Physics of Granular and Amorphous Solids
Granular and amorphous (disordered) solids are a condensed form of matter which show elastic response but lack periodic structure. In our group we use simulations and theory to try to explain different aspects of these materials with emphasis on an irreversibility transition which we have recently co-discovered. The irreversibility transition is a non-equilibrium phase transition in which an amorphous solid subject to oscillatory forcing transitions between reversible and irreversible behavior. Since the phase transition occurs in a system that is not in thermodynamic equilibrium, it cannot be explained by studying the free-energy and we have to develop novel methods to understand it. Specifically, we are working on a theory in which the set of stable configurations of the system is mapped into a random network. By studying the topology of this network and developing theories that explain it, we hope to understand the energy landscape and dynamics of amorphous solids and the irreversibility transition.
Yield in amorphous solids is a non-equilibrium phase transition
Amorphous solids are disordered
Glasses have a complex potential energy landscape
Power-law scaling at
the critical point
Network representation of the configuration space
(a) Detailed view of the mesostate transitions associated with the 0.05 limit-cycles depicted in Fig. 1 (b). Transitions out of the endpoints X and Y are marked as green triangles and will be ignored. Regions of interest have colored backgrounds and refer to (b) and Fig. 3(c). (b) Network motifs involving one and two soft-spots, (i) and (ii) - (iv), respectively. Soft-spots are shown as black ellipses with states corresponding to their orientation. Motif background color and transition pattern highlighted in (a) coincide. (c) The particle displacements associated with the transitions of the avalanche motif in (iv) and (a). (d) Tree representation of the hierarchy of loops and sub-loops making up the limit cycle shown in (a).
Biophysics and Pattern Formation in Growing Plants
Similarly to animals, plants sense their environment and respond to changes. This includes the direction at which gravity acts, the humidity of the soil and the concentration of nutrients. However, contrary to animals, plants respond to their environment by changing their modes of growth since they cannot move. The growth itself is also affected by the mechanical properties of the plant and its environment. The feedback between growth and sensing can give rise to unusual growth patterns which were observed under laboratory conditions. When grown on tilted plates, roots of certain plants grow in a wavy pattern and when the plates are flat, they form circles. We work on understanding these growth patterns using lab experiments and theoretical models.
Root waving and coiling
Elastic instability during root waving
(A) An illustration of root waving.
Root waving and coiling:
(B) An illustration of root coiling. pattern to a coiling pattern.
(D) An illustration of the experimental apparatus containing an agarose covered plastic plate (petri-dish) the normal of which can be set at different angles with respect to the vertical. The plate is shown from the profile.
Comparison of a model explaining waving as an elastic instability with waving observed in experiments.