Cooperative Phenomena Group
Condensed Matter Physics Group
Department of Physics
University of Oslo

### 1 Introduction

The Cooperative Phenomena Group at the University of Oslo is doing systematic basic research in condensed matter physics. Some of our work is concerned with the growth of patterns and structures -- for instance, the structures that arise if oil is displacing water in a porous rock, or the fracture pattern formed in a brittle plate that fractures under the influence of external stress. Other work deals with transport processes. How do the grains in a pile of sand move? How do waves in a crystal propagate?

Observation of a transport process. Rice grains are falling and sliding along the sloped surface of a rice pile.

Growth always implies transport -- transport of matter, or transport of energy, for instance. Growth and transport processes are closely linked, and reflect basic physical properties of the materials involved. The study of materials, including biomaterials, is another main activity of the group.

Much of our understanding of the physical world is formulated in terms of discrete units or particles'' and the interactions between them. A crystal is made of a large number of atoms, and similarly, a fluid consists of a large number of molecules. However, some of the most astonishing properties of many materials (or systems'') do not depend on the detail properties of the individual particles: All crystals melt at sufficiently high temperature, and all fluids freeze at sufficiently low temperature. The exact melting and freezing temperatures depend on the details of particle properties -- the phenomena of melting and freezing do not.

Melting and freezing are familiar examples of processes that can only occur in systems consisting of many particles. Other processes of this sort include magnetic phase transitions in ferromagnets, glass transitions in polymers, transitions to superconductive and superfluid states, and pattern formation processes. Collective behavior of many, single elements is common also among living individuals: the synchronized motion of a school of fish, a herd of sheep, and flights of migrant birds are well-known examples. Processes that occur in many-particle systems exhibiting ordered structures are frequently referred to as {\em cooperative} phenomena -- hence the name The Cooperative Phenomena Group''.

Examples taken from recent experiments and simulations. (a) Formation of a water cone in a porous model representing a three-fluid layered oil reservoir. (b) Fracture patterns observed on the surface of a clay slab exposed to external stress. (c) Simulation of the slow displacement of water by oil (light structure) in a fracture. (d) The slime mold {\rm Physarum polycephalum} growing on a substrate of discrete agar based nutrient drops. (e) Simulation of a river meandering through a changing landscape. (f) Air (light structure) displacing dyed water that is flowing in a porous medium.

The work of our research group is devoted to the study of systems consisting of many microscopic particles, bringing about macroscopic phenomena that cannot be understood by considering the single particles alone. Cooperative phenomena are usually non-linear processes. The non-linearities indicate that these processes occur far from the thermodynamic equilibrium and are not macroscopically reversible. Non-linear processes cannot be explained by traditional thermodynamics, due to the linear mathematical structure of this theory.

In recent decades the understanding of cooperative phenomena has improved substantially. The development of fractal'' geometry has provided us with a set of theoretical tools that can be used to describe complex natural shapes in simple quantitative terms. Similarly, the development of scaling concepts'' and the renormalization group'' has provided a way to describe quantitatively the growth kinetics of both fractal and non-fractal objects. This development is crucial because describing natural processes in quantitative terms is necessary before a theoretical understanding can be developed. During this same period, a new understanding of non-linear phenomena has emerged. Work on non-linear systems demonstrated that apparently complex processes could have simple origins and provided a variety of concepts that helped to motivate the work described in this booklet. Back to Frontpage
Projects and Methods