Critical Phenomena in Morphology Transitions of Growth Models with Competition

Saitō, Yukio; Müller‐Krumbhaar, H.

doi:10.1103/physrevlett.74.4325

Cited by 55 publications

(105 citation statements)

References 13 publications

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“…This consists in covering, without overlapping, the whole cluster by squares of same sizes, and counting the number of squares which have at least one nip +1 (or −1), then modify the square sizes. We have distinguished between the fractal This value is similar to that obtained in binary Eden growth models [61,62] and in simple ballistic deposition models [60].…”

Section: Fractal Dimensionsupporting

confidence: 59%

“…A 2D pile of these entities is built by vertically depositing grains from an extended horizontal source, with the help of a Metropolis rule. This ballistic deposition process should not be confused with the binary Eden growth model on a 1D substrate [61], later on extended toward the case of a central seed growth [62] in 2D, nor with other chemical deposition models. During the present deposition process the grain can change its direction (the grain can rotate from vertical to horizontal, or conversely, whence the nip changes from +1 to −1 or conversely) with some probability q.…”

Section: Introductionmentioning

confidence: 99%

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Exponential and Power Law Distribution of Mass Clusters in a (Magnetic-Like) Deposition Model of Elongated Grains in 2d Piles

Trojan¹,

Ausloos²,

Cloots³

2004

Int. J. Mod. Phys. C

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A generalized so called magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, called "nip", their interaction being described through a Hamiltonian. Results are discussed in order to search for the effect of nip flip (or grain rotation from vertical to horizontal and conversely) probability in building a granular pile. The characteristics of creation of + (or −) nip's clusters and clusters of holes (missing nips) are analyzed. Two different cluster-mass regimes have been identified, through the cluster-mass distribution function which can be exponential or have a power law form depending on whether the nip flip (or grain rotation) probability is large or small. Analytical forms of the exponent are empirically found in terms of the Hamiltonian parameters.

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Section: Fractal Dimensionsupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Exponential and Power Law Distribution of Mass Clusters in a (Magnetic-Like) Deposition Model of Elongated Grains in 2d Piles

Trojan¹,

Ausloos²,

Cloots³

2004

Int. J. Mod. Phys. C

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“…Then evolution of the domain size on the surface is of interest. The scaling in this case has been recently studied by Saito and Müller-Krumbhaar [9] in another generalization of the Eden model (different from MEM). They obtained ψ = 2/3 for growth of domain size, but they did not investigate kinetic roughening.…”

mentioning

confidence: 99%

“…We are not going to model growth of any specific material but we shall concentrate on the scaling behaviour. The problem of growth in a system with two or more components is interesting from pure statistical-mechanical point of view, because growth process may belong to a new universality class [7,8,9]; such system might also exhibit a nonequilibrium phase transition between the low and high temperature region.…”

mentioning

confidence: 99%

Interplay between kinetic roughening and phase ordering

Kotrla

Předota

1997

Europhys. Lett.

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PACS. 05.70L -Nonequilibrium thermodynamics, irreversible processes. PACS. 75.70Kw -Domain structure. PACS. 75.40M -Numerical simulation studies.Abstract. -We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties was investigated by Monte Carlo simulations for various strengths of coupling. We found that the initial growth is strongly affected by interaction between species, scaling exponents are enhanced and the ordering on the surface is observed. However, after certain time, ordering along the surface stops and the scaling exponents cross over to exponents of the Kardar-Parisi-Zhang universality class. For sufficiently strong strength of coupling, ordering in vertical direction is present and leads to columnar structure persisting for a long time.Recently there has been considerable interest in growth induced surface roughening called kinetic roughening [1] and in phase ordering [2] independently. In kinetic roughening one is interested in the evolution of roughness during a nonequilibrium growth process. Phase ordering deals with the approach to equilibrium of a system quenched from a homogeneous high temperature phase into a two-component region. In both fields concept of scaling allowed to classify physical processes into universality classes. However, not very much is known so far about scaling exponents in systems where both processes, roughening as well as ordering, are relevant.Growth of many-component systems is in fact quite common situation. Many real materials are composed of two or more components but often the dynamics of one component is dominant and one can use a single-component growth model. For example, one can consider only kinetics of Ga atoms in studies of GaAs growth [3]. We are interested here in a more complex case when dynamics of Typeset using EURO-L a T E X

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“…A less well studied phenomenon is the competing growth of two materials. The interface between two growing clusters (competition interface) presents a random direction on the same scale as the deterministic shape [3,12,17]. In this letter we describe quite explicitly this phenomenon in a simple model.…”

mentioning

confidence: 92%

Roughening and inclination of competition interfaces

2006

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We study the competition interface between two clusters growing over a random vacant sector of the plane in a simple set-up which allows us to perform formal computations and obtain analitical solutions. We demonstrate that a phase transition occurs for the asymptotic inclination of this interface when the final macroscopic shape goes from curved to non curved. In the first case it is random while in the second one it is deterministic. We also show that the flat case (stationary growth) is a critical point for the fluctuations: for curved and flat final profiles the fluctuations are in the KPZ scale (2/3); for non curve final profile the fluctuations are in the same scale of the fluctuations of the initial conditions, which in our model are Gaussian (1/2). Introduction The behavior of the interface of a growing material has been investigated using the Eden model [4], ballistic deposition and other random systems. Typically, the growing region converges to an asymptotic deterministic shape and its fluctuations depend on the geometry of the initial condition [11,13]. A less well studied phenomenon is the competing growth of two materials. The interface between two growing clusters (competition interface) presents a random direction on the same scale as the deterministic shape [3,12,17]. In this letter we describe quite explicitly this phenomenon in a simple model. On gronds of universality, this will provide a guide to understand the interplay between the asymptotics of the competition interface and the final macroscopic shape in models with different growth and competition mechanisms.

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Critical Phenomena in Morphology Transitions of Growth Models with Competition

Cited by 55 publications

References 13 publications

Exponential and Power Law Distribution of Mass Clusters in a (Magnetic-Like) Deposition Model of Elongated Grains in 2d Piles

Exponential and Power Law Distribution of Mass Clusters in a (Magnetic-Like) Deposition Model of Elongated Grains in 2d Piles

Interplay between kinetic roughening and phase ordering

Roughening and inclination of competition interfaces

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