Statistical physics of error-correcting codes

In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.

Waveform type evaluation in congenital nystagmus

Congenital nystagmus is an ocular-motor disorder characterised by involuntary, conjugated and bilateral to and fro ocular oscillations. In this study a method to recognise automatically jerk waveform inside a congenital nystagmus recording and to compute foveation time and foveation position variability is presented. The recordings were performed with subjects looking at visual targets, presented in nine eye gaze positions; data were segmented into blocks corresponding to each gaze position. The nystagmus cycles were identified searching for local minima and maxima (SpEp sequence) in intervals centred on each slope change of the eye position signal (position criterion). The SpEp sequence was then refined using an adaptive threshold applied to the eye velocity signal; the outcome is a robust detection of each slow phase start point, fundamental to accurately compute some nystagmus parameters. A total of 1206 slow phases was used to compute the specificity in waveform recognition applying only the position criterion or adding the adaptive threshold; results showed an increase in negative predictive value of 25.1% using both features. The duration of each foveation window was measured on raw data or using an interpolating function of the congenital nystagmus slow phases; foveation time estimation less sensitive to noise was obtained in the second case. © 2010.

Aspects of 350 ºC (500 ºF) embrittlement in a CrMoV steel

A study has been made of the fracture modes associated with toughness minima, observed in notched impact tests at 173K, for a weldable CrMoV steel, quenched from different austenitising temperatures, and tempered in the range 300-900K. The fracture mode at 623K varied from 100% transgranular cleavage for an austenitising temperature of 1523K. The results are discussed in terms of mechanisms for 350 ºC embrittlement, such mechanisms require modification to allow for the difficulty of dissolving alloy carbides at low austenitising temperatures.

Molecular Dynamics implementation of BN2D or 'Mercedes Benz' water model

Two-dimensional 'Mercedes Benz' (MB) or BN2D water model (Naim, 1971) is implemented in Molecular Dynamics. It is known that the MB model can capture abnormal properties of real water (high heat capacity, minima of pressure and isothermal compressibility, negative thermal expansion coefficient) (Silverstein et al., 1998). In this work formulas for calculating the thermodynamic, structural and dynamic properties in microcanonical (NVE) and isothermal-isobaric (NPT) ensembles for the model from Molecular Dynamics simulation are derived and verified against known Monte Carlo results. The convergence of the thermodynamic properties and the system's numerical stability are investigated. The results qualitatively reproduce the peculiarities of real water making the model a visually convenient tool that also requires less computational resources, thus allowing simulations of large (hydrodynamic scale) molecular systems. We provide the open source code written in C/C++ for the BN2D water model implementation using Molecular Dynamics.

Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction

We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results.