Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Ostrowski Type Inequalities over Spherical Shells

2000 Mathematics Subject Classification: 26D10, 26D15.

The non-linear acousto-mechanical and thermodynamic response of spherical absorbers to laser pulses of various temporal profiles

This study is to theoretically investigate shockwave and microbubble formation due to laser absorption by microparticles and nanoparticles. The initial motivation for this research was to understand the underlying physical mechanisms responsible for laser damage to the retina, as well as the predict threshold levels for damage for laser pulses with of progressively shorter durations. The strongest absorbers in the retina are micron size melanosomes, and their absorption of laser light causes them to accrue very high energy density. I theoretically investigate how this absorbed energy is transferred to the surrounding medium. For a wide range of conditions I calculate shockwave generation and bubble growth as a function of the three parameters; fluence, pulse duration and pulse shape. In order to develop a rigorous physical treatment, the governing equations for the behavior of an absorber and for the surrounding medium are derived. Shockwave theory is investigated and the conclusion is that a shock pressure explanation is likely to be the underlying physical cause of retinal damage at threshold fluences for sub-nanosecond pulses. The same effects are also expected for non-biological micro and nano absorbers. ^

DEVELOPMENT OF A MECHANISM AND PROCESS TO CONTINUOUSLY PRODUCE SPHERICAL, TORREFIED BIOMASS PELLETS

A recently developed novel biomass fuel pellet, the Q’ Pellet, offers significant improvements over conventional white pellets, with characteristics comparable to those of coal. The Q’ Pellet was initially created at bench scale using a proprietary die and punch design, in which the biomass was torrefied in-situ¬ and then compressed. To bring the benefits of the Q’ Pellet to a commercial level, it must be capable of being produced in a continuous process at a competitive cost. A prototype machine was previously constructed in a first effort to assess continuous processing of the Q’ Pellet. The prototype torrefied biomass in a separate, ex-situ reactor and transported it into a rotary compression stage. Upon evaluation, parts of the prototype were found to be unsuccessful and required a redesign of the material transport method as well as the compression mechanism. A process was developed in which material was torrefied ex-situ and extruded in a pre-compression stage. The extruded biomass overcame multiple handling issues that had been experienced with un-densified biomass, facilitating efficient material transport. Biomass was extruded directly into a novel re-designed pelletizing die, which incorporated a removable cap, ejection pin and a die spring to accommodate a repeatable continuous process. Although after several uses the die required manual intervention due to minor design and manufacturing quality limitations, the system clearly demonstrated the capability of producing the Q’ Pellet in a continuous process. Q’ Pellets produced by the pre-compression method and pelletized in the re-designed die had an average dry basis gross calorific value of 22.04 MJ/kg, pellet durability index of 99.86% and dried to 6.2% of its initial mass following 24 hours submerged in water. This compares well with literature results of 21.29 MJ/kg, 100% pellet durability index and <5% mass increase in a water submersion test. These results indicate that the methods developed herein are capable of producing Q’ Pellets in a continuous process with fuel properties competitive with coal.

