Abstract In time delay estimation the correlator or, equivalently, matched filter estimator is widely used. Examples of its usage can be found in the global positioning system (GPS), radars and code division multiple access (CDMA) communication systems. Although widely used its performance is not studied in general case until recently. Partially this study is done in this thesis. If interfering signals like multipath or multiple access signals exist in addition to additive white Gaussian noise, as in GPS and CDMA, the correlator is not a maximum likelihood (ML) estimator. However, it is known that the correlator produces consistent estimates in the existence of multipath interference if the delay separation is larger than the correlation time of the signal (in direct sequence spread spectrum applications such as GPS and CDMA, the correlation time approximately equals the chip duration of the spreading code). It also performs well in the existence of multiple access interference (MAI), if the powers of the MAI signals are equal to the power of the desired signal. In this thesis the asymptotic distribution of the correlator estimator is derived in multisignal environments. Using the result, it can be analytically shown, that in these benign interference cases the exact ML estimator and the correlator estimators perform equally well in the sense that their asymptotic covariance matrices are equal. The thesis also verifies the well known result that if the signals are orthogonal, then the correlator and ML estimators perform equally. In addition, the correlator's asymptotic performance is investigated also in the inconsistent case by slightly extending the earlier results found in the literature. Also the resolution of the correlator estimator is investigated. It is numerically shown that the correlator estimator can produce consistent estimators even if the delay separation is less that the chip duration, which is commonly believed to be the resolution limit of the correlator. This can happen in fading channels where the multipath amplitudes are uncorrelated or just slightly correlated. This result seems to be fairly unknown. In addition to the classical ML estimator, where all the unknowns are assumed to be deterministic, also an improved ML estimator is investigated. This other ML estimator is obtained by assuming that the amplitudes are Gaussian distributed. It is an improved estimator in the sense that its asymptotic covariance, say CML, is less positive definite than that of the classical ML estimator CCML, i.e., CCML-CML is positive semidefinite. More importantly, this result is valid independent of the fact are the amplitudes really deterministic or Gaussian. This well known result is shown in this thesis to be valid also if the signals contain more than one unknown parameter, which occurs, for example, in direction-of-arrival estimation when two angles per arrival are to be estimated.

Abstract In this thesis, we study quantum waveguides and their spectral properties. A quantum waveguide is a system of narrow strips or tubes. That is, the waveguide has large longitudinal but small transverse sizes. The study of quantum waveguides is essential in the semi-conductor industry, and the waveguides are used to model the electron behavior in these devices. We consider two- and three-dimensional waveguides with sharp bends and question whether the quantum particle can propagate in the waveguide. It is well known that a certain type of bends and bulges cause the resonance phenomena, that is, at some energy levels the electron motion is localized in a finite area, and the propagation is disturbed. The study of waveguides leads to the interesting field of mathematics - the spectral analysis of differential operators. For a waveguide having high purity and a crystalline structure, the electron motion can be considered as a free particle motion with effective mass. This gives rise to the spectral problem, that is, the eigenvalue problem of the Laplace operator. On the boundary we set the Dirichlet conditions. This thesis consists of three parts and in each part we study waveguides which form sharp bends in the junctions where two or three outlets are joined together. To be precise, we consider waveguides which resemble the letters Y, Z, and C. We study the discrete spectrum corresponding to these waveguides and the behavior of the bound modes when the geometry is slightly changed. For this, we apply the variational, numerical, and asymptotic methods. For the Y-shaped waveguide, we let one outlet become wider than the others and found that a critical width exists, so that for smaller width values, exactly one bound state exists, but for larger values, no bound modes exist. We also let the angle between the strips to vary and found that the number of the bound modes highly depends on the opening angle of the outlets in the Y-shaped waveguide. For the Z- and C-shaped waveguides, we let the height of the waveguide change. We saw that there may appear two bound states at most. Moreover, for the C-shaped waveguide, the first is monotone increasing as a function of height and the second eigenvalue is monotone decreasing. For the Z-shaped waveguide, we show that the lowest eigenvalue as a function of the height is not monotone. / Tiivistelmä Tässä väitöskirjassa tutkitaan kvanttiaaltojohteisiin liittyvää ominaisarvo-ongelmaa. Kvanttiaaltojohteessa aallon eteneminen on rajoitettu tiettyyn suuntaan, ja johde on poikittaissuunnassa nanokokoluokkaa. Kvanttiaaltojohteiden tutkimus on tärkeä osa nykyistä puolijohdeteknologiaa. Tutkimuksessamme