A Deep Learning Technique to Control the Non-linear Dynamics of a Gravitational-wave Interferometer

In this work we developed a deep learning technique that successfully solves a non-linear dynamic control problem. Instead of directly tackling the control problem, we combined methods in probabilistic neural networks and a Kalman-Filter-inspired model to build a non-linear state estimator for the system. We then used the estimated states to implement a trivial controller for the now fully observable system. We applied this technique to a crucial non-linear control problem that arises in the operation of the LIGO system, an interferometric gravitational-wave observatory. We demonstrated in simulation that our approach can learn from data to estimate the state of the system, allowing a successful control of the interferometer's mirror . We also developed a computationally efficient model that can run in real time at high sampling rate on a single modern CPU core, one of the key requirements for the implementation of our solution in the LIGO digital control system. We believe these techniques could be used to help tackle similar non-linear control problems in other applications

Gravità bidimensionale e Teoria Quantistica di Liouville

La teoria di Liouville sulla sfera è legata alla gravità bidimensionale accoppiata a campi scalari di materia e alla teoria di stringa in dimensione non critica. A livello classico la teoria è invariante per azione del gruppo conforme bidimensionale se il campo non è uno scalare, ma trasforma come il fattore conforme di una metrica. In una prima parte della tesi rivediamo la quantizzazione canonica della teoria di Liouville sul cilindro, seguendo il procedimento di Curtright e Thorn (Phys.Rev.Lett 48, 1309); la simmetria conforme rimane valida a livello quantistico se si modifica la legge di trasformazione del campo. Gli operatori di vertice sono campi primari conformi con dimensione quantistica diversa da quella classica. Come in ogni teoria di campo quantistica è fondamentale disporre di uno sviluppo perturbativo. Sulla pseudosfera questo è possibile sviluppando attorno ad un campo di background regolare. Sulla sfera invece non è direttamente possibile a causa di restrizioni topologiche, legate al teorema di Gauss-Bonnet. Lo scopo di questo lavoro di tesi è lo sviluppo di un procedimento che permetta tale approccio perturbativo. Infatti sulla sfera esiste un background classico stabile in presenza di almeno tre sorgenti puntiformi. In analogia con il problema dell'uniformizzazione delle superfici di Riemann, l'equazione classica del campo di Liouville in presenza di tali sorgenti è riconducibile ad un'equazione differenziale fuchsiana che dipende da alcuni parametri completamente determinati dalle sorgenti, e dai parametri accessori di Poincaré. Questi devono soddisfare un sistema lineare che permette di determinarli completamente solo per tre sorgenti. In questo caso ricaviamo esplicitamente la soluzione classica e il limite semiclassico della funzione a tre punti. Calcoliamo le dimensioni conformi semiclassiche degli operatori di vertice e la costante di struttura per la funzione a tre punti. Il risultato è in accordo con quanto previsto dalla congettura DOZZ (Zamolodchikov e Zamolodchikov Nucl.Phys. B477, 577). Per il calcolo delle correzioni quantistiche alla funzione a tre punti si pone il problema di ottenere la funzione di Green sul background. Questo viene fatto studiando il problema classico connesso di tre sorgenti finite e una infinitesima, perturbando la soluzione trovata precedentemente. Otteniamo una formula esplicita per la funzione di Green, che si generalizza al caso di un background stabile generico. Questo apre la strada ad uno sviluppo perturbativo della teoria. Ricaviamo anche dei risultati semiclassici sulle funzioni a N punti, con n sorgenti finite e m infinitesime, nonché la forma del parametro accessorio corrispondente alla sorgente infinitesima. Riguardo il caso completamente quantistico, le funzioni di correlazione sono definite come usuale da un integrale funzionale che qui viene suddiviso in un contributo di background e in uno di fluttuazione quantistica. La prima correzione quantistica è data dal determinante funzionale dell'operatore differenziale che compare nella parte quaadratica dell'azione del campo quantistico, ovvero essenzialmente l'operatore di Laplace-Beltrami sul background classico, ovvero su una superficie a curvatura costante negativa in presenza di tre difetti conici corrispondenti alle tre sorgenti. Questo calcolo viene impostato sviluppando le tecniche di heat kernel

Probing microplasticity in small scale FCC crystals via Dynamic Mechanical Analysis

In small-scale metallic systems, collective dislocation activity has been correlated with size effects in strength and with a step-like plastic response under uniaxial compression and tension. Yielding and plastic flow in these samples is often accompanied by the emergence of multiple dislocation avalanches. Dislocations might be active pre-yield, but their activity typically cannot be discerned because of the inherent instrumental noise in detecting equipment. We apply Alternate Current (AC) load perturbations via Dynamic Mechanical Analysis (DMA) during quasi-static uniaxial compression experiments on single crystalline Cu nano-pillars with diameters of 500 nm, and compute dynamic moduli at frequencies 0.1, 0.3, 1, and 10 Hz under progressively higher static loads until yielding. By tracking the collective aspects of the oscillatory stress-strain-time series in multiple samples, we observe an evolving dissipative component of the dislocation network response that signifies the transition from elastic behavior to dislocation avalanches in the globally pre-yield regime. We postulate that microplasticity, which is associated with the combination of dislocation avalanches and slow viscoplastic relaxations, is the cause of the dependency of dynamic modulus on the driving rate and the quasi-static stress. We construct a continuum mesoscopic dislocation dynamics model to compute the frequency response of stress over strain and obtain a consistent agreement with experimental observations. The results of our experiments and simulations present a pathway to discern and quantify correlated dislocation activity in the pre-yield regime of deforming crystals.Comment: 5 pages, 3 figure

