UC Davis

This dissertation focuses on nonlinear dynamical systems with net responses. In particular, we discover a steady field induced within liquids by a sinusoidal potential, referred to as Asymmetric Rectified Electric Field (AREF). AREF helps explain several long-standing discrepancies regarding the behavior of particles and electrically induced fluid flows in response to oscillatory potentials, broadly impacts the interpretation of the experiments, and offers new avenues for research in electrokinetics. Additionally, we demonstrate that non-antiperiodic, zero-time-average, excitation of a spatially symmetric system can yield net responses. We consider an object atop a flat surface that undergoes a dual-mode horizontal vibration. Our calculations, and subsequent experimental observations, show that the object experiences a net drift if the applied frequencies are the ratio of odd and even numbers (e.g., 1 Hz and 2 Hz). As a corollary, our theory suggests that swapping the powered (non-antiperiodic potential) and the grounded parallel electrodes of an electrochemical cell alters the system behavior, a prediction verified by our experimental observations on the AREF-induced electrophoresis.