Magnetic and Acoustic Investigations of Turbulent Spherical Couette Flow

Title of dissertation: MAGNETIC AND ACOUSTIC INVESTIGATIONS OF TURBULENT SPHERICAL COUETTE FLOW Matthew M. Adams, Doctor of Philosophy, 2016 Dissertation directed by: Professor Daniel Lathrop Department of Physics This dissertation describes experiments in spherical Couette devices, using both gas and liquid sodium. The experimental geometry is motivated by the Earth's outer core, the seat of the geodynamo, and consists of an outer spherical shell and an inner sphere, both of which can be rotated independently to drive a shear flow in the fluid lying between them. In the case of experiments with liquid sodium, we apply DC axial magnetic fields, with a dominant dipole or quadrupole component, to the system. We measure the magnetic field induced by the flow of liquid sodium using an external array of Hall effect magnetic field probes, as well as two probes inserted into the fluid volume. This gives information about possible velocity patterns present, and we extend previous work categorizing flow states, noting further information that can be extracted from the induced field measurements. The limitations due to a lack of direct velocity measurements prompted us to work on developing the technique of using acoustic modes to measure zonal flows. Using gas as the working fluid in our 60~cm diameter spherical Couette experiment, we identified acoustic modes of the container, and obtained excellent agreement with theoretical predictions. For the case of uniform rotation of the system, we compared the acoustic mode frequency splittings with theoretical predictions for solid body flow, and obtained excellent agreement. This gave us confidence in extending this work to the case of differential rotation, with a turbulent flow state. Using the measured splittings for this case, our colleagues performed an inversion to infer the pattern of zonal velocities within the flow, the first such inversion in a rotating laboratory experiment. This technique holds promise for use in liquid sodium experiments, for which zonal flow measurements have historically been challenging.

Inverse Spectral Methods in Acoustic Normal Mode Velocimetry of High Reynolds Number Spherical Couette Flows

Experimental geophysical fluid dynamics often examines regimes of fluid flow infeasible for computer simulations. Velocimetry of zonal flows present in these regimes brings many challenges when the fluid is opaque and vigorously rotating; spherical Couette flows with molten metals are one such example. The fine structure of the acoustic spectrum can be related to the fluid’s velocity field, and inverse spectral methods can be used to predict and, with sufficient acoustic data, mathematically reconstruct the velocity field. The methods are to some extent inherited from helioseismology. This work develops a Finite Element Method suitable to matching the geometries of experimental setups, as well as modelling the acoustics based on that geometry and zonal flows therein. As an application, this work uses the 60-cm setup Dynamo 3.5 at the University of Maryland Nonlinear Dynamics Laboratory. Additionally, results obtained using a small acoustic data set from recent experiments in air are provided.

Fabrication of Mg foams for biomedical applications by means of a replica method based upon spherical carbon particles

Interest in Mg foams is increasing due to their potential use as biomaterials. Fabrication methods determine to a great extent their structure and, in some cases, may pollute the foam. In this work Mg foams are fabricated by a replica method that uses as skeleton packed spheres of active carbon, a material widely utilized in medicine. After Mg infiltration, carbon particles are eliminated by an oxidizing heat treatment. The latter covers Mg with MgO which improves performance. In particular, oxidation retards degradation of the foam, as the polarization curves of the Mg foam with and without oxide indicate. The sphericity and regularity of C particles allows control of the structure of the produced open-cell foams.

Effect of third-order aberrations on dynamic accommodation

We investigate the potential for the third-order aberrations coma and trefoil to provide a signed cue to accommodation. It is first demonstrated theoretically (with some assumptions) that the point spread function is insensitive to the sign of spherical defocus in the presence of odd-order aberrations. In an experimental investigation, the accommodation response to a sinusoidal change in vergence (1–3 D, 0.2 Hz) of a monochromatic stimulus was obtained with a dynamic infrared optometer. Measurements were obtained in 10 young visually normal individuals with and without custom contact lenses that induced low and high values of r.m.s. trefoil (0.25, 1.03 μm) and coma (0.34, 0.94 μm). Despite variation between subjects, we did not find any statistically significant increase or decrease in the accommodative gain for low levels of trefoil and coma, although effects approached or reached significance for the high levels of trefoil and coma. Theoretical and experimental results indicate that the presence of Zernike third-order aberrations on the eye does not seem to play a crucial role in the dynamics of the accommodation response.

