” accounts for the observed exponents. Interestingly, the 1/f spectr...
متن کاملNon-order parameter Langevin equation for a bounded Kardar-Parisi-Zhang universality class
We introduce a Langevin equation describing the pinning-depinning phase transition experienced by Kardar-Parisi-Zhang interfaces in the presence of a bounding “lower-wall”. This provides a continuous description for this universality class, complementary to the different and already well documented one for the case of an “upper-wall”. The Langevin equation is written in terms of a field that is...
متن کاملExtremal paths, the stochastic heat equation, and the three-dimensional Kardar-Parisi-Zhang universality class.
Following our numerical work [Phys. Rev. Lett. 109, 170602 (2012)] focused upon the 2+1 Kardar-Parisi-Zhang (KPZ) equation with flat initial condition, we return here to study, in depth, the three-dimensional (3D) radial KPZ problem, comparing common scaling phenomena exhibited by the pt-pt directed polymer in a random medium (DPRM), the stochastic heat equation (SHE) with multiplicative noise ...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2016
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti1334