Dynamic hysteresis and transitions controlled by asymmetry in potential barrier shaping

Abstract

Our study unveils the precise role of the underlying potential in regulating the fundamental processes of dynamic hysteresis, which manifests in numerous natural and designed systems. We identify that it is possible to induce symmetry breaking in dynamic hysteresis, and consequently to observe dynamic transitions under moderate conditions, which is absent for the symmetric case, if appropriate asymmetry is implemented in the design of the underlying potential. This kind of asymmetry appears through the disparate widths of the two wells of the intrinsic bistable potential governing the dynamics and the barrier separating them. It is characteristically distinct from the potential in which the two minima are energetically dissimilar. Our understanding suggests that only the intrinsic asymmetry of the former type can substantially influence the elemental dynamics of the processes to generate significant effects on the outcomes. Our study presents a novel approach to quantitatively regulate the outputs, to increase or decrease the extent of dynamic hysteresis, based on the requirements, by effectively controlling the proper asymmetry of the intrinsic potential.

Figures (4)

• Figure 1: (a) Bistable potential with different values of $c$ which affect the curvature of the potential minima and maximum, and accounts for the degree of asymmetry in the potential. (b) Modulation in the shape of the potential due to the external periodic force over a complete period of forcing.
• Figure 2: (a) Lag: $P_{R}(t)$ vs $t$ in comparison to $F(t)$ vs $t$ at $F_0 = 0.5$, (b) Hysteresis loops: $P_{R}(t)$ versus $F(t)$ at $F_0 = 0.5$, $D = 0.5$ and $\omega = 0.1$, Turn over: Hysteresis loop area versus $c$ at $F_0 = 0.5$ for the parametric variation of (c) the noise strength $D$ at $\omega = 0.5$ and (d) the frequency of oscillation $\omega$ at $D = 0.3$.
• Figure 3: $Q$ versus $c$ for parametric variation of (a) the noise strength $D$ with $F_0 = 0.5$ and $\omega = 0.01$, (b) the forcing frequency $\omega$ with $D = 0.4$ and $F_0 =0.5$ and (c) the forcing amplitude $F_0$ with $D=0.4$ and $\omega = 0.05$.
• Figure 4: (a) Lag: $P_{R}(t)$ vs $t$ in comparison to $F(t)$ vs $t$ at $F_{0} = 0.5$, $D = 0.5$ and $\omega = 0.1$, (b) Hysteresis loops: $P_{R}(t)$ versus $F(t)$ at $F_{0} = 0.5$, $D = 0.3$ and $\omega = 0.1$, (c) Turnover: Hysteresis loop area versus $c$, and (d) the order parameter $Q$ versus $c$ at $F_{0} = 0.5$ at $D=0.3$ and $\omega=0.01$. The results are obtained through the semi-analytical approach.