Prediction of fluidization behaviour and a quasi-stationary approach to drying kinetics of irregular particulate food materials

Changes in fluidization behaviour behaviour was characterised for parallelepiped particles with three aspect ratios, 1:1, 2:1 and 3:1 and spherical particles. All drying experiments were conducted at 500C and 15 % RH using a heat pump dehumidifier system. Fluidization experiments were undertaken for the bed heights of 100, 80, 60 and 40 mm and at 10 moisture content levels. Due to irregularities in shape minimum fluidisation velocity of parallelepiped particulates (potato) could not fitted to any empirical model. Also a generalized equation was used to predict minimum fluidization velocity. The modified quasi-stationary method (MQSM) has been proposed to describe drying kinetics of parallelepiped particulates at 30o C, 40o C and 50o C that dry mostly in the falling rate period in a batch type fluid bed dryer.

Deposition of combustion aerosols in the human respiratory tract : comparison of theoretical predictions with experimental data

Total deposition of petrol, diesel and environmental tobacco smoke (ETS) aerosols in the human respiratory tract for nasal breathing conditions was computed for 14 nonsmoking volunteers, considering the specific anatomical and respiratory parameters of each volunteer and the specific size distribution for each inhalation experiment. Theoretical predictions were 34.6% for petrol, 24.0% for diesel, and 18.5% for ETS particles. Compared to the experimental results, predicted deposition values were consistently smaller than the measured data (41.4% for petrol, 29.6% for diesel, and 36.2% for ETS particles). The apparent discrepancy between experimental data on total deposition and modeling results may be reconciled by considering the non-spherical shape of the test aerosols by diameter-dependent dynamic shape factors to account for differences between mobility-equivalent and volume-equivalent or thermodynamic diameters. While the application of dynamic shape factors is able to explain the observed differences for petrol and diesel particles, additional mechanisms may be required for ETS particle deposition, such as the size reduction upon inspiration by evaporation of volatile compounds and/or condensation-induced restructuring, and, possibly, electrical charge effects.

Effect of orthokeratology on peripheral aberrations of the eye

Purpose: To investigate the effect of orthokeratology on peripheral aberrations in two myopic volunteers. Methods: The subjects wore reverse geometry orthokeratology lenses overnight and were monitored for 2 weeks of wear. They underwent corneal topography, peripheral refraction (out to ±34° along the horizontal visual field) and peripheral aberration measurements across the 42° × 32° central visual field using a modified Hartmann-Shack aberrometer. Results: Spherical equivalent refraction was corrected for the central 25° of the visual fields beyond which it gradually returned to its preorthokeratology values. There were increases in axial coma, spherical aberration, higher order root mean square aberrations, and total root-mean-squared aberrations (excluding defocus). The rates of change of vertical and horizontal coma across the field changed in sign. Total root mean square aberrations showed a quadratic rate of change across the visual field which was greater subsequent to orthokeratology. Conclusion: Although orthokeratology can correct peripheral relative hypermetropia it induces dramatic increases in higher-order aberrations across the field

Nanoparticle melting as a Stefan moving boundary problem

The melting of spherical nanoparticles is considered from the perspective of heat flow in a pure material and as a moving boundary (Stefan) problem. The dependence of the melting temperature on both the size of the particle and the interfacial tension is described by the Gibbs-Thomson effect, and the resulting two-phase model is solved numerically using a front-fixing method. Results show that interfacial tension increases the speed of the melting process, and furthermore, the temperature distribution within the solid core of the particle exhibits behaviour that is qualitatively different to that predicted by the classical models without interfacial tension.

Corneal topography with Scheimpflug imaging and videokeratography : comparative study of normal eyes

