Press Releases
Dec. 9, 2009

Universality in Spreading Phenomena

—First experimental evidence found in liquid crystal turbulence—
Presenters
  • Kazumasa A. Takeuchi (PhD student, Department of Physics, Univ. of Tokyo)
  • Masaki Sano (professor, Department of Physics, Univ. of Tokyo)

Abstract

Figure 1

Fig. Evolution of topological turbulence. It disappears for low voltages but spreads if voltage is high enough, just like water percolating downward in pumice. Photos show spreading at applied voltage 36.65V, where black patches of topological turbulence spread (inside red circles) and reach the entire field of view (500 µm squared) at 140 sec.

Universal laws expected behind spreading phenomena, such as epidemics, fires, and percolation of water, found their first experimental evidence in spreading turbulence of liquid crystals. Known under the name of “directed percolation” universality, those universal laws which describe critical spreading in various situations have been very well established except in one essential aspect: no experiment, so far, could show convincing evidence of this universal behavior despite substantial efforts. This long-standing puzzle is solved here, opening the door towards the question of to what extent such spreading phenomena, which are ubiquitous in our daily lives, can be described by universal laws of physics.

Spreading phenomena can be observed everywhere in our daily lives. Epidemic spreading, which calls our attention recently, forest fires, rumors, and percolation of water in pumice are some prototypical examples which are easy to imagine. Such phenomena can also be found in every field of science, like in catalytic reactions, signal communications in cells, and galactic evolution. Those spreading phenomena, of course, comprise completely different physical processes, so that physical laws which describe them have in general nothing in common. Nevertheless, physicists have found in theory and simulations that, in critical situations marking the onset of unbounded spreading, they often obey the same universal laws prescribing how activity grows, how it is distributed, how it fluctuates, etc. Known under the name of “directed percolation” universality, those universal laws are now theoretically very well established.

Then, what happens for spreading in the real world? As an important problem from the viewpoint of both pure science and applications, substantial efforts have been made in the experimental side over almost 30 years, but the theoretically expected universal behavior has been somehow quite elusive. The lack of experimental evidence has been therefore recognized as an outstanding open problem.

This long-standing puzzle is solved here, in the context of liquid crystal turbulence. Certain nematic liquid crystals(*1) exhibit convection driven by electric field, which becomes turbulent when high voltage is applied. There are two turbulent states there, composed of lots of vortices call topological defects(*2) or only few of them. The topological turbulence spreads for sufficiently high voltages, otherwise disappears. At criticality in between, patches of topological turbulence “percolate” in time, just similarly to water in pumice which penetrates downward (figure 1). We directly measured 11 sorts of properties characterizing spreading, extinction, and distributions of the topological turbulence, and found all of them in quantitative agreement with the theoretical predictions of the universal behavior. We thereby demonstrated for the first time that the universal critical behavior of the directed percolation does exist in a real phenomenon, putting an end to the fundamental problem of lack of experimental evidence.

This is an important result both for pure science and applications. From the academic point of view, universality in critical phenomena was discovered in materials at equilibrium, i.e., without any effective exchange of energy with surroundings, which substantially changed our view of statistical mechanics since the mid 20th century. Spreading phenomena are obviously not in this category, being able to exist only in situations where energy is constantly supplied, just like in our experiments. The existence of universal behavior in such systems is a good litmus test in the ongoing search for universal structure in physics of out-of-equilibrium systems, and therefore of great fundamental importance.

Moreover, as mentioned in the beginning, spreading phenomena are ubiquitous in our daily lives. The universal laws found in this study determine how activity grows, is distributed, and fluctuates, in critical situations determining the fate of spreading. Understanding conditions for this universal behavior thus may lead to strategies to, e.g., prevent epidemics and broadcast information efficiently. Our finding would be the very first step in this direction.

This is a joint work of Kazumasa A. Takeuchi, Masafumi Kuroda, Masaki Sano (Department of Physics, Univ. of Tokyo), and Hugues Chate (Service de Physique de l’Etat Condense, CEA-Saclay, France). Financial supports from Grant-in-Aid for Scientific Research (Priority Area “Soft Matter Physics” from MEXT and Fellowships for Young Scientists from JSPS) are acknowledged.

Publications

  • Physical Review Letters Vol. 99, 234503, American Physical Society (a prompt report of partial results; published online on December 5th, 2007).
  • Physical Review E Vol. 80, 051116, Americal Physical Society (published online on November 16, 2009)
  • Highlighted in Physics, Vol. 2, 96, American Physical Society (published online on November 16, 2009)

Notes

*1: nematic liquid crystal
Liquid crystal with typically a rod-like molecule structure, which flows like liquid, but with long axes of molecules aligned.
*2: topological defect
Mathematically, it denotes a singular point which cannot be removed by continuous transformations. In the context of liquid crystals, when molecules are aligned like a vortex or in a radial manner, the direction of the alignment cannot be defined at the center, so that this is a topological defect.