title: Steady and unsteady visco-resistive reconnection in the presence of the Hall effect

authors: McMahon, Liam

subjects: Magnetic Reconnection

abstract: In this thesis we investigate the effects of viscosity and the Hall effect on magnetic reconnection. Magnetic reconnection is a process of releasing large amounts of magnetic energy as observed in solar flares. In the first two chapters, we describe the basic mathematics and early models of reconnection.

In Chapter 3, we search for a visco-resistive length scale in reconnection solutions. This is demonstrated in reconnective annihilation and a quasi-one-dimensional series expansion. We find that the visco-resistive length scale appears organically unless a specific geometry is chosen. Upon adding small scale perturbations, the visco-resistive length scale always appears.

 In Chapter 4, we build on Litvinenko’s (2007) self-similar solution that showed singularities appear with a Hall MHD X-point geometry for a certain set of initial conditions. These singularities signal current sheet formation. We consider a general set of initial conditions and find that the singularities will form in this self-similar solution unless the axial field is many orders of magnitude larger than the planar field. 

In Chapter 5, we review the Craig and McClymont (1991) linear, oscillatory  model of reconnection. In Chapter 6, we attempt to quantify a general model that includes viscosity, pressure and axial effects, the Hall effect and electron inertia. We perform a dimensional analysis to find order-of magnitude estimates for how the aforementioned effects perturb the Craig and McClymont (1991) solution. We verify these estimates with numerical simulations. 

In Chapter 7, we give an overview of the thesis and make suggestions for future work.

text: Steady and unsteady visco-resistive reconnection in the presence of the Hall effect In this thesis we investigate the effects of viscosity and the Hall effect on magnetic reconnection. Magnetic reconnection is a process of releasing large amounts of magnetic energy as observed in solar flares. In the first two chapters, we describe the basic mathematics and early models of reconnection.

In Chapter 3, we search for a visco-resistive length scale in reconnection solutions. This is demonstrated in reconnective annihilation and a quasi-one-dimensional series expansion. We find that the visco-resistive length scale appears organically unless a specific geometry is chosen. Upon adding small scale perturbations, the visco-resistive length scale always appears.

 In Chapter 4, we build on Litvinenko’s (2007) self-similar solution that showed singularities appear with a Hall MHD X-point geometry for a certain set of initial conditions. These singularities signal current sheet formation. We consider a general set of initial conditions and find that the singularities will form in this self-similar solution unless the axial field is many orders of magnitude larger than the planar field. 

In Chapter 5, we review the Craig and McClymont (1991) linear, oscillatory  model of reconnection. In Chapter 6, we attempt to quantify a general model that includes viscosity, pressure and axial effects, the Hall effect and electron inertia. We perform a dimensional analysis to find order-of magnitude estimates for how the aforementioned effects perturb the Craig and McClymont (1991) solution. We verify these estimates with numerical simulations. 

In Chapter 7, we give an overview of the thesis and make suggestions for future work.

year: 2021

title: Wavelength Tuneable Frequency Domain Photon Migration Spectrometer for Tissue-like Media

authors: Cletus, Biju

subjects: Photon Migration

abstract: Frequency domain spectrometers use intensity modulated light to quantitatively interrogate turbid media. The modulation frequencies employed are in the radiofrequency range. Intensity modulated light launched into a turbid medium generates photon density fluctuations with wave like character that oscillates at the modulation frequency. These density fluctuations are named diffuse photon density waves, and it has been shown that the amplitude and phase of the photon density wave inside the medium depends on its optical properties. Hence by measuring the amplitude and phase of the photon density wave the optical properties of the medium can be estimated. This is the basic working principle of a frequency domain photon migration spectrometer. 
Frequency domain spectrometers fabricated with laser diodes are limited to discrete wavelengths thereby making compromises on the information about the media under test. In this research a wavelength tuneable frequency domain spectrometer was constructed by modulating the output intensity of a titanium: sapphire laser using an acousto-optic modulator. A low noise avalanche photodiode module in conjunction with a lock-in amplifier was used to measure the amplitude attenuation and phase lag inside a turbid sample. The frequency domain spectrometer was tested for accuracy and precision by estimating the optical properties of an important tissue simulation phantom, Intralipid , at a representative wavelength 790 nm. The results indicated that the spectrometer estimates absorption with an accuracy of 10%. The instrument estimates the absorption and reduced scattering coefficients with a precision of 3% and 6%, respectively. 
Optical properties of Intralipid  were measured from 710-850 nm in the therapeutic window. The results were compared with published data measured by other methods and similar frequency domain techniques. The absorption coefficient agrees within 10% with results from a time domain measurement. The reduced scattering coefficient was within the error limits of other reported measurements. At 750 nm the reduced scattering agrees within 5% with the results from a continuous wave, time domain and within 1% from another frequency domain measurement, and at 811 and 849 nm this agreement is within 9%. A Mie theory prediction of the reduced scattering coefficient based on a measurement of the particle size distribution by a Mastersizer 2000 is larger than the frequency domain results by 6%. 
The spectrometer was used to determine the optical temperature coefficient of Intralipid , exploring its potential as a non invasive temperature monitoring device. The measured minute change in the absorption coefficient suggests a minimum observable temperature change of   4'C, which for most practical applications means that the precision needs to improve. The effect of glucose on the optical properties of Intralipid  indicates that the absorption coefficient decreases steadily at 730 nm up to 1000mg/dL. The reduced scattering coefficient decreases with increasing glucose concentration at most of the wavelengths. 
This work quantified the absorption and reduced scattering of Intralipid  over a larger wavelength range (in the therapeutic window) than before. This is the first time the effects of temperature on the optical properties of a turbid medium monitored with a frequency domain spectrometer.  Specific information about the precision and accuracy which can be achieved with the current technology is documented. Current precision is not sufficient for many applications that would benefit from separation of absorption and scattering.

