My work is dedicated both to the fundamentals and to applications of dynamical systems; to what I have termed the dynamics of natural systems.

In physics a couple of centuries ago there occurred a revolution, or as some would have it, a paradigm shift, when statistical methods were introduced. These have gradually spread throughout the sciences and today statistical tools are applied to all areas of knowledge, and there exist statisticians and institutes and faculties of statistics. More recently, another paradigm shift has brought to the attention of physicists the importance of understanding nonlinear dynamical systems. From this revolution there has come another set of multipurpose tools, that like the earlier statistical ones, can be applied to problems in all areas of science. With them can be understood phenomena that arise from nonlinear interactions between the elements of a system. Chaos, pattern formation, and complexity, are just a few of the consequences of nonlinear dynamics.

At present nonlinear dynamics has only partially been assimilated into the edifice of science: there are few dynamicists, and fewer institutes dedicated to dynamics in general. The foundations of the field are not yet complete, either. There is still much to understand regarding the fundamentals of many aspects of nonlinear systems.

Current research interests — which are frequently entangled — include work with Antonio Checa and Ignacio Sainz here in the IACT in Granada:

1. • Ice morphology — with Ignacio Sainz (Bruno Escribano worked on this in his PhD with Ignacio and myself).

   

   Ice is all around us; ice or snow covers a small but significant part of the Earth's surface, both land and sea; ice is found in our atmosphere and plays a similarly important role there, ice is present on many other planetary bodies and it coats grains of dust in interstellar space. Ice is not a static medium but a dynamical one; it shows strong variations of its characteristics with time and place, as is easily experienced on any ski slope.  A better understanding of ice structures, patterns, and processes is thus a topic of current research. We are interested in understanding the myriad morphologies one can observe in ice. This understanding can be applied to questions ranging from the shape of icy particles in space, to how ice grows in a thundercloud and how the ice growth charges up the cloud to initiate a thunderstorm.
   
2. • Nacre self-assembly — with Antonio Checa (Bruno Escribano worked on this in his PhD). Pearls and nacre (mother-of-pearl) make beautiful jewellery, but are also a high-performance material that reminds us how far we still have to go before being able to imitate nature with artificial products.

   

   Imagine if one could build a brick wall by simply putting clay, lime, water, and so on, together, and walking away. This is how a mollusc makes nacre. All of the ingredients are produced by the animal and released in the right quantities at given moments, but they then assemble themselves without outside influence into crystals, liquid crystals, and membranes which come together in an exquisite hierarchical sequence to produce nacre. By understanding the physics of how nacre builds itself, we gain insight into the self-organization of biological materials, and one day similar self-assembling artificial composite materials may become more than just a dream.
   

And work with Diego González in Bologna and Oreste Piro in Mallorca:

1. • Nonlinear hearing — with Diego González and Oreste Piro. While microphones and other recording devices are 

   

   essentially passive systems designed only to convert linearly sound pressure into an electric voltage, the biological ear is a very complex and nonlinear dynamical apparatus that not only detects sounds but also provides a great quantity of sound signal preprocessing mechanisms. Nonlinear dynamics is thus an essential element present in — and exploited by — nature, the importance of which has not been realized in the complex neurally based implementations of artificial auditory systems. Our hypothesis is that most of the important features of hearing can be understood and coded in terms of robust properties of moderately low dimensional dynamical systems. We are pursuing an interdisciplinary research effort to understand aspects of sound perception from pitch and timbre to rhythm and harmony.
   
2. • Biological fluid dynamics: cilia and embriogenesis — with Oreste Piro (Idan Tuval worked on this in his PhD with Oreste).

   

   How does the developing embryo tell its left side from its right, to know to put the heart on the left, the liver on the right, and so on? It turns to physics; to fluid mechanics: Fluid flow driven by rotating cilia in the node, a structure present in the early stages of growth of vertebrate embryos, is responsible for determining the normal development of the left–right axis. Fluids are ubiquitous in biological systems, so it is not surprising that fluid dynamics should play an important role in the physical and chemical processes shaping ontogeny. However, only in a few cases have the strands been teased apart to see exactly how fluid forces operate to guide development. We are engaged in a programme to understand the role of fluid dynamics during the development of an organism; the physical processes operating (transport, mixing, liquid crystallization, Rayleigh-Taylor instability, ...) and their driving mechanisms (cilia, peristalsis, osmotic pressure, ...).
   

My colleagues and I form a diverse group coming from different areas of science and we work in an interdisciplinary manner that involves applying a mixture of theory, computer simulation and laboratory observations and experiments to tackle problems. I welcome inquiries from students about joining us; I always have ideas for undergraduate projects and for PhD and postdoc research topics.

Julyan Cartwright

"Science is not about devising hugely complex descriptions of the world. It is about devising descriptions that illuminate the world and make it comprehensible. The reason that Newton's law of gravity is important is not because it describes the movement of every particle in the solar system. It is important because it opens up the possibility of simple models of the solar system that are comprehensible to human beings - models with 2 bodies, or 3, or 20, but not quadrillions. Similarly, any kind of equation for life has to be comprehensible, as well as to correspond to how organisms function - on some level of description."
Ian Stewart, Life's other secret (1998).