In this dissertation we study the dynamics of loop quantum gravity and its applications. We propose a tunneling phenomenon of a black hole-white hole transition and derive an amplitude for such transition using the spinfoam framework. We investigate a special class of kinematical states for loop quantum gravity - Bell spin networks - and show that their entanglement entropy obeys the area law. We develop a new spinfoam vertex amplitude that has the correct semi-classical limit. We then apply this new amplitude to calculate the graviton propagator and a cosmological transition amplitude. The results of these calculations show feasibility of computations with the new amplitude and its viability as a spinfoam model. Finally, we use physical principles to radically constrain ambiguities in the cosmological dynamics and derive unique Hamiltonian dynamics for Friedmann-Robertson-Walker and Bianchi I cosmologies. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

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Modeling loops is an often necessary step in protein structure and function determination, even with experimental X-ray and NMR data. It is well known to be difficult. Database techniques have the advantage of producing a higher proportion of predictions with sub-angstrom accuracy when compared with ab initio techniques, but the disadvantage of often being able to produce usable results as they depend entirely on the loop already being represented within the database. My contribution is the LoopWeaver protocol, a database method that uses multidimensional scaling to rapidly achieve better clash-free, low energy placement of loops obtained from a database of protein structures. This maintains the above- mentioned advantage while avoiding the disadvantage by permitting the use of lower quality matches that would not otherwise fit. Test results show that this method achieves significantly better results than all other methods, including Modeler, Loopy, SuperLooper, and Rapper before refinement. With refinement, the results (LoopWeaver and Loopy combined) are better than ROSETTA's, with 0.53Å RMSD on average for 206 loops of length 6, 0.75Å local RMSD for 168 loops of length 7, 0.93Å RMSD for 117 loops of length 8, and 1.13Å RMSD loops of length 9, while ROSETTA scores 0.66Å , 0.93Å , 1.23Å , 1.56Å , respectively, at the same average time limit (3 hours on a 2.2 GHz Opteron). When ROSETTA is allowed to run for over a week against LoopWeaver's and Loopy's combined 3 hours, it approaches, but does not surpass, this accuracy.

The hamiltonian number problem is a generalization of hamiltonian cycle problem in graph theory. It is well known that the hamiltonian cycle problem in graph theory is NP-complete [16]. So the hamiltonian number problem is also NP-complete. On the other hand, the hamiltonian number problem is the traveling salesman problem with each edge having weight 1. A hamiltonian walk of a graph G is a closed spanning walk of minimum length. The length of a hamiltonian walk in G is called the hamiltonian number. For graphs, we give some bounds for hamiltonian numbers of graphs. First, we improve some results in [14] and give a necessary and sufficient condition for h(G) < e(G) where e(G) is the minimum length of a closed walk passing through all edges of G. Next, we prove that if two nonadjacent vertices u and v satisfying that deg(u)+deg(v) ≥ |G|, then h(G) = h(G + uv). This result generalizes a theorem of Bondy and Chv¡¬atal for the hamiltonian cycle. Finally, we show that if 0 ≤ k ≤ n − 2 and G is a 2-connected graph of order n satisfying deg(u) + deg(v) + deg(w) ≥ 3n−k−2 for every independent set {u, v,w} of three vertices in G, then h(G) ≤ n+k. It is a generalization of a Bondy¡¦s result. For digraphs, we give some bounds for hamiltonian numbers of digraphs first. We prove that if a digraph D of order n is strongly connected, thenn ≤ h(D) ≤ ⌊(n+1)^2/4 ⌋. Next, we also present some digraphs of order n ≥ 5 which have hamiltonian number k for n ≤ k ≤ ⌊(n+1)^2/4 ⌋. Finally, we study hamiltonian numbers of M¡Lobius double loop networks. We introduce M¡Lobius double loop network and every strongly connected double loop network is isomorphic to some M¡Lobius double loop network. Next, we give an upper bound for the hamiltonian numbers of M¡Lobius double loop networks. Then, we find some necessary and sufficient conditions for M¡Lobius double loop networks MDL(d, m, ℓ) to have hamiltonian numbers dm, dm + 1 or dm + 2.

An ideal polymerase chain reaction (PCR) system should be capable of rapidly amplifying a wide range of targets in both single and multiplex formats. Unfortunately, the timescales and complexities involved in many existing technologies impose significant limitations on achievable throughput. Buoyancy driven PCR is emerging as a simplified version of thermally driven bio-analysis systems. Here, we demonstrate a simplified convectively driven thermocycler capable of performing single and multiplex PCR for amplicons ranging from 191 bp to 1.3 kb within 10 to 50 minutes using 10 to 25 µL reaction volumes. By positioning two independent thermoelectric heating elements along the perimeter of a flow loop reactor constructed using ordinary plastic tubing, a buoyancy-driven flow is established that continuously circulates reagents through temperature zones associated with the PCR process. Unlike conventional benchtop thermocyclers, this arrangement allows reactions to be performed without the need for dynamic temperature control of inactive hardware components while maintaining comparable product yields and requiring no modifications to standard PCR protocols. We also provide a general correlation that can be applied to design reactor geometries satisfying virtually any combination of reagent volume and cycling time. In addition to offering an attractive combination of cost and performance, this system is readily adaptable for portable battery powered operation, making it feasible to perform PCRbased assays in a broader array of settings.

