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

Trojan, Kamil; Ausloos, Marcel; Cloots, Rudi

doi:10.1142/s0129183104006571

Cited by 3 publications

(5 citation statements)

References 71 publications

(114 reference statements)

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“…I. No relaxation -the no-relaxation process is the pure q-MBD, [7], i.e. the spin sticks to the cluster immediately.…”

Section: Methodsmentioning

confidence: 99%

“…A crossover effect likewise occurs in presence of relaxation. The whole data analysis is not reproduced here; it was done as for the case I in [7]. The differences are particularly noticeable in the power law region i.e.…”

Section: The Size (Mass) Distribution Of Clustersmentioning

confidence: 99%

“…We have studied such a model [6,7], within a (magnetic) ballistic deposition process; it is similar to the Tetris model [8], but more simplified. Basically the (2-dimensional) grains are anisotropic and are deposited vertically as in a gravity controlled rain.…”

Section: Introductionmentioning

confidence: 99%

“…We have previously examined clustering effects as in [6,7], through the cluster fractal dimension, the pile overall density, the distribution of grain orientations, ... and have found through percolation arguments [10,11] the existence of different cluster growth "mechanisms".…”

Section: Introductionmentioning

confidence: 99%

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Effects of relaxation processes during deposition of anisotropic grains on a flat substrate

Trojan

Ausloos

2005

Physica A: Statistical Mechanics and its Applications

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The ballistic deposition on a one dimensional substrate of grains with one degree of freedom, called spin, is studied with respect to relaxation processes during deposition. The "spin" represents the grain anisotropy, e.g. its longest axis with respect to the vertical. The grains interact through some contact energy (J) and are allowed to flip with a probability q during deposition and relaxation. Different relaxation processes are investigated. The pile structure is investigated, i.e. the density and "magnetisation", as a function of q and J. A percolation transition is found across which the cluster size changes from exponential-like to a power law-like dependence. The differences between "ferromagnetic" and "anti-ferromagnetic"-like contact energies are emphasized as a function of q.

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“…I. No relaxation -the no-relaxation process is the pure q-MBD, [7], i.e. the spin sticks to the cluster immediately.…”

Section: Methodsmentioning

confidence: 99%

Section: The Size (Mass) Distribution Of Clustersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of relaxation processes during deposition of anisotropic grains on a flat substrate

Trojan

Ausloos

2005

Physica A: Statistical Mechanics and its Applications

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“…It seems (31) that one can distinguish pile growth conditions and pile structure depending on whether q < q c (J) or q > q c (J). Two different cluster-mass regimes have been identified, through the cluster-mass distribution function.…”

Section: Ballistic Magnetic Deposition Modelmentioning

confidence: 99%

Granular matter: A wonderful world of clusters in far-from-equilibrium systems

Ausloos¹,

Lambiotte

Trojan

et al. 2005

Physica A: Statistical Mechanics and its Applications

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In this paper, we recall various features of non equilibrium granular systems. Clusters with specific properties are found depending on the packing density, going from loose (a granular gas) to sintered (though brittle) polycrystalline materials. The phase space available can be quite different. Unexpected features, with respect to standard or expected ones in classical fluids or solids, are observed, -like slow relaxation processes or anomalous electrical and thermoelectrical transport property dependences. The cases of various pile structures and the interplay between classical phase transitions and self-organized criticality for avalanches are also outlined.

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Magnetic hierarchical deposition

Posazhennikova¹,

Indekeu²

2014

Physica A: Statistical Mechanics and its Applications

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We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals $1/\lambda^n$ in generation $n$, in terms of a rescaling factor $\lambda$. Without interactions between the blocks, this model is described by a logarithmic fractal, studied previously, which is characterized by a constant increment of the length, area or volume upon proliferation. We study to what extent the logarithmic fractality survives, if each block is equipped with an Ising (pseudo-)spin $s=\pm 1$ and the interactions between those spins are switched on (ranging from antiferromagnetic to ferromagnetic). It turns out that the dependence of the surface topology on the interaction sign and strength is not trivial. For instance, deep in the ferromagnetic regime, our numerical experiments and analytical results reveal a sharp crossover from a Euclidean transient, consisting of aggregated domains of aligned spins, to an asymptotic logarithmic fractal growth. In contrast, deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins. Finally, in the weak interaction regime, we demonstrate that the non-interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength. In all regimes, we demonstrate the adequacy of a mean-field approximation whenever vacancies are rare. In sum, the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process.Comment: 17 pages, 8 figure

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

Cited by 3 publications

References 71 publications

Effects of relaxation processes during deposition of anisotropic grains on a flat substrate

Effects of relaxation processes during deposition of anisotropic grains on a flat substrate

Granular matter: A wonderful world of clusters in far-from-equilibrium systems

Magnetic hierarchical deposition

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