olemme keskittyneet kaksi- ja kolmiulotteisiin aaltojohteisiin, jotka geometrialtaan muistuttavat Y-, Z- tai C-kirjainta. Haluamme tietää millaisissa tilanteissa elektronin liike aaltojohteessa estyy. Yleisesti tiedetään, että aaltojohteessa olevat pullistumat ja mutkat johtavat niin sanottuun sidottuun tilaan, ts. tilanteeseen että tietyllä taajuudella tai energiatasolla oleva partikkeli jää lokalisoituun tilaan. Aaltojohde rakentuu puhtaasta kiderakennemateriaalista, joka on kokoluokaltaan pieni poikittaissuunnassa, niin että elektronin liikettä voidaan kuvata vapaan elektronin mallilla Schrödingerin yhtälössä, jossa elektronilla on effektiivinen massa. Tämä johtaa Laplace-operaattorin ominaisarvo-ongelmaan, reunaehtoina on aaltojohteille käytetty Dirichlet nollareuna-arvoja. Tässä väitöstutkimuksessa on tutkittu kolmea erityyppistä aaltojohdetta, joiden geometriaa voidaan kuvata kirjainten Y, C ja Z avulla. Jokaisessa tapauksessa on tutkittu spektristä erityisesti diskreettiä osaa, ja erityisesti mahdollisia muutoksia diskreetissä spektrissä geometristen parametrien muuttuessa. Diskreetin spektrin tutkimiseen on käytetty variaatiomenetelmiä, asymptoottista analyysiä sekä numeerisista menetelmistä elementtimenetelmää. Geometrialtaan kirjainta Y muistuttava aaltojohde koostuu kolmesta haarasta, joista yhden leveyden annetaan varioida. Tällöin voidaan löytää kriittinen raja, siten että jalan leveyden ollessa tätä rajaa pienempi on diskreetti spektri epätyhjä kun taas leveyden ollessa kriittistä rajaa suurempi, diskreetti spektri on tyhjä. Toisessa tapauksessa jalan leveydet pidetään samana, mutta annetaan kulman kahden haaran välillä muuttua. Voidaan nähdä, että diskreetissä spektrissä olevien ominaisarvojen lukumäärä riippuu aaltojohteen kulmasta siten että mitä pienempi kulma kahden haaran välillä, sitä enemmän ominaisarvoja on diskreetissä spektrissä. Vastaavasti Z- ja C- aaltojohteissa, aaltojohteen korkeutta säädellään. Havaitaan, että korkeuden kasvaessa, voi aaltojohteessa esiintyä korkeintaan kaksi ominaisarvoa diskreetissä spektrissä. Lisäksi C-aaltojohteen ensimmäisen ominaisarvon voidaan havaita olevan kasvava aaltojohteen korkeuden funktiona kun taas toinen ominaisarvoista on vähenevä. Toisaalta taas Z-aaltojohteen pienin ominaisarvo korkeuden funktiona ei ole monotoninen.

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Les algorithmes Branch-and-Bound (B&B) font partie des méthodes exactes pour la résolution de problèmes d’optimisation combinatoire. Les calculs induits par un algorithme B&B sont extrêmement couteux surtout lorsque des instances de grande tailles sont considérées. Un algorithme B&B peut être vu comme une exploration implicite d’un espace représenté sous la forme d’un arbre qui a pour spécificité d’être hautement irrégulier. Pour accélérer l’exploration de cet espace, les calculs parallèles et distribués à très large échelle sont souvent utilisés. Cependant, atteindre des performances parallèles optimales est un objectif difficile et jalonné de plusieurs défis, qui découlent essentiellement de deux facteurs: (i) l’irrégularité des calculs inhérents à l’arbre B&B et (ii) l’hétérogénéité inhérente aux environnements de calcul large échelle. Dans cette thèse, nous nous intéressons spécifiquement à la résolution de ces deux défis. Nous nous concentrons sur la conception d’algorithmes distribués pour l’équilibrage de charge afin de garantir qu’aucune entité de calcul n’est surchargée ou sous-utilisée. Nous montrons comment résoudre l’irrégularité des calculs sur différents type d’environnements, et nous comparons les approches proposées par rapport aux approches de références existantes. En particulier, nous proposons un ensemble de protocoles spécifiques à des contextes homogènes, hétérogène en terme de puissance de calcul (muti-coeurs, CPU et GPU), et hétérogènes en terme de qualité des lien réseaux. Nous montrons à chaque fois la supériorité de nos protocoles à travers des études expérimentales extensives et rigoureuses. / Branch and Bound (B&B) algorithms are exact methods used to solve combinatorial optimization problems (COPs). The computation process of B&B is extremely time-intensive when solving large problem instances since the algorithm must explore a very large space which can be viewed as a highly irregular tree. Consequently, B&B algorithms are usually parallelized on large scale distributed computing environments in order to speedup their execution time. Large scale distributed computing environments, such as Grids and Clouds, can provide a huge amount of computing resources so that very large B&B instances can be tackled. However achieving high performance is very challenging mainly because of (i) the irregular characteristics of B&B workload and (ii) the heterogeneity exposed by large scale computing environments. This thesis addresses and deals with the above issues in order to design high performance parallel B&B on large scale heterogeneous computing environments. We focus on dynamic load balancing techniques which are to guarantee that no computing resources are underloaded or overloaded during execution time. We also show how to tackle the irregularity of B&B while running on different computing environments, and consider to compare our proposed solutions with the state-of-the-art algorithms. In particular, we propose several dynamic load balancing algorithms for homogeneous, node-heterogeneous and link-heterogeneous computing platforms. In each context, our approach is shown to perform much better than the state-of-the-art approaches.

