Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)

Megjelent: PHYSICAL REVIEW E: COVERING STATISTICAL NONLINEAR BIOLOGICAL AND SOFT MATTER PHYSICS
(2016-) 2470-0045 2470-0053 102 (1) Paper: 012122 , 14 p. 2020

- SJR Scopus - Condensed Matter Physics: Q1

Azonosítók

- MTMT: 31490544
- DOI: 10.1103/PhysRevE.102.012122
- WoS: 000555733700004
- Scopus: 85089543566
- PubMed: 32795063

Szakterületek:

The Preisach model has been useful as a null model for understanding memory formation
in periodically driven disordered systems. In amorphous solids, for example, the athermal
response to shear is due to localized plastic events (soft spots). As shown recently
by Mungan et al. [Phys. Rev. Lett. 123. 178002 (2019)], the plastic response to applied
shear can be rigorously described in terms of a directed network whose transitions
correspond to one or more soft spots changing states. The topology of this graph depends
on the interactions between soft spots and when such interactions are negligible,
the resulting description becomes that of the Preisach model. A first step in linking
transition graph topology with the underlying soft-spot interactions is therefore
to determine the structure of such graphs in the absence of interactions. Here we
perform a detailed analysis of the transition graph of the Preisach model. We highlight
the important role played by return-point memory in organizing the graph into a hierarchy
of loops and subloops. Our analysis reveals that the topology of a large portion of
this graph is actually not governed by the values of the switching fields that describe
the hysteretic behavior of the individual elements but by a coarser parameter, a permutation
rho which prescribes the sequence in which the individual hysteretic elements change
their states as the main hysteresis loop is traversed. This in turn allows us to derive
combinatorial properties, such as the number of major loops in the transition graph
as well as the number of states vertical bar R vertical bar constituting the main
hysteresis loop and its nested subloops. We find that vertical bar R vertical bar
is equal to the number of increasing subsequences contained in the permutation rho.

2022-01-28 04:22