The Complexity Of The NP-Class

This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal Geometrical Structures and the Travelling Salesman Problems. The main results are the polynomial reduction procedure and the solution to the Noted Conjecture of the NP-Class

Detection of hidden structures on all scales in amorphous materials and complex physical systems: basic notions and applications to networks, lattice systems, and glasses

Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate correlations between their constituents. For a detailed understanding, there is a need for tools that enable the detection of pertinent structures on all spatial and temporal scales. Towards this end, we suggest a new method by invoking ideas from network analysis and information theory. Our method efficiently identifies basic unit cells and topological defects in systems with low disorder and may analyze general amorphous structures to identify candidate natural structures where a clear definition of order is lacking. This general unbiased detection of physical structure does not require a guess as to which of the system properties should be deemed as important and may constitute a natural point of departure for further analysis. The method applies to both static and dynamic systems.Comment: (23 pages, 9 figures

Understanding and design of molecular dynamics based simulation methods.

Several new strategies for employing modified molecular dynamics (MD) protocols for finding energy minima were developed developed. First, we derived a new method of searching for the lowest energy conformation by employ employing the results of our work to explain "mean mean-field" molecular dynamics simulation methods. Called ensembles extracted by atomic coordinate transformations (EXACT), the method allows simulations to be performed with a variable degree of approximation. Then, we examine the previously published locally enhanced sampling (LES) approximation. The method makes copies of a small part of interest in a larger system, and allows the dynamics to unfold. The method works by making the copies invisible to each other and allowing them to interact only with the remainder of the system, called the bath. The bath, on the other hand, interacts with an averaged representation of the copied part. This averaged interaction allows the copied particles to move into geometries they might not visit in a conventional MD simulation, which allows a greater variety of structures to be sampled. We derive the algorithm by copying the entire system, and then by employing holonomic constraints between the bath particles between the various systems. Using this new approach, we explore several issues previously noted in the literature. We also use the EXACT approximation method to illustrate the nature of the LES approximation. Finally, we present another optimization method, which add adds pressure along with temperature in analogue with simulated annealing. The method is tested against simulated annealing for condensed phase systems of argon, monoglyme, and tetraglyme. The method noticeably improves the results for the glyme systems, but does not seem to hurt the results for the argon system

Single atom imaging with time-resolved electron microscopy

Developments in scanning transmission electron microscopy (STEM) have opened up new possibilities for time-resolved imaging at the atomic scale. However, rapid imaging of single atom dynamics brings with it a new set of challenges, particularly regarding noise and the interaction between the electron beam and the specimen. This thesis develops a set of analytical tools for capturing atomic motion and analyzing the dynamic behaviour of materials at the atomic scale. Machine learning is increasingly playing an important role in the analysis of electron microscopy data. In this light, new unsupervised learning tools are developed here for noise removal under low-dose imaging conditions and for identifying the motion of surface atoms. The scope for real-time processing and analysis is also explored, which is of rising importance as electron microscopy datasets grow in size and complexity. These advances in image processing and analysis are combined with computational modelling to uncover new chemical and physical insights into the motion of atoms adsorbed onto surfaces. Of particular interest are systems for heterogeneous catalysis, where the catalytic activity can depend intimately on the atomic environment. The study of Cu atoms on a graphene oxide support reveals that the atoms undergo anomalous diffusion as a result of spatial and energetic disorder present in the substrate. The investigation is extended to examine the structure and stability of small Cu clusters on graphene oxide, with atomistic modelling used to understand the significant role played by the substrate. Finally, the analytical methods are used to study the surface reconstruction of silicon alongside the electron beam-induced motion of adatoms on the surface. Taken together, these studies demonstrate the materials insights that can be obtained with time-resolved STEM imaging, and highlight the importance of combining state-ofthe- art imaging with computational analysis and atomistic modelling to quantitatively characterize the behaviour of materials with atomic resolution.The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement 291522–3DIMAGE, as well as from the European Union Seventh Framework Programme under Grant Agreement 312483-ESTEEM2 (Integrated Infrastructure Initiative -I3)