Analytical modelling of bacterial migration and accumulation with rate-limited sorption in discrete fractures

An analytical model for bacterial accumulation in a discrete fractllre has been developed. The transport and accumlllation processes incorporate into the model include advection, dispersion, rate-limited adsorption, rate-limited desorption, irreversible adsorption, attachment, detachment, growth and first order decay botl1 in sorbed and aqueous phases. An analytical solution in Laplace space is derived and nlln1erically inverted. The model is implemented in the code BIOFRAC vvhich is written in Fortran 99. The model is derived for two phases, Phase I, where adsorption-desorption are dominant, and Phase II, where attachment-detachment are dominant. Phase I ends yvhen enollgh bacteria to fully cover the substratllm have accllillulated. The model for Phase I vvas verified by comparing to the Ogata-Banks solution and the model for Phase II was verified by comparing to a nonHomogenous version of the Ogata-Banks solution. After verification, a sensitiv"ity analysis on the inpllt parameters was performed. The sensitivity analysis was condllcted by varying one inpllt parameter vvhile all others were fixed and observing the impact on the shape of the clirve describing bacterial concentration verSllS time. Increasing fracture apertllre allovvs more transport and thus more accllffilliation, "Vvhich diminishes the dllration of Phase I. The larger the bacteria size, the faster the sllbstratum will be covered. Increasing adsorption rate, was observed to increase the dllration of Phase I. Contrary to the aSSllmption ofllniform biofilm thickness, the accllffilliation starts frOll1 the inlet, and the bacterial concentration in aqlleous phase moving towards the olitiet declines, sloyving the accumulation at the outlet. Increasing the desorption rate, redllces the dliration of Phase I, speeding IIp the accllmlilation. It was also observed that Phase II is of longer duration than Phase I. Increasing the attachment rate lengthens the accliffililation period. High rates of detachment speeds up the transport. The grovvth and decay rates have no significant effect on transport, althollgh increases the concentrations in both aqueous and sorbed phases are observed. Irreversible adsorption can stop accllillulation completely if the vallIes are high.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

Autonomic regulation and blood pressure in children

Vagal baroreflex sensitivity (BRS) is a measure of short term blood pressure (BP) regulation through alterations in heart rate. Low BRS reflects impaired autonomic system regulation and has been found to be a surrogate marker for cardiovascular health. In particular, it has found to be associated with the pathogenesis of adult hypertension. However, only limited information exists as to the negative consequences of childhood BP on baroreflex function. The objective of this study was to investigate BRS in children with 2 different BP profiles while controlling for the effects of age, maturation, sex, and body composition. A preliminary subsample of 11-14 year-old children from the HBEAT (Heart Behavioural Environmental Assessment Team) Study was selected. The children were divided into 2 BP groups; high BP (HBP; 2:95tl1 percentile, n=21) and normal BP (NBP; <90th percentile, n=85). Following an initial 15 minutes of supine rest, 5 minutes of continuous beat-to-beat BP (Finapres) and RR interval (RRI) were recorded (standard ECG). Spectral indices were computed using Fast Fourier Transform and transfer function analysis was used to compute BRS. High frequency (HF) and low frequency (LF) power spectral areas were set to 0.15-0.4 Hz and 0.04-0.15 Hz, respectively. Body composition was measured using body mass index. After adjusting for body composition, maturation, age and sex ANCOV A results were as follows; LF and HF BRS, LF and HF RRI, and RRI total power were lower in the HBP versus NBP participants (p<0.05). As well, LF IHF SBP ratio was significantly higher in the HBP compared to the NBP group (p<0.05). The regression coefficients (unstandardized B) indicated that in changing groups (NBP to HBP) LF and HF BRS decreases by 4.04 and 6.18 ms/mmHg, respectively. Thus, as BP increases, BRS decreases. These data suggest that changes in autonomic activity occur in children who have HBP, regardless of age, sex, maturation, and body composition. Thus, despite their young age and relatively short amount of time having high BP compared with adults, these children are already demonstrating poor BP regulation and reduced cardiovagal activity. Given that childhood BP is associated with hypertension in adulthood, there is a growing concern in regards to the current cardiovascular health of our children and future adults.

Baroreflex sensitivity and developmental coordination disorder

Developmental coordination disorder (DCD) is a motor coordination disorder that is characterized by impairment of motor skills which leads to challenges with performing activities of daily living. Children with DCD have been shown to be less physically active and have increased body fatness. This is an important finding since a sedentary lifestyle and obesity are risk factors for cardiovascular disease. One indicator of cardiovascular health is baroreflex sensitivity (BRS), which is a measure of short term BP regulation that is accomplished through changes in HR. Diminished BRS is predictive of cardiovascular morbidity and mortality. The purpose of this study was to investigate BRS in 117 children aged 12 to 13 years with probable DCD (pOCO) and their matched controls with normal coordination. Following 15 minutes of supine rest, five minutes of continuous beat-by-beat blood pressure (Finapres) and RR interval were recorded (standard ECG). Spectral indices were computed using Fast Fourier Transform and transfer function analysis was used to compute BRS. High frequency and low frequency power spectral areas were set to 0.15-0.6 Hz and 0.04-0.15 Hz, respectively. BRS was compared between groups with an independent t-test and the difference was not significant. It is likely that a difference in BRS was not seen between groups since the difference in BMI between groups was small. As well, differences in BRS may not have manifested yet at this early age. However, the cardiovascular health of this population still deserves attention since differences in body composition and fitness were found between groups.