In this thesis we study the edge currents and the multi-band superconductivity in the unconventional superconductor Sr2RuO4. Numerous measurements have given strong support for a topologically non-trivial time-reversal symmetry breaking chiral p-wave state in this material. However, the spontaneous edge current expected for this order has eluded experimental detection. In this thesis, we present a general theoretical description of the edge currents in chiral superconductors. Our results elucidate the connection between the edge currents and the topological property of the chiral pairing. On this basis, we argue that superconducting gap anisotropy, combined with surface disorder, may provide an explanation for the absence of observable edge currents in Sr2RuO4. In addition, contrary to intuitive expectations, the integrated edge current is found to identically vanish for any non-p-wave chiral superconductor in the continuum limit-- a result which may be connected with the orbital angular momentum problem in chiral superfluids, such as the A phase of He-3. In lattice models, the integrated edge current may not vanish in non-p-wave superconductors but, in general, is substantially smaller compared to that of a simple chiral p-wave. In a separate study, we investigate the multi-band nature of the superconductivity in Sr2RuO4, via explicit microscopic calculations of the multi-band interactions. Our results indicate comparable pairing correlations on all of the bands and the existence of soft collective phase fluctuations--a Leggett mode. We also examine the possibility of alternative time-reversal symmetry breaking multi-band superconductivity which does not necessarily require chiral p-wave pairing. / Thesis / Doctor of Philosophy (PhD)

Proper design of bridge structures requires an appreciation for the possible failure mechanisms that can develop over the lifetime of the bridge, many of which are related to natural hazards. For example, scour is one of the most common causes of bridge failures. Scour occurs due to the erosion of soil and sediment within a channel with flowing water. During a flood event, the extent of scour can be so great that it can destabilize an existing bridge structure. In order to evaluate the scour potential of a bridge, it is necessary to have information regarding the substructure, particularly the bridge foundations. However, as of 2011 there are more than 40,000 bridges across United States with unknown foundations. Generally for these bridges there are no design or as-built plans available to show the type, depth, geometry, or materials incorporated into the foundations. Several non-destructive testing (NDT) methods have been developed to evaluate these unknown foundations. The primary objective of this research is to identify the most current and widely used NDT methods for determining the embedment depth of unknown bridge foundations and to compare these methods to an ultrasonic P-wave reflection imaging system. The ultrasonic P-wave reflection system has tremendous potential to provide more information and address several short-comings of other NDT methods. A laboratory study was initiated to explore various aspects related to the P-wave system performance, in order to characterize the limitations of the system in evaluation of unknown foundations prior to deployment in field studies. Moreover, field testing was performed using the P-wave system and a number of the current NDT methods at two selected bridge foundations to allow comparison between the results. / Civil Engineering

<p>The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing.</p><p>This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory.</p><p>The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2<i>n</i>^-1, pertinent to nonabelian statistics, in the presence of 2<i>n</i> quasiholes in the Moore-Read state and generalise this result to 2<i>n</i>-<i>k</i> quasiholes and <i>k </i>quasielectrons.</p><p>In the third approach, we study the topological nature of the degeneracy 2<i>n</i>^-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-<i>T</i>c superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2<i>n</i>^-1 for 2<i>n</i> vortices.</p>

The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing. This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory. The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2n-1, pertinent to nonabelian statistics, in the presence of 2n quasiholes in the Moore-Read state and generalise this result to 2n-k quasiholes and k quasielectrons. In the third approach, we study the topological nature of the degeneracy 2n-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-Tc superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2n-1 for 2n vortices.

