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University of Otago

1. Lee, Au-Chen. Dipolar Bose-Einstein Condensate with a Vortex .

Degree: University of Otago

We theoretically consider the properties of a dipolar Bose-Einstein condensate with a vortex. Our theory includes the influence of the leading order quantum fluctuation corrections which allows the condensate to stabilize into a droplet state in the regime of dominant dipole interactions. We develop numerical techniques to accurately and efficiently calculate the stationary vortex states and the quasi-particle excitations. These methods are carefully benchmarked where possible. We make a brief study of self-bound vortex droplets, considering their basic properties, and presenting a phase diagram for where they exist. We also compare our calculations to results which appeared from another group during our research. We show that their results suffer from serious numerical issues and are unreliable. We focus on studying the properties of a vortex line in an elongated dipolar Bose-Einstein condensate confined by a prolate trap. Increasing the strength of the dipole-dipole interactions relative to the short ranged contact interactions we find that the system crosses over to a self-bound vortex droplet stabilized from collapse by quantum fluctuations. We calculate the quasiparticle excitation spectrum of the vortex state, which is important in characterizing the vortex response, and assessing its stability. When the DDIs are sufficiently strong we find that the vortex is dynamically unstable to quadrupolar modes. Advisors/Committee Members: Blakie, Blair (advisor).

Subjects/Keywords: Bose-einstein condensates; BEC; nonlinear; condensate; Gross-Pitaevskii; nonlinear Schrödinger equation; vortices; Collective excitations; vortex self-bound droplets; dipolar BEC; dipolar quantum; quantum fluctuations; Bogoliubov-de Gennes; instability; quadrupolar modes; dynamical stability; dipole interaction; density approximation; dipolar Bose-Einstein condensate; quasi-particle excitations; vortex; Hankel Transformation; Bessel function; cosine transformation; Cylindrical; BdG; Bogoliubov-de Gennes Equation; numerical calculations; DDI; dipole-dipole interactions; phonon dispersion; dynamical instability; eigenvalue problem; eigenvector; imaginary time evolution; laplacian operator; GPE; Gross–Pitaevskii equation; zero-norm; Kohn modes; Bessel grid; DDIs; numerical techniques; dipolar; dipolar BECs; LHY term; local density treatment; vortex stationary states; Kelvin wave (helical) excitations; stabilized from collapse; quasi-particle; leading order quantum fluctuation correction; lanthanides dysprosium; dysprosium; Dy; s-wave interaction; many-body physics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lee, A. (n.d.). Dipolar Bose-Einstein Condensate with a Vortex . (Masters Thesis). University of Otago. Retrieved from http://hdl.handle.net/10523/9254

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Chicago Manual of Style (16th Edition):

Lee, Au-Chen. “Dipolar Bose-Einstein Condensate with a Vortex .” Masters Thesis, University of Otago. Accessed April 14, 2021. http://hdl.handle.net/10523/9254.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

MLA Handbook (7th Edition):

Lee, Au-Chen. “Dipolar Bose-Einstein Condensate with a Vortex .” Web. 14 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Vancouver:

Lee A. Dipolar Bose-Einstein Condensate with a Vortex . [Internet] [Masters thesis]. University of Otago; [cited 2021 Apr 14]. Available from: http://hdl.handle.net/10523/9254.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Council of Science Editors:

Lee A. Dipolar Bose-Einstein Condensate with a Vortex . [Masters Thesis]. University of Otago; Available from: http://hdl.handle.net/10523/9254

Note: this citation may be lacking information needed for this citation format:
No year of publication.

2. Mashrafi, Sheikh. X-ray microscope performance enhancement through control architecture change.

Degree: MS, 0133, 2014, University of Illinois – Urbana-Champaign

The goal of this thesis is to apply control algorithms to improve the performance of nanopositioning devices used on the beamline in Advanced Photon Source (APS) at Argonne National Laboratory (ANL). A prototype device, better known as the Early User Instrument (EUI) was the subject of this work. It consists of X-ray optics stage group that focuses the X-ray beam as a source-size-limited spot onto a sample held on the sample stage group. The controller algorithms that are used should provide the closed-loop with robust stability, large bandwidth, high resolution, disturbance rejection and noise attenuation. Conveniently, the field of scanning probe microscopes (SPMs) have already flourished on this aspect of controller algorithms proven to give desired closed-loop properties. Controller algorithms such as Proportional Integral Derivative (PID), Glover-McFarlane H-infinty algorithm, and 1DOF H-infinty controller were designed and implemented on the EUI system. The controller hardware used for implementation is National Instruments (NI) CompactRIO hardware that consists of a real-time controller, a FPGA built into the hardware chassis, analog I/O modules, and digital I/O modules. NI LabVIEW, the dedicated software to the NI hardware, was used to represent the discrete controllers as biquads structures that ran in the FPGA as a part of the closed-loop . The largest closed-loop bandwidth achieved is of 65 Hz through the 1DOF H-infinty controller and is a 171% improvement over the traditional PID controller. Highest closed- loop resolution achieved by the EUI with a 50 Hz bandwidth 1DOF H-infinty controller is 1.4 nanometers, which is a 180% improvement over the open loop resolution of 7 nanometers. Advisors/Committee Members: Salapaka, Srinivasa M. (advisor), Preissner, Curt (advisor).

