Diode lasers are a convenient and economical source of near-infrared radiation, which may usefully be applied to a host of different sensitive detection methods; this thesis presents novel extensions of these methods, making use of the favourable characteristics of this type of light source. The first part of this thesis details the development of an optical feedback cavity-enhanced absorption spectroscopy (OF-CEAS) apparatus, including the development of the optical system, the sample handling, and the electronics for feedback phase control. A preliminary demonstration of the system is reported, presenting the detection of atmospheric water absorptions close to 1596 nm. Optimisation and application of the OF-CEAS spectrometer are then demonstrated, after which the spectrometer is applied to the sensitive detection of carbon dioxide absorptions suitable as a diagnostic aid in identifying Heliobacter pylori infection. A time-normalised α-min value of 5.8 × 10⁻⁹ cm⁻¹s^1/2 was measured for these spectra. Further optimisation of the system leads to an ultimate detection sensitivity of 1.42 × 10⁻⁹ cm⁻¹s^1/2, measured on absorption transitions in acetylene close to 1532 nm. In order further to characterise the performance of the OF-CEAS system, analogous experiments are presented using the OF-CEAS setup and a standard diode-laser cavity-enhanced absorption spectroscopy (CEAS) apparatus. Detection is carried out on the P(6) line of the ν₁ + ν₃ vibrational band of the mixed isotopologue of acetylene, ¹²-C¹³-CH₂. Direct comparison is made between the sensitivities of the two methods, and in light of this the suitability of each technique for detection in different environments is considered. The well-characterised and consistent frequency scale which is inherent to the OF-CEAS technique is then applied to a line shape analysis for the presented absorption spectra. Pressure-broadening coefficients are determined for selected absorptions in the ν₁ + ν₃ band of acetylene. In spite of the low resolution associated with this technique, this accurate frequency scaling allows observation of subtle line shape effects such as Dicke collisional narrowing using the data presented in Chapter 3 for the R(60) line in the 3ν₁ + ν₃ vibrational band of CO₂. These effects are quantified through use of a Galatry fit to each absorption spectrum. The statistical significance associated with the use of such a model, and the physical meaning of the results, are examined and discussed. An alternative strategy for increasing the sensitivity of a diode-laser-based gas monitoring technique lies in moving detection to the mid-infrared region, where the absorption cross-sections are generally larger. With this motivation, difference frequency generation is presented, to produce radiation close to 3.5 µm which is then applied to a series of different enhanced spectroscopy techniques. The optimal sensitivity, of 32 ppb NO2 at 45 Torr total sample pressure, was achieved using wavelength modulation spectroscopy. The different techniques are compared and possible improvements to them are put forward. Finally, proof-of-principle work is presented seeking to combine the enhanced circulating power associated with the optical-feedback-locked techniques and non-linear optical techniques to move detection to a more favourable spectral region. Light close to 429 nm is generated by second harmonic generation in a crystal of potassium niobate, with resonance-enhancement afforded by a feedback V-cavity of the sort employed in OF-CEAS. The potential of such a system for diode-laser-based generation of blue and ultraviolet light is demonstrated and discussed, along with improvements that might be implemented to increase the efficiency of the system.

CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Sistemas descritos por Hamiltonianos do tipo Dirac são ubíquos. Surgindo em materiais como grafeno, isolantes topológicos ou recentemente nos semimetais de Weyl. Devido ao interesse tecnológico e acadêmico desses materiais, caracterizar suas propriedades é essencial. Uma abordagem matemática para efetuar o estudo de tais sistemas consiste em discretizar o Hamiltoniano no espaço das posições, mas tal abordagem esbarra no problema da duplicação de férmions. De forma breve, esse problema atesta pela impossibilidade de simulação de férmions livres não massivos em uma rede discreta sem que alguma simetria ou propriedade da Hamiltoniana seja quebrada. No presente trabalho demonstramos que tal problemática não deveria ser causa de preocupação para o estudo de sistemas na matéria condensada, pois podemos utilizar a simetria quebrada para confinar os portadores de carga no sistema para remover os estados duplicados. Tal remoção é conseguida com a inserção de um termo quadrático em relação ao momento, conhecido como massa de Wilson. Nesse sentido podemos inserir um termo de Wilson com quebra de simetria necessária para o confinamento, tornando o problema de duplicação de férmions irrelevante, essa relação não tinha sido notada até o presente trabalho, e recentes resultados na literatura erroneamente atribuem a massa de Wilson com a quebra de uma simetria de reversão temporal, o que não necessariamente é verdade. Nesse contexto além de abordar essa relação a presente dissertação objetiva também elucidar alguns mal entendimentos a respeitos das massas de Wilson, quiralidade e outras simetrias. Para validar nosso argumento central estudamos diversos sistemas de interesse e comparamos com os resultados na literatura. / Hamiltonians of Dirac type are ubiquitous. Appearing in materials such as graphene, topological insulators or recently in the Weyl semimetals. Due to the technological and academic interest of these materials, characterizing their properties is essential. A mathematical approach to study these systems consists of discretizing the Hamiltonian in the space of positions, but such an approach causes the problem of doubling fermions (FDP). We demonstrate the FDP should not be a cause of concern for the study of confined systems because we can use the broken symmetry to confine in the system to remove the duplicate states. Such removal is achieved by inserting a quadratic term with respect to the moment, known as the Wilson mass. In this sense we can insert a Wilson term with symmetry breaking required for confinement, rendering the fermion duplication problem irrelevant, this relationship had not been noticed until the present work, and recent literature results erroneously attribute Wilson’s mass to break of a symmetry of time reversal, which is not necessarily true. In this context, in addition to addressing this relationship, the present dissertation also aims to elucidate some misconceptions regarding the Wilson masses, chirality and other symmetries. In order to validate our central argument we study several systems of interest and compare it with the results in the literature. / Dissertação (Mestrado)

