| In this thesis, we investigate the ability to implement desired changes in dynamical systems of nonlinear oscillators and also in a particular complex material system. In brief: we explore the dynamics and memory capabilities of a harmonically driven integrate-and-fire oscillator; we consider the network dynamics of nanoscale implementations of such oscillators with fast and strong coupling, and propose a computational scheme that provides logical manipulation of attractor-logic states of the oscillators via gating the interactions among the oscillators; and in an experimental investigation, we show that electron-beam lithographic techniques can be used to selectively change the material properties of mesoporous silica at the nanoscale. This thesis employs a wide range of investigative techniques, and delivers important analytical, computational, and experimental results for the systems under consideration.;In Chapter 2 of this thesis, we investigate the presence, dynamics, and basin structure of coexisting attractors for a harmonically driven integrate-and-fire oscillator. These coexisting attractors may be phase-shifted versions of the same mode-locked waveform or may be members of different waveforms. Coexisting attractors can represent distinct robust logic states since small perturbations will decay and keep the oscillator with the memory of its original attractor-logic state. They can also be used for computation since the basin structure describes the necessary strength and timing for impulsive interactions to move the oscillator to a new robust attractor-logic state.;In the following chapter, we present a new scheme for information processing in a network of locally coupled driven nonlinear oscillators, realizable at the nanoscale. Using this scheme, any logical rule can be implemented among the oscillators at any time via gated interactions. In the course of our exposition, we give the first general account of the dynamics of any capacitively coupled single-electron-tunneling-junction network and we show how the dynamics simplify for the limiting regime of strong and fast coupling, which are both critical steps towards designing useful computational systems from such oscillators. We use these results to show how this non-autonomous dynamical system can be made into a basis for powerful information processing. For bistable oscillators, we show that each physical gate can act as every possible logic gate through appropriately selected bias voltages. As an example of the flexibility of this computational substrate, we also apply our scheme to demonstrate that, with the necessary external influence, a simple network of oscillators can implement any of the 256 possible elementary cellular automata rules.;In the final chapter of this thesis, we describe the first account of using a focused electron beam to directly write nanoscale features into thin films of mesoporous silica. We show that we can both modulate film thickness and induce chemical resistance in patterned regions. We show that this chemical resistance can be achieved with the same conditions and comparable electron dosages as are used in more common applications of electron beam lithography (EBL). We further show that gentle polar solvents, including de-ionized water, are sufficient etchants, readily discriminating between the features and the unexposed film. Taken together, our results suggest a novel yet simple strategy to tailor mesoporous silica with conventional nanoscale lithographic techniques. |
