Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets

H. Cohn et. al. proposed an association scheme of 64 points in R^{14} which is conjectured to be a universally optimal code. We show that this scheme has a generalization in terms of Kerdock codes, as well as in terms of maximal real mutually unbiased bases. These schemes also related to extremal line-sets in Euclidean spaces and Barnes-Wall lattices. D. de Caen and E. R. van Dam constructed two infinite series of formally dual 3-class association schemes. We explain this formal duality by constructing two dual abelian schemes related to quaternary linear Kerdock and Preparata codes.Comment: 16 page

Experimental study of energy-minimizing point configurations on spheres

In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.Comment: 41 pages, 12 figures, to appear in Experimental Mathematic

Multidimensional Constellation Shaping for Coherent Optical Communication Systems

To overcome the increasing demands for Internet traffic, exploiting the available degrees of freedom in optical communication systems is necessary. In this thesis, we study how constellation shaping can be achieved in various dimensions and how various shaping schemes affect the whole performance in real systems. This thesis investigates the performance of constellation shaping methods including geometric shaping and probabilistic shaping in coherent fiber-optic systems.To study geometric shaping, we explore multidimensional lattice-based constellations. These constellations provide a regular structure with fast and low-complexity encoding and decoding. We show the possibility of transmitting and detecting constellations with a size of more than 10^{28} points, which can be done without a look-up table to store the constellation points. Moreover, we experimentally realize our proposed multidimensional modulation formats in long-haul optical communication systems.Finally, we investigate the performance of probabilistically shaped quadrature amplitude modulation and compare it with uniform cross quadrature amplitude modulation in the presence of transmitter impairments, and with uniform quadrature amplitude modulation in links where higher-order modulation formats co-propagate with on-off keying wavelength channels

Theoretical Study of Dust in RF Discharges and Tokamak Plasmas

Dusty plasma systems are common in all aspects of plasma physics, from space, to our Earth's atmosphere, to low temperature discharges and fusion devices. In this work the basic plasma dust interactions are studied, with the main focus being on RF discharges and tokamak plasmas. One very important physical characteristic of a dust grain immersed in a plasma environment, which plays a central role in the study of its dynamical behaviour, is its charge. It determines the ion and electron fluxes on the dust and through that, one can calculate the forces exerted on the solid particle and the energy fluxes onto it. In this work an overview of the basic charging theory used in dusty plasma, the Orbital Motion Limited (OML) approach, will be presented, and its implications will be studied in the context of RF discharges and tokamak plasmas. In the case of RF discharges, modifications of the OML approach will be explored for the accommodation of time varying phenomena. This will have two directions. The first, concerning the presence of time varying electric fields in a uniform plasma background and the second, the presence of different forms of time dependent current carrying electron distributions. In the tokamak case, the work is focused on the modelling of the dynamical behaviour of dust particles in a tokamak plasma environment. An improved version of the existing Dust in TOKamakS (DTOKS) code has been developed. Results for the Mega Amp Spherical Tokamak (MAST) and ITER are presented, as well as an assessment of the importance of the various aspects of the physical model from the plasma background, the dust grain charge, the forces on the particle and the dust heating model. Furthermore, the first basic comparison between DTOKS and the DUST Transport (DUSTT) code, the only other similar code available at the moment, is being presented

Multidimensional Optimized Optical Modulation Formats

This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. Then, the chapter discusses optimization of modulation formats in coded systems. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. It further explains how to simply determine the transmitted symbol from the received 4D vector, without resorting to a full search of the Euclidean distances to all points in the whole constellation

Anisotropic shock response of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)

