All That Matters

For the past weeks this blog has been more quiet than usual. Mostly, I was busy with a number of projects, including the co-organisation of a Nature Conference – ‘Frontiers in Electronic Materials: Correlation Effects and Memristive Phenomena‘. The conference took place in Aachen/Germany, and was organized in collaboration with the Jülich-Aachen Research Alliance (JARA) formed by the RWTH Aachen University and the Helmholtz research centre in Jülich – who did a great job in getting this meeting off the ground. Rainer Waser in particular dedicated a tremendous amount of work to the conference. And with close to 600 attendees, the popularity of the conference certainly exceeded all our expectations.

I do not intend to summarize all the interesting talks at the conference here. Instead, I like to focus on two aspects that I think contributed in particular to the success of the conference, and that could be of interest also to those that couldn’t attend the meeting. They’re related to the scope of the conference and its organisation. […]

Symphonies are some of the most complex musical pieces. They involve different instruments, each with their own unique sound, and each instruments section playing their own tunes. Yet, what are symphonies in comparison to the complexity of life? Proteins for example, they are made of a limited number of building blocks, amino acids, but take highly complex shapes and assume a broad range of functions in the body.

Still, there is a commonality underlying such complex systems, in many cases they are hierarchical, which means they’re made of different objects on different scales – instruments playing tunes, amino acids forming proteins and so on. As David Spivak, Markus Buehler and others from MIT have described in a recent paper, a mathematical approach, known as category theory, can be used as a versatile tool that is capable of modelling complex systems by using the underlying rules governing a structure’s components. This is a very powerful approach and there is a lot to be gained by using this mechanism in materials science, to describe biomolecules or other hierarchical materials. Moreover, their approach makes it easy to connect different complex system. To put it crudely, understanding a Beethoven symphony may also provide insights into the properties of a protein, because category theory helps us links various complex systems.

Photo by Wayne Dixon via flickr.

To understand how this works, let’s take a look at an example provided by Buehler and colleagues – spider webs. These are made of individual fibres, consisting of smaller fibrils. The fibrils are made of a nanocomposite of crystal-like structures connected by flexible links. These structures are in turn made of various amino acids.

The complex structural hierarchy of spider silk (and other systems) is of course well-known. The problem researchers face is, however, that knowing the individual components of a material doesn’t necessarily mean that the properties of  the full system are known. For example, even though the molecular composition of a protein may be known, predicting its three-dimensional shape is notoriously difficult. It is the behaviour of structural elements in the context of their use that can be so difficult to understand. And this is where category theory is useful. […]

The study of materials is one of the major areas of science, with legions of researchers in physics, chemistry and materials science working on this topic. Condensed matter physics is one of the largest research areas in physics. Yet, it makes me often uneasy how the benefits of materials science are promoted. It is all too often about applications, and not about fundamental physics. How materials such as graphene might revolutionize electronics. And how new physical concepts could be used to develop materials for energy applications: solar cells, batteries and so on. In classical materials science it’s often about tougher materials, such as enhanced steels, and less about the fundamental insights they are based on. Of course, applications are an important aspect in the study of materials. But does this mean that too often fundamental insights are neglected in favour of a material’s commercial potential?

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