Darbo tikslas: Sukurti kiekybinius signalų morfologijos, atspindinčių širdies veiklos reguliavimą, jos audinių gyvybingumą bei centrinę hemodinamiką, vertinimo metodus. Uždaviniai: 1. Ištirti signalų dekompozicijos baigtiniu bazinių funkcijų rinkiniu (truncated signal representation) metodų tinkamum��, širdies veiklą, jos audinių gyvybingumą bei centrinę hemodinamiką aprašančių signalų, morfologijos analizei; 2. Sukurti signalų, atspindinčių širdies audinių gyvybingumą, optimalaus aprašymo metodą; 3. Sukurti centrinę hemodinamiką atspindinčio krūtinės ląstos impedanso signalo struktūrinės bei morfologinės analizės metodą; 4. Sukurti elektrokardiogramos P-bangos morfologijos dinamikos, atspindinčios širdies veiklos autonominį reguliavimą, kiekybinio įvertinimo metodą. / The aim: To elaborate the quantitative methods for evaluation of morphology of the signals reflecting viability of heart tissue, heart function control and central/peripheral hemodynamics. Objectives: 1. Investigation of usefulness truncated signal representation methods for analysis of morphology of the signals reflecting viability of heart tissue, heart function control and central/peripheral hemodynamics; 2. Elaboration of method for optimal representation of signals reflecting heart tissue viability; 3. Elaboration of method for quantitative evaluation of ECG P-wave morphology dynamics reflecting autonomous heart function control; 4. Elaboration of method for structural and morphological analysis of the chest impedance signals reflecting central hemodynamics.

