Nilpotent orbits and the Coulomb branch of Tσ(G)T^\sigma (G) theories: special orthogonal vs orthogonal gauge group factors

Coulomb branches of a set of $3d\ \mathcal{N}=4$ supersymmetric gauge theories are closures of nilpotent orbits of the algebra $\mathfrak{so}(n)$. From the point of view of string theory, these quantum field theories can be understood as effective gauge theories describing the low energy dynamics of a brane configuration with the presence of orientifold planes. The presence of the orientifold planes raises the question to whether the orthogonal factors of a the gauge group are indeed orthogonal $O(N)$ or special orthogonal $SO(N)$. In order to investigate this problem, we compute the Hilbert series for the Coulomb branch of $T^\sigma(SO(n)^\vee)$ theories, utilizing the monopole formula. The results for all nilpotent orbits from $\mathfrak {so} (3)$ to $\mathfrak{so}(10)$ which are special and normal are presented. A new relationship between the choice of $SO/O(N)$ factors in the gauge group and the Lusztig's Canonical Quotient of the corresponding nilpotent orbit is observed. We also provide a new way of projecting several magnetic lattices of different $SO(N)$ gauge group factors by the simultaneous action of a $\mathbb Z_2$ group.Comment: 33 pages, 3 figures, 28 table

CFD Evaluation of Blood Flow in an Improved Blalock-Taussig Shunt Using Patient Specific Geometries

Blalock-Taussig (BT) Shunt is a palliative surgical procedure used during a Norwood surgery on a newborn baby suffering from cyanotic heart defects. The BT Shunt can increase blood flow in patients’ pulmonary artery which can ease the “Blue Baby Syndrome.” Currently used BT Shunts do not produce a balanced flow distribution to the pulmonary arteries (PAs) which can cause high wall shear stress (WSS) and blood flow separation resulting in blood clots. A modified BT Shunt was designed to partially solve this problem. In our previous work [1], the modified BT Shunt was shown by numerical simulations to have the ability to better control the flow distribution between Innominate Artery (IA) and PA with lower and gradually varying WSS and with improved flow balance to the pulmonary artery at the T-junction of the shunt. The goal of this paper is to computationally evaluate the flow in the modified BT shunt model between innominate and pulmonary artery using a patient specific aorta model. The simulations are performed using the commercial CFD software ANSYS Fluent. The improved modified BT shunt is connected between IA and PA. A change in the length of the shunt can be made to fit it under different conditions of actual patients. In numerical simulations, a full geometry of patient’s aorta is considered. Results for different lengths of the shunt are compared to determine the length that generates the lowest WSS and improved flow distribution to the PAs. It was found that the length of nearly 26mm creates lower WSS and flow rate difference between the two sides of PA at the T-junction attachment of the shunt. A sophisticated computational model was created using SolidWorks and Blender software to create the realistic geometry which included the IA, PA and modified BT shunt. The numerical simulations provide details of the flow field including velocity and pressure field, WSS, and blood damage. Several parameters in shunt design weigh heavily in reducing the thrombosis. This study demonstrates how CFD can be effectively utilized in the design of a medical device such as BT shunt to improve the clinical outcomes in patients

Superradiance and its implementation in cold atoms inside a hollow-core waveguide

In this thesis, I am intending to understand the cooperative effect of an ensemble of quantum emitters, which constitutes the preliminary elements of our current experimental investigations towards realization of an ultra-narrow linewidth superriant laser. In the first part of the thesis, I investigate the basics of the theory of superradiance (SR), which includes the full derivation of the Hamiltonian and the Lindblad equation for an ensemble of two-level atoms in both free-space and a single-mode waveguide. In addition, I construct the simulations for observing the transition from single-atom uncorrelated spontaneous emission to superradiance in various physical settings, as well as a simulation for the understanding of the cooperative effects of an ensemble of two-level atoms inside an optical cavity. Then, in the second part of the thesis, I introduce the experimental progress we have been making to observe SR with an ensemble of laser-cooled Cs atoms inside a hollow-core photonic crystal fiber (HCPCF). In our experiment, the Cs atoms, initially cooled using a magneto-optical trap (MOT), are guided and confined inside a short piece of HCPCF with a magic-wavelength dipole trap. Currently we have successfully implemented a novel detection methods for studying superradiance

Frequency-domain method for measuring alpha factor by self-mixing interferometry

Linewidth enhancement factor, also known as the alpha factor, is a fundamental characteristic parameter of a laser diode (LD). It characterises the broadening of the laser linewidth, the frequency chirp, the injection lock range and the response to external optical feedback. In the past few decades, extensive researches have been dedicated to the measurement of alpha. Among all the existing approaches, the methods based on selfmixing interferometry (SMI) are considered the most simple and effective. The core components of a SMI consist of an LD, a lens and a moving target. When a portion of laser light backscattered or reflected by the external target and re-enters the laser cavity, a modulated lasing field will be generated. The modulated laser power is also called SMI signal, which carries the information of target movement and LD related parameters, including alpha