Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Hardware design of cryptographic accelerators

With the rapid growth of the Internet and digital communications, the volume of sensitive electronic transactions being transferred and stored over and on insecure media has increased dramatically in recent years. The growing demand for cryptographic systems to secure this data, across a multitude of platforms, ranging from large servers to small mobile devices and smart cards, has necessitated research into low cost, flexible and secure solutions. As constraints on architectures such as area, speed and power become key factors in choosing a cryptosystem, methods for speeding up the development and evaluation process are necessary. This thesis investigates flexible hardware architectures for the main components of a cryptographic system. Dedicated hardware accelerators can provide significant performance improvements when compared to implementations on general purpose processors. Each of the designs proposed are analysed in terms of speed, area, power, energy and efficiency. Field Programmable Gate Arrays (FPGAs) are chosen as the development platform due to their fast development time and reconfigurable nature. Firstly, a reconfigurable architecture for performing elliptic curve point scalar multiplication on an FPGA is presented. Elliptic curve cryptography is one such method to secure data, offering similar security levels to traditional systems, such as RSA, but with smaller key sizes, translating into lower memory and bandwidth requirements. The architecture is implemented using different underlying algorithms and coordinates for dedicated Double-and-Add algorithms, twisted Edwards algorithms and SPA secure algorithms, and its power consumption and energy on an FPGA measured. Hardware implementation results for these new algorithms are compared against their software counterparts and the best choices for minimum area-time and area-energy circuits are then identified and examined for larger key and field sizes. Secondly, implementation methods for another component of a cryptographic system, namely hash functions, developed in the recently concluded SHA-3 hash competition are presented. Various designs from the three rounds of the NIST run competition are implemented on FPGA along with an interface to allow fair comparison of the different hash functions when operating in a standardised and constrained environment. Different methods of implementation for the designs and their subsequent performance is examined in terms of throughput, area and energy costs using various constraint metrics. Comparing many different implementation methods and algorithms is nontrivial. Another aim of this thesis is the development of generic interfaces used both to reduce implementation and test time and also to enable fair baseline comparisons of different algorithms when operating in a standardised and constrained environment. Finally, a hardware-software co-design cryptographic architecture is presented. This architecture is capable of supporting multiple types of cryptographic algorithms and is described through an application for performing public key cryptography, namely the Elliptic Curve Digital Signature Algorithm (ECDSA). This architecture makes use of the elliptic curve architecture and the hash functions described previously. These components, along with a random number generator, provide hardware acceleration for a Microblaze based cryptographic system. The trade-off in terms of performance for flexibility is discussed using dedicated software, and hardware-software co-design implementations of the elliptic curve point scalar multiplication block. Results are then presented in terms of the overall cryptographic system.

Ab initio calculations of group 4 metallocene reaction mechanisms: atomic layer deposition and bond activation catalysis