Topological phases of matter represent a new phase which cannot be understood in terms of Landau’s theory of symmetry breaking and are characterized by non-local topological properties emerging from purely local (microscopic) degrees of freedom. It is the non-trivial topology of the bulk band structure that gives rise to topological phases in condensed matter systems. Quantum Hall systems are prominent examples of such topological phases. Different quantum Hall states cannot be distinguished by a local order parameter. Instead, non-local measurements are required, such as the Hall conductance, to differentiate between various quantum Hall states. A signature of a topological phase is the existence of robust properties that do not depend on microscopic details and are insensitive to local perturbations which respect appropriate symmetries. Examples of such properties are the presence of protected gapless edge states at the boundary of the system for topological insulators and the remarkably precise quantization of the Hall conductance for quantum Hall states. The robustness of these properties can be under-stood through the existence of a topological invariant, such as the Chern number for quantum Hall states which is quantized to integer values and can only be changed by closing the bulk gap. Two other examples of topological phases of matter are topological superconductors and Weyl semimetals. The study of transport in various kinds of junctions of these topological materials is highly interesting for their applications in modern electronics and quantum computing. Another intriguing area to study is how to generate new kind of gapless edge modes in topological systems. In this thesis I have studied various aspects of topological phases of matter, such as electronic transport in junctions of topological insulators and topological superconductors, the generation of new kinds of boundary modes in the presence of granularity, and the effects of periodic driving in topological systems. We have studied the following topics. 1. transport across a line junction of two three-dimensional topological insulators, 2. transport across a junction of topological insulators and a superconductor, 3. surface and edge states of a topological insulator starting from a lattice model, 4. effects of granularity in topological insulators, 5. Majorana modes and conductance in systems with junctions of topological superconducting wires and normal metals, and 6. generation of new surface states in a Weyl semimetal in the presence of periodic driving by the application of electromagnetic radiation. A detailed description of each chapter is given below. • In the first chapter we introduce a number of concepts which are used in the rest of the thesis. We will discuss the ideas of topological phases of matter (for example, topological insulators, topological superconductors and Majorana modes, and Weyl semimetals), the renormalization group theory for weak interactions, and Floquet theory for periodically driven systems. • In the second chapter we study transport across a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time-reversal invariant system, we show that the line junction is characterized by an arbitrary real parameter α; this determines the scattering amplitudes (reflection and transmission) from the junction. The physical origin of α is a potential barrier that may be present at the junction. If the surface velocities have the same sign, edge states exist that propagate along the line junction with a velocity and orientation of the spin which depend on α and the ratio of the velocities. Next, we study what happens if the two surfaces are at an angle φ with respect to each other. We study the scattering and differential conductance across the line junction as functions of φ and α. We also show that there are edge states which propagate along the line junction with a velocity and spin orientation which depend on φ. Finally, if the surface velocities have opposite signs, we find that the electrons must necessarily transmit into the two-dimensional interface separating the two topological insulators. • In the third chapter we discuss transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. This junction is more complicated than the line junction discussed in the previous chapter because of the presence of the superconductor. In a topological insulator spin-up and spin-down electrons get coupled while in a superconductor electrons and holes get coupled. Hence we have to use a four-component spinor formalism to describe both spin and particle-hole degrees of freedom. The junction can have three time-reversal invariant barriers on the three sides. We compute the subgap charge conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters which characterize the barriers. We find that the presence of topological insulators and a superconductor leads to both Dirac and Schrodinger-like features in the charge conductances. We discuss the effects of bound states on the superconducting side on the conductance; in particular, we show that for triplet p-wave superconductors such a junction may be used to determine the spin state of its Cooper pairs. • In the fourth chapter we derive the surface Hamiltonians of a three-dimensional topological insulator starting from a microscopic model. (This description was not discussed in the previous chapters where we directly started from the surface Hamiltonians without deriving them form a bulk Hamiltonian). Here we begin from the bulk Hamiltonian of a three-dimensional topological insulator Bi2Se3. Using this we derive the surface Hamiltonians on various surfaces of the topological insulator, and we find the states which appear on the different surfaces and along the edge between pairs of surfaces. The surface Hamiltonians depend on the orientation of the surfaces and are therefore quite different from the previous chapters. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based directly on a lattice discretization of the bulk Hamiltonian in order to find surface and edge states. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge are studied as a function of the edge potential. We show that a magnetic field applied in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states. • In the fifth chapter we study a system made of topological insulator (TI) nanocrystals which are coupled to each other. Our theoretical studies are motivated by the following experimental observations. Electrical transport measurements were carried out on thin films of nanocrystals of Bi2Se3 which is a TI. The measurements reveal that the entire system behaves like a single TI with two topological surface states at the two ends of the system. The two surface states are found to be coupled if the film thickness is small and decoupled above a certain film thickness. The surface state penetration depth is found to be unusually large and it decreases with increasing temperature. To explain all these experimental results we propose a theoretical model for this granular system. This consists of multiple grains of Bi2Se3 stacked next to each other in a regular array along the z-direction (the c-axis of Bi2Se3 nanocrystals). We assume translational invariance along the x and y directions. Each grain has top and bottom surfaces on which the electrons are described by Hamiltonians of the Dirac form which can be derived from the bulk Hamiltonian known for this material. We introduce intra-grain tunneling couplings t1 between the opposite surfaces of a single grain and inter-grain couplings t2 between nearby surfaces of two neighboring grains. We show that when t1 < t2 the entire system behaves like a single topological insulator whose outermost surfaces have gapless spectra described by Dirac Hamiltonians. We find a relation between t1, t2 and the surface state penetration depth λ which explains the properties of λ that are seen experimentally. We also present an expression for the surface state Berry phase as a function of the hybridization between the surface states and a Zeeman magnetic field that may be present in the system. At the end we theoretically studied the surface states on one of the side surfaces of the granular system and showed that many pairs of surface states can exist on the side surfaces depending on the length of the unit cell of the granular system. • In the sixth chapter we present our work on junctions of p-wave superconductors (SC) and normal metals (NM) in one dimension. We first study transport in a system where a SC wire is sandwiched between two NM wires. For such a system it is known that there is a Majorana mode at the junction between the SC and each NM lead. If the p-wave pairing changes sign at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the subgap conductance between the leads and the SC. We derive an analytical expression as a function of and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the energies oscillate and decay exponentially as L is increased. The energies exactly match the locations of the peaks in the conductance. We find that the subgap conductances do not change noticeably with the sign of . So there is no effect of the extra Majorana modes which appear inside the SC (due to changes in the signs of Δ) on the subgap conductance. Next we study junctions of three p-wave SC wires which are connected to the NM leads. Such a junction is of interest as it is the simplest system where braiding of Majorana modes is possible. Another motivation for studying this system is to see if the subgap transport is affected by changes in the signs of . For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads. In addition, depending on the signs of the Δ’s in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various subgap conductances have peaks occurring at the energies of all these modes; we therefore get a rich pattern of conductance peaks. Next we study the effects of interactions between electrons (in the NM leads) on the transport. We use a renormalization group approach to study the effect of interactions on the conductance at energies far from the SC gap. Hence the earlier part of this chapter where we studied the transport at an energy E inside the SC gap (so that − < E < Δ) differs from this part where we discuss conductance at an energy E where |E| ≫ . For the latter part we assume the region of three SC wires to be a single region whose only role is to give rise to a scattering matrix for the NM wires; this scattering matrix has both normal and Andreev elements (namely, an electron can be reflected or transmitted as either an electron or a hole). We derive a renormalization group equation for the elements of the scattering matrix by assuming the interaction to be sufficiently weak. The fixed points of the renormalization group flow and their stabilities are studied; we find that the scattering matrix at the stable fixed point is highly symmetric even when the microscopic scattering matrix and the interaction strengths are not symmetric. Using the stability analysis we discuss the dependence of the conductances on the various length scales of the problem. Finally we propose an experimental realization of this system which can produce different signs of the p-wave pairings in the different SCs. • In the seventh chapter we show that the application of circularly polarized electro-magnetic radiation on the surface of a Weyl semimetal can generate states at that surface. The surface states can be characterized by their momenta due to translation invariance. The Floquet eigenvalues of these states come in complex conjugate pairs rather than being equal to ±1. If the amplitude of the radiation is small, we find some unusual bulk-boundary relations: the Floquet eigenvalues of the surface states lie at the extrema of the Floquet eigenvalues of the bulk system when the latter are plotted as a function of the momentum perpendicular to the surface, and the peaks of the Fourier transforms of the surface state wave functions lie at the momenta where the bulk Floquet eigenvalues have extrema. For the case of zero surface momentum, we can analytically derive interesting scaling relations between the decay lengths of the surface states and the amplitude and penetration depth of the radiation. For topological insulators, we again find that circularly polarized radiation can generate states on the surfaces; these states have much larger decay lengths (which can be tuned by the radiation amplitude) than the topological surface states which are present even in the absence of radiation. Finally, we show that radiation can generate surface states even for trivial insulators.

