# Universality in quasiperiodic Rayleigh-Benard convection

## Abstract

We study universal scaling properties of quasiperiodic Rayleigh-Benard convection in a {sup 3}He--superfluid-{sup 4}He mixture. The critical line is located in a parameter space of Rayleigh and Prandtl numbers using a transient-Poincare-section technique to identify transitions from nodal periodic points to spiral periodic points within resonance horns. We measure the radial and angular contraction rates and extract the linear-stability eigenvalues (Flouquet multipliers) of the periodic point. At the crossings of the critical line with the lines of fixed golden-mean-tail winding number we determine the universality class of our experimental dynamics using {ital f}({alpha}) and trajectory-scaling-function analyses. A technique is used to obtain a robust five-scale approximation to the universal trajectory scaling function. Different methods of multifractal analysis are employed and an understanding of statistical and systematic errors in these procedures is developed. The power law of the inflection point of the map, determined for three golden-mean-tail winding numbers, is 2.9{plus minus}0.3, corresponding to the universality class of the sine-circle map.

- Authors:

- (Physics Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States))

- Publication Date:

- OSTI Identifier:
- 5103408

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review A. General Physics; (United States)

- Additional Journal Information:
- Journal Volume: 44:12; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; HELIUM 3; CONVECTION; HELIUM 4; BINARY MIXTURES; MAPPING; SCALING LAWS; DISPERSIONS; ENERGY TRANSFER; EVEN-EVEN NUCLEI; EVEN-ODD NUCLEI; HEAT TRANSFER; HELIUM ISOTOPES; ISOTOPES; LIGHT NUCLEI; MASS TRANSFER; MIXTURES; NUCLEI; STABLE ISOTOPES; 665420* - Superfluidity- (1992-)

### Citation Formats

```
Ecke, R.E., Mainieri, R., and Sullivan, T.S.
```*Universality in quasiperiodic Rayleigh-Benard convection*. United States: N. p., 1991.
Web. doi:10.1103/PhysRevA.44.8103.

```
Ecke, R.E., Mainieri, R., & Sullivan, T.S.
```*Universality in quasiperiodic Rayleigh-Benard convection*. United States. doi:10.1103/PhysRevA.44.8103.

```
Ecke, R.E., Mainieri, R., and Sullivan, T.S. Sun .
"Universality in quasiperiodic Rayleigh-Benard convection". United States. doi:10.1103/PhysRevA.44.8103.
```

```
@article{osti_5103408,
```

title = {Universality in quasiperiodic Rayleigh-Benard convection},

author = {Ecke, R.E. and Mainieri, R. and Sullivan, T.S.},

abstractNote = {We study universal scaling properties of quasiperiodic Rayleigh-Benard convection in a {sup 3}He--superfluid-{sup 4}He mixture. The critical line is located in a parameter space of Rayleigh and Prandtl numbers using a transient-Poincare-section technique to identify transitions from nodal periodic points to spiral periodic points within resonance horns. We measure the radial and angular contraction rates and extract the linear-stability eigenvalues (Flouquet multipliers) of the periodic point. At the crossings of the critical line with the lines of fixed golden-mean-tail winding number we determine the universality class of our experimental dynamics using {ital f}({alpha}) and trajectory-scaling-function analyses. A technique is used to obtain a robust five-scale approximation to the universal trajectory scaling function. Different methods of multifractal analysis are employed and an understanding of statistical and systematic errors in these procedures is developed. The power law of the inflection point of the map, determined for three golden-mean-tail winding numbers, is 2.9{plus minus}0.3, corresponding to the universality class of the sine-circle map.},

doi = {10.1103/PhysRevA.44.8103},

journal = {Physical Review A. General Physics; (United States)},

issn = {1050-2947},

number = ,

volume = 44:12,

place = {United States},

year = {1991},

month = {12}

}