In this thesis, we present two e cent algorithms to compute shortest path between pair of vertices in directed and undirected double-loop networks. The algorithm for undirected double-loop networks is based on the concept "packed basis" proposed by Janez Zerrovnik and Toma z Pisanski. With O(logN) preprocessing time, both algorithms need only constant time to compute the shortest path between any pair of vertices in the network. This is an improvement of the best known algorithm, which needs O(l) time, where l is the length of the path in the directed double-loop networks. These algo- rithms are useful in message routing in the double-loop networks. Once the network has been constructed, the parameters for computing the shortest paths can be computed. At the time a message is to be delivered, the algo- rithm needs only constant time to determine which edge the message should be sent.

In most techniques to improve performance for loops or nested loops, they are often to do pipelined scheduling according to know loop execution times at compiler time. But it is hardly to pipeline the execution of loop whose execution length is unknown before loop execution at compiler time. In this thesis, a Common-Case based approach is proposed to improve the performance of loops with variable execution length. Besides, we use the modulo schedule to achieve the goal under resource constraint and without violating data dependence. The Common-Case approach not only reduces the execution time efficiently, but also reduces the power consumption largely due to the reduction of execution time. Through the searching for good Common-Case, we can surely supply a better solution to the loops whose execution length is unknown before loop execution at compiler time. Moreover, since the loop is divided into Common-Case and exception parts, we can further reduce power consumption by using Clock-Gating and Finite State Machine decomposition techniques. Finally, experiments on three real examples (Morris-Pratt Algorithm, Insertion Sort, Running Length Encoding) are used to demonstrate that our flow is correct and can achieve the goal of performance and energy optimizations.

Abstract This thesis presents that the closed-loop sensitivity function shaping combined with -synthesis applies to design the controller with structured uncertainties. The sensitivity function shaping is directly based on the indices of the closed-loop performances. The closed-loop frequency response and the robust stability for the system could approach the designed performances by adjusting weighting functions. Since the robust performance of the closed-loop systems bases on the index of the open-loop function in the loop shaping, it may not accomplish the requirement of the designer. The loop shaping can¡¦t be applied to design controllers for the system with structured uncertainties. Therefore, using the closed-loop sensitivity function shaping to design controller will contain the system with structured uncertainties and satisfy the closed-loop performance.

Loop heat pipes seem a promising approach for application in modern technologies where such thermal devices as cooling fans and radiators cannot satisfy overall requirements. Even though a loop heat pipe has a big potential to remove the thermal energy from a high heat flux source, the heat removal performance of heat pipes cannot be predicted well since a first principles of evaporation has not been established. An evaporation model based on statistical rate theory has been recently suggested by Ward and developed for a single pore by Oinuma. A loop heat pipe with coherent pore wick structure has been proposed as a design model. To limit product development risk and to enhance performance assurance, design model features and performance parameters have been carefully reviewed during the concept development phase and have been deliberately selected so as to be well-founded on the limited existing loop heat pipe knowledge base. A first principles evaporation model has been applied for evaporator geometry optimization. A number of iteration calculations have been performed to satisfy design and operating limitations. A set of recommendations for design optimization has been formulated. An optimal model has been found and proposed for manufacture and experimental investigation.

The purpose of this thesis is to design and fabricate cross-loop cavity filter. We fabricated optical filter by bended waveguide and 2x2 90-degree MMI crossing model. By this design, we get the power splitter with coupling coefficient is 0, 0.15, 0.5, 0.85. By MatFhcad and BPM simulation, we showed that the device volume was decrease to 34%. In the quantum dot lasers, we fabricated the Fabry-Perot laser by optical waveguide and cleavage surface. In the material, a 1.3£gm quantum dots InGaAs epitaxial wafer is used to fabricate the lasers. Broad area lasers and ridge waveguide lasers are fabricated and their static properties (IV, LI) are analyzed experimentally. In fabrication process, first, we defined the device pattern by using photo-lithography technique. Second, we etched ridge waveguide by using dry etching method. Finally, we used the etching solution HBr:HCl:H2O2:H2O=5:4:1:70 to smooth the sidewall and reduce the scattering loss. We showed that the waveguide loss was decrease to 27.9dB/cm. In the QD lasers characteristic, we can not observe laser characteristics, partly because of the low optical power. Through the optimization of QD growth conditions, we can increase the QD sheet density and increase the number of QD layers. We can also optimize the device processing techniques and laser structure design in order to reduce the series resistance and to increase the optical confinement factor. By using the methods mentioned above, we believe the laser signal can be further increase. In the cross-loop cavity filter characteristic, we get the FSR=300GHz (simulation value FSR=50GHz) in throughput port and drop port. We attribute this appearance induced by cross couple for 2x2 90-degree MMI. The contracts for the drop port of 10.22dB have been achieved.