@@ -22,7 +22,7 @@ where $`V_u`$ is the volume of the unit cell, $`Z_{Ti}^*`$, $`Z_{Ba}^*`$, $`Z_{O
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The relative atomic motion of Ti-atom as shown in fig. (A) determines the unit cell's local polarization for a given system. Orange and blue regions are two different symmetric ‘domains’ – domain with Pup and Pdown respectively, with a domain-wall between them. Under an electric-field, say one pointing up, the domain-wall moves so as to increase the fraction of UP domains. At a particular electric-field, all domains (or almost all) will be converted to a single UP domain. Reversal of the electric-field will result in an increase in the DOWN domain fraction, and the total polarization pointing up will reduce in magnitude till the macroscopic polarization is flipped. Interestingly, a plot of the total polarization of the box, when as a function of the electric-field, does not show perfect reversible motion – one sees a so-called hysteresis loop, as shown in fig. (B) – where a change in the total polarization depends on which state it started from, and in which direction the field was applied. This motion (i.e., kinetics and dynamics) of domain walls under fields can be different heterogeneities, such as defects, are present. While in a static snapshot of the local polarization at an instant in time, as shown in fig. (A) above, one only sees two domains, different parts of the same domain could show different dynamics as well as kinetics. We want to identify how many different such ‘dynamical’ states (i.e., regions with different dynamics) exist in our MD simulation when it is in equilibrium? How do these dynamical states evolve under an applied electric-field? How are these dynamical states modified in the presence of heterogeneities thereby leading to a change in the hysteretic response?
The relative atomic motion of Ti-atom as shown in fig. (A) determines the unit cell's local polarization for a given system. Orange and blue regions are two different symmetric ‘domains’ – domain with P_up_ and P_down_ respectively, with a domain-wall between them. Under an electric-field, say one pointing up, the domain-wall moves so as to increase the fraction of UP domains. At a particular electric-field, all domains (or almost all) will be converted to a single UP domain. Reversal of the electric-field will result in an increase in the DOWN domain fraction, and the total polarization pointing up will reduce in magnitude till the macroscopic polarization is flipped. Interestingly, a plot of the total polarization of the box, when as a function of the electric-field, does not show perfect reversible motion – one sees a so-called hysteresis loop, as shown in fig. (B) – where a change in the total polarization depends on which state it started from, and in which direction the field was applied. This motion (i.e., kinetics and dynamics) of domain walls under fields can be different heterogeneities, such as defects, are present. While in a static snapshot of the local polarization at an instant in time, as shown in fig. (A) above, one only sees two domains, different parts of the same domain could show different dynamics as well as kinetics. We want to identify how many different such ‘dynamical’ states (i.e., regions with different dynamics) exist in our MD simulation when it is in equilibrium? How do these dynamical states evolve under an applied electric-field? How are these dynamical states modified in the presence of heterogeneities thereby leading to a change in the hysteretic response?
The current state-of-the-art methods to extract dynamical information from molecular dynamics simulations combine Koopman’s operator theory of dynamical systems [3] or methods such as dynamic mode decomposition (DMD) [4] with Variational autoencoders (VAEs) and Time-lagged independent component analysis (TICA)[5]. We are interested in extending the current state-of-the-art approaches to identify dynamical states in hysteretic solids.