Le but de ce travail est de comprendre les relations entre la déformation et la diagenèse dans les carbonates. Pour cela, l’échelle du m au dam est adéquate car elle permet de séparer les effets matriciels, des fractures et des failles. Celle-ci est sous la résolution de la sismique, donc peu de données géophysiques et diagénétiques spatiale et quantitatives sont disponibles, le plus souvent limitées aux données 1D de puit.Nous avons choisi 4 affleurements présentant des hétérogénéités et des intensités de déformation et de diagenèse diverses. Un protocole multi-échelle et multidisciplinaire a été développé, comprenant de la géophysique à l’échelle du cm au dam, de la diagenèse structurale et de la géochimie sur les ciments de fracture. Nous montrons un fort effet d’échelle entre les Vp en laboratoire et à l’affleurement dû à des hétérogénéités sédimentaire, d’enfouissement et structurale, qui conduisent à différents motifs géostatistiques.Les fractures ont l’effet le plus fort sur les Vp, modulé par leur cimentation, et qui peut entièrement effacer la signature initiale du faciès. La réactivation des fractures induit une anisotropie directionnelle de 10% due à des changements dans le remplissage des fractures, caractérisés par de multiples phases de cimentation, broyage et dissolution.Dans les zones de faille, l’anisotropie sismique est amplifiée, conduisant à un fort affaiblissement de la roche au cisaillement et à une diminution de Vp autour de la faille. Les données géochimiques tracent plusieurs flux de fluides diagénétiques et soulignent les fortes interactions entre l’évolution de la perméabilité, la diagenèse structurale et la signature géophysique des carbonates. / The aim of this work was to understand the relationships between deformations and diagenesis in carbonates. The relevant scale to study it may be the m to dkm scale which allows individualizing fracture, fault and matrix effects. This scale is under the seismic resolution, so few quantitative diagenetic and geophysical spatial data are available, mainly constrained to 1D borehole.Therefore, we selected 4 dkm scale outcrops displaying various heterogeneities and intensities of deformation and diagenesis. We developed a multidisciplinary/multiscale protocol including geophysics from cm to dkm scale along with structural diagenesis study and geochemical measurements on fractures cements. We found a strong scale effect between laboratory and outcrop Vp due to sedimentary, burial and structural heterogeneities that lead to different geostatistical patterns. Fractures have the strongest effect on Vp, being modulated by their cementation and can erase the initial facies acoustic signature. The fracture reactivation induce a 10% Vp directional anisotropy due to microscale changes in the fractures infillings characterized by multiple cementation, crushing and dissolution phases. In fault-zones the seismic anisotropy magnitude is amplified, leading to a strong directional rock shear weakening and a Vp decrease around the fault, caused by higher discontinuities aperture and brecciation. Geochemical data indicate that the Vp signature evolution is linked to different diagenetic fluids flow origins occurring during each deformation phase. This underlines the strong interplay between permeability evolution, structural diagenesis and geophysical signature in carbonates.

