Axially Uniform Magnetic Field-Modulation Excitation for Electron Paramagnetic Resonance in Rectangular and Cylindrical Cavities by Slot Cutting

In continuous-wave (CW) Electron Paramagnetic Resonance (EPR) a low-frequency time-harmonic magnetic field, called field modulation, is applied parallel to the static magnetic field and incident on the sample. Varying amplitude of the field modulation incident on the sample has consequences on spectral line-shape and line-height over the axis of the sample. Here we present a method of coupling magnetic field into the cavity using slots perpendicular to the sample axis where the slot depths are designed in such a way to produce an axially uniform magnetic field along the sample. Previous literature typically assumes a uniform cross-section and axial excitation due to the wavelength of the field modulation being much larger than the cavity. Through numerical analysis and insights obtained from the eigenfunction expansion of dyadic Green’s functions, it is shown that evanescent standing-wave modes with complex cross-sections are formed within the cavity. From this analysis, a W-band (94 GHz) cylindrical cavity is designed where modulation slots are optimized to present a uniform 100 kHz field modulation over the length of the sample

A note on the 1-prevalence of continuous images with full Hausdorff dimension

We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large as possible, namely 1. We extend this result by showing that `prevalent' can be replaced by `1-prevalent', i.e. it is possible to \emph{witness} this prevalence using a measure supported on a one dimensional subspace. Such one dimensional measures are called \emph{probes} and their existence indicates that the structure and nature of the prevalence is simpler than if a more complicated `infinite dimensional' witnessing measure has to be used.Comment: 8 page

The Hausdorff dimension of graphs of prevalent continuous functions

We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on $[0,1]^d$ for $d \in \mathbb{N}$ and use this to obtain results on the `horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function

Design and Manufacture of a Biodegradable Ureteral Stent

Approximately 92,000 ureteral stents are implanted every year to maintain urine flow after treatment of kidney stones, kidney transplants, and urinary incontinence. However, current ureteral stents have several downsides that include encrustation, urgency due to the proximal curl pressing on the bladder, patient pain from inflexible stents, and most importantly, the need for a follow up removal surgery. To address many of these current issues, a novel biodegradable stent was designed, fabricated, and characterized in the present studies. The innovative stent design features the use of biodegradable, FDA approved polydioxanone polymer material that was aimed to reduce encrustation and eliminate the need for a removal surgery. Additionally, the stent\u27s novel coiled shape is intended to provide flexibility and anchor into the ureter. By eliminating the clinically conventional double J anchors, this could prevent the issue of the proximal anchor pressing on the bladder, remove the risk of encrustation on the distal anchor, and provide for better patient comfort by creating a more axially flexible stent. The novel stent was fabricated by winding a PDO suture around a mandrel and annealing at 100 °C. This annealing step increased the stiffness of the polymer as determined by cantilever bend testing. The source of this stiffness increase was determined to be due to an increase in crystallinity as verified by Differential Scanning Calorimetry and Wide Angle X-Ray Scattering. The results of custom testing in the present study also provided evidence that the stent exhibits adequate anchor strength and radial strength to maintain patency, which would allow standard ureteral flow conditions. Finally, an in vitro experiment demonstrated that the stent degrades in four weeks under normal physiological conditions, which is believed to be the ideal degradation time for the majority of ureteral stent applications. The results of this thesis provide strong supporting evidence that the proposed stent design has the ability to improve patient outcomes by addressing the drawbacks of current stent technology. However, further characterization efforts using animal models will be necessary to assure the safety and efficacy of this technology before it is ready for clinical use

Enumeration of idempotents in planar diagram monoids

We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley-Lieb) and Kauffman monoids. The classification is in terms of certain vertex- and edge-coloured graphs associated to Motzkin diagrams. The enumeration is necessarily algorithmic in nature, and is based on parameters associated to cycle components of these graphs. We compare our algorithms to existing algorithms for enumerating idempotents in arbitrary (regular *-) semigroups, and give several tables of calculated values.Comment: Majorly revised (new title, new abstract, one additional author), 24 pages, 6 figures, 8 tables, 5 algorithm