Destructive Impact of Molecular Noise on Nanoscale Electrochemical Oscillators

We study the loss of coherence of electrochemical oscillations on meso- and nanosized electrodes with numeric simulations of the electrochemical master equation for a prototypical electrochemical oscillator, the hydrogen peroxide reduction on Pt electrodes in the presence of halides. On nanoelectrodes, the electrode potential changes whenever a stochastic electron-transfer event takes place. Electrochemical reaction rate coefficients depend exponentially on the electrode potential and become thus fluctuating quantities as well. Therefore, also the transition rates between system states become time-dependent which constitutes a fundamental difference to purely chemical nanoscale oscillators. Three implications are demonstrated: (a) oscillations and steady states shift in phase space with decreasing system size, thereby also decreasing considerably the oscillating parameter regions; (b) the minimal number of molecules necessary to support correlated oscillations is more than 10 times as large as for nanoscale chemical oscillators; (c) the relation between correlation time and variance of the period of the oscillations predicted for chemical oscillators in the weak noise limit is only fulfilled in a very restricted parameter range for the electrochemical nano-oscillator.Comment: 18 pages, 9 figure

Unusual synchronization phenomena during electrodissolution of silicon: the role of nonlinear global coupling

The photoelectrodissolution of n-type silicon constitutes a convenient model system to study the nonlinear dynamics of oscillatory media. On the silicon surface, a silicon oxide layer forms. In the lateral direction, the thickness of this layer is not uniform. Rather, several spatio-temporal patterns in the oxide layer emerge spontaneously, ranging from cluster patterns and turbulence to quite peculiar dynamics like chimera states. Introducing a nonlinear global coupling in the complex Ginzburg-Landau equation allows us to identify this nonlinear coupling as the essential ingredient to describe the patterns found in the experiments. The nonlinear global coupling is designed in such a way, as to capture an important, experimentally observed feature: the spatially averaged oxide-layer thickness shows nearly harmonic oscillations. Simulations of the modified complex Ginzburg-Landau equation capture the experimental dynamics very well.Comment: To appear as a chapter in "Engineering of Chemical Complexity II" (eds. A.S. Mikhailov and G.Ertl) at World Scientific in Singapor

Scaling full seismic waveform inversions

The main goal of this research study is to scale full seismic waveform inversions using the adjoint-state method to the data volumes that are nowadays available in seismology. Practical issues hinder the routine application of this, to a certain extent theoretically well understood, method. To a large part this comes down to outdated or flat out missing tools and ways to automate the highly iterative procedure in a reliable way. This thesis tackles these issues in three successive stages. It first introduces a modern and properly designed data processing framework sitting at the very core of all the consecutive developments. The ObsPy toolkit is a Python library providing a bridge for seismology into the scientific Python ecosystem and bestowing seismologists with effortless I/O and a powerful signal processing library, amongst other things. The following chapter deals with a framework designed to handle the specific data management and organization issues arising in full seismic waveform inversions, the Large-scale Seismic Inversion Framework. It has been created to orchestrate the various pieces of data accruing in the course of an iterative waveform inversion. Then, the Adaptable Seismic Data Format, a new, self-describing, and scalable data format for seismology is introduced along with the rationale why it is needed for full waveform inversions in particular and seismology in general. Finally, these developments are put into service to construct a novel full seismic waveform inversion model for elastic subsurface structure beneath the North American continent and the Northern Atlantic well into Europe. The spectral element method is used for the forward and adjoint simulations coupled with windowed time-frequency phase misfit measurements. Later iterations use 72 events, all happening after the USArray project has commenced, resulting in approximately 150`000 three components recordings that are inverted for. 20 L-BFGS iterations yield a model that can produce complete seismograms at a period range between 30 and 120 seconds while comparing favorably to observed data