Energy spectrum of fermionized bosonic atoms in optical lattices

We investigate the energy spectrum of fermionized bosonic atoms, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and the retarded Green's function method. The results show that the energy spectrum splits into two energy bands with single-occupation; the fermionized bosonic atom occupies nonvanishing energy state and left hole has a vanishing energy at any given momentum, and the system is in Mott-insulating state with a energy gap. Using the characteristic of energy spectra we obtained a criterion with which one can judge whether the Tonks-Girardeau (TG) gas is achieved or not.

Energy spectrum of two-component Bose-Einstein condensates in optical lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.

Energy spectrum of ground state and excitation spectrum of quasi-particle for hard-core boson in optical lattices

We investigate the energy spectrum of ground state and quasi-particle excitation spectrum of hard-core bosons, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and Bogoliubov approach. The results show that the energy spectrum has a single band structure, and the energy is lower near zero momentum; the excitation spectrum gives corresponding energy gap, and the system is in Mott-insulating state at Tonks limit. The analytic result of energy spectrum is in good agreement with that calculated in terms of Green's function at strong correlation limit.

Strength, Deformation and Fracture in Metallic Nanostructures

An understanding of the mechanics of nanoscale metals and semiconductors is necessary for the safe and prolonged operation of nanostructured devices from transistors to nanowire- based solar cells to miniaturized electrodes. This is a fascinating but challenging pursuit because mechanical properties that are size-invariant in conventional materials, such as strength, ductility and fracture behavior, can depend critically on sample size when materials are reduced to sub- micron dimensions. In this thesis, the effect of nanoscale sample size, microstructure and structural geometry on mechanical strength, deformation and fracture are explored for several classes of solid materials. Nanocrystalline platinum nano-cylinders with diameters of 60 nm to 1 μm and 12 nm sized grains are fabricated and tested in compression. We find that nano-sized metals containing few grains weaken as sample diameter is reduced relative to grain size due to a change from deformation governed by internal grains to surface grain governed deformation. Fracture at the nanoscale is explored by performing in-situ SEM tension tests on nanocrystalline platinum and amorphous, metallic glass nano-cylinders containing purposely introduced structural flaws. It is found that failure location, mechanism and strength are determined by the stress concentration with the highest local stress whether this is at the structural flaw or a microstructural feature. Principles of nano-mechanics are used to design and test mechanically robust hierarchical nanostructures with structural and electrochemical applications. 2-photon lithography and electroplating are used to fabricate 3D solid Cu octet meso-lattices with micron- scale features that exhibit strength higher than that of bulk Cu. An in-situ SEM lithiation stage is developed and used to simultaneously examine morphological and electrochemical changes in Si-coated Cu meso-lattices that are of interest as high energy capacity electrodes for Li-ion batteries.

Key to the larvae of the genera of the sub-family Orthocladiinae from Larvae and Pupae of midges of the sub-family Orthocladiinae of the fauna of the USSR. [Translation from: Larvae and pupae of midges of the subfamily Orthocladiinae of the fauna of the USSR (Diptera, Chironomidae = Tendipedidae) (ed. Pankratova V.Ya.), 51-55. Leningrad, Nauka, 1970. ]

A key to the larvae of the genera of the sub-family Orthocladiinae from Larvae and Pupae of midges of the sub-family Orthocladiinae. Parts of the key refer to the rest of the publication which is not included in this partial translation.

(Ce,Cu)∶LiNbO3晶体非挥发全息记录理论研究与优化

根据双中心带输运模型,对(Ce,Cu)∶LiNbO3晶体双中心非挥发全息记录进行了理论研究与优化。推导了(Ce,Cu)∶LiNbO3晶体的微观参量,采用数值方法通过严格求解模拟双中心带输运方程来模拟全息记录过程。分析了记录过程中,记录与敏化光强、Ce和Cu掺杂浓度以及晶体微观参量对(Ce,Cu)∶LiNbO3晶体双中心全息记录的影响。发现(Ce,Cu)∶LiNbO3晶体非挥发全息记录中实现高衍射效率与固定效率的主导因素是深中心Cu,在记录过程中,深中心Cu建立起了很强的空间电荷场。数值模拟的结果经过实验验

LiNbO3∶Fe∶Rh晶体近红外非挥发全息记录

采用双中心记录方案在双掺杂LiNbO3∶Fe∶Rh晶体中实现了近红外非挥发全息记录,研究了LiNbO3∶Fe∶Rh晶体在633 nm,752 nm,799 nm波长下的全息记录性能。结果表明,在使用近红外记录光时,其记录灵敏度随敏化光强的变化趋势与双中心短波长记录时的不同。通过和LiNbO3∶Fe∶Mn等传统双掺杂铌酸锂晶体的近红外波段记录效果对比,发现同时掺杂Fe和Rh可增强晶体对近红外光的吸收,获得更高的浅中心Fe光生伏特系数,从而能够在LiNbO3∶Fe∶Rh晶体中实现近红外波段的光折变全息记录。

Hyperfine interactions and nuclear structure

An automatic experimental apparatus for perturbed angular correlation measurements, capable of incorporating Ge(Li) detectors as well as scintillation counters, has been constructed.

The gamma-gamma perturbed angular correlation technique has been used to measure magnetic dipole moments of several nuclear excited states in the osmium transition region. In addition, the hyperfine magnetic fields, experienced by nuclei of 'impurity' atoms embedded in ferromagnetic host lattices, have been determined for several '4d' and '5d' impurity atoms.

The following magnetic dipole moments were obtained in the osmium transition region μ_2⁺(¹⁹⁰Os) = 0.54 ± 0.06 nm μ_4⁺(¹⁹⁰Os) = 0.88 ± 0.48 nm μ_2⁺(¹⁹²Os) = 0.56 ± 0.08 nm μ_2⁺(¹⁹²Pt) = 0.56 ± 0.06 nm μ_2^+’(¹⁹²Pt) = 0.62 ± 0.14 nm.

These results are discussed in terms of three collective nuclear models; the cranking model, the rotation-vibration model and the pairing-plus-quadrupole model. The measurements are found to be in satisfactory agreement with collective descriptions of low lying nuclear states in this region.

The following hyperfine magnetic fields of 'impurities' in ferromagnetic hosts were determined; H_int(Cd Ni) = - (64.0 ± 0.8)kG H_int(Hg Fe) = - (440 ± 105)kG H_int(Hg Co) = - (370 ± 78)kG H_int(Hg Ni) = - (86 ± 22)kG H_int(Tl Fe) = - (185 ± 70)kG H_int(Tl Co) = - (90 ± 35)kG H_int(Ra Fe) = - (105 ± 20)kG H_int(Ra Co) = - (80 ± 16)kG H_int(Ra Ni) = - (30 ± 10)kG, where in H_int(AB); A is the impurity atom embedded in the host lattice B. No quantitative theory is available for comparison. However, these results are found to obey the general systematics displayed by these fields. Several mechanisms which may be responsible for the appearance of these fields are mentioned.

Finally, a theoretical expression for time-differential perturbed angular correlation measurement, which duplicates experimental conditions is developed and its importance in data analysis is discussed.

Multiplication in Riesz spaces

A.G. Vulih has shown how an essentially unique intrinsic multiplication can be defined in certain types of Riesz spaces (vector lattices) L. In general, the multiplication is not universally defined in L, but L can always be imbedded in a large space L^# in which multiplication is universally defined.

If ф is a normal integral in L, then ф can be extended to a normal integral on a large space L₁(ф) in L^#, and L₁(ф) may be regarded as an abstract integral space. A very general form of the Radon-Nikodym theorem can be proved in L₁(ф), and this can be used to give a relatively simple proof of a theorem of Segal giving a necessary and sufficient condition that the Radon-Nikodym theorem hold in a measure space.

In another application, the multiplication is used to give a representation of certain Riesz spaces as rings of operators on a Hilbert space.

A Multiwavelength Study of the Intracluster Medium and the Characterization of the Multiwavelength Sub/millimeter Inductance Camera

The first part of this thesis combines Bolocam observations of the thermal Sunyaev-Zel’dovich (SZ) effect at 140 GHz with X-ray observations from Chandra, strong lensing data from the Hubble Space Telescope (HST), and weak lensing data from HST and Subaru to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive, dynamically relaxed galaxy clusters. For five of the six clusters, the full multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The multiwavelength analysis yields considerably better constraints on the total mass and concentration compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulent and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95% confidence, where r500c refers to radius at which the average enclosed density is 500 times the critical density of the Universe. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for the clusters in this sample.

The second part of this thesis focuses on the characterization of the Multiwavelength Sub/millimeter Inductance Camera (MUSIC), a photometric imaging camera that was commissioned at the Caltech Submillimeter Observatory (CSO) in 2012. MUSIC is designed to have a 14 arcminute, diffraction-limited field of view populated with 576 spatial pixels that are simultaneously sensitive to four bands at 150, 220, 290, and 350 GHz. It is well-suited for studies of dusty star forming galaxies, galaxy clusters via the SZ Effect, and galactic star formation. MUSIC employs a number of novel detector technologies: broadband phased-arrays of slot dipole antennas for beam formation, on-chip lumped element filters for band definition, and Microwave Kinetic Inductance Detectors (MKIDs) for transduction of incoming light to electric signal. MKIDs are superconducting micro-resonators coupled to a feedline. Incoming light breaks apart Cooper pairs in the superconductor, causing a change in the quality factor and frequency of the resonator. This is read out as amplitude and phase modulation of a microwave probe signal centered on the resonant frequency. By tuning each resonator to a slightly different frequency and sending out a superposition of probe signals, hundreds of detectors can be read out on a single feedline. This natural capability for large scale, frequency domain multiplexing combined with relatively simple fabrication makes MKIDs a promising low temperature detector for future kilopixel sub/millimeter instruments. There is also considerable interest in using MKIDs for optical through near-infrared spectrophotometry due to their fast microsecond response time and modest energy resolution. In order to optimize the MKID design to obtain suitable performance for any particular application, it is critical to have a well-understood physical model for the detectors and the sources of noise to which they are susceptible. MUSIC has collected many hours of on-sky data with over 1000 MKIDs. This work studies the performance of the detectors in the context of one such physical model. Chapter 2 describes the theoretical model for the responsivity and noise of MKIDs. Chapter 3 outlines the set of measurements used to calibrate this model for the MUSIC detectors. Chapter 4 presents the resulting estimates of the spectral response, optical efficiency, and on-sky loading. The measured detector response to Uranus is compared to the calibrated model prediction in order to determine how well the model describes the propagation of signal through the full instrument. Chapter 5 examines the noise present in the detector timestreams during recent science observations. Noise due to fluctuations in atmospheric emission dominate at long timescales (less than 0.5 Hz). Fluctuations in the amplitude and phase of the microwave probe signal due to the readout electronics contribute significant 1/f and drift-type noise at shorter timescales. The atmospheric noise is removed by creating a template for the fluctuations in atmospheric emission from weighted averages of the detector timestreams. The electronics noise is removed by using probe signals centered off-resonance to construct templates for the amplitude and phase fluctuations. The algorithms that perform the atmospheric and electronic noise removal are described. After removal, we find good agreement between the observed residual noise and our expectation for intrinsic detector noise over a significant fraction of the signal bandwidth.

Combinatorial properties of finite geometric lattices

Let L be a finite geometric lattice of dimension n, and let w(k) denote the number of elements in L of rank k. Two theorems about the numbers w(k) are proved: first, w(k) ≥ w(1) for k = 2, 3, ..., n-1. Second, w(k) = w(1) if and only if k = n-1 and L is modular. Several corollaries concerning the "matching" of points and dual points are derived from these theorems.

Both theorems can be regarded as a generalization of a theorem of de Bruijn and Erdös concerning ʎ= 1 designs. The second can also be considered as the converse to a special case of Dilworth's theorem on finite modular lattices.

These results are related to two conjectures due to G. -C. Rota. The "unimodality" conjecture states that the w(k)'s form a unimodal sequence. The "Sperner" conjecture states that a set of non-comparable elements in L has cardinality at most max/k {w(k)}. In this thesis, a counterexample to the Sperner conjecture is exhibited.

The ecological impact of different mechanisms of chronic sub-lethal toxicity on feeding and respiratory physiology

Sub-lethal toxicity tests, such as the scope-for-growth test, reveal simple relationships between measures of contaminant concentration and effect on respiratory and feeding physiology. Simple models are presented to investigate the potential impact of different mechanisms of chronic sub-lethal toxicity on these physiological processes. Since environmental quality is variable, even in unimpacted environments, toxicants may have differentially greater impacts in poor compared to higher quality environments. The models illustrate the implications of different degrees and mechanisms of toxicity in response to variability in the quality of the feeding environment, and variability in standard metabolic rate. The models suggest that the relationships between measured degrees of toxic stress, and the maintenance ration required to maintain zero scope-for-growth, may be highly nonlinear. In addition it may be possible to define critical levels of sub-lethal toxic effect above which no environment is of sufficient quality to permit prolonged survival.

Padrões geoacústicos de fundo e sub-fundo na Baía de Sepetiba: implicações no conhecimento da geologia do holoceno

A Baía de Sepetiba, localizada entre a Baía de Guanabara e a Baía de Ilha Grande, Estado do Rio de Janeiro, está inserida em um cenário estratégico para o desenvolvimento econômico do Estado. Isto ocorre devido ao aumento da concentração populacional, que está diretamente relacionado com o turismo, com a presença de portos e de áreas industriais. Sendo assim, se faz necessário estudar sua estrutura geológica e dinâmica sedimentar para entender sua evolução ao longo do tempo e para uma utilização mais racional desta área. Utilizando-se da sísmica rasa de alta resolução e da sonografia de varredura lateral juntamente com dados pretéritos de amostragem superficial de sedimentos, o presente trabalho tem como objetivo principal analisar sua geologia holocênica. A investigação, em subsuperfície, da geologia estrutural e sedimentar dessa baía, através da interpretação de 09 perfis sísmicos, baseada na determinação de diferentes tipos de ecotexturas, revelou a presença de diferentes pacotes sedimentares depositados ao longo do Holoceno. Ao todo, foram encontrados 15 tipos de ecotexturas perfazendo 14 camadas sedimentares, que estão relacionados em 4 Grupos de acordo com sua distribuição. Já a investigação em superfície através dos registros sonográficos, baseada nos diferentes graus de reflexão acústica (backscattering) e parametrizada pelos dados de amostragem direta pretérita, identificou 6 padrões sonográficos distintos. Com isso foi confeccionado um novo mapa de distribuição textural dos sedimentos superficiais da Baía de Sepetiba. Com a correlação dos dados de sísmica rasa com os dados sonográficos, foi possível ainda sugerir a provável existência de neotectonismo na área de estudo.

激光二极管端面抽运Nd∶YVO4固体激光器热致光束畸变非对称的平衡

由于a轴切割Nd∶YVO4晶体的非对称性,使得激光二极管(LD)端面抽运Nd∶YVO4固体激光器不同于Nd∶YAG激光器,输出的激光经常产生非对称结果。用有限元法分析激光二极管端面抽运a轴切割Nd∶YVO4固体激光器的晶体热效应,包括温度分布、内部应力和产生的形变。分析结果表明端面抽运a轴切割Nd∶YVO4晶体产生了椭球热透镜效应。从结构方面和抽运方面提出了热透镜非对称性的平衡方法,实验验证了方法的可行性。