PURPOSE: To compare the repeatability within anterior corneal topography measurements and agreement between measurements with the Pentacam HR rotating Scheimpflug camera and with a previously validated Placido disk–based videokeratoscope (Medmont E300). ------ SETTING: Contact Lens and Visual Optics Laboratory, School of Optometry, Queensland University of Technology, Brisbane, Queensland, Australia. ----- METHODS: Normal eyes in 101 young adult subjects had corneal topography measured using the Scheimpflug camera (6 repeated measurements) and videokeratoscope (4 repeated measurements). The best-fitting axial power corneal spherocylinder was calculated and converted into power vectors. Corneal higher-order aberrations (HOAs) (up to the 8th Zernike order) were calculated using the corneal elevation data from each instrument. ----- RESULTS: Both instruments showed excellent repeatability for axial power spherocylinder measurements (repeatability coefficients <0.25 diopter; intraclass correlation coefficients >0.9) and good agreement for all power vectors. Agreement between the 2 instruments was closest when the mean of multiple measurements was used in analysis. For corneal HOAs, both instruments showed reasonable repeatability for most aberration terms and good correlation and agreement for many aberrations (eg, spherical aberration, coma, higher-order root mean square). For other aberrations (eg, trefoil and tetrafoil), the 2 instruments showed relatively poor agreement. ----- CONCLUSIONS: For normal corneas, the Scheimpflug system showed excellent repeatability and reasonable agreement with a previously validated videokeratoscope for the anterior corneal axial curvature best-fitting spherocylinder and several corneal HOAs. However, for certain aberrations with higher azimuthal frequencies, the Scheimpflug system had poor agreement with the videokeratoscope; thus, caution should be used when interpreting these corneal aberrations with the Scheimpflug system.

Peripheral ocular monochromatic aberrations

Aberrations affect image quality of the eye away from the line of sight as well as along it. High amounts of lower order aberrations are found in the peripheral visual field and higher order aberrations change away from the centre of the visual field. Peripheral resolution is poorer than that in central vision, but peripheral vision is important for movement and detection tasks (for example driving) which are adversely affected by poor peripheral image quality. Any physiological process or intervention that affects axial image quality will affect peripheral image quality as well. The aim of this study was to investigate the effects of accommodation, myopia, age, and refractive interventions of orthokeratology, laser in situ keratomileusis and intraocular lens implantation on the peripheral aberrations of the eye. This is the first systematic investigation of peripheral aberrations in a variety of subject groups. Peripheral aberrations can be measured either by rotating a measuring instrument relative to the eye or rotating the eye relative to the instrument. I used the latter as it is much easier to do. To rule out effects of eye rotation on peripheral aberrations, I investigated the effects of eye rotation on axial and peripheral cycloplegic refraction using an open field autorefractor. For axial refraction, the subjects fixated at a target straight ahead, while their heads were rotated by ±30º with a compensatory eye rotation to view the target. For peripheral refraction, the subjects rotated their eyes to fixate on targets out to ±34° along the horizontal visual field, followed by measurements in which they rotated their heads such that the eyes stayed in the primary position relative to the head while fixating at the peripheral targets. Oblique viewing did not affect axial or peripheral refraction. Therefore it is not critical, within the range of viewing angles studied, if axial and peripheral refractions are measured with rotation of the eye relative to the instrument or rotation of the instrument relative to the eye. Peripheral aberrations were measured using a commercial Hartmann-Shack aberrometer. A number of hardware and software changes were made. The 1.4 mm range limiting aperture was replaced by a larger aperture (2.5 mm) to ensure all the light from peripheral parts of the pupil reached the instrument detector even when aberrations were high such as those occur in peripheral vision. The power of the super luminescent diode source was increased to improve detection of spots passing through the peripheral pupil. A beam splitter was placed between the subjects and the aberrometer, through which they viewed an array of targets on a wall or projected on a screen in a 6 row x 7 column matrix of points covering a visual field of 42 x 32. In peripheral vision, the pupil of the eye appears elliptical rather than circular; data were analysed off-line using custom software to determine peripheral aberrations. All analyses in the study were conducted for 5.0 mm pupils. Influence of accommodation on peripheral aberrations was investigated in young emmetropic subjects by presenting fixation targets at 25 cm and 3 m (4.0 D and 0.3 D accommodative demands, respectively). Increase in accommodation did not affect the patterns of any aberrations across the field, but there was overall negative shift in spherical aberration across the visual field of 0.10 ± 0.01m. Subsequent studies were conducted with the targets at a 1.2 m distance. Young emmetropes, young myopes and older emmetropes exhibited similar patterns of astigmatism and coma across the visual field. However, the rate of change of coma across the field was higher in young myopes than young emmetropes and was highest in older emmetropes amongst the three groups. Spherical aberration showed an overall decrease in myopes and increase in older emmetropes across the field, as compared to young emmetropes. Orthokeratology, spherical IOL implantation and LASIK altered peripheral higher order aberrations considerably, especially spherical aberration. Spherical IOL implantation resulted in an overall increase in spherical aberration across the field. Orthokeratology and LASIK reversed the direction of change in coma across the field. Orthokeratology corrected peripheral relative hypermetropia through correcting myopia in the central visual field. Theoretical ray tracing demonstrated that changes in aberrations due to orthokeratology and LASIK can be explained by the induced changes in radius of curvature and asphericity of the cornea. This investigation has shown that peripheral aberrations can be measured with reasonable accuracy with eye rotation relative to the instrument. Peripheral aberrations are affected by accommodation, myopia, age, orthokeratology, spherical intraocular lens implantation and laser in situ keratomileusis. These factors affect the magnitudes and patterns of most aberrations considerably (especially coma and spherical aberration) across the studied visual field. The changes in aberrations across the field may influence peripheral detection and motion perception. However, further research is required to investigate how the changes in aberrations influence peripheral detection and motion perception and consequently peripheral vision task performance.

