Polymer Fluid Dynamics: Continuum and Molecular Appoaches

To solve problems in polymer fluid dynamics, one needs the equation of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (1) one can write a continuum expression for the stress tensor in terms of kinematic tensors, or (2) one can select a molecular model that represents the polymer molecule, and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. In this review, we restrict the discussion primarily to the simplest stress tensor expressions or “constitutive equations” containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. The virtue of studying the simplest models is that we can discover some general notions as to which types of empiricisms or which types of molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows. These are the flows that are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.

The adaptive response of humans to exercise: Impact of exercise intensity, fibre-type specific responses and molecular patterns of response

In an attempt to improve the current understanding of the adaptive response to exercise in humans, this dissertation performed a series of studies designed to examine the impact of training intensity and mode on aerobic capacity and performance, fibre-type specific adaptations to training, and individual patterns of response across molecular, morphological and genetic factors. Project #1 determined that training intensity, session dose, baseline VO2max and total training volume do not influence the magnitude of change in VO2max by performing a meta-regression, and meta-analysis of 28 different studies. The intensity of training had no effect on the magnitude of increase in maximal oxygen uptake in young healthy participants, but similar adaptations were achieved with lower training doses following high intensity training. Project # 2 determined the acute molecular response, and training-induced adaptations in aerobic performance, aerobic capacity and muscle phenotype following high-intensity interval training (HIT) or endurance exercise (END). The acute molecular response (fibre recruitment and signal activation) and training-induced adaptations in aerobic capacity, aerobic performance, and muscle phenotype were similar following HIT and END. Project # 3 examined the impact of baseline muscle morphology and molecular characteristics on the training response, and if muscle adaptations are coordinated. The muscle phenotype of individuals who experience the largest improvements (high responders) were lower before training for some muscle characteristics and molecular adaptations were coordinated within individual participants. Project # 4 examined the impact of 2 different intensities of HIT on the expression of nuclear and mitochondrial encoded genes targeted by PGC-1α. A systematic upregulation of nuclear and mitochondrial encoded genes was not present in the early recovery period following acute HIT, but the expression of mitochondrial genes were coordinated at an individual level. Collectively, results from the current dissertation contribute to our understanding of the molecular mechanisms influencing skeletal muscle and whole-body adaptive responses to acute exercise and training in humans.

RELIBILITY ANALYSIS OF SIMPLE SLOPES AND SOIL-STRUCTURES WITH LINEAR LIMIT STATES

The first objective of this research was to develop closed-form and numerical probabilistic methods of analysis that can be applied to otherwise conventional methods of unreinforced and geosynthetic reinforced slopes and walls. These probabilistic methods explicitly include random variability of soil and reinforcement, spatial variability of the soil, and cross-correlation between soil input parameters on probability of failure. The quantitative impact of simultaneously considering the influence of random and/or spatial variability in soil properties in combination with cross-correlation in soil properties is investigated for the first time in the research literature. Depending on the magnitude of these statistical descriptors, margins of safety based on conventional notions of safety may be very different from margins of safety expressed in terms of probability of failure (or reliability index). The thesis work also shows that intuitive notions of margin of safety using conventional factor of safety and probability of failure can be brought into alignment when cross-correlation between soil properties is considered in a rigorous manner. The second objective of this thesis work was to develop a general closed-form solution to compute the true probability of failure (or reliability index) of a simple linear limit state function with one load term and one resistance term expressed first in general probabilistic terms and then migrated to a LRFD format for the purpose of LRFD calibration. The formulation considers contributions to probability of failure due to model type, uncertainty in bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety (OFS). Bias is defined as the ratio of measured to predicted value. Parametric analyses were carried out to show that ignoring possible correlations between random variables can lead to conservative (safe) values of resistance factor in some cases and in other cases to non-conservative (unsafe) values. Example LRFD calibrations were carried out using different load and resistance models for the pullout internal stability limit state of steel strip and geosynthetic reinforced soil walls together with matching bias data reported in the literature.