This thesis encompasses a body of experimental work on the dynamics of twisted light. We first deal with the generation and reconstruction of twisted light for applications in classical and quantum physics, respectively. In the first case, we present a novel device that has the ability to generate twisted light in a manner that is completely wavelength-independent. Such a device may find applications in various fields of classical physics, ranging from nano to astronomical imaging. In the second work, we study the dynamics of twisted light in the case of laser-induced radial birefringence. This is done by studying the optical features resulting from elastic properties of silver-doped glass. In the last work on generation of twisted light, we present a nano-scale twisted light generator having the capacity to generate an optical mode with a controllable number of twists. In the context of quantum communication and quantum computations, this device has a great potential due to its small size and integrability. In the second part of the thesis, we study the propagation of twisted light both at the classical and quantum regime. In the first case, we observe exotic group velocities of light pulses in vacuum due to the twisting of its wavefront. In the second case, we study the effect of quantum decoherence of twisted light due to the coupling of photonic internal degrees of freedom. We present a technique to recover the lost coherence, which we name recoherence, by a practical unitary transformation.

In this collection I have explored the paradox of perfection. The collection is an epic tribute to my prior self and discovers how the unperfect can be transformed to something, perceived, perfect. I flirt with my past obsessions in finding mathematically measured legs, exact tailored arms and perfectly fitted stockings. In a fun, poetic and melancholy way I invite the viewer on a highly visual voyage to my childhood where the obsession of finding costume perfection "Vemoden" the act of control becomes visual through statuesque frozen looks, where the previous unperfect becomes perfection.

The bifurcation phenomenon occurring in twisted square plates with free edges subject to contrary self-equilibrating corner loading was examined. In order to eliminate lateral deflection of the test plates due to their own weight, a special loading apparatus was constructed which held the plates in a vertical plane. The complete strain field occurring at the plate centre was measured using two strain gauge rosettes mounted on opposing sides of the plate at the centre. Principal curvatures were calculated and related to corner load for several plates with differing edge length/thickness ratios. A Southwell plot was used relating mean curvature to the ratio mean curvature/Gaussian curvature, from which the Gaussian curvature occurring at bifurcation was determined. The critical dimensionless twist ka was then calculated for each plate size. It was found that there is a linear relation between the critical dimensionless twist ka occurring at bifurcation, and the thickness to edge length ratio h/a ratio, specifically: ka = 10.8h/a. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This thesis develops some general calculational techniques for finding the orders of knots in the topological concordance group C . The techniques currently available in the literature are either too theoretical, applying to only a small number of knots, or are designed to only deal with a specific knot. The thesis builds on the results of Herald, Kirk and Livingston [HKL10] and Tamulis [Tam02] to give a series of criteria, using twisted Alexander polynomials, for determining whether a knot is of infinite order in C. There are two immediate applications of these theorems. The first is to give the structure of the subgroups of the concordance group C and the algebraic concordance group G generated by the prime knots of 9 or fewer crossings. This should be of practical value to the knot-theoretic community, but more importantly it provides interesting examples of phenomena both in the algebraic and geometric concordance groups. The second application is to find the concordance orders of all prime knots with up to 12 crossings. At the time of writing of this thesis, there are 325 such knots listed as having unknown concordance order. The thesis includes the computation of the orders of all except two of these. In addition to using twisted Alexander polynomials to determine the concordance order of a knot, a theorem of Cochran, Orr and Teichner [COT03] is applied to prove that the n-twisted doubles of the unknot are not slice for n ≠ 0,2. This technique involves analysing the `second-order' invariants of a knot; that is, slice invariants (in this case, signatures) of a set of metabolising curves on a Seifert surface for the knot. The thesis extends the result to provide a set of criteria for the n-twisted double of a general knot K to be slice; that is, of order 0 in C. The structure of the knot concordance group continues to remain a mystery, but the thesis provides a new angle for attacking problems in this field and it provides new evidence for long-standing conjectures.

There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.

This study investigates the optical properties of the twisted-nematic liquid-crystals at oblique directions and their applications. A large difference in the phase retardation and the twisted angle of the TN-LC from different viewing directions occurs at the low voltage regime. The proposed viewing angle switching (VAS) panel is developed using this large optically anisotropic behavior of the TN-LC. The proposed VAS panel is only perceived clearly at normal and downward directions in a narrow viewing angle mode to ensure high privacy protection, it highly promising for mobile device applications.

There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.

The thesis focuses on the area of copper twisted pair based wireline communications. As one of the most widely deployed communication media, the copper twisted pair cable plays an important role in the communication network cabling infrastructure. This thesis looks to exploit diversity to improve twisted pair channels for data communications in two common application areas, namely Ethernet over Twisted Paris and digital subscriber line over twisted pair based telephone network. The first part of the thesis addresses new approaches to next generation Ethernet over twisted pair cable. The coming challenge for Ethernet over twisted pair cable is to realise a higher data rate beyond the 25/40GBASE-T standard, in relatively short reach scenarios. The straight-forward approaches, such as improving cable quality and extending frequency bandwidth, are unlikely to provide significant improvement in terms of data rate. However, other system diversities, such as spectrum utilization are yet to be fully exploited, so as to meet the desired data rate performance. The current balanced transmission over the structured twisted pair cable and its parallel single-in-single-out channel model is revisited and formulated as a full-duplex multiple-in-multiple-out (MIMO) channel model. With a common ground (provided by the cable shield), the balanced transmission is converted into unbalanced transmission, by replacing the differential-mode excitation with single-ended excitation. In this way, MIMO adoption may offer spectrum utilization advantages due to the doubled number of the channels. The S-parameters of the proposed MIMO channel model is obtained through the full wave electromagnetic simulation of a short CAT7A cable. The channel models are constructed from the resulting S-parameters, also the corresponding theoretical capacity is evaluated by exploiting different diversity scenarios. With higher spectrum efficiency, the orthogonal-frequency-division-multiplexing (OFDM) modulation can significantly improve the theoretical capacity compared with single-carrier modulation, where the channel frequency selectivity is aided. The MIMO can further enhance the capacity by minimising the impact of the crosstalk. When the crosstalk is properly handled under the unbalanced transmission, this thesis shows that the theoretical capacity of the EoTP cable can reach nearly 200GBit/s. In order to further extend the bandwidth capability of twisted pair cables, Phantom Mode transmission is studied, aiming at creating more channels under balanced transmission operation. The second part of the thesis focuses on the research of advanced scheduling algorithms for VDSL2 QoS enhancement. For VDSL2 broadband access networks, multi-user optimisation techniques have been developed, so as to improve the basic data rate performance. Spectrum balancing improves the network performance by optimising users transmit power spectra as the resource allocation, to mitigate the impact from the crosstalk. Aiming at enhancing the performance for the upstream VDSL2 service, where the users QoS demand is not known by all other users, a set of autonomous spectrum balancing algorithms is proposed. These optimise users transmit power spectra locally with only direct channel state information. To prevent selfish behaviour, the concept of a virtual user is introduced to represent the impact on both crosstalk interference and queueing status of other users. Moreover, novel algorithms are developed to determine the parameters and the weight of the virtual user. Another type of resource allocation in the VDSL2 network is crosstalk cancellation by centralised signal coordination. The history of the data queue is considered as a time series, on which different smooth filter characteristics are investigated in order to investigate further performance improvement. The use of filter techniques accounts for both the instantaneous queue length and also the previous data to determine the most efficient dynamic resource allocation. With the help of this smoothed dynamic resource allocation, the network will benefit from both reduced signalling communication and improved delay performance. The proposed algorithms are verified by numerical experiments.

No description available.

No description available.