Cyclic annealing as an iterated random map

Abstract

Disordered magnets, martensitic mixed crystals, and glassy solids can be irreversibly deformed by subjecting them to external deformation. The deformation produces a smooth, reversible response punctuated by abrupt relaxation "glitches". Under appropriate repeated forward and reverse deformation producing multiple glitches, a strict repetition of a single sequence of microscopic configurations often emerges. We exhibit these features by describing the evolution of the system configuration from glitch to glitch as a mapping of $\mathcal{N}$ states into one-another. A map $\mathbf{U}$ controls forward deformation; a second map $\mathbf{D}$ controls reverse deformation. Iteration of a given sequence of forward and reverse maps, e.g. $\mathbf{DDDDUUU}$ necessarily produces a convergence to a fixed cyclic repetition of states covering multiple glitches. The repetition may have a period of more than one strain cycle, as recently observed in simulations. Using numerical sampling, we characterize the convergence properties of four types of random maps implementing successive physical restrictions. The most restrictive is the much-studied Preisach model. These maps show only the most qualitative resemblance to annealing simulations. However, they suggest further properties needed for a realistic mapping scheme.

13 pages, 5 figures, minor changes from v1 (to appear in Phys. Rev. E)

References in corpus (16)

• Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
• Amorphous Systems in Athermal, Quasistatic Shear
• The yielding transition in amorphous solids under oscillatory shear deformation
• Onset of Irreversibility and Chaos in Amorphous Solids Under Periodic Shear
• Persistent memory in athermal systems in deformable energy landscapes
• Multiple transient memories in experiments on sheared non-Brownian suspensions
• Generic transient memory formation in disordered systems with noise
• Closing probabilities in the Kauffman model: an annealed computation
• Strength of Mechanical Memories is Maximal at the Yield Point of a Soft Glass
• Period proliferation in periodic states in cyclically sheared jammed solids
• Multiple transient memories in sheared suspensions: robustness, structure, and routes to plasticity
• Role of disorder in finite-amplitude shear of a 2D jammed material
• The structure of state transition graphs in hysteresis models with return point memory: I. General Theory
• Subharmonics and Aperiodicity in Hysteresis Loops
• Memory Effects in Schematic Models of Glasses Subjected to Oscillatory Deformation
• The computational complexity of Kauffman nets and the P versus NP problem

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• Global Memory from Local Hysteresis in an Amorphous Solid
• Multiple memory formation in glassy landscapes
• Multiperiodic orbits from interacting soft spots in cyclically-sheared amorphous solids
• Topology of the energy landscape of sheared amorphous solids and the irreversibility transition
• State transition graph of the Preisach model and the role of return point memory
• Models for the yielding behaviour of amorphous solids
• Cooperative effects driving the multi-periodic dynamics of cyclically sheared amorphous solids
• Mapping out the glassy landscape of a mesoscopic elastoplastic model
• Metastability as a mechanism for yielding in amorphous solids under cyclic shear
• Absorbing phase transitions in systems with mediated interactions
• Competition between energy and dynamics in memory formation
• Loss of memory of an elastic line on its way to limit cycles
• Random organization criticality with long-range hydrodynamic interactions
• Yielding and memory in a driven mean-field model of glasses
• Yielding versus random organization: convex absorbing transitions in soft matter