Order hidden in disorder
Partitioning space into cells with optimum geometrical properties is a central challenge in many fields of science and technology. Researchers of Karlsruhe Institute of Technology (KIT) and colleagues from several countries have now found that in amorphous, i.e. disordered, systems optimization of the individual cells gradually results in the same structure, although it remains amorphous. The disordered structure quickly converges to hyperuniformity – a hidden order on large scales. This is reported in Nature Communications. (DOI: 10.1038/s41467-019-08360-5)
No matter whether you search for an optimum foam or for a method to pack spheres as closely as possible – ideal tessellation of three-dimensional space, that means complete partitioning into cells with special geometrical properties, has been studied for a long time by scientists. It is not only of theoretical interest, but relevant to many practical applications, among others for telecommunications, image processing, or complex granules.
Researchers of KIT's Institute of Stochastics have now studied a special problem of tessellation, the quantizer problem. “The goal is to partition space into cells and all points in a cell to be located as closely as possible to the cell center, intuitively speaking,” says Dr. Michael Andreas Klatt, former staff member of the Institute, who now works at Princeton University in the USA.
Solutions of the quantizer problem can be used for the development of novel materials and may contribute to a better understanding of the unique properties of complex cell tissue in future.
The theoretical work that combines methods of stochastic geometry and statistical physics is now reported in Nature Communications. The researchers of KIT, Princeton University, Friedrich-Alexander-Universität (FAU) Erlangen-Nuremberg, Ru?er Boškovi?
Institute in Zagreb, and Murdoch University in Perth used the so-called Lloyd algorithm, a method to partition space into uniform regions. Every region has exactly one center and contains those points in space that are closer to this than to any other center. Such regions are referred to as Voronoi cells. The Voronoi diagram is made up of all points having more than one closest center and, hence, forming the boundaries of the regions.
The scientists studied stepwise local optimization of various point patterns and found that all completely amorphous, i.e. disordered, states do not only remain completely amorphous, but that the initially diverse processes converge to a statistically indistinguishable ensemble. Stepwise local optimization also rapidly compensates extreme global fluctuations of density. “The resulting structure is nearly hyperuniform. It does not exhibit any obvious, but a hidden order on large scales,” Klatt says.
Hence, this order hidden in amorphous systems is universal, i.e. stable and independent of properties of the initial state. This provides basic insight into the interaction of order and disorder and can be used among others for the development of novel materials. Of particular interest are photonic metamaterials similar to a semiconductor for light or so-called block copolymers, i.e. nanoparticles composed of longer sequences or blocks of various molecules that form regular and complex structures in a self-organized way.
The work reported in Nature Communications was carried out by the research group “Geometry & Physics of Spatial Random Systems” funded by the German Research Foundation (DFG). The interdisciplinary team consists of groups of KIT, FAU, and the University of Aarhus (Denmark) with experts in stochastic geometry, spatial statistics, and statistical physics, among others. Publication of the work was funded by the KIT publication fund.
Original publication (open access):
Michael A. Klatt, Jakov Lovri?, Duyu Chen, Sebastian C. Kapfer, Fabian M. Schaller, Philipp W. A. Schönhöfer, Bruce S. Gardiner, Ana-Sunčana Smith, Gerd E. Schröder-Turk & Salvatore Torquato: Universal hidden order in amorphous cellular geometries. Nature Communications, 2019. (DOI: 10.1038/s41467-019-08360-5)
Animation relating to the publication:
Phone: +49 721 608-21165
Being “The Research University in the Helmholtz Association,” KIT creates and imparts knowledge for the society and the environment. It is the objective to make significant contributions to the global challenges in the fields of energy, mobility and information. For this, about 9,300 employees cooperate in a broad range of disciplines in natural sciences, engineering sciences, economics, and the humanities and social sciences. KIT prepares its 25,100 students for responsible tasks in society, industry, and science by offering research-based study programs. Innovation efforts at KIT build a bridge between important scientific findings and their application for the benefit of society, economic prosperity, and the preservation of our natural basis of life.
This press release is available on the internet at http://www.
Alle Nachrichten aus der Kategorie: Materials Sciences
Materials management deals with the research, development, manufacturing and processing of raw and industrial materials. Key aspects here are biological and medical issues, which play an increasingly important role in this field.
innovations-report offers in-depth articles related to the development and application of materials and the structure and properties of new materials.
Smart sensors for future fast charging batteries
European project “Spartacus” launched Faster charging, longer stability of performance not only for electric vehicles but also for smartphones and other battery powered products. What still sounds like science fiction…
Small molecules control bacterial resistance to antibiotics
Antibiotics have revolutionized medicine by providing effective treatments for infectious diseases such as cholera. But the pathogens that cause disease are increasingly developing resistance to the antibiotics that are most…