Thesis advisor: Kevin S. Bedell / One of the many achievements of renowned physicist L.D. Landau was the formulation of Fermi Liquid Theory (FLT). Originally debuted in the 1950s, FLT has seen abundant success in understanding degenerate Fermi systems and is still used today when trying to understand the physics of a new interacting Fermi system. Of its many advantages, FLT excels in explaining why interacting Fermi systems behave like their non-interacting counterparts, and understanding transport phenomena without cumbersome and confusing mathematics. In this work, FLT is applied to systems whose low energy excitations obey the massless Dirac equation; i.e. the energy dispersion is linear in momentum, ε α ρ, as opposed to the normal quadratic, ε α ρ². Such behavior is seen in numerous, seemingly unrelated, materials including graphene, high T[subscript]c superconductors, Weyl semimetals, etc. While each of these materials possesses its own unique properties, it is their low energy behavior that provides the justification for their grouping into one family of materials called Dirac materials (DM). As will be shown, the linear spectrum and massless behavior leads to profound differences from the normal Fermi liquid behavior in both equilibrium and transport phenomena. For example, with mass having no meaning, we see the usual effective mass relation from FLT being replaced by an effective velocity ratio. Additionally, as FLT in d=2 has been poorly studied in the past, and since the most famous DM in graphene is a d=2 system, a thorough analysis of FLT in d=2 is presented. This reduced dimensionality leads to substantial differences including undamped collective modes and altered quasiparticle lifetime. In chapter 3, we apply the Virial theorem to DM and obtain an expression for the total average ground state energy $E=\frac{B}{r_s}$ where $B$ is a constant independent of density and $r_s$ is a dimensionless parameter related to the density of the system: the interparticle spacing $r$ is related to $r_s$ through $r=ar_s$ where $a$ is a characterstic length of the system (for example, in graphene, $a=1.42$ \AA). The expression derived for $E$ is unusual in that it's typically impossible to obtain a closed form for the energy with all interactions included. Additionally, the result allows for easy calculation of various thermodynamic quantities such as the compressibility and chemical potential. From there, we use the Fermi liquid results from the previous chapter and obtain an expression for $B$ in terms of constants and Fermi liquid parameters $F_0^s$ and $F_1^s$. When combined with experimental results for the compressibility, we find that the Fermi liquid parameters are density independent implying a unitary like behavior for DM. In chapter 4, we discuss the alleged universal KSS lower bound in DM. The bound, $\frac{\eta}{s}\geq\frac{\hbar}{4\pi k_B}$, was derived from high energy/string theory considerations and was conjectured to be obeyed by all quantum liquids regardless of density. The bound provides information on the interactions in the quantum liquid being studied and equality indicates a nearly perfect quantum fluid. Since its birth, the bound has been highly studied in various systems, mathematically broken, and poorly experimented on due to the difficult nature of measuring viscosity. First, we provide the first physical example of violation by showing $\frac{\eta}{s}\rightarrow 0$ as $T\rightarrow T_c$ in a unitary Fermi gas. Next, we determine the bound in DM in d=2,3 and show unusual behavior that isn't seen when the bound is calculated for normal Fermi systems. Finally we conclude in chapter 5 and discuss the outlook and other avenues to explore in DM. Specifically, it must be pointed out that the physics of what happens near charge neutrality in DM is still poorly understood. Our work in understanding the Fermi liquid state in DM is necessary in understanding DM as a whole. Such a task is crucial when we consider the potential in DM, experimentally, technologically, and purely for our understanding. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

<div><div><div><p>Numerous fundamental quests and technological advances require trapping light waves. Generally, light is trapped by the absence of radiation channels or by forbid- ding access to them. Unconventional bound states of light, called bound states in the continuum (BICs), have recently gained tremendous interest due to their peculiar and extreme capabilities of trapping light in open structures with access to radiation. A BIC is a localized state of an open structure with access to radiation channels, yet it remains highly confined with, in theory, infinite lifetime and quality factor. There have been many realizations of such exceptional states in dielectric systems without loss. However, realizing BICs in lossy systems such as those in plasmonics remains a challenge. This thesis explores the realization of BICs in a hybrid plasmonic-photonic structure consisting of a plasmonic grating coupled to a dielectric optical waveguide with diverging radiative quality factors. The plasmonic-photonic system supports two distinct groups of BICs: symmetry protected BICs and Friedrich-Wintgen BICs. The photonic waveguide modes are strongly coupled to the gap plasmons in the grating leading to an avoided crossing behavior with a high value of Rabi splitting of 150 meV . Additionally, it is shown that the strong coupling significantly alters the band diagram of the hybrid system, revealing opportunities for supporting stopped light at an off-Γ wide angular span.</p><p>In another study, we demonstrate the design of a BIC-based all-dielectric metasurface and its application as a nanolaser. Metasurfaces have received an ever-growing interest due to their unprecedented ability to control light using subwavelength structures arranged in an ultrathin planar profile. However, the spectral response of meta- surfaces is generally broad, limiting their use in applications requiring high quality (Q) factors. In this study, we design, fabricate, and optically characterize metasur- faces with very high Q-factors operating near the BIC regime. The metasurfaces are coated with an organic lasing dye as an active medium, and their lasing action is experimentally characterized. The proposed BIC-based metasurfaces nanolaser have very favorable characteristics including low threshold, easily tunable resonances, polarization-independent response, and room temperature operation.</p><div><div><div><p>The second part of the thesis deals with the nonlinear phenomenon in nanopho- tonic structures. We developed an advanced full-wave framework to model nonlinear light-matter interactions. Rate equations, describing atomic relaxations and excita- tion dynamics, are coupled to the Maxwell equations using a Lorentzian oscillator that models the kinetics-dependent light-matter interaction in the form of averaged polarization. The coupled equations are discretized in space and time using a finite- difference time-domain method that provides a versatile multiphysics framework for designing complex structures and integrating diverse material models. The proposed framework is used to study gain dynamics in silver nanohole array, reverse saturable absorption dynamic in optical limiters, and saturable absorption in random lasers. This framework provides critical insights into the design of photonic devices and their complementary optical characterization, and serve as an invaluable utility for guiding the development of synthetic materials. It allows accurate physics-based numerical modeling and optimization of the devices with complex micro- and nano-structured materials and complex illumination sources such as non-paraxial structured beams.</p></div></div></div></div></div></div>

High performance computing (HPC) platforms are evolving to more heterogeneous configurations to support the workloads of various applications. The current hardware landscape is composed of traditional multicore CPUs equipped with hardware accelerators that can handle high levels of parallelism. Graphical Processing Units (GPUs) are popular high performance hardware accelerators in modern supercomputers. GPU programming has a different model than that for CPUs, which means that many numerical kernels have to be redesigned and optimized specifically for this architecture. GPUs usually outperform multicore CPUs in some compute intensive and massively parallel applications that have regular processing patterns. However, most scientific applications rely on crucial memory-bound kernels and may witness bottlenecks due to the overhead of the memory bus latency. They can still take advantage of the GPU compute power capabilities, provided that an efficient architecture-aware design is achieved. This dissertation presents a uniform design strategy for optimizing critical memory-bound kernels on GPUs. Based on hierarchical register blocking, double buffering and latency hiding techniques, this strategy leverages the performance of a wide range of standard numerical kernels found in dense and sparse linear algebra libraries. The work presented here focuses on matrix-vector multiplication kernels (MVM) as repre- sentative and most important memory-bound operations in this context. Each kernel inherits the benefits of the proposed strategies. By exposing a proper set of tuning parameters, the strategy is flexible enough to suit different types of matrices, ranging from large dense matrices, to sparse matrices with dense block structures, while high performance is maintained. Furthermore, the tuning parameters are used to maintain the relative performance across different GPU architectures. Multi-GPU acceleration is proposed to scale the performance on several devices. The performance experiments show improvements ranging from 10% and up to more than fourfold speedup against competitive GPU MVM approaches. Performance impacts on high-level numerical libraries and a computational astronomy application are highlighted, since such memory-bound kernels are often located in innermost levels of the software chain. The excellent performance obtained in this work has led to the adoption of code in NVIDIAs widely distributed cuBLAS library.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第17895号 / 農博第2018号 / 新制||農||1017(附属図書館) / 学位論文||H25||N4791(農学部図書室) / 30715 / 京都大学大学院農学研究科応用生命科学専攻 / (主査)教授 加納 健司, 教授 三芳 秀人, 教授 小川 順 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

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