A method for the experimental measurement of bulk and shear loss angles in amorphous thin films

Brownian thermal noise is a limiting factor for the sensitivity of many high precision metrology applications, among other gravitational-wave detectors. The origin of Brownian noise can be traced down to internal friction in the amorphous materials that are used for the high reflection coatings. To properly characterize the internal friction in an amorphous material, one needs to consider separately the bulk and shear losses. In most of previous works the two loss angles were considered equal, although without any first principle motivation. In this work we present a method that can be used to extract the material bulk and shear loss angles, based on current state-of-the-art coating ring-down measurement systems. We also show that for titania-doped tantala, a material commonly used in gravitational-wave detector coatings, the experimental data strongly favor a model with two different and distinct loss angles, over the simpler case of one single loss angle

Structure and morphology of low mechanical loss TiO₂-doped Ta₂O₅

The exceptional stability required from high finesse optical cavities and high precision interferometers is fundamentally limited by Brownian motion noise in the interference coatings of the cavity mirrors. In amorphous oxide coatings these thermally driven fluctuations are dominant in the high index layer compared to those in the low index SiO₂ layer in the stack. We present a systematic study of the evolution of the structural and optical properties of ion beam sputtered TiO₂-doped Ta₂O₅ films with annealing temperature. We show that low mechanical loss in TiO₂-doped Ta₂O₅ with a Ti cation ratio = 0.27 is associated with a material that consists of a homogeneous titanium-tantalum-oxygen mixture containing a low density of nanometer sized Ar-filled voids. When the Ti cation ratio is 0.53, phase separation occurs leading to increased mechanical loss. These results suggest that amorphous mixed oxides with low mechanical loss could be identified by considering the thermodynamics of ternary phase formation

Structure and morphology of low mechanical loss TiO₂-doped Ta₂O₅

The exceptional stability required from high finesse optical cavities and high precision interferometers is fundamentally limited by Brownian motion noise in the interference coatings of the cavity mirrors. In amorphous oxide coatings these thermally driven fluctuations are dominant in the high index layer compared to those in the low index SiO₂ layer in the stack. We present a systematic study of the evolution of the structural and optical properties of ion beam sputtered TiO₂-doped Ta₂O₅ films with annealing temperature. We show that low mechanical loss in TiO₂-doped Ta₂O₅ with a Ti cation ratio = 0.27 is associated with a material that consists of a homogeneous titanium-tantalum-oxygen mixture containing a low density of nanometer sized Ar-filled voids. When the Ti cation ratio is 0.53, phase separation occurs leading to increased mechanical loss. These results suggest that amorphous mixed oxides with low mechanical loss could be identified by considering the thermodynamics of ternary phase formation

Semiclassical and quantum Liouville theory on the sphere

We solve the Riemann-Hilbert problem on the sphere topology for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincare' accessory parameters. In this way we compute the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infinitesimal. With the same technique we compute the exact Green function on the sphere with three finite singularities. Turning to the full quantum problem we address the calculation of the quantum determinant on the background of three finite charges and the further perturbative corrections. The zeta function technique provides a theory which is not invariant under local conformal transformations. Instead by employing a regularization suggested in the case of the pseudosphere by Zamolodchikov and Zamolodchikov we obtain the correct quantum conformal dimensions from the one loop calculation and we show explicitly that the two loop corrections do not change such dimensions. We expect such a result to hold to all order perturbation theory.Comment: 26 pages, latex, 1 figure, references added, 2 typos correcte

Investigation of effects of assisted ion bombardment on mechanical loss of sputtered tantala thin films for gravitational wave interferometers

Reduction of Brownian thermal noise due to mechanical loss in high-reflectivity mirror coatings is critical for improving the sensitivity of future gravitational wave detectors. In these mirrors, the mechanical loss at room temperature is dominated by the high refractive index component, amorphous tantala (Ta₂O₅) or tantala doped with titania (Ti∶Ta₂O₅). Toward the goal of identifying mechanisms that could alter mechanical loss, this work investigates the use of assist ion bombardment in the reactive ion beam sputtering deposition of tantala single layers. Low-energy assist ion bombardment can enhance adatom diffusion. Low-energy assist Ar⁺ and Xe⁺ ion bombardment at different conditions was implemented during deposition to identify trends in the mechanical loss with ion mass, ion energy, and ion dose. It is shown that the atomic structure and bonding states of the tantala thin films are not significantly modified by low-energy assist ion bombardment. The coatings mechanical loss remains unaltered by ion bombardment within errors. Based on an analysis of surface diffusivity, it is shown that the dominant deposition of tantala clusters and limited surface diffusion length of oxygen atoms constrain structural changes in the tantala films. A slower deposition rate coupled with a significant increase in the dose of the low-energy assist ions may provide more favorable conditions to improve adatom diffusivity