A Technique for Calculating Flexural Rigidity of Nonlinear Systems

Faculty Adviser: Guy Genin Geometric, kinematic, force, and material nonlinearity arise in manufactured products. Flexural rigidity, or relative stiffness of a beam, cannot be measured accurately for flexible, composite medical devices like catheters and sheaths using linear beam theory because they undergo high deformations when subject to relatively small loads. Surgeons depend on the relative stiffness of their catheters to determine the maneuverability of their devices. For neurovascular interventions, surgeons rely on stiffness to determine if their catheter can navigate arduous vasculature, especially around the aortic arch1. Navigation has become increasingly difficult as surgeons have adopted the transradial approach to neurovascular angioplasty procedures. In these procedures, surgeons must steer their guide catheter through the radial artery, across narrow bends through the subclavian artery, and around the aortic arch. It is unrealistic to consistently use particularly flexible catheters since they do not provide enough support to guide medical devices to the brain. To overcome this issue, surgeons pair flexible intermediate guide catheters with stiffer sheaths in a coaxial system. They navigate the guide catheter into position, run the stiff sheath over the guide catheter, and send more devices (microcatheters, stents, coils, etc.) through that system. Medical device companies now commonly design catheters with sections that vary in stiffness throughout the length of the catheter to help overcome these issues2. Although the relative stiffness of these devices are critical to the success of the procedure, stiffness values for these devices are unknown to surgeons. More generally, cardiovascular, peripheral vascular, and other general vascular surgeons experience similar difficulty in selecting catheters to navigate other arterial systems. Cardiovascular surgeons experience similar difficulty navigating bends through the aortic arch for different procedures. Beyond vascular surgery, flexural rigidity calculations are important throughout mechanical analysis, and these calculations become especially difficult for manufactured products with soft or composite materials. Previous studies have found flexural rigidity calculations of thin films for aerospace engineering3, of flat plates in mountains for geophysics4, of microtubules for cell biophysics5, and of jute fibers and yarns6. Euler-Bernoulli and Timoshenko beam theories provide relatively accurate approximations for beams under small deformations7. Applications of these theories are fitting to measure the flexural rigidity of catheters and other nonlinear systems. Beams with flexible materials undergoing large deformations require more complicated definitions to solve for flexural rigidity through deflection analysis. A nonlinear approach to beam theory does provide a more accurately measured flexural rigidity for high deformations than linear beam theory8. By applying the definition of curvature to the general equation for Euler-Bernoulli beam theory, the flexural rigidity can be calculated accurately. Other techniques have been applied to manufactured systems to measure mechanical properties of catheters and other medical devices9. Previous studies found the flexural rigidity of central venous catheters based on deflections10,11, which differs from the angle calculations used in this research. Another method from previous studies examines the buckling load of the device when the force is applied axially12,13. Yet another group compared stiffness between catheters based on the critical angle at which the catheter could physically bend14. These methods for measuring flexural rigidity are distinctly different from the technique used in this research, which instead measures the value based on the angle of rotation where the point load is applied. For measurement of manufactured products, the flexural rigidity can be calculated through image analysis paired with the nonlinear application of the general beam theory equation. Flexural rigidity can be found by examining the mechanical reaction of a fixed-free beam under a given load. This technique was tested using finite element analysis in COMSOL by measuring angles via displacements using the software applications and through image analysis of the deflection provided by the software. These values were compared to calculated flexural rigidity values, which are based on the elastic modulus and second area moment of inertia of the cross section. This strategy provides researchers with an accurate means to measure the flexural rigidity of medical devices like catheters that undergo large deformations under applied forces

Dark cloud chemistry in initially H-rich regions

The chemistry in dark regions of dense cores is explored as a function of the initial abundance ratio of H to H 2, on the assumption that some cores form on a timescale and are younger than the time required for the H :H 2 ratio to attain its equilibrium value. Observational diagnostics of non-equilibrium values of the initial H :H 2 ratio are identified. In initially H-rich material, the abundances of OH, NH 3, CN, and HNC are for some time higher than they are in initially H-poor material. In initially H-poor regions, the abundances of CO, species containing multiple carbon atoms in each molecule, and CS are larger for an (observationally significant) period than in initially H-rich material

