STATISTICAL PHYSICS OF COMPLEX SYSTEMS
The Regev Research Group
פיסיקה סטטיסטית של מערכות מורכבות
קבוצת המחקר של עדו רגב
Physics of Amorphous Solids
Amorphous (disordered) solids, some times referred to as glasses, 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 plastic deformation, memory retention and an irreversibility transition which we have co-discovered.
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
Memory in Amorphous Solids
Thu study of memory formation and retention is a multidisciplinary research field which is on the crossroads of physics, biology, chemistry, computer science among others. Memory can be stored in a system if it can be “programmed” to a state that is stored for a long period of time without changing and that can be read using an appropriate device. A physical system in thermodynamic equilibrium cannot store any information since its state is constantly changing. Memory retention is thus a property of materials far from thermodynamic equilibrium. We study memory in a specific non equilibrium system - amorphous and granular materials, materials that have random structure. In such materials memory is imprinted and read by applying plastic deformation which allows them to reach periodic states called "limit-cycles". We study the appearance of memory as well as memory retention using computer simulations of particle systems as well as toy models that we create. We then study and describe these models by representing the configuration space using a network. This is used to extract different properties and as a basis for theoretical modeling.
Network representation of memory and hysteresis in amorphous solids
(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).
The irreversibility transition
When an amorphous solid experiences oscillating shear strain at a constant level, its initial response is usually irreversible. However, if the strain amplitude is below the a critical point, the material eventually becomes reversible - after one or more cycles of applied force, plastic events will repeat indefinitely. The number of irreversible cycles before reaching reversibility increases as the strain amplitude gets closer to the yield point. If the amplitude exceeds the yield point, the material can never achieve a reversible state, and its response will always be irreversible. This shift from reversible to irreversible behavior is known as “the irreversibility transition.” Although most researchers agree that this transition is a non-equilibrium phase transition, the exact reasons for and the nature of this transition remain unclear. Understanding this phenomena is important for understanding the limits of imprinting memory in materials as well as for understanding materials strength, especially in the context of nanotechnology.
(a)
(c)
(b)
(a) The irreversibility transition - the potential energy of an amorphous solid subject to oscillatory shear for different forcing amplitude (top - smallest amplitude, bottom - largest amplitude). For sub-yield amplitudes (top two shown), the response is initially random, but eventually becomes periodic. For large amplitudes (bottom graph) the response is completely random. Periodic response - once the system reached a limit-cycle, particle positions repeat during consecutive cycles (b) which leads the potential energy to also repeat (c). One can see that there are plastic events but they repeat in each cycle.