text: Wavelength Tuneable Frequency Domain Photon Migration Spectrometer for Tissue-like Media Frequency domain spectrometers use intensity modulated light to quantitatively interrogate turbid media. The modulation frequencies employed are in the radiofrequency range. Intensity modulated light launched into a turbid medium generates photon density fluctuations with wave like character that oscillates at the modulation frequency. These density fluctuations are named diffuse photon density waves, and it has been shown that the amplitude and phase of the photon density wave inside the medium depends on its optical properties. Hence by measuring the amplitude and phase of the photon density wave the optical properties of the medium can be estimated. This is the basic working principle of a frequency domain photon migration spectrometer. 
Frequency domain spectrometers fabricated with laser diodes are limited to discrete wavelengths thereby making compromises on the information about the media under test. In this research a wavelength tuneable frequency domain spectrometer was constructed by modulating the output intensity of a titanium: sapphire laser using an acousto-optic modulator. A low noise avalanche photodiode module in conjunction with a lock-in amplifier was used to measure the amplitude attenuation and phase lag inside a turbid sample. The frequency domain spectrometer was tested for accuracy and precision by estimating the optical properties of an important tissue simulation phantom, Intralipid , at a representative wavelength 790 nm. The results indicated that the spectrometer estimates absorption with an accuracy of 10%. The instrument estimates the absorption and reduced scattering coefficients with a precision of 3% and 6%, respectively. 
Optical properties of Intralipid  were measured from 710-850 nm in the therapeutic window. The results were compared with published data measured by other methods and similar frequency domain techniques. The absorption coefficient agrees within 10% with results from a time domain measurement. The reduced scattering coefficient was within the error limits of other reported measurements. At 750 nm the reduced scattering agrees within 5% with the results from a continuous wave, time domain and within 1% from another frequency domain measurement, and at 811 and 849 nm this agreement is within 9%. A Mie theory prediction of the reduced scattering coefficient based on a measurement of the particle size distribution by a Mastersizer 2000 is larger than the frequency domain results by 6%. 
The spectrometer was used to determine the optical temperature coefficient of Intralipid , exploring its potential as a non invasive temperature monitoring device. The measured minute change in the absorption coefficient suggests a minimum observable temperature change of   4'C, which for most practical applications means that the precision needs to improve. The effect of glucose on the optical properties of Intralipid  indicates that the absorption coefficient decreases steadily at 730 nm up to 1000mg/dL. The reduced scattering coefficient decreases with increasing glucose concentration at most of the wavelengths. 
This work quantified the absorption and reduced scattering of Intralipid  over a larger wavelength range (in the therapeutic window) than before. This is the first time the effects of temperature on the optical properties of a turbid medium monitored with a frequency domain spectrometer.  Specific information about the precision and accuracy which can be achieved with the current technology is documented. Current precision is not sufficient for many applications that would benefit from separation of absorption and scattering.

year: 2010

title: Boat electrofishing surveys of fish populations in the Ohau Channel in 2011 and 2012

authors: Hicks, Brendan J.

abstract: The aim of the survey was to provide on-going monitoring of the fish communities and abundance in the Ohau Channel, especially fish species that are taonga to Maori (eels, goldfish, and koura). In the current study we present the findings from the fifth and sixth years of sampling (2011 and 2012) in view of previous surveys using boat electrofishing in the Ohau Channel.

We used the University of Waikato’s 4.5 m-long, aluminium-hulled electrofishing boat to catch a total of 399 fish (29.4 kg) from 10 sites in 2011 (2,420 linear m, 9,680 m² area) and 301 fish (12.8 kg) at 11 sites in 2012 (3,625 linear m, 14,500 m² area). Koura and 7 fish species were present in both years, with common bully the most abundant in 2011 and common smelt the most abundant in 2012. Common smelt were more abundant in 2012 (131 fish) than in 2011 (39 fish). Goldfish were most abundant at sites in the lower channel, especially at site 7.

