On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment

In a probabilistic assessment of the performance of structures subjected to uncertain environmental loads such as earthquakes, an important problem is to determine the probability that the structural response exceeds some specified limits within a given duration of interest. This problem is known as the first excursion problem, and it has been a challenging problem in the theory of stochastic dynamics and reliability analysis. In spite of the enormous amount of attention the problem has received, there is no procedure available for its general solution, especially for engineering problems of interest where the complexity of the system is large and the failure probability is small.

The application of simulation methods to solving the first excursion problem is investigated in this dissertation, with the objective of assessing the probabilistic performance of structures subjected to uncertain earthquake excitations modeled by stochastic processes. From a simulation perspective, the major difficulty in the first excursion problem comes from the large number of uncertain parameters often encountered in the stochastic description of the excitation. Existing simulation tools are examined, with special regard to their applicability in problems with a large number of uncertain parameters. Two efficient simulation methods are developed to solve the first excursion problem. The first method is developed specifically for linear dynamical systems, and it is found to be extremely efficient compared to existing techniques. The second method is more robust to the type of problem, and it is applicable to general dynamical systems. It is efficient for estimating small failure probabilities because the computational effort grows at a much slower rate with decreasing failure probability than standard Monte Carlo simulation. The simulation methods are applied to assess the probabilistic performance of structures subjected to uncertain earthquake excitation. Failure analysis is also carried out using the samples generated during simulation, which provide insight into the probable scenarios that will occur given that a structure fails.

Developing peptide based capture agents for diagnostics and therapeutics

Iterative in situ click chemistry (IISCC) is a robust general technology for development of high throughput, inexpensive protein detection agents. In IISCC, the target protein acts as a template and catalyst, and assembles its own ligand from modular blocks of peptides. This process of ligand discovery is iterated to add peptide arms to develop a multivalent ligand with increased affinity and selectivity. The peptide based protein capture agents (PCC) should ideally have the same degree of selectivity and specificity as a monoclonal antibody, along with improved chemical stability. We had previously reported developing a PCC agent against bovine carbonic anhydrase II (bCAII) that could replace a polyclonal antibody. To further enhance the affinity or specificity of the PCC agent, I explore branching the peptide arms to develop branched PCC agents against bCAII. The developed branched capture agents have two to three fold higher affinities for the target protein. In the second part of my thesis, I describe the epitope targeting strategy, a strategy for directing the development of a peptide ligand against specific region or fragment of the protein. The strategy is successfully demonstrated by developing PCC agents with low nanomolar binding affinities that target the C-terminal hydrophobic motif of Akt2 kinase. One of the developed triligands inhibits the kinase activity of Akt. This suggests that, if targeted against the right epitope, the PCC agents can also influence the functional properties of the protein. The exquisite control of the epitope targeting strategy is further demonstrated by developing a cyclic ligand against Akt2. The cyclic ligand acts as an inhibitor by itself, without any iteration of the ligand discovery process. The epitope targeting strategy is a cornerstone of the IISCC technology and opens up new opportunities, leading to the development of protein detection agents and of modulators of protein functions.

Noise Cancellation for Gravitational Wave Detectors

The LIGO gravitational wave detectors are on the brink of making the first direct detections of gravi- tational waves. Noise cancellation techniques are described, in order to simplify the commissioning of these detectors as well as significantly improve their sensitivity to astrophysical sources. Future upgrades to the ground based detectors will require further cancellation of Newtonian gravitational noise in order to make the transition from detectors striving to make the first direct detection of gravitational waves, to observatories extracting physics from many, many detections. Techniques for this noise cancellation are described, as well as the work remaining in this realm.

Quantum Electromechanics with Two Tone Drive

In the field of mechanics, it is a long standing goal to measure quantum behavior in ever larger and more massive objects. It may now seem like an obvious conclusion, but until recently it was not clear whether a macroscopic mechanical resonator -- built up from nearly 10¹³ atoms -- could be fully described as an ideal quantum harmonic oscillator. With recent advances in the fields of opto- and electro-mechanics, such systems offer a unique advantage in probing the quantum noise properties of macroscopic electrical and mechanical devices, properties that ultimately stem from Heisenberg's uncertainty relations. Given the rapid progress in device capabilities, landmark results of quantum optics are now being extended into the regime of macroscopic mechanics.

The purpose of this dissertation is to describe three experiments -- motional sideband asymmetry, back-action evasion (BAE) detection, and mechanical squeezing -- that are directly related to the topic of measuring quantum noise with mechanical detection. These measurements all share three pertinent features: they explore quantum noise properties in a macroscopic electromechanical device driven by a minimum of two microwave drive tones, hence the title of this work: "Quantum electromechanics with two tone drive".

In the following, we will first introduce a quantum input-output framework that we use to model the electromechanical interaction and capture subtleties related to interpreting different microwave noise detection techniques. Next, we will discuss the fabrication and measurement details that we use to cool and probe these devices with coherent and incoherent microwave drive signals. Having developed our tools for signal modeling and detection, we explore the three-wave mixing interaction between the microwave and mechanical modes, whereby mechanical motion generates motional sidebands corresponding to up-down frequency conversions of microwave photons. Because of quantum vacuum noise, the rates of these processes are expected to be unequal. We will discuss the measurement and interpretation of this asymmetric motional noise in a electromechanical device cooled near the ground state of motion.

Next, we consider an overlapped two tone pump configuration that produces a time-modulated electromechanical interaction. By careful control of this drive field, we report a quantum non-demolition (QND) measurement of a single motional quadrature. Incorporating a second pair of drive tones, we directly measure the measurement back-action associated with both classical and quantum noise of the microwave cavity. Lastly, we slightly modify our drive scheme to generate quantum squeezing in a macroscopic mechanical resonator. Here, we will focus on data analysis techniques that we use to estimate the quadrature occupations. We incorporate Bayesian spectrum fitting and parameter estimation that serve as powerful tools for incorporating many known sources of measurement and fit error that are unavoidable in such work.