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Related papers: Patterns in the Kardar-Parisi-Zhang equation

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We have studied the Kardar-Parisi-Zhang equation in the strong coupling regime in the mode-coupling approximation. We solved numerically in dimension d=1 for the correlation function at wavevector k. At large times t we found the predicted…

Statistical Mechanics · Physics 2009-11-07 Francesca Colaiori , M. A. Moore

A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the…

Condensed Matter · Physics 2009-10-28 M. Marsili , A. J. Bray

We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface,…

Statistical Mechanics · Physics 2018-08-08 J. Whitehouse , R. A. Blythe , M. R. Evans , D. Mukamel

The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its…

Statistical Mechanics · Physics 2017-06-26 R. A. L. Almeida , S. O. Ferreira , I. Ferraz , T. J. Oliveira

We study the surface dynamics of silica films grown by low pressure chemical vapor deposition. Atomic force microscopy measurements show that the surface reaches a scale invariant stationary state compatible with the Kardar-Parisi-Zhang…

Statistical Mechanics · Physics 2009-10-31 Fernando Ojeda , Rodolfo Cuerno , Roberto Salvarezza , Luis Vazquez

We investigate the noisy Burgers equation (Kardar--Parisi--Zhang equation in 1+1 dimensions) using the dynamical renormalization group (to two--loop order) and mode--coupling techniques. The roughness and dynamic exponent are fixed by…

Condensed Matter · Physics 2009-10-28 Erwin Frey , Uwe Claus Täuber , Terence Hwa

Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give…

We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav

Inspired by the recent results on totally asymmetric simple exclusion processes on a periodic lattice with short-ranged quenched hopping rates [A. Haldar, A. Basu, Phys Rev Research 2, 043073 (2020)], we study the universal scaling…

Statistical Mechanics · Physics 2021-08-18 Astik Haldar

We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from…

Statistical Mechanics · Physics 2009-11-11 Satya N. Majumdar , Chandan Dasgupta

In its original version the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over past years the corresponding two-dimensional field theory has been applied to models with different…

Statistical Mechanics · Physics 2020-06-24 Herbert Spohn

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…

Statistical Mechanics · Physics 2014-12-23 I. S. S. Carrasco , K. A. Takeuchi , S. C. Ferreira , T. J. Oliveira

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been…

Statistical Mechanics · Physics 2026-04-08 Ricardo Gutierrez , Rodolfo Cuerno

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved…

Statistical Mechanics · Physics 2013-05-15 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

We introduce a new kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-…

Statistical Mechanics · Physics 2009-10-31 H. Kaya , A. Kabakcioglu , A. Erzan

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and…

Probability · Mathematics 2023-06-08 Kohei Hayashi

In this work we write down a classical (not quantum) action for the surface height for the Kardar-Parisi-Zhang (KPZ) equation for surface growth. We do so starting with the regular Martin-Siggia-Rose (MSR) action (which is quantum -…

Statistical Mechanics · Physics 2024-05-06 Garry Goldstein

We present results from extensive numerical integration of the KPZ equation in $1 + 1$ dimensions aimed to check the long-time behavior of the dynamical structure factor of that system. Over a number of decades in the size of the structure…

Statistical Mechanics · Physics 2008-04-21 Eytan Katzav , Moshe Schwartz

The conserved Kardar-Parisi-Zhang equation in the presence of long-range nonlinear interactions is studied by the dynamic renormalization group method. The long-range effect produces new fixed points with continuously varying exponents and…

Statistical Mechanics · Physics 2009-10-31 Youngkyun Jung , In-mook Kim , Jin Min Kim