As reflected in total numbers, common bullies had the highest densities of any fish species in 2011 (up to 7.4 fish 100 m⁻²), the majority of which were taken from edge habitats at sites 4, 5 and site 7. In 2012, common bully abundance was much reduced. However, despite the lower bully densities in 2012, mean bully biomass was higher in 2012 (1.00 g m⁻²) than in 2011 (0.04 g m⁻²) because bullies were smaller in 2011.

Common smelt had variable densities, the largest number of which was found in and around the excavated side branch at site 7 edge habitats (up to 14.7 fish 100 m⁻²) below the weir (site 1).

Mean density of rainbow trout in the Ohau Channel was similar in both years (0.27 fish 100 m⁻² in 2011,0.24 fish 100 m⁻² in 2012). Mean biomass of rainbow trout was much greater in 2012 (0.69 g m⁻² in 2011, 11.2 g m⁻² in 2012). Goldfish densities were greater in 2012, partly because goldfish at site 7 were targeted in 2012, and mean biomass was correspondingly greater (0.48 g m⁻² in 2011, 47.7 g m⁻² in 2012). Site 7 had 282 g m⁻² of goldfish biomass in 2012.

Catch per unit effort (CPUE) for common bullies in 2011 was twice that in 2012, reflecting lower densities in 2012. Common smelt CPUE in 2012, however, was 5 times greater than in 2011. Despite the much higher biomass of goldfish in 2012, CPUE was much the same.
The increased goldfish biomass in 2012 arose because of targeted fishing in the excavated side branch, which clearly offers good habitat for goldfish. In 2012, the first shortfin eel encountered in these surveys was caught. The abundance of common bully appears to have a clear trend of reducing abundance since these surveys started in 2007. The cause of this is not apparent, and not accounted for by water clarity expressed as black disk (BD) distance or water conductivity (Table 7). Poor water clarity can reduce the efficiency of electrofishing, but BD was greater in 2012 than in 2011. It is possible that smelt abundance has declined too, but the relatively inefficient sampling resulting from boat electrofishing must be considered. Independent verification is required.

text: Boat electrofishing surveys of fish populations in the Ohau Channel in 2011 and 2012 The aim of the survey was to provide on-going monitoring of the fish communities and abundance in the Ohau Channel, especially fish species that are taonga to Maori (eels, goldfish, and koura). In the current study we present the findings from the fifth and sixth years of sampling (2011 and 2012) in view of previous surveys using boat electrofishing in the Ohau Channel.

We used the University of Waikato’s 4.5 m-long, aluminium-hulled electrofishing boat to catch a total of 399 fish (29.4 kg) from 10 sites in 2011 (2,420 linear m, 9,680 m² area) and 301 fish (12.8 kg) at 11 sites in 2012 (3,625 linear m, 14,500 m² area). Koura and 7 fish species were present in both years, with common bully the most abundant in 2011 and common smelt the most abundant in 2012. Common smelt were more abundant in 2012 (131 fish) than in 2011 (39 fish). Goldfish were most abundant at sites in the lower channel, especially at site 7.

As reflected in total numbers, common bullies had the highest densities of any fish species in 2011 (up to 7.4 fish 100 m⁻²), the majority of which were taken from edge habitats at sites 4, 5 and site 7. In 2012, common bully abundance was much reduced. However, despite the lower bully densities in 2012, mean bully biomass was higher in 2012 (1.00 g m⁻²) than in 2011 (0.04 g m⁻²) because bullies were smaller in 2011.

Common smelt had variable densities, the largest number of which was found in and around the excavated side branch at site 7 edge habitats (up to 14.7 fish 100 m⁻²) below the weir (site 1).

Mean density of rainbow trout in the Ohau Channel was similar in both years (0.27 fish 100 m⁻² in 2011,0.24 fish 100 m⁻² in 2012). Mean biomass of rainbow trout was much greater in 2012 (0.69 g m⁻² in 2011, 11.2 g m⁻² in 2012). Goldfish densities were greater in 2012, partly because goldfish at site 7 were targeted in 2012, and mean biomass was correspondingly greater (0.48 g m⁻² in 2011, 47.7 g m⁻² in 2012). Site 7 had 282 g m⁻² of goldfish biomass in 2012.

Catch per unit effort (CPUE) for common bullies in 2011 was twice that in 2012, reflecting lower densities in 2012. Common smelt CPUE in 2012, however, was 5 times greater than in 2011. Despite the much higher biomass of goldfish in 2012, CPUE was much the same.
The increased goldfish biomass in 2012 arose because of targeted fishing in the excavated side branch, which clearly offers good habitat for goldfish. In 2012, the first shortfin eel encountered in these surveys was caught. The abundance of common bully appears to have a clear trend of reducing abundance since these surveys started in 2007. The cause of this is not apparent, and not accounted for by water clarity expressed as black disk (BD) distance or water conductivity (Table 7). Poor water clarity can reduce the efficiency of electrofishing, but BD was greater in 2012 than in 2011. It is possible that smelt abundance has declined too, but the relatively inefficient sampling resulting from boat electrofishing must be considered. Independent verification is required.

year: 2013