GFLean: An Autoformalisation Framework for Lean via GF

We present an autoformalisation framework for the Lean theorem prover, called GFLean. GFLean uses a high-level grammar writing tool called Grammatical Framework (GF) for parsing and linearisation. GFLean is implemented in Haskell. We explain the functionalities of GFLean, its inner working and discuss its limitations. We also discuss how we can use neural network based translation programs and rule based translation programs together complimenting each other to build robust autoformalisation frameworks.Comment: 19 Pages, 3 Figure

Isomerization and fragmentation of polyatomic molecules induced by ultraviolet and extreme UV light

Doctor of PhilosophyDepartment of PhysicsDaniel RollesImaging molecular structures evolving at their natural timescales, during a chemical reaction, with an atomic-scale resolution has been a long-standing goal for physicists and chemists. With the recent developments in experimental techniques, as well as the light sources, such as synchrotron radiation sources, free-electron lasers (FELs), ultrafast lasers, and high-harmonic sources, it is now possible to study the molecular dynamics and structural changes with femtosecond (in some cases attosecond) time-resolution, for near-infrared to x-ray wavelengths. These advancements are particularly useful in studying a wide range of photoinduced chemical reactions and photoinduced fragmentation. In this thesis, some of the advanced techniques are used to study photoinduced isomerization and fragmentation. This thesis also partly focuses on developing the tools and techniques which can be used to study these molecular structural changes. Several molecular systems are studied throughout the thesis. Some of them are studied with the goal of understanding the chemistry post photoexcitation and photo-fragmentation, while others were aiming for method development for future experiments. Specifically, some of the experiments are performed on a prototypical heterocyclic ring molecule, thiophenone. One such experiment studies photochemistry after ultraviolet light absorption, using time-resolved photoelectron spectroscopy at a free-electron laser. The experimental results are combined with ab-initio molecular dynamics and electronic structure calculation for the ground state and excited state molecules, which revealed insights about the electronic and nuclear dynamics. Ring-opening is the most dominant process upon photoexcitation, driven by a ballistic extension of C-S bond, and is completed within $\sim$350 fs. The ground state trajectories also confirm the formation of three ring-opened products, providing detailed insights into this reaction. Ring-opening reactions of similar types are considered as candidates for designing fast molecular switches. In another study, the fragmentation pathways of thiophenone are studied using ion-electron coincidence experiments. With these experiments, it is observed that some of the fragmentation pathways may be decoupled purely based upon the photoelectron energy, which is also a measure of the internal energy of an ion. Another method, which is often used to study dissociation, fragmentation, and isomerization pathways, is coincident ion momentum imaging. The sensitivity of this method in distinguishing similar-looking structures is demonstrated by distinguishing conformational isomers of 1,2-dibromoethane, which only differ by a rotation around a single bond and coexist in a particular ratio at any given temperature. Sequential and concerted breakup pathways were disentangled using a newly developed Native frames method to obtain information about the initial molecular geometry. These experiments may trigger future time-resolved studies to monitor subtle molecular structural changes using coincidence ion momentum imaging. The work presented in this thesis uses a wide variety of techniques to understand light-induced isomerization and fragmentation dynamics, from simple molecules to moderately complex systems. This work contributes to the understanding developed for the prototypical systems, which may help formulate general principles underlying some light-induced reactions and processes

A Designer’s Approach for Estimation of Nuclear-Air-Blast-Induced Ground Motion

A reliable estimate of free-field ground displacement induced by nuclear-air-blast is required for design of underground strategic structures. A generalized pseudostatic formulation is proposed to estimate nuclear-air-blast-induced ground displacement that takes into account nonlinear stress-strain behaviour of geomaterials, stress-dependent wave propagation velocity, and stress wave attenuation. This proposed formulation is utilized to develop a closed-form solution for linearly decaying blast load applied on a layered ground medium with bilinear hysteretic behaviour. Parametric studies of closed-form solution indicated that selection of appropriate constrained modulus consistent with the overpressure is necessary for an accurate estimation of peak ground displacement. Stress wave attenuation affects the computed displacement under low overpressure, and stress-dependent wave velocity affects mainly the occurrence time of peak displacement and not its magnitude. Further, peak displacements are estimated using the proposed model as well as the UFC manual and compared against the field data of atmospheric nuclear test carried out at Nevada test site. It is found that the proposed model is in good agreement with field data, whereas the UFC manual significantly underestimates the peak ground displacements under higher overpressures

