No abstract

We study the rate dependent response of a bistable chain subjected to thermal fluctuations. The study is motivated by the fact that the behavior of this model system is prototypical to a wide range of nonlinear processes in materials physics, biology and chemistry. To account for the stochastic nature of the system response, we formulate a set of governing equations for the evolution of the probability density of meta-stable configurations. Based on this approach, we calculate the behavior for a wide range of parametric values, such as rate, temperature, overall stiffness, and number of elements in the chain. Our results suggest that fundamental characteristics of the response, such as average transition stress and hysteresis, can be captured by a simple law which folds the influence of all these factors into a single non-dimensional quantity. We also show that the applicability of analytical results previously obtained for single-well systems can be extended to systems having multiple wells by proper definition of rate and of the transition stress.

A stochastic and rate-dependent response originating from thermal fluctuations over a highly nonconvex energy landscape is a prevailing aspect of the mechanical behavior of nanoscale structures. The overdamped dynamics of a bistable chain subjected to thermal fluctuations is prototypical of such behavior. Based on this approach, we find a new nondimensional quantity, similar in its mathematical structure to Boltzmann's factor, which captures the intricate competition between rate, temperature, and energy barriers underlying the system dynamics. In turn, we obtain simple universal laws for predicting statistical properties of the mechanical response.

Titin is a giant protein that functions as a shock absorber in sarcomeres—the basic contractile unit of muscles. When stretched, thermal disturbances are expected to make titin follow the Maxwell path (global minimizer) of its energy. This path involves neither energy dissipation nor hysteresis. Therefore, a basic question is how does titin releases energy so efficiently? By adopting a simple mechanical model of a chain comprised from bistable elements, we show that dissipation depends on both system size and the height of the energy barrier separating equilibrium configurations. In this sense, titin is an optimal product of evolution.

The “jerky” motion of a twin boundary in the ferromagnetic shape memory alloy NiMnGa is studied experimentally and theoretically. We employ a bi-stable chain model in order to interpret macroscopic stress-strain experiments and extract important micro-level properties. The analysis reveals the existence of a periodic barrier for type I twin boundary motion with an average distance of 19 μm and amplitude of 0.16 J/m2. Further, we show that the macroscopic mechanical response depends on the length of the crystal and predict a significant decrease of the hysteresis in sub-mm length specimens.