### Abstract

We study the complex behavior in soft-mode turbulence (SMT), a recently discovered type of spatiotemporal chaos observed in electrohydrodynamic instability (EHD) of a nematic liquid crystal with homeotropic alignment. A particle, small compared to the characteristic length of the macroscopic flow, injected in SMT travels with random velocity such as an active Brownian motion. Tracking the particle trajectory induces changes in the flow velocity as a function of space and time (the Lagrange picture). The mean amplitude of the velocity is linearly proportional to the control parameter ε, normalized voltage in EHD. The probability density distribution of the particle velocity changes from Lévy for small ε to Gaussian distribution for large ε through intermediate distributions. The different regimes of anomalous diffusions are also observed. The stochastic properties of SMT are discussed based on these results.

Original language | English |
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Pages (from-to) | 157-168 |

Number of pages | 12 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 306 |

DOIs | |

Publication status | Published - Apr 1 2002 |

Event | 21th IUPAP Conference on Invited Papares (STATPHYS 21) - Cancun, Mexico Duration: Jul 15 2001 → Jul 21 2001 |

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### All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*306*, 157-168. https://doi.org/10.1016/S0378-4371(02)00494-6

**Anomalous diffusion and Lévy distribution of particle velocity in soft-mode turbulence in electroconvection.** / Tamura, Koyo; Hidaka, Yoshiki; Yusuf, Yusril; Kai, Shoichi.

Research output: Contribution to journal › Conference article

*Physica A: Statistical Mechanics and its Applications*, vol. 306, pp. 157-168. https://doi.org/10.1016/S0378-4371(02)00494-6

}

TY - JOUR

T1 - Anomalous diffusion and Lévy distribution of particle velocity in soft-mode turbulence in electroconvection

AU - Tamura, Koyo

AU - Hidaka, Yoshiki

AU - Yusuf, Yusril

AU - Kai, Shoichi

PY - 2002/4/1

Y1 - 2002/4/1

N2 - We study the complex behavior in soft-mode turbulence (SMT), a recently discovered type of spatiotemporal chaos observed in electrohydrodynamic instability (EHD) of a nematic liquid crystal with homeotropic alignment. A particle, small compared to the characteristic length of the macroscopic flow, injected in SMT travels with random velocity such as an active Brownian motion. Tracking the particle trajectory induces changes in the flow velocity as a function of space and time (the Lagrange picture). The mean amplitude of the velocity is linearly proportional to the control parameter ε, normalized voltage in EHD. The probability density distribution of the particle velocity changes from Lévy for small ε to Gaussian distribution for large ε through intermediate distributions. The different regimes of anomalous diffusions are also observed. The stochastic properties of SMT are discussed based on these results.

AB - We study the complex behavior in soft-mode turbulence (SMT), a recently discovered type of spatiotemporal chaos observed in electrohydrodynamic instability (EHD) of a nematic liquid crystal with homeotropic alignment. A particle, small compared to the characteristic length of the macroscopic flow, injected in SMT travels with random velocity such as an active Brownian motion. Tracking the particle trajectory induces changes in the flow velocity as a function of space and time (the Lagrange picture). The mean amplitude of the velocity is linearly proportional to the control parameter ε, normalized voltage in EHD. The probability density distribution of the particle velocity changes from Lévy for small ε to Gaussian distribution for large ε through intermediate distributions. The different regimes of anomalous diffusions are also observed. The stochastic properties of SMT are discussed based on these results.

UR - http://www.scopus.com/inward/record.url?scp=0036539068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036539068&partnerID=8YFLogxK

U2 - 10.1016/S0378-4371(02)00494-6

DO - 10.1016/S0378-4371(02)00494-6

M3 - Conference article

AN - SCOPUS:0036539068

VL - 306

SP - 157

EP - 168

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -