ULTRACOLD QUANTUM GASES

In this thesis, we discuss ultracold quantum gases both in continuum and optical lattices. For the continuum Fermi gases in BCS-BEC crossover, we present an effective field theory study on the recently discovered puzzling damping phenomena on the BCS side of the crossover. We find that in contrast to the previous proposed pair-breaking mechanism of damping, the damping process is due to the interaction between superfluid phonons and thermally excited fermionic quasi particles. Results from our effective field theory are compared quantitatively with experiments, showing a good agreement. For the ultracold fermionic atoms in optical lattices, we propose two novel quantum phases. Firstly, we show that a novel superconducting pairing occurs for spin-imbalanced Fermi gases with the spin up and down Fermi levels lying within the px- and s- orbital bands of a quasi-one-dimensional optical lattice. The pairs condense at a finite momentum equal to the sum of the two Fermi momenta of spin up and down fermions, and form a p-orbital condensate. The phase diagram shows that the p-orbital pair condensate occurs in a wide range of fillings. Secondly, we study instabilities of single-species fermionic atoms in the p-orbital bands in two-dimensional square optical lattices. From the nearly-perfect nesting Fermi surfaces, charge density wave and orbital density wave orderings with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superconducting phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible liquid crystal phases in our system. For bosons, we study ultracold bosonic atoms loaded in a one-dimensional optical lattice of two-fold p-orbital degeneracy at each site, and find an anti-ferro-orbital, a homogeneous px Mott insulator phase and two kinds of superfluid phases distinguished by the orbital ordering

Synthesis Of Biodiesel From Animal Fat And Polymerization Of Glycerin

Biodiesel was synthesized using raw beef fat using esterification and transesterification reaction. The obtained biodiesel-glycerin mixture was tested using Fourier transform infrared resonance (FT-IR) and compared with the FT-IR of raw beef fat, glycerin, biodiesel made from vegetable oil and commercial biodiesel. The FT-IR spectrum of the synthesized biodiesel was identical to that of biodiesel made from vegetable oil. Poly-glycerin was synthesized from glycerin by water elimination reaction, where solid NaOH was used as a catalyst under a stream of nitrogen gas. The water-elimination reaction obeys the “N-1†rule. “N-1†is the degree of polymerization and “N†is the number of glycerin molecules. The polymers were produced either by patch synthesis or continuous synthesis. In the former, the trimer, pentamer, heptamer, and the decamer were individually synthesized. In the latter, a higher degree of polymers were produced by continuously heating glycerin where the mass of water that was reduced from the reaction was monitored and samples of the polymer were obtained at regular time. FT-IR samples were acquired and the viscosity of the glycerin and the final product was obtained at different temperatures. FT-IR, viscosity, 1H and 13C nuclear magnetic resonance (1H and 13C NMR), and principal component analysis (PCA) based on FT-IR data were used to monitor and study the polymerization process. The results indicate that among the spectroscopy methods that we used, FT-IR yields consistent data on monitoring the polymerization reaction. PCA calculations indicate that the amount of dimer peaks an hour after the initiation of the polymerization reaction then it goes down as higher- degree polymers are made

Metrics of critical pair identification

Critical Pair Identification works as a potential assistive tool for human air traffic controllers by identifying potentially dangerous situations that are not detected by proposed automated separation assurance systems. This concept specifically considers conflicts that might arise if aircraft unexpectedly deviate from their planned flight path in the near future. Five metrics of the critical pair concept, Critical Pair Count, Time to Risk Exposure, Lead Time, Risk Exposure Duration and Blunder Sensitivity Index, have been developed and mathematically defined to characterize the safety level of an aircraft pair or a volume of air space. Algorithm that computes proposed metrics is developed in the study. The metrics are calculated in four-aircraft test scenario simulation and the results have shown that aircraft pairs that have separated by automated separation assurance tools may still have critical pair metric values that suggest a potentially dangerous situation

Finite temperature damping of collective modes of a BCS-BEC crossover superfluid

A new mechanism is proposed to explain the puzzling damping of collective excitations, which was recently observed in the experiments of strongly interacting Fermi gases below the superfluid critical temperature on the fermionic (BCS) side of Feshbach resonance. Sound velocity, superfluid density and damping rate are calculated with effective field theory. We find that a dominant damping process is due to the interaction between superfluid phonons and thermally excited fermionic quasiparticles, in contrast to the previously proposed pair-breaking mechanism. Results from our effective model are compared quantitatively with recent experimental findings, showing a good agreement.Comment: final version, 9 pages, 4 figure

Stripe, checkerboard, and liquid-crystal ordering from anisotropic p-orbital Fermi surfaces in optical lattices

We study instabilities of single-species fermionic atoms in the p-orbital bands in two-dimensional optical lattices at noninteger filling against interactions. Charge density wave and orbital density wave orders with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superfluid phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible phase-transitions from orbital stripe order to liquid-crystal phases and obtain the phase diagram. The condition of nearly-perfect Fermisurface nesting, which is key to the above results, is shown robustly independent of fermion fillings in such p-orbital systems, and the $(2k_F,\pm2k_F)$ momentum of density wave oscillation is highly tunable. Such remarkable features show the promise of making those exotic orbital phases, which are of broad interest in condensed-matter physics, experimentally realizable with optical lattice gases.Comment: final version, 8 pages, 5 figure

Consistency and Consensus Driven for Hesitant Fuzzy Linguistic Decision Making with Pairwise Comparisons

Hesitant fuzzy linguistic preference relation (HFLPR) is of interest because it provides an efficient way for opinion expression under uncertainty. For enhancing the theory of decision making with HFLPR, the paper introduces an algorithm for group decision making with HFLPRs based on the acceptable consistency and consensus measurements, which involves (1) defining a hesitant fuzzy linguistic geometric consistency index (HFLGCI) and proposing a procedure for consistency checking and inconsistency improving for HFLPR; (2) measuring the group consensus based on the similarity between the original individual HFLPRs and the overall perfect HFLPR, then establishing a procedure for consensus ensuring including the determination of decision-makers weights. The convergence and monotonicity of the proposed two procedures have been proved. Some experiments are furtherly performed to investigate the critical values of the defined HFLGCI, and comparative analyses are conducted to show the effectiveness of the proposed algorithm. A case concerning the performance evaluation of venture capital guiding funds is given to illustrate the availability of the proposed algorithm. As an application of our work, an online decision-making portal is finally provided for decision-makers to utilize the proposed algorithms to solve decision-making problems.Comment: Pulished by Expert Systems with Applications (ISSN: 0957-4174

Time reversal symmetry breaking of pp-orbital bosons in a one-dimensional optical lattice

We study bosons loaded in a one-dimensional optical lattice of two-fold $p$-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p$_x$+ip$_y$, a homogeneous p$_x$ Mott insulator phase and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and para-orbital). The anti-ferro-orbital order breaks time reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time reversal symmetry breaking in the first Mott phase.Comment: 4+ pages, version accepted by Phys. Rev. Let

A method for incremental discovery of financial event types based on anomaly detection

Event datasets in the financial domain are often constructed based on actual application scenarios, and their event types are weakly reusable due to scenario constraints; at the same time, the massive and diverse new financial big data cannot be limited to the event types defined for specific scenarios. This limitation of a small number of event types does not meet our research needs for more complex tasks such as the prediction of major financial events and the analysis of the ripple effects of financial events. In this paper, a three-stage approach is proposed to accomplish incremental discovery of event types. For an existing annotated financial event dataset, the three-stage approach consists of: for a set of financial event data with a mixture of original and unknown event types, a semi-supervised deep clustering model with anomaly detection is first applied to classify the data into normal and abnormal events, where abnormal events are events that do not belong to known types; then normal events are tagged with appropriate event types and abnormal events are reasonably clustered. Finally, a cluster keyword extraction method is used to recommend the type names of events for the new event clusters, thus incrementally discovering new event types. The proposed method is effective in the incremental discovery of new event types on real data sets.Comment: 11 pages,4 figure