Subjects/Keywords: control; Control Architecture; Advanced Photon Source (APS); Argonne National Laboratory (ANL); control algorithms; nanopositioning; nanopositioning devices; Early User Instrument (EUI); X-ray; optics; robust stability; bandwidth; resolution; disturbance rejection; noise attenuation; scanning probe microscope (SPM); closed-loop properties; Proportional Integral Derivative (PID); Glover-McFarlane h-infinity algorithm; 1DOF h-infinity controller; h-infinity; Glover-McFarlane controller; Keith Glover; Duncan McFarlane; controller; controller implementation; National Instruments (NI); CompactRIO; real-time controller; Field-Programmable Gate Array (FPGA); LabVIEW; biquads structures; closed-loop bandwidth; U.S. Department of Energy (DOE); Office of Science; DE-AC02-06CH11357; DE-SC0004283; Cross Power Spectral Density (CPSD); Power Spectral Density (PSD); Degree Of Freedom (DOF); Discrete-Time Fourier Transform (DTFT); Hardware Description language (HDL); High-Level Synthesis (HLS); Hard X-ray Nanoprobe (HXN); In Situ Nanoprobe (ISN); Laser Doppler Displacement Meter (LDDM); Physik Instrumente (PI); Reconfigurable Input/Output (RIO); Advanced Photon Source (APS) beamline; full-field imaging microscopy; fluorescence mapping; nanodiffraction; transmission imaging; reliability and repeatability of positioning systems; modeling uncertainties; insensitive modeling uncertainties; quantifying trade-offs; trade-offs; design flexibility; design methodology; feedforward; feedback; performance objectives; robustness; Advanced Photon Source (APS) user; beamline scientist; imaging resolution and bandwidth; imaging resolution; nanoprobe; model fitting; curve fitting; model reduction; feedback controllers; X-ray nanoprobe instrument; third-generation synchrotron radiation source; zone plate optics; zone plate; flexure stages; piezoelectric actuators stacks; flexure; Piezoelectric; high-stiffness stages; high-resolution weak-link stages; piezoelectric-transducer; sub-nanometer resolution; subnanometer; optical heterodyning; heterodyning; Optodyne; frequency-shifted laser beam; PID controller; digital to analog converter (DAC); analog input modules; digital input modules; analog output modules; cRIO-9118; Virtex-5; Virtex-5 LX110 FPGA chassis; NI-9223; NI-9402; NI-9263; System Identification; Identification; black-box identification; parametric model; non-parametric model; welch; pwelch; tfestimate; invfreqs; time domain data; band-limited uniform Gaussian white noise; band-limited; white noise; resonant peak; Balance Realization; minimal realization; controllability; observability; Experimental Frequency response; transfer function; Hankel singular values; Hankel norm; balanced truncation; noise histogram; Open Loop Resolution; closed Loop Resolution; Simulink simulation; LabVIEW simulation; discrete controller; continuous controllers; discrete; Tustin; tustins method; discretization; complementary sensitivity transfer function; sensitivity transfer function; robust stabilization; coprime factorization; Bezout identity; Bezout; stability margin; algebraic Riccati equation; Riccati equation; sub-optimal; suboptimal; sub-optimal controller; optimal controller; mixed-sensitivity optimization; sensitivity optimization; generalized framework; generalized controller framework; stabilizing controller; closed-loop objectives; generalized plant; nominal plant; linear fractional transformation; weighting transfer functions; weighted sensitivity; hinfsyn; bode integral law; waterbed effect; second waterbed formula; Skogestad; Poslethwaite; sensitivity weighting; sensitivity weighting transfer function; nanopositioner; nanopositioning device; nanopositioning system; second order sections; ASPE 28th Annual Meeting; American Society for Precision Engineering (ASPE); Synchrotron Radiation Instrumentation; Synchrotron; Nanoprobe Instrument

…the minimal realization of the system and apply a certain state transformation. When the… …observable and controllable states are eliminated. Through balance realization the Hankel singular… …to large Hankel singular values are strongly controllable and observable. So, by balanced… …truncation technique the states with small Hankel singular values are truncated. While following… 

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Mashrafi, S. (2014). X-ray microscope performance enhancement through control architecture change. (Thesis). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/46671

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Mashrafi, Sheikh. “X-ray microscope performance enhancement through control architecture change.” 2014. Thesis, University of Illinois – Urbana-Champaign. Accessed April 14, 2021. http://hdl.handle.net/2142/46671.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Mashrafi, Sheikh. “X-ray microscope performance enhancement through control architecture change.” 2014. Web. 14 Apr 2021.

Vancouver:

Mashrafi S. X-ray microscope performance enhancement through control architecture change. [Internet] [Thesis]. University of Illinois – Urbana-Champaign; 2014. [cited 2021 Apr 14]. Available from: http://hdl.handle.net/2142/46671.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mashrafi S. X-ray microscope performance enhancement through control architecture change. [Thesis]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/46671

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.