On the affinity of Chuaria–Tawuia complex : a multidisciplinary study

In this study, biometric and structural engineering tool have been used to examine a possible relationship within Chuaria–Tawuia complex and micro-FTIR (Fourier Transform Infrared Spectroscopy) analyses to understand the biological affinity of Chuaria circularis Walcott, collected from the Mesoproterozoic Suket Shales of the Vindhyan Supergroup and the Neoproterozoic Halkal Shales of the Bhima Group of peninsular India. Biometric analyses of well preserved carbonized specimens show wide variation in morphology and uni-modal distribution. We believe and demonstrate to a reasonable extent that C. circularis most likely was a part of Tawuia-like cylindrical body of algal origin. Specimens with notch/cleft and overlapping preservation, mostly recorded in the size range of 3–5 mm, are of special interest. Five different models proposed earlier on the life cycle of C. circularis are discussed. A new model, termed as ‘Hybrid model’ based on present multidisciplinary study assessing cylindrical and spherical shapes suggesting variable cell wall strength and algal affinity is proposed. This model discusses and demonstrates varied geometrical morphologies assumed by Chuaria and Tawuia, and also shows the inter-relationship of Chuaria–Tawuia complex. Structural engineering tool (thin walled pressure vessel theory) was applied to investigate the implications of possible geometrical shapes (sphere and cylinder), membrane (cell wall) stresses and ambient pressure environment on morphologically similar C. circularis and Tawuia. The results suggest that membrane stresses developed on the structures similar to Chuaria–Tawuia complex were directly proportional to radius and inversely proportional to the thickness in both cases. In case of hollow cylindrical structure, the membrane stresses in circumferential direction (hoop stress) are twice of the longitudinal direction indicating that rupture or fragmentation in the body of Tawuia would have occurred due to hoop stress. It appears that notches and discontinuities seen in some of the specimens of Chuaria may be related to rupture suggesting their possible location in 3D Chuaria. The micro-FTIR spectra of C. circularis are characterized by both aliphatic and aromatic absorption bands. The aliphaticity is indicated by prominent alkyl group bands between 2800–3000 and 1300–1500 cm−1. The prominent absorption signals at 700–900 cm−1 (peaking at 875 and 860 cm−1) are due to aromatic CH out of plane deformation. A narrow, strong band is centred at 1540 cm−1 which could be COOH band. The presence of strong aliphatic bands in FTIR spectra suggests that the biogeopolymer of C. circularis is of aliphatic nature. The wall chemistry indicates the presence of ‘algaenan’—a biopolymer of algae.