Kardar, Parisi, and Zhang Respond

Kardar, Mehran; Parisi, Giorgio; Zhang, Yi Cheng

doi:10.1103/physrevlett.57.1810

Cited by 623 publications

(1,072 citation statements)

References 2 publications

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“…The slope of the intensity decay gives access to the roughness parameter h. Curves calculated from eqn. Logarithmic roughness is expected for systems growing according to the linear version of the growth equation of Kardar, Parisi, and Zhang (KPZ) in 2+1 dimensions [9]. The results of the Q,-resolved data also indicate that the growth of the multilayer was govered by the KPZ equation.…”

Section: Resultssupporting

confidence: 52%

Characterization of roughness correlations in W/Si multilayers by diffuse x-ray scattering

Salditt¹,

Metzger²,

Peisl³

1994

J. Phys. IV France

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Abstract:We present diffuse, nonspecular x-ray measurements of the interface height-height self-correlations in an amorphous WlSi multilayer. The measurements have been performed in a scattering geometry that is placed out of the plane of reflection, giving access to a much larger range in parallel momentum transfer than in conventional nonspecular geometries. For the sample studied a logarithmic form of the correlation function is found.

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Section: Resultssupporting

confidence: 52%

Characterization of roughness correlations in W/Si multilayers by diffuse x-ray scattering

Salditt¹,

Metzger²,

Peisl³

1994

J. Phys. IV France

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“…(31) reduce to the EK [3] equations. Although the complete phase diagram of the latter is not known, they do have a locally stable renormalization-group fixed point belonging to the universality class of the KPZ equation [16], with χ + = χ − = 1/2 and z + = z − = 3/2. Secondly, in the absence of the nonlinear terms coupling h + and h − , the kinematic wave terms can be removed separately in each equation by opposite Galilean transformations, yielding scaling properties independent of the wavespeed.…”

Section: Analytical Demonstration Of Weak Dynamic Scalingmentioning

confidence: 99%

“…The most relevant terms at the linear fixed point are the quadratic nonlinear terms. Thus we would expect that these terms would govern the dissipation and give rise to the Kardar-Parisi-Zhang (KPZ) value z = 3/2 [16] for both the modes.…”

Section: A Symmetries Of the Equationsmentioning

confidence: 99%

Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves

et al. 2001

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We study the coupled dynamics of the displacement fields in a one dimensional coupled-field model for drifting crystals, first proposed by R. S.Ramaswamy [Phys. Rev. Lett. 79, 1150 (1997)]. We present some exact results for the steady state and the current in the lattice version of the model, for a special subspace in the parameter space, within the region where the model displays kinematic waves. We use these to construct the effective continuum equations corresponding to the lattice model. These equations decouple at the linear level in terms of the eigenmodes. We examine the long-time, large-distance properties of the correlation functions of the eigenmodes by using symmetry arguments, Monte Carlo simulations and self-consistent mode coupling methods. For most parameter values, the scaling exponents of the Kardar-Parisi-Zhang equation are obtained. However, for certain symmetry-determined values of the coupling constants the two eigenmodes, although nonlinearly coupled, are characterized by two distinct dynamic exponents. We discuss the possible application of the dynamic renormalization group in this context.

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“…2. We have also checked that similar scaling collapses occur when we use other models of surface fluctuations with widely different values of z (z = 3/2 for KardarParisi-Zhang (KPZ) [11] surfaces, and z ≃ 4 for the Das Sarma-Tamborenea model [12]). …”

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confidence: 99%

Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws

2000

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We study a system of hard-core particles sliding downwards on a fluctuating one-dimensional surface which is characterized by a dynamical exponent z. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale ∼ t 1/z . The structure factor deviates from the Porod law in some cases. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provides insight into the origin of this behaviour.PACS numbers: 05.70. Ln, 64.75.+g, 05.70.Jk How do density fluctuations evolve in a system of particles moving on a fluctuating surface? Can the combination of random vibrations and an external force such as gravity drive the system towards a state with large-scale clustering of particles? Such large-scale clustering driven by a fluctuating potential represents an especially interesting possibility for the behaviour of two coupled systems, one of which evolves autonomously but influences the dynamics of the other. Semi-autonomous systems are currently of interest in diverse contexts, for instance, advection of a passive scalar by a fluid [1], phase ordering in rough films [2], the motion of stuck and flowing grains in a sandpile [3], and the threshold of an instability in a sedimenting colloidal crystal [4].In this paper, we show that there is an unusual sort of phase ordering in a simple model of this sort, namely a system of particles sliding downwards under a gravitational field on a fluctuating one-dimensional surface. The surface evolves through its own dynamics, while the motion of particles is guided by local downward slopes; since random surface vibrations cause slope changes, they constitute a source of nonequilibrium noise for the particle system. The mechanism which promotes clustering is simple: fluctuations lead particles into potential minima or valleys, and once together the particles tend to stay together as illustrated in Fig. 1. The question is whether this tendency towards clustering persists up to macroscopic scales. We show below that in fact the particle density exhibits coarsening towards a phase-ordered state. This state has uncommonly large fluctuations which affect its properties in a qualitative way, and make it quite different from that in other driven, conserved, systems which exhibit coarsening [5].It is useful to state our principal results at the outset. (1) In an infinite system, an initially randomly distributed particle density exhibits coarsening with a characteristic growing length scale L(t) ∼ t 1/z where z is the dynamical exponent governing fluctuations of the surface. For some of the models we study, the scaled structure factor varies as |kL(t)| −(1+α) with α < 1, which represents a marked deviation from the Porod law (α = 1) for coarsening systems [6]. Further, a finite...

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Kardar, Parisi, and Zhang Respond

Cited by 623 publications

References 2 publications

Characterization of roughness correlations in W/Si multilayers by diffuse x-ray scattering

Characterization of roughness correlations in W/Si multilayers by diffuse x-ray scattering

Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves

Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws

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