The thermo-mechanical response of shock-induced pore collapse has been studied using non-reactive all-atom molecular dynamics (MD) and Eulerian continuum simulations for the molecular crystal 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). Three crystal orientations, bracketed by the limiting cases with respect to the crystal structure anisotropy in TATB, are considered in the MD simulations, while an isotropic constitutive model is used for the continuum simulations. Simulations with three impact speeds from 0.5 km s[superscript -1] to 2.0 km s[superscript -1] are investigated. Results from MD and continuum simulations are in agreement in terms of shock wave speeds, temperature distributions, and pore-collapse mechanisms. However, differences arise for other quantities that are also important in hotspot ignition and growth, for example, the skewness of high-temperature distributions and the local temperature field around the post-collapse hotspot, indicating the urgent need to incorporate anisotropic crystal plasticity and strength models into the continuum descriptions. The deformation mechanisms of TATB crystals in the shock-induced pore collapse MD simulations were studied using Strain Functional Analysis. This new approach maps discrete quantities from atomistic simulations onto continuous fields via a Gaussian kernel, from which a unique and complete set of rotationally invariant Strain Functional Descriptors (SFD) is obtained from the high-order central moments of local configurations, expressed in a Solid Harmonics polynomial basis by SO(3) decomposition. Coupled with unsupervised machine learning techniques, the SFD successfully identifies and distinguishes the deformations presented in the MD simulations of shock-compressed TATB crystals. It enables automated detection of disordered structures in the system and can be readily applied to materials with any symmetry class.Includes bibliographical references (pages 142-168)

Three-dimensional space representation in the human brain

Brain structures that support spatial cognition by encoding one’s position and direction have been extensively studied for decades. In the majority of studies, neural substrates have been investigated on a horizontal two-dimensional plane, whereas humans and other animals also move vertically in a three-dimensional (3D) world. In this thesis, I investigated how 3D spatial information is represented in the human brain using functional MRI experiments and custom-built 3D virtual environments. In the first experiment, participants moved on flat, tilted-up or tilted-down pathways in a 3D lattice structure. Multivoxel pattern analysis revealed that the anterior hippocampus expressed 3D location information that was similarly sensitive to the vertical and horizontal axes. The retrosplenial cortex and posterior hippocampus represented direction information that was only sensitive to the vertical axis. In the second experiment, participants moved in a virtual building with multiple levels and rooms. Using an fMRI repetition suppression analysis, I observed a hierarchical representation of this 3D space, with anterior hippocampus representing local information within a room, while retrosplenial cortex, parahippocampal cortex and posterior hippocampus represented room information within the wider building. As in the first experiment, vertical and horizontal location information was similarly encoded. In the last experiments, participants were placed into a virtual zero-gravity environment where they could move freely along all 3 axes. The thalamus and subiculum expressed horizontal heading information, whereas retrosplenial cortex showed dominant encoding of vertical heading. Using novel fMRI analyses, I also found preliminary evidence of a 3D grid code in the entorhinal cortex. Overall, these experiments demonstrate the capacity of the human brain to implement a flexible and efficient representation of 3D space. The work in this thesis will, I hope, serve as a stepping-stone in our understanding of how we navigate in the real – 3D – world

Neutron scattering studies of the geometrically frustrated SrLn2O4 materials

Geometrical frustration in condensed matter is a phenomenon induced by competing magnetic interactions being in a situation of incompatibly with the crystal lattice geometry. In highly frustrated magnets, the competition can be such that a unique magnetic ground state cannot be stabilised, even at the lowest temperatures. Such a situation of instability is known to give rise to unusual and novel properties stimulating our interest for this class of materials. The members of the SrLn2O4 (Ln = Nd, Gd, Tb, Dy, Ho, Er, Tm, Yb) crystalline family, present the characteristics of highly frustrated systems. The magnetic sublattice of these materials consists of interconnected triangular ladders forming a three dimensional distorted honey-comb lattice. This lattice is also bipartite, in a sense that the Ln3+ magnetic ions are hosted by two crystallographically inequivalent sites, resulting in the presence of two different types of magnetic ladders in the system. Many different types of triangular structures are thus combined within these materials, resulting in the strong frustration of the antiferromagnetic Ln3+ exchange interactions. This thesis presents an investigation of the low temperature magnetic properties of the Nd, Gd and Er variants of the SrLn2O4 family. The use of neutron scattering techniques in the determination of the different magnetic orders stabilised by these systems stands as a central aspect of this work. In fact, the structural characteristics of the orders have revealed fundamental aspects of the magnetic properties of this family of material. Of particular interest, it was understood that strong dipolar interaction can stabilise up-down-up-down (udud) N_eel orders progressing along the ladders in SrLn2O4 systems containing the Ln3+ ions bearing the larger magnetic moments. On the other hand, near neighbour antiferromagnetic exchange interactions have the possibility to stabilise right-left-right-left (rlrl) Néel or (rrll) double Néel orders along the ladders, the moments lying within the a - b plane of the materials. An investigation of the low temperature field induced properties of the SrEr2O4 material is moreover proposed in this thesis