published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Civil Engineering / Master / Master of Philosophy

It has been customary practice in galactic dynamics to implicitly assume that the corresponding N-body problem is (near) integrable. After a review of some relevant ideas from non-linear dynamics, I discuss the evidence suggesting that the above assumption is not generally satisfied and the consequences of such a situation. Next, I discuss the characterization of such "chaotic" behaviour. A geometric method-which I argue is best suited for measuring the instability properties of N-body systems-is tested on systems of 231 particles integrated with high precision and displaying "obvious" instabilities like violent relaxation and collective processes. The predicted instability time-scales show good agreement with those inferred from the spatial evolution. As a further test I study closed systems which relax towards definite equilibrium states. The times of relaxation towards such states are then compared to the exponential instability time-scales in an attempt to identify the physical interpretation of the exponential instability that appears to be always present in N -body systems. As an application of the method, the variation of the exponential divergence time-scales in N -body Plummer models with particle number, rotation, softening, and central mass is studied. I also study the extent of chaotic behaviour in some non-axisymmetric but smooth potentials representing galaxies with triaxial halos. This is done with the aid of Liapunov exponents, Poincare maps, and stability analysis of resonant orbits. It is found that a significant amount of chaos is usually present and increases dramatically with the addition of rotating bar perturbations, or of central masses. The degree of instability may also depend on the presence of external noise. It is also shown that dissipative perturbations have the important effect of producing an inflow of matter to the central areas. The consequences of the above processes are then discussed and it is suggested that they may explain some aspects of the observed relative bulge-disk-halo contributions to galaxy rotation curves.

Molecular dynamics (MD) provides an atomically detailed description of the dynamics of a system of atoms. It is a useful tool to understand how protein function arises from the dynamics of the atoms of the protein and of its environment. When the MD model is accurate, analyzing a MD trajectory unveils features of the proteins that are not available from a single snapshot or a static structure. When the sampling of the accessible configurations is accurate, we can employ statistical mechanics (SM) to connect the trajectory generated by MD to experimentally measurable kinetic and thermodynamic quantities that are related to function. In this dissertation I describe three applications of MD and SM in the field of biochemistry. First, I discuss the theory of alchemical methods to compute free energy differences. In these methods a fragment of a system is computationally modified by removing its interactions with the environment and creating the interactions of the environment with the new species. This theory provides a numerical scheme to efficiently compute protein-ligand affinity, solvation free energies, and the effect of mutations on protein structure. I investigated the theory and stability of the numerical algorithm. The second research topic that I discuss considers a model of the dynamics of a set of coarse variables. The dynamics in coarse space is modeled by the Smoluchowski equation. To employ this description it is necessary to have the correct potential of mean force and diffusion tensor in the space of coarse variables. I describe a new method that I developed to extract the diffusion tensor from a MD simulation. Finally, I employed MD simulations to explain at a microscopic level the stereospecificity of the enzyme ketoreductase. To do so, I ran multiple simulations of the enzyme bound with the correct ligand and its enantiomer in a reactive configuration. The simulations showed that the enzyme retained the correct stereoisomer closer to the reactive configuration, and highlighted which interactions are responsible for the specificity. These weak physical interactions enhance binding with the correct ligand even prior to the steps of chemical modification. / text

Topological insulators and superconductors, which are featured by not only the topological characteristics of their gapped bulk band structure but also the special edge or surface states, have attracted great attention in the past few years. A complete classification of topological insulators and superconductors in terms of symmetry and spatial dimension has been established, while the application of their surface states remains a challenge. The gapless phases which have topologically stable Fermi surfaces could also exhibit peculiar surface states and topological transport phenomena in the bulk. In this thesis, the topological DIII-classs superconducting chains and the application of its Majorana edge states are studied. On the other hand, Weyl semimetals, as the representative example of topological gapless phases, and its exotic transport phenomena are also investigated. Majorana edge states have been a focus of condensed matter research for their potential applications in topological quantum computation, which appear in the topological DIII-class superconducting chains protected by both the particle-hole and time reversal symmetries. We utilize two charge-qubit arrays to explicitly simulate one type of DIII-class superconducting chains and the universal quantum operations performed on the Majorana edge states. It is shown that combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. It is further shown that in a similar way, a controlled-NOT gate for two topological qubits can be simulated in four charge-qubit arrays. Although the current scheme may not truly realize topological quantum operations, we elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations. Weyl semimetals possess nontrivial Fermi surface topology in that the pair of Weyl points with opposite topological charges is separated from each other in momentum space. The physical manifestations of this Fermi surface topology are protected surface states and exotic transport phenomena including the anomalous Hall effect as well as the chiral magnetic effect. By studying the path integral measure under the chiral transformation, it is shown that these transport phenomena can be described by the chiral anomaly which appears when the chiral Weyl fermion couples to the topologically nontrivial gauge field. The case of the gauge anomaly for the Weyl fermion coupled to a non-Abelian gauge field is also discussed. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

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