Annihilative Fractals Formed in Rayleigh-Taylor Instability

Shimokawa, Michiko; Ohta, Souichi

doi:10.1142/s0218348x12500090

Cited by 6 publications

(6 citation statements)

References 27 publications

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“…16) The fractal pattern was similar to that of Rayleigh-Benard convection in that the vertical flow determined the surface pattern. When the fractal pattern is observed, the HDS sinks and the LDS rises vertically toward the surface from the bottom of an experimental container owing to gravitational instability.…”

Section: Introductionmentioning

confidence: 59%

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Experimental Study on Transition in Fractal Patterns Derived from Vertical Flow

Shimokawa

2012

J. Phys. Soc. Jpn.

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A fractal pattern was observed on the surface of a lower-density solution owing to gravitational instability, when a droplet of a higher-density solution was placed on the lower-density solution surface. The relationship between the fractal pattern and the vertical flow was studied in containers of different configurations and sizes in order to understand the formation dynamics. It was found that fractal patterns of similar structure emerge independent of the configuration. The transition from a fractal pattern to a cell pattern occurs at r % h in experiments involving the use of various sizes of containers, where r and h are the radius of the container and the depth of the lower-density solution, respectively. The vertical flow for fractal patterns is different from that for cell patterns and has an axisymmetric structure. These results indicate that an axisymmetric flow is necessary for the formation of a fractal pattern.

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Section: Introductionmentioning

confidence: 59%

“…The result in ref. 16 implies a strong relationship between the fractal pattern and the vertical flow, as is the case for Rayleigh-Benard convection. No results, however, were reported regarding the relationship between the fractal pattern and the vertical flow.…”

Section: Introductionmentioning

confidence: 85%

Experimental Study on Transition in Fractal Patterns Derived from Vertical Flow

Shimokawa

2012

J. Phys. Soc. Jpn.

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“…The above discussion is confirmed through a comparison between the brightness σ(t) from experiments and σ theory (t) in Eq. (6). As shown in Fig.…”

Section: Fitting Functions Of σ(T) In Formation Of Fractal and Hole/cmentioning

confidence: 82%

“…[1][2][3][4][5] Recently, interfacial instability between two solutions is observed in not only a vertical but also a horizontal direction. 6,7,9 Although the initial vertical dynamics is directly induced by density difference under the gravity, the horizontal one is considered to be a secondary effect after a sinking phenomenon of the HDS. We studied a pattern formation due to the secondary effect in the previous paper.…”

Section: Introductionmentioning

confidence: 99%

Effect of fluid viscosity on surface patterns formed by gravitational instability

Shimokawa

Takami

2015

Mod. Phys. Lett. B

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When a droplet of a higher-density solution (HDS) is placed on the top of a lower-density solution (LDS), the HDS on the surface of the LDS sinks due to gravitational instability. In the sinking process, the HDS draws a fractal pattern or a hole/cell pattern on the surface of the LDS. It is observed that the surface pattern is determined by an aspect ratio of the container and viscosity of the LDS. In the formation of the surface pattern, a time series of the HDS density is analyzed. It is found that the profile of the series for the fractal pattern is different from that for the hole/cell pattern. In order to clarify the difference, we propose a phenomenological model for the time series to obtain fitting functions for both patterns.

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“…physical systems such as frosts and river basins [1]- [3]. In particular, one of the most popular structures is the tree-shaped network pattern.…”

Section: Introductionmentioning

confidence: 99%

Tree Network Formation in Poisson Equation Models and the Implications for the Maximum Entropy Production Principle

Shinmoto¹,

Amemiya²,

Itoh³

2014

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This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.

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Annihilative Fractals Formed in Rayleigh-Taylor Instability

Cited by 6 publications

References 27 publications

Experimental Study on Transition in Fractal Patterns Derived from Vertical Flow

Experimental Study on Transition in Fractal Patterns Derived from Vertical Flow

Effect of fluid viscosity on surface patterns formed by gravitational instability

Tree Network Formation in Poisson Equation Models and the Implications for the Maximum Entropy Production Principle

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