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Τα πρωτότυπα αποτελέσματα της διατριβής περιέχονται στα κεφ. 2, 3 και 4. Στο κεφ. 2 μελετούμε με αριθμητικές μεθόδους ένα 3-διάστατο διακριτό μοντέλο μακροοικονομίας με σταθερές ισοτιμίες. Χρησιμοποιώντας μια μέθοδο πλέγματος, βρίσκουμε την περιοχή ευστάθειας στον παραμετρικό χώρο, προσδιορίζουμε την καμπύλη διακλαδώσεων Hopf-Neimark και θεωρούμε σύντομα την εμφάνιση “γλωσσών” Arnold. Υπολογίζονται διαγράμματα διακλαδώσεων και εκθέτη Lyapunov που δίνουν πληροφορίες για τους επιχειρηματικούς κύκλους και την πολύπλοκη δυναμική του μοντέλου και. παρουσιάζουμε παραδείγματα κυκλικών και χαοτικών ελκυστών. Στο κεφ. 3 μελετούμε με τις ίδιες μεθόδους ένα διακριτό μοντέλο αλληλεπίδρασης περιοχών με σταθερές ισοτιμίες, επέκταση του προηγούμενου μοντέλου σε 5 διαστάσεις. Στόχος ήταν να δείξουμε πόσο εφικτή και αποτελεσματική είναι μία αριθμητική μελέτη για ηπίως πολυδιάστατα διακριτά δυναμικά συστήματα με πολλές παραμέτρους. Βρήκαμε ότι η κίνηση κεφαλαίων δεν αρκεί για τη δημιουργία κύκλων όταν είναι χαμηλή η εμπορική αλληλεπίδραση. Το κατώφλι εμπορίου προβλέπεται περίπου στο 15% των εμπορικών συναλλαγών. Αντίθετα, το μοντέλο δεν προβλέπει αναγκαίο ελάχιστο επίπεδο κίνησης κεφαλαίων για την εμφάνιση των κύκλων. Δίνουμε παραδείγματα διαγραμμάτων διακλάδωσης και εκθέτη Lyapunov που δείχνουν την εμφάνιση κύκλων ή ακολουθίας διπλασιασμού περιόδου, και παραδείγματα της ανάπτυξής τους. Το κεφ. 4 περιέχει σύντομη περιγραφή συμπληρωματικών αποτελεσμάτων στα παραπάνω μοντέλα, και στα αντίστοιχα μοντέλα μεταβλητής ισοτιμίας συναλλάγματος, καθώς και κατευθύνσεις μελλοντικής έρευνας. Στο κεφ. 5 περιγράφονται σύντομα οι υπολογιστικές τεχνικές που χρησιμοποιήσαμε. Η διατριβή δείχνει την αποτελεσματικότητα της αριθμητικής προσέγγισης για πολυδιάστατα διακριτά μοντέλα. / The original results of the dissertation are contained in ch. 2, 3 and 4, and concern mainly the problem of business cycles. In ch. 2 we explore numerically a 3D discrete Kaldorian macrodynamic model of open economy with fixed exchange rates. Using a grid search method we determine the stability region in parameter space, and the Hopf-Neimark bifurcation curve, and discuss briefly the occurrence of Arnold tongues. Bifurcation and Lyapunov exponent diagrams are computed providing information on the business cycles and illustrating the complex dynamics involved. Examples of cycles and chaotic attractors are presented. In ch. 3 we explore a 5D extension of the previous model using the same methods. The aim was to demonstrate the feasibility and effectiveness of the numerical approach for discrete dynamical systems of moderately high dimensionality and several parameters. We found that capital movement is not sufficient to generate interregional business cycles when trade interaction is low. The trade threshold is predicted at about 15% of trade transactions. By contrast, no minimum level of capital mobility exists as a requirement for the emergence of business cycles. Examples of bifurcation and Lyapunov exponent diagrams illustrating the occurrence of cycles or period doubling, and examples of their development, are given. Ch. 4 contains a short description of complementary results on the above models, and on two other models which extend the previous models to the case of flexible exchange rates, as well as some lines of future research. In ch. 5, the computational techniques employed in the present study are briefly described. The dissertation indicates the effectiveness of the numerical approach for high dimensional discrete models.

Indiana University-Purdue University Indianapolis (IUPUI) / Blömmer, Otto, and Seifert presented a fault attack on elliptic curve scalar multiplication called the Sign Change Attack, which causes a fault that changes the sign of the accumulation point. As the use of a sign bit for an extended integer is highly unlikely, this appears to be a highly selective manipulation of the key stream. In this thesis we describe two plausible fault attacks on a smart card implementation of elliptic curve cryptography. King and Wang designed a new attack called counter fault attack by attacking the scalar multiple of discrete-log cryptosystem. They then successfully generalize this approach to a family of attacks. By implementing King and Wang's scheme on RSA, we successfully attacked RSA keys for a variety of sizes. Further, we generalized the attack model to an attack on any implementation that uses NAF and wNAF key.