State-Selective Photodissociation Dynamics of Formaldehyde: Near Threshold Studies of the H+HCO Product Channel

The laser-induced photodissociation of formaldehyde in the wavelength range 309<λ<330nm 309<λ<330nm has been investigated using H (Rydberg) atom photofragment translational spectroscopy. Photolysis wavelengths corresponding to specific rovibronic transitions in the A ˜ A 2 1 