Real-Time Musical Analysis of Polyphonic Guitar Audio

In this thesis, we analyze the audio signal of a guitar to extract musical data in real-time. Specifically, the pitch and octave of notes and chords are displayed over time. Previous work has shown that non-negative matrix factorization is an effective method for classifying the pitches of simultaneous notes. We explore the effect of window size, hop length, and other parameters to maximize the resolution and accuracy of the output.Other groups have required prerecorded note samples to build a library of note templates to search for. We automate this step and compute the library at run-time, tuning it specifically for the input guitar. The program we present generates a musical visualization of the results in addition to suggestions for fingerings of chords in the form of a fretboard display and tablature notation. This program is built as an applet and is accessible from the web browser

The modifcation by diffuse radiation of "cometary tail" formation behind globules

We study the evolution of a globule of neutral material immersed in the more tenuous hotter plasma of an H II region surrounding newly born OB stars. The neutral globule is illuminated by the direct ionizing radiation of OB stars, and by diffuse radiation emitted by recombination in the surrounding ionized gas. We perform 2D, time dependent axisymmetric hydrodynamic simulations, and find that, for values of the diffuse field of the order of 10% of the direct field, the evolution of the globule is completely different to its evolution when the diffuse field is neglected

Erratum: The chemistry of transient molecular cloud cores

We assume that some, but not all, of the structure observed in molecular clouds is associated with transient features which are not bound by self-gravity. We investigate the chemistry of a transient density fluctuation, with properties similar to those of a core within a molecular cloud. We run a multipoint chemical code through a core's condensation from a diffuse medium to its eventual dispersion, over a period of ∼1 Myr. The dynamical description adopted for our study is based on an understanding of a particular mechanism, involving slow-mode wave excitation, for transient structure formation which so far has been studied in detail only with plane-parallel models in which self-gravity has not been included. We find a significant enhancement of the chemical composition of the core material on its return to diffuse conditions, whilst the expansion of the core as it disperses moves this material out to large distances from the core centre. This process transports molecular species formed in the high-density regions out into the diffuse medium. Chemical enrichment of the cloud as a whole also occurs, as other cores of various sizes, life-spans and separations evolve throughout. Enrichment is strongly affected by freeze-out on to dust grains, which takes place in high-density, high visual extinction regions. As the core disperses after reaching its peak density and the visual extinction drops below a critical value, grain mantles are evaporated back into the gas phase, initiating more chemistry. The influence of the sizes, masses and cycle periods of cores will be large both for the level of chemical enrichment of a dark cloud and ultimately for the low-mass star formation rate. The cores in which stars form are almost certainly bound by their self-gravity and are not transient in the sense that the cores on which most of our study is focused are transient. Obviously, enrichment of the chemistry of low-density material will not take place if self-gravity prevents the re-expansion of a core. We also consider the case of a self-gravitating core, by holding its peak density conditions for a further 0.4 Myr. We find that the differences near the peak densities between transient and gravitationally bound cores are generally small, and the resultant column densities for objects near the peak densities do not provide definitive criteria for discriminating between transient and bound cores. However, increases in fractional abundances due to reinjection of mantle-borne species may provide a criterion for detection of a non-bound core

Magnetic ionization fronts II: Jump conditions for oblique magnetization

We present the jump conditions for ionization fronts with oblique magnetic fields. The standard nomenclature of R- and D-type fronts can still be applied, but in the case of oblique magnetization there are fronts of each type about each of the fast- and slow-mode speeds. As an ionization front slows, it will drive first a fast- and then a slow-mode shock into the surrounding medium. Even for rather weak upstream magnetic fields, the effect of magnetization on ionization front evolution can be important. [Includes numerical MHD models and an application to observations of S106.]Comment: 9 pages, 10 figures, Latex, to be published in MNRA

Nanodust shedding and its potential influence on dust related phenomena in the mesosphere

We explore the possibility that some meteoric smoke particles that collide with larger nanoparticles near the mesopause can escape from the larger particles by capturing surface electrons. If the process were sufficiently efficient, under certain conditions it would influence the responses of polar mesospheric summer echoes to artificial heating in a manner that is compatible with observations that are unexplained with previous models. The process would have a number of other possible consequences for nanoparticles near the mesopause

Generation of density inhomogeneities by magnetohydrodynamic waves in two dimensions

Using two dimensional simulations, we study the formation of structures with a high-density contrast by magnetohydrodynamic waves in regions in which the ratio of thermal to magnetic pressure is small. The initial state is a uniform background perturbed by fast-mode wave. Our most significant result is that dense structures persist for far longer in a two-dimensional simulation than in the one-dimensional case. Once formed, these structures persist as long as the fast-mode amplitude remains high.Comment: 6 pages, 7 figures, accepted by MNRA