Thin film dielectrics based on titanium, zirconium or hafnium oxides are being introduced to increase the permittivity of insulating layers in transistors for micro/nanoelectronics and memory devices. Atomic layer deposition (ALD) is the process of choice for fabricating these films, as it allows for high control of composition and thickness in thin, conformal films which can be deposited on substrates with high aspect-ratio features. The success of this method depends crucially on the chemical properties of the precursor molecules. A successful ALD precursor should be volatile, stable in the gas-phase, but reactive on the substrate and growing surface, leading to inert by-products. In recent years, many different ALD precursors for metal oxides have been developed, but many of them suffer from low thermal stability. Much promise is shown by group 4 metal precursors that contain cyclopentadienyl (Cp = C5H5-xRx) ligands. One of the main advantages of Cp precursors is their thermal stability. In this work ab initio calculations were carried out at the level of density functional theory (DFT) on a range of heteroleptic metallocenes [M(Cp)4-n(L)n], M = Hf/Zr/Ti, L = Me and OMe, in order to find mechanistic reasons for their observed behaviour during ALD. Based on optimized monomer structures, reactivity is analyzed with respect to ligand elimination. The order in which different ligands are eliminated during ALD follows their energetics which was in agreement with experimental measurements. Titanocene-derived precursors, TiCp*(OMe)3, do not yield TiO2 films in atomic layer deposition (ALD) with water, while Ti(OMe)4 does. DFT was used to model the ALD reaction sequence and find the reason for the difference in growth behaviour. Both precursors adsorb initially via hydrogen-bonding. The simulations reveal that the Cp* ligand of TiCp*(OMe)3 lowers the Lewis acidity of the Ti centre and prevents its coordination to surface O (densification) during both of the ALD pulses. Blocking this step hindered further ALD reactions and for that reason no ALD growth is observed from TiCp*(OMe)3 and water. The thermal stability in the gas phase of Ti, Zr and Hf precursors that contain cyclopentadienyl ligands was also considered. The reaction that was found using DFT is an intramolecular α-H transfer that produces an alkylidene complex. The analysis shows that thermal stabilities of complexes of the type MCp2(CH3)2 increase down group 4 (M = Ti, Zr and Hf) due to an increase in the HOMO-LUMO band gap of the reactants, which itself increases with the electrophilicity of the metal. The reverse reaction of α-hydrogen abstraction in ZrCp2Me2 is 1,2-addition reaction of a C-H bond to a Zr=C bond. The same mechanism is investigated to determine if it operates for 1,2 addition of the tBu C-H across Hf=N in a corresponding Hf dimer complex. The aim of this work is to understand orbital interactions, how bonds break and how new bonds form, and in what state hydrogen is transferred during the reaction. Calculations reveal two synchronous and concerted electron transfers within a four-membered cyclic transition state in the plane between the cyclopentadienyl rings, one π(M=X)-to-σ(M-C) involving metal d orbitals and the other σ(C-H)-to-σ(X-H) mediating the transfer of neutral H, where X = C or N. The reaction of the hafnium dimer complex with CO that was studied for the purpose of understanding C-H bond activation has another interesting application, namely the cleavage of an N-N bond and resulting N-C bond formation. Analysis of the orbital plots reveals repulsion between the occupied orbitals on CO and the N-N unit where CO approaches along the N-N axis. The repulsions along the N-N axis are minimized by instead forming an asymmetrical intermediate in which CO first coordinates to one Hf and then to N. This breaks the symmetry of the N-N unit and the resultant mixing of MOs allows σ(NN) to be polarized, localizing electrons on the more distant N. This allowed σ(CO) and π(CO) donation to N and back-donation of π*(Hf2N2) to CO. Improved understanding of the chemistry of metal complexes can be gained from atomic-scale modelling and this provides valuable information for the design of new ALD precursors. The information gained from the model decomposition pathway can be additionally used to understand the chemistry of molecules in the ALD process as well as in catalytic systems.

Identification of RNA editing in the human exome and development of DARNED DatabaseSF

RNA editing is a biological phenomena that alters nascent RNA transcripts by insertion, deletion and/or substitution of one or a few nucleotides. It is ubiquitous in all kingdoms of life and in viruses. The predominant editing event in organisms with a developed central nervous system is Adenosine to Inosine deamination. Inosine is recognized as Guanosine by the translational machinery and reverse-transcriptase. In primates, RNA editing occurs frequently in transcripts from repetitive regions of the genome. In humans, more than 500,000 editing instances have been identified, by applying computational pipelines on available ESTs and high-throughput sequencing data, and by using chemical methods. However, the functions of only a small number of cases have been studied thoroughly. RNA editing instances have been found to have roles in peptide variants synthesis by non-synonymous codon substitutions, transcript variants by alterations in splicing sites and gene silencing by miRNAs sequence modifications. We established the Database of RNA EDiting (DARNED) to accommo-date the reference genomic coordinates of substitution editing in human, mouse and fly transcripts from published literatures, with additional information on edited genomic coordinates collected from various databases e.g. UCSC, NCBI. DARNED contains mostly Adenosine to Inosine editing and allows searches based on genomic region, gene ID, and user provided sequence. The Database is accessible at http://darned.ucc.ie RNA editing instances in coding region are likely to result in recoding in protein synthesis. This encouraged me to focus my research on the occurrences of RNA editing specific CDS and non-Alu exonic regions. By applying various filters on discrepancies between available ESTs and their corresponding reference genomic sequences, putative RNA editing candidates were identified. High-throughput sequencing was used to validate these candidates. All predicted coordinates appeared to be either SNPs or unedited.