Aspects of Markov Chains and Particle Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Mode Localization in a Nearly Cyclic Symmetric System

Thesis (Ph.D.)--University of Washington, 2016-06

Entanglement induced by spontaneous emission in spatially extended two-atom systems

The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.

Comparative study of symmetric and asymmetric cylindrical MRI gradient Y-coils in terms of induced eddy currents

We have recently introduced the concept of whole-body asymmetric MRI systems [1]. In this theoretical study, we investigate the PNS characteristics of whole-body asymmetric gradient systems as compared to conventional symmetric systems. Recent experimental evidence [2] supports the hypothesis of transverse gradients being the largest contributor of PNS due to induced electric currents. Asymmetric head gradient coils have demonstrated benefits in the past [3]. The numerical results are based on an anatomically-accurate 2mm-human voxel-phantom NORMAN [4]. The results of this study can facilitate the optimization of whole-body asymmetric gradients in terms of patient comfort/safety (less PNS), while prospering the use of asymmetric MRI systems for in-vivo medical interventions.

Inference by replication in densely connected systems

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance. © 2007 The American Physical Society.

A study of the aerodynamic characteristics of captor hoods in local exhaust ventilation systems

The research objectives were:- 1.To review the literature to establish the factors which have traditionally been regarded as most crucial to the design of effectlve exhaust ventilation systems. 2. To design, construct, install and calibrate a wind tunnel. 3. To develop procedures for air velocity measurement followed by a comprehensive programme of aerodvnamic data collection and data analysis for a variety of conditions. The major research findings were:- a) The literature in the subject is inadequate. There is a particular need for a much greater understanding of the aerodynamics of the suction flow field. b) The discrepancies between the experimentally observed centre-line velocities and those predicted by conventional formulae are unacceptably large. c) There was little agreement between theoretically calculated and observed velocities in the suction zone of captor hoods. d) Improved empirical formulae for the prediction of centre-line velocity applicable to the classical geometrically shaped suction openings and the flanged condition could be (and were) derived. Further analysis of data revealed that: - i) Point velocity is directly proportional to the suction. flow rate and the ratio of the point velocity to the average face velocity is constant. ii) Both shape, and size of the suction opening are significant factors as the coordinates of their points govern the extent of the effect of the suction flow field. iii) The hypothetical ellipsoidal potential function and hyperbolic streamlines were found experimentally to be correct. iv) The effect of guide plates depends on the size, shape and the angle of fitting. The effect was to very approximately double the suction velocity but the exact effect is difficult to predict. v) The axially symmetric openings produce practically symmetric flow fields. Similarity of connection pieces between the suction opening and the main duct in each case is essential in order to induce a similar suction flow field. Additionally a pilot study was made in which an artificial extraneous air flow was created, measured and its interaction with the suction flow field measured and represented graphically.

Channel estimation and compensation in chromatic dispersion limited optical fast OFDM systems

We experimentally investigate the channel estimation and compensation in a chromatic dispersion (CD) limited 20Gbit/s optical fast orthogonal frequency division multiplexing (F-OFDM) system with up to 840km transmission. It is shown that symmetric extension based guard interval (GI) is required to enable CD compensation using one-tap equalizers. As few as one optical F-OFDM symbol with four and six pilot tones per symbol can achieve near-optimal channel estimation and compensation performance for 600km and 840km respectively.

Channel estimation and compensation in chromatic dispersion limited optical fast OFDM systems

We experimentally investigate the channel estimation and compensation in a chromatic dispersion (CD) limited 20Gbit/s optical fast orthogonal frequency division multiplexing (F-OFDM) system with up to 840km transmission. It is shown that symmetric extension based guard interval (GI) is required to enable CD compensation using one-tap equalizers. As few as one optical F-OFDM symbol with four and six pilot tones per symbol can achieve near-optimal channel estimation and compensation performance for 600km and 840km respectively.

Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations

We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems.

Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual o-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving nonclassical damping is proposed. An example of modal control sucessfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving non-classical damping is proposed. An example of modal control successfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

DnaG interacts with a linker region that joins the N- and C-domains of DnaB and induces the formation of 3-fold symmetric rings

Loading of the replicative ring helicase onto the origin of replication (oriC) is the final outcome of a well coordinated series of events that collectively constitute a primosomal cascade. Once the ring helicase is loaded, it recruits the primase and signals the switch to the polymerization mode. The transient nature of the helicase-primase (DnaB-DnaG) interaction in the Escherichia coli system has hindered our efforts to elucidate its structure and function. Taking advantage of the stable DnaB-DnaG complex in Bacillus stearothermophilus, we have reviewed conflicting mutagenic data from other bacterial systems and shown that DnaG interacts with the flexible linker that connects the N- and C-terminal domains of DnaB. Furthermore, atomic force microscopy (AFM) imaging experiments show that binding of the primase to the helicase induces predominantly a 3-fold symmetric morphology to the hexameric ring. Overall, three DnaG molecules appear to interact with the hexameric ring helicase but a small number of complexes with two and even one DnaG molecule bound to DnaB were also detected. The structural/functional significance of these data is discussed and a speculative structural model for this complex is suggested.

A Microleakage Study Of Gutta-percha/ah Plus And Resilon/real Self-etch Systems After Different Irrigation Protocols.

The development and maintenance of the sealing of the root canal system is the key to the success of root canal treatment. The resin-based adhesive material has the potential to reduce the microleakage of the root canal because of its adhesive properties and penetration into dentinal walls. Moreover, the irrigation protocols may have an influence on the adhesiveness of resin-based sealers to root dentin. The objective of the present study was to evaluate the effect of different irrigant protocols on coronal bacterial microleakage of gutta-percha/AH Plus and Resilon/Real Seal Self-etch systems. One hundred ninety pre-molars were used. The teeth were divided into 18 experimental groups according to the irrigation protocols and filling materials used. The protocols used were: distilled water; sodium hypochlorite (NaOCl)+eDTA; NaOCl+H3PO4; NaOCl+eDTA+chlorhexidine (CHX); NaOCl+H3PO4+CHX; CHX+eDTA; CHX+ H3PO4; CHX+eDTA+CHX and CHX+H3PO4+CHX. Gutta-percha/AH Plus or Resilon/Real Seal Se were used as root-filling materials. The coronal microleakage was evaluated for 90 days against Enterococcus faecalis. Data were statistically analyzed using Kaplan-Meier survival test, Kruskal-Wallis and Mann-Whitney tests. No significant difference was verified in the groups using chlorhexidine or sodium hypochlorite during the chemo-mechanical preparation followed by eDTA or phosphoric acid for smear layer removal. The same results were found for filling materials. However, the statistical analyses revealed that a final flush with 2% chlorhexidine reduced significantly the coronal microleakage. A final flush with 2% chlorhexidine after smear layer removal reduces coronal microleakage of teeth filled with gutta-percha/AH Plus or Resilon/Real Seal SE.