A new high-order Fourier continuation-based elasticity solver for complex three-dimensional geometries

This thesis presents a new approach for the numerical solution of three-dimensional problems in elastodynamics. The new methodology, which is based on a recently introduced Fourier continuation (FC) algorithm for the solution of Partial Differential Equations on the basis of accurate Fourier expansions of possibly non-periodic functions, enables fast, high-order solutions of the time-dependent elastic wave equation in a nearly dispersionless manner, and it requires use of CFL constraints that scale only linearly with spatial discretizations. A new FC operator is introduced to treat Neumann and traction boundary conditions, and a block-decomposed (sub-patch) overset strategy is presented for implementation of general, complex geometries in distributed-memory parallel computing environments. Our treatment of the elastic wave equation, which is formulated as a complex system of variable-coefficient PDEs that includes possibly heterogeneous and spatially varying material constants, represents the first fully-realized three-dimensional extension of FC-based solvers to date. Challenges for three-dimensional elastodynamics simulations such as treatment of corners and edges in three-dimensional geometries, the existence of variable coefficients arising from physical configurations and/or use of curvilinear coordinate systems and treatment of boundary conditions, are all addressed. The broad applicability of our new FC elasticity solver is demonstrated through application to realistic problems concerning seismic wave motion on three-dimensional topographies as well as applications to non-destructive evaluation where, for the first time, we present three-dimensional simulations for comparison to experimental studies of guided-wave scattering by through-thickness holes in thin plates.

Synthesis and characterization of 1,1-di-tert-butyldiazene

The synthesis and direct observation of 1,1-di-tert-butyldiazene (16) at -127°C is described. The absorption spectrum of a red solution of 1,1-diazene 16 reveals a structured absorption band with λ max at 506 run (Me_2O, -125°C). The vibrational spacing in S_1 is about 1200 cm^(-1). The excited state of 16 emits weakly with a single maximum at 715 run observed in the fluorescence spectrum (Me_2O:CD_2Cl_2, -196°C). The proton NMR spectrum of 16 occurs as a singlet at 1.41 ppm. Monitoring this NMR absorption at -94^0 ± 2°C shows that 1,1-diazene 16 decomposes with a first-order rate of 1.8 x 10^(-3) sec(-1) to form isobutane, isobutylene and hexarnethylethane. This rate is 10^8 and 10^(34) times faster than the thermal decomposition of the corresponding cis and trans 1,2-di-tert-butyldiazene isomers. The free energy of activation for decomposition of 1,1-diazene 16 is found to be 12.5 ± 0.2 kcal/mol at -94°C which is much lower than the values of 19.1 and 19.4 kcal/lmole calculated at -94°C for N-(2,2,6,6- tetramethylpiperidyl)nitrene (3) and N-(2,2,5,5- tetrarnethylpyrrolidyl)nitrene (4), respectively. This difference between 16 and the cyclic-1,1-diazenes 3 and 4 can be attributed to a large steric interaction between the tert-butyl groups in 1,1-diazene 16.

In order to investigate the nature of the singlet-triplet gap in 1,1-diazenes, 2,5-di-tert-butyl-N-pyrrolynitrene (22) was generated but was found to be too reactive towards dimerization to be persistent. In the presence of dimethylsulfoxide, however, N-pyrrolynitrene (22) can be trapped as N-(2,5-di-tert-butyl- N'-pyrrolyl)dimethylsulfoxirnine (38). N-(2,5-di-tert-butyl-N'-pyrrolyl)dimethylsulfoximine (38-d^6) exchanges with free dimethylsulfoxide at 50°C in solution, presumably by generation and retrapping of pyrrolynitrene 22.

The power of quantum Fourier sampling

How powerful are Quantum Computers? Despite the prevailing belief that Quantum Computers are more powerful than their classical counterparts, this remains a conjecture backed by little formal evidence. Shor's famous factoring algorithm [Shor97] gives an example of a problem that can be solved efficiently on a quantum computer with no known efficient classical algorithm. Factoring, however, is unlikely to be NP-Hard, meaning that few unexpected formal consequences would arise, should such a classical algorithm be discovered. Could it then be the case that any quantum algorithm can be simulated efficiently classically? Likewise, could it be the case that Quantum Computers can quickly solve problems much harder than factoring? If so, where does this power come from, and what classical computational resources do we need to solve the hardest problems for which there exist efficient quantum algorithms?

We make progress toward understanding these questions through studying the relationship between classical nondeterminism and quantum computing. In particular, is there a problem that can be solved efficiently on a Quantum Computer that cannot be efficiently solved using nondeterminism? In this thesis we address this problem from the perspective of sampling problems. Namely, we give evidence that approximately sampling the Quantum Fourier Transform of an efficiently computable function, while easy quantumly, is hard for any classical machine in the Polynomial Time Hierarchy. In particular, we prove the existence of a class of distributions that can be sampled efficiently by a Quantum Computer, that likely cannot be approximately sampled in randomized polynomial time with an oracle for the Polynomial Time Hierarchy.

Our work complements and generalizes the evidence given in Aaronson and Arkhipov's work [AA2013] where a different distribution with the same computational properties was given. Our result is more general than theirs, but requires a more powerful quantum sampler.

A two-step phase-retrieval method in Fourier-transform ghost imaging

A two-step phase-retrieval method, based on Fourier-transform ghost imaging, was demonstrated. For the complex objects, the phase-retrieval process was divided into two steps: first got the complex object's amplitude from the Fourier-transform patterns of the squared object function, then combining with the Fourier-transform patterns of the object function to get the phase. The theoretical basis of this technique is outlined, and the experimental results are presented. (C) 2008 Elsevier B.V. All rights reserved.