Automatic detection and delineation of ECG characteristic points is a basic procedure of any analyze of ECG using computer. This detection is a necessary step to simplify the work of cardiologists to evaluate long ECG records. In this thesis is proposed and evaluate a method of detection and delineation in a single-lead ECG using dyadic wavelet transform followed by correction in pseudo-orthogonal lead system taken from standard 12-lead system. The method uses information about position of positive maximum – negative minimum pair to detect ECG characteristic waves. At first the QRS complex is detected and than its morphology (waves Q and S) and the onset and end of the complex. After that the T-wave is detected and delineated within a searching window dependent on QRS position. And last the P-wave is detected and delineated. There are used two types of wavelets in developed method, “haar” and “quadratic spline”. The developed method was evaluated on CSE database. When haar wavelet was used the QRS detector sensitivity was 99.14%. In the work is also evaluated the accuracy of delineation characteristic points. As the P-wave and QRS complex delineation produced quite good results the T-wave end delineator produced relatively big deviations. All deviations are presented in histograms.

The aim of this diploma thesis is to introduce methods of detection of the QRS complex and the subsequent detection of P waves. The intention is to create a program by specified method in the software Matlab which will be able to implement this method. The thesis describes the basic and important methods of detection and subsequent algorithm to detect P waves. Solution of the algorithm is tested on real data. It also describes the automatic signal evaluation and the results of this automatic function.

Spring water inflow is distinct at Pah Tempe Hot Springs (also known as Dixie Hot Springs) situated within the damage zone of the Hurricane Fault in Timpoweap Canyon in Hurricane, Utah. Excising of the footwall by the Virgin River has created Timpoweap Canyon and allowed an unusual opportunity to study the spring inflow in relation to the fault damage zone. While correlation of these springs with the damage zone and visible fracture patterns on the canyon wall has been made, no subsurface faulting has been imaged to verify connection to these visible fractures and spring inflows (Nelson et al., 2009). The stream was logged and contoured to note the varying locations of spring water inflows in contrast with unsaturated Virgin River water. Seismic surveys were conducted and subsurface profiles made to locate offsets and faults. Photogrammetry was conducted and a three-dimensional model of the canyon and cliff wall was created to facilitate remote fracture mapping of this wallSubsurface features correlate to fractures, spring water inflow locations, and surface faults mapped by Biek (2002). This suggests that faulting and fracturing from the Hurricane Fault provides subsurface conduits for these thermal waters to rise. In one area in the stream, thermal inflow correlates with both subsurface offsets and major surface fractures. Numerous correlations between just spring water entry and subsurface offsets or surface fractures are also found. Fracture and fault density is atypical at Pah Tempe as these features do not diminish with distance from the main strand of the fault. This has led to the Sevier Orogeny accounting for creating the observed fracture conduits at Pah Tempe. Fractures in the canyon wall at Pah Tempe open west to east. This is indicative of the maximum horizontal compressive stress of southern Utah being north to south (Zoback and Zoback, 2015). Therefore the spring inflow at Pah Tempe is likely a result of the damage from the Hurricane Fault creating conduits for spring water to rise, rather than the Sevier Orogeny.