On the link between pole-zero distance and maximum reachable damping in MIMO systems

peer reviewedThis paper studies the possibility of extending the already proved link between the pole-zero distance and the maximum reachable damping ratio in single input single output (SISO) systems to multiple inputs multiple outputs (MIMO) ones. This extension is shown to be possible when the considered system presents specific properties: (i) it is equipped with collocated transducers with small authority, (ii) the system has a small modal density in the frequency band of interest and (iii) a low authority control law is used. It is indeed demonstrated that when these three conditions are satisfied, the analytical development of the closed-loop poles convergence is equivalent to the one observed with SISO cases, except that the anti-resonances are replaced by the transmission zeros (TZs). Consequently, it is concluded that the maximum reachable damping ratio is directly proportional to the pole-transmission zero distance for such MIMO systems. This conclusion is demonstrated with two numerical examples (a cantilever beam and a simply supported plate) and experimentally validated on a cantilever beam where all the studied systems are equipped with two collocated pairs of piezoelectric patches

On transmission Zeros of piezoelectric structures

The evaluation of transmission zeros is of great importance for the control engineering applications. The structures equipped with piezoelectric patches are complex to model and usually require finite element approaches supplemented by model reduction. This study rigorously investigates the influence of mesh size, model reduction, boundary conditions (free and clamped), and sensor/actuator configuration (collocated and non-collocated) on the evaluation of transmission zeros of the piezoelectric structures. The numerical illustrations are presented for a thin rectangular plate equipped with a single pair of piezoelectric voltage sensor/ voltage actuator. Through the examples considered in this study, a link is presented between the static response (or static deflected shape) and the transmission zeros of the piezoelectric structures. This interesting observation forms the basis of: (i) a local mesh refinement strategy for computationally efficient estimation of the transmission zeros and (ii) a physical interpretation of the pole-zero pattern in the case of piezoelectric structures. The physical interpretation developed in this study helps in qualitatively explaining the pole-zero patterns observed for different configurations. It is also shown that this understanding of the relation between the static deformed shape and the transmission zeros can be used by the practitioners to modify the pole-zero pattern through a careful selection of the orientation and the size of the piezoelectric patches

High Harmonic Generation in Mixed Xuv and Nir Fields at a Free-Electron Laser

We Present the Results of an Experiment Investigating the Generation of High-Order Harmonics by a Femtosecond Near-Infrared (NIR) Laser Pulse in the Presence of an Extreme Ultraviolet (XUV) Field Provided by a Free-Electron Laser (FEL), a Process Referred to as XUV-Assisted High-Order Harmonic Generation (HHG). Our Experimental Findings Show that the XUV Field Can Lead to a Small Enhancement in the Harmonic Yield When the XUV and NIR Pulses overlap in Time, while a Strong Decrease of the HHG Yield and a Red Shift of the HHG Spectrum is Observed When the XUV Precedes the NIR Pulse. the Latter Observations Are in Qualitative Agreement with Model Calculations that Consider the Effect of a Decreased Number of Neutral Emitters but Are at Odds with the Predicted Effect of the Correspondingly Increased Ionization Fraction on the Phase Matching. Our Study Demonstrates the Technical Feasibility of XUV-Assisted HHG Experiments at FELs, Which May Provide New Avenues to Investigate Correlation-Driven Electron Dynamics as Well as Novel Ways to Study and Control Propagation Effects and Phase Matching in HHG

Multiple-core-hole resonance spectroscopy with ultraintense X-ray pulses

Understanding the interaction of intense, femtosecond X-ray pulses with heavy atoms is crucial for gaining insights into the structure and dynamics of matter. One key aspect of nonlinear light-matter interaction was, so far, not studied systematically at free-electron lasers -- its dependence on the photon energy. Using resonant ion spectroscopy, we map out the transient electronic structures occurring during the complex charge-up pathways. Massively hollow atoms featuring up to six simultaneous core holes determine the spectra at specific photon energies and charge states. We also illustrate how the influence of different X-ray pulse parameters that are usually intertwined can be partially disentangled. The extraction of resonance spectra is facilitated by the fact that the ion yields become independent of the peak fluence beyond a saturation point. Our study lays the groundwork for novel spectroscopies of transient atomic species in exotic, multiple-core-hole states that have not been explored previously.Comment: Supplementary information is include

Ultrafast electronic relaxation pathways of the molecular photoswitch quadricyclane

The light-induced ultrafast switching between molecular isomers norbornadiene and quadricyclane can reversibly store and release a substantial amount of chemical energy. Prior work observed signatures of ultrafast molecular dynamics in both isomers upon ultraviolet excitation but could not follow the electronic relaxation all the way back to the ground state experimentally. Here we study the electronic relaxation of quadricyclane after exciting in the ultraviolet (201 nanometres) using time-resolved gas-phase extreme ultraviolet photoelectron spectroscopy combined with non-adiabatic molecular dynamics simulations. We identify two competing pathways by which electronically excited quadricyclane molecules relax to the electronic ground state. The fast pathway (<100 femtoseconds) is distinguished by effective coupling to valence electronic states, while the slow pathway involves initial motions across Rydberg states and takes several hundred femtoseconds. Both pathways facilitate interconversion between the two isomers, albeit on different timescales, and we predict that the branching ratio of norbornadiene/quadricyclane products immediately after returning to the electronic ground state is approximately 3:2