The effect of screening on entropy production in pattern formation

Kaufman, James H.; Melroy, O. R.; Dimino, G. M.

doi:10.1007/bf01042603

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…Once a general solution to has been found, here we propose a theoretical approach to determine χ ( d ). This approach is based on a particular finding from the study of the rate of information-entropy production of random fractals 60,61 . This finding suggests that DLA can be associated to a critical state that defines the point of maximum information-entropy production along the DBM morphological transition 62–65 .…”

Section: Resultsmentioning

confidence: 99%

A universal dimensionality function for the fractal dimensions of Laplacian growth

Nicolás-Carlock

Carrillo-Estrada

2019

Sci Rep

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Laplacian growth, associated to the diffusion-limited aggregation (DLA) model or the more general dielectric-breakdown model (DBM), is a fundamental out-of-equilibrium process that generates structures with characteristic fractal/non-fractal morphologies. However, despite diverse numerical and theoretical attempts, a data-consistent description of the fractal dimensions of the mass-distributions of these structures has been missing. Here, an analytical model of the fractal dimensions of the DBM and DLA is provided by means of a recently introduced dimensionality equation for the scaling of clusters undergoing a continuous morphological transition. Particularly, this equation relies on an effective information-function dependent on the Euclidean dimension of the embedding-space and the control parameter of the system. Numerical and theoretical approaches are used in order to determine this information-function for both DLA and DBM. In the latter, a connection to the Rényi entropies and generalized dimensions of the cluster is made, showing that DLA could be considered as the point of maximum information-entropy production along the DBM transition. The results are in good agreement with previous theoretical and numerical estimates for two- and three-dimensional DBM, and high-dimensional DLA. Notably, the DBM dimensions conform to a universal description independently of the initial cluster-configuration and the embedding-space.

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Section: Resultsmentioning

confidence: 99%

A universal dimensionality function for the fractal dimensions of Laplacian growth

Nicolás-Carlock

Carrillo-Estrada

2019

Sci Rep

View full text Add to dashboard Cite

show abstract

“…This approach is based on a particular finding from the study of the rate of information-entropy production of random fractals. 60,61 This finding suggests that DLA can be associated to a critical state that defines the point of maximum information-entropy production along the DBM morphological transition. [62][63][64][65] Then, if this is indeed the case, this could manifest itself in the fractality of the system.…”

Section: Solution To Dbm: Finding a General χ(D)mentioning

confidence: 85%

The fractal dimensions of Laplacian growth: an analytical approach based on a universal dimensionality function

Nicolás-Carlock,

Carrillo-Estrada

2016

Preprint

View full text Add to dashboard Cite

Laplacian growth, associated to the diffusion-limited aggregation (DLA) model or the more general dielectric-breakdown model (DBM), is a fundamental out-of-equilibrium process that generates structures with characteristic fractal/non-fractal morphologies. However, despite of diverse numerical and theoretical attempts, a data-consistent description of the fractal dimensions of the mass-distributions of these structures has been missing. Here, an analytical description to the fractal dimensions of the DBM and DLA is provided by means of a recently introduced general dimensionality equation for the scaling of clusters undergoing a continuous morphological transition. Particularly, this equation relies on an effective information-function dependent on the Euclidean dimension of the embedding-space and the control parameter of the system. Numerical and theoretical approaches are used in order to determine this information-function for both DLA and DBM. In the latter, a connection to the R ényi entropies and generalized dimensions of the cluster is made, showing that DLA could be considered as the point of maximum information-entropy production along the DBM transition. These findings are in good agreement with previous theoretical and numerical results (two-and threedimensional DBM, and high-dimensional DLA). Notably, the DBM dimensions can be conformed to a universal description independently of the initial cluster-configuration and the embedding-space.

show abstract

The effect of screening on entropy production in pattern formation

Cited by 2 publications

References 9 publications

A universal dimensionality function for the fractal dimensions of Laplacian growth

A universal dimensionality function for the fractal dimensions of Laplacian growth

The fractal dimensions of Laplacian growth: an analytical approach based on a universal dimensionality function

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