Nonlinear material properties shape locomotor performance in hydrozoan jellyfish
Nonlinear mechanics and dynamics are pervasive at all levels of biological organization. Chapter 1 presents an overview of the diversity of nonlinear mechanics across various spatial scales and nonlinear dynamics over different temporal scales. This chapter sets the stage for an integrated perspective of the role of nonlinear material properties in hydrozoan locomotion.Composite swimming behavior of hydrozoan jellyfish incorporates neuronal control, muscle forces, passive mechanics, and fluid stresses. In Chapter 2, I measure passive mechanical properties of mesoglea from Polyorchis penicillatus and Mitrocoma cellularia and find different nonlinear dependencies on strain but no interspecific difference in stiffness. Fits to stress-strain curves estimate an exponent of nonlinearity for each species which is incorporated into a simple dynamical system to model the passive mechanical properties of mesoglea. Nonlinearity yields oscillation amplitude augmentation and added frequency components that depend on its magnitude.Coupling the frequency of muscle activation with the resonant frequency of a locomotor structure leads to large oscillation amplitudes for small periodic forces and may enable energetic savings. In Chapter 3, I explore resonant phenomena in medusa Mitrocoma cellularia. Experimental perturbation by manipulation of seawater viscosity tests whether emergent responses are more consistent with nonlinear or linear resonant behavior. Shifting bell position, without concurrent shifts in driving frequency, suggests that passive exploitation of strain-dependent bell stiffness may enable recovery from perturbation. A recovery mechanism independent of neural feedback is consistent with predictions of nonlinear resonant phenomena.In Chapter 4, a coupled fluid-solid model enables integration of aspects of locomotion to predict forward swimming velocity. Navigating a multi-dimensional parameter space, which includes bell size, shape, stiffness, and patterns of force production, maps nonlinear material properties against structural and temporal variables. Nonlinearity often enhances swimming velocity, but creates a landscape of tuning optima in which combinations of parameters contribute differentially to swimming performance. Smaller jellyfish exploit a larger set of "suitable" combinations of shape, stiffness, and muscle timing parameters than large jellyfish. Nonlinearity enhances peaks and troughs in performance and interacts with temporal patterns of force production to confer sensitivity over a fine scale, but robustness to perturbation over a longer scale.
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