On Time Correlations for KPZ Growth in One Dimension

Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance with two approaches: (1) the variational problem and (2) deriving the covariance of the time-integrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the l arge time behavior for the covariance of the height gradients

Issues and Challenges in Orbital-free Density Functional Calculations

Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential calculations and, if the latter, construction of the pseudo-potential. Another is the stability, speed, and accuracy of solution algorithms. Underlying both is the fundamental issue of satisfactory quality of the approximate functionals (kinetic energy and exchange-correlation). We address both computational issues and illustrate them by some comparative performance testing of our recently developed modified-conjoint generalized gradient approximation kinetic energy functionals. Comparisons are given for atoms, diatomic molecules, and some simple solids.Comment: submitted to Computer Physics Communication

Towards 6 Degrees of Freedom Seakeeping Simulations Using a Fully Nonlinear Potential Flow Method

In recent years, the International Maritime Organization introduced a new set of rules in order to try to reduce emissions of ships by improving their efficiency. To assess the energy efficiency of a new ship, the regulations require to estimate the Energy Efficiency Design Index (EEDI), which represent the amount of Carbon Dioxide produced per mile in relation to the amount of cargo carried, and verify that it is smaller than a prescribed value. For a proper evaluation of the EEDI, it is necessary to estimate the added resistance in waves with high accuracy. There are different ways to evaluate added resistance: empirical methods, adding a safety factor to the calm water resistance called sea margin, numerical simulations and model test experiments. Nowadays, the most used way during the design stage to do that is employing numerical simulations. Numerical simulations are not only used for the estimation of added resistance, but also to predict ship motions. If the motions are known at an early design stage, it is possible to modify the design of a ship to minimize them in order to improve the performance of the ship and to increase the safety and comfort of those who are on board.The main objective of the PhD project is to evaluate added resistance and ship motions in oblique waves. In the work presented in this thesis, an existing fully nonlinear unsteady potential flow method is used to perform seakeeping numerical simulations in head and beam sea. Since viscosity is disregarded in potential flow methods but it is still very important for some cases, such as roll motion, viscous damping coefficients were added into the equation of motions. For the last two papers, an unstructured adaptive grid refinement, a nonlinear decomposition of the velocity potential, a formulation for the acceleration potential and a Barnes-Hut algorithm were introduced in the code. The method has been used to simulate roll motion in beam sea, parametric rolling, added resistance and ship motions in head waves as well as ship-ship interaction in calm water. Numerical results were compared with experiments and with other methods. Overall, the method presented here proved to be able to handle the tested scenarios, showing a good agreement between the simulations and the experiments. The work summarized in this thesis contributed to a better understanding of the numerical method used and helped to outline the next steps to be taken in order to achieve numerical seakeeping simulations in 6 degrees of freedom in oblique waves

Subspace discovery for video anomaly detection

PhDIn automated video surveillance anomaly detection is a challenging task. We address this task as a novelty detection problem where pattern description is limited and labelling information is available only for a small sample of normal instances. Classification under these conditions is prone to over-fitting. The contribution of this work is to propose a novel video abnormality detection method that does not need object detection and tracking. The method is based on subspace learning to discover a subspace where abnormality detection is easier to perform, without the need of detailed annotation and description of these patterns. The problem is formulated as one-class classification utilising a low dimensional subspace, where a novelty classifier is used to learn normal actions automatically and then to detect abnormal actions from low-level features extracted from a region of interest. The subspace is discovered (using both labelled and unlabelled data) by a locality preserving graph-based algorithm that utilises the Graph Laplacian of a specially designed parameter-less nearest neighbour graph. The methodology compares favourably with alternative subspace learning algorithms (both linear and non-linear) and direct one-class classification schemes commonly used for off-line abnormality detection in synthetic and real data. Based on these findings, the framework is extended to on-line abnormality detection in video sequences, utilising multiple independent detectors deployed over the image frame to learn the local normal patterns and infer abnormality for the complete scene. The method is compared with an alternative linear method to establish advantages and limitations in on-line abnormality detection scenarios. Analysis shows that the alternative approach is better suited for cases where the subspace learning is restricted on the labelled samples, while in the presence of additional unlabelled data the proposed approach using graph-based subspace learning is more appropriate

Hybrid Evolutionary Shape Manipulation for Efficient Hull Form Design Optimisation

‘Eco-friendly shipping’ and fuel efficiency are gaining much attention in the maritime industry due to increasingly stringent environmental regulations and volatile fuel prices. The shape of hull affects the overall performance in efficiency and stability of ships. Despite the advantages of simulation-based design, the application of a formal optimisation process in actual ship design work is limited. A hybrid approach which integrates a morphing technique into a multi-objective genetic algorithm to automate and optimise the hull form design is developed. It is envisioned that the proposed hybrid approach will improve the hydrodynamic performance as well as overall efficiency of the design process