Megacylops viridis Jurine, abyssal form in Lake Maggiore. [Translation of: Memorie dell'Istituto Italiano di Idrobiologia Dott.Marco de Marchi 17 57-79, 1964]

Megacyclops viridis Jurine, noticed in Lago Maggiore in 1912 by De Marchi from the littoral vegetation of Pallanza, is a normal member of the littoral plankton of the lake. The subgenus Megacyclops, created by Kiefer in his revision of the viridis-vernalis group, contains european and american species some of which are today considered as varieties of the species viridis. This paper examines morphology and of the distribution of the Italian viridis in Lake Maggiore.

Study on the dynamics of the population of a copepod (Eudiaptomus vulgaris Schmeil). [Translation from: Memorie dell'Istituto Italiano di Idrobiologia Dott.Marco de Marchi 13 179-202, 1961. ]

Eudiaptomus vulgaris Schmeil is the most abundant copepod in Lake Maggiore and forms also, in respect to other entomostraca, the most important element, through its average biomass and because it is fairly numerous throughout the year. Plankton samples collected in a systematic and quantitative way, gave the opportunity to study some aspects of the dynamics of the population of this copepod, in safety in view of the uncertainty which in this kind of study can ensue when samples are taken only at a single station - in consequence of the changes in size of population between different water masses. The results of the biometrical observations are of the population of Eudiaptomus vulgaris is presented.

Ecological significance of seasonal variation in clutch-size of Arctodiaptomus bacillifer in alpine lakes of high altitudes (Val Bognanco) [Translation from: Bollettino di Zoologia 37 491-492, 1970]

This brief paper describes the significance of seasonal variation in clutch-size of the copepod Arctodiaptomus bacillifer in alpine lakes of high altitudes (Val Bognanco). Seasonal dynamics of the zooplankton of these lakes was studied during summer and autumn of 1968 and 1969and results are summarised.

Observing the fractional Fourier transform by free-space Fresnel diffraction

The fractional Fourier transform of an object can be observed in the free-space Fresnel diffraction pattern of the object. (C) 1997 Optical Society of America

Scaled fractional Fourier transform and its optical implementation

The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of phi and output scale. In addition, physically it relates the FRT with the general lens transform-the optical diffraction between two asymmetrically positioned planes before and after a lens. (C) 1997 Optical Society of America.

Predation and selection in copepod populations of Alpine waters [Translation from: Bollettino di Zoologia 21 541-545, 1954]

Zooplankton was studied in four alpine lakes in Switzerland, France and Italy. The presence the presence of the invertebrate predator Heterocope in three lakes was stated. It is then discussed why in three of these four lakes, the copepod Arctodiaptomus denticornis is present in the absence of Arctodiaptomus bacillifer, and vice versa respectively in the second and first parts of the lacustrine summer.

Selective plankton feeding by the coregonid ”bondella” (Coregonus sp.) of Lake Maggiore [Translation from: Translation from: Memorie dell'Istituto Italiano di Idrobiologia Dott.Marco de Marchi 31 181-203, 1974]

In recent times, some specialists have begun to study the subject of food selection of fish in an organized way, thus highlighting its importance. In the present work, the author intends to evaluate the impact of predation on the eupelagic zooplanktonic biocenosis of Lake Maggiore, producing, in this way, as far as possible, a basis for a better understanding of the population dynamics of the species of zooplankton directly involved. Another aspect which has been studied is that related to the mechanism of selective capture set in action by the predator. To this end the study tries to bear in mind that the subject should be interpreted as a function of numerous factors acting contemporaneously, that is as the interaction of characters peculiar to the predator and to the prey. The species studied, locally called ”bondella”, belongs to the family Salmonidae, subfamily Coregoninae and was introduced into Lake Maggiore in 1950.

The problem of the co-existence of Arctodiaptomus bacillifer (Koelb.), Acanthodiaptomus denticornis (Wierz.) and Heterocope saliens Lill [Translation from: Memorie dell'Istituto Italiano di Idrobiologia Dott.Marco de Marchi 8 81-94, 1954]

In freshwater environments of modest size and without notable ecological structure, there is usually present only one diaptomid species. When two or more diaptomid species are present in the same habitat, generally their body dimensions are distinctly different. There are only four examples of co-existence of Arctodiaptomus bacillifer (Koelb.) and Acanthodiaptomus denticornis (Wierz.) situated at higher altitudes alpine lakes. The article discusses the results of sampling in the summer of 1953 and the problem of the co-existence of Arctodiaptomus bacillifer, Acanthodiaptomus denticornis and Heterocope saliens.

Flood circulation in oligomictic lakes: an undervalued reason for restriction of zooplankton production [Translation from: Memorie dell'Istituto Italiano di Idrobiologia Dott.Marco de Marchi 22 9-52, 1967]

Dormancy has been observed in several species of Cyclops. Animals in dormancy are characterised by almost complete inactivity of the main appendages and sluggish intestinal peristalsis. In Cyclops vicinus dormancy can take place in copepod stages III (19%), IV (78%) and V (3%) but one and the same animal only in one developmental stage. The author gives his own results between frequency of dormancy and photoperiod (20 C, 1000 lux). He concludes that dormancy in C. vicinus can be influenced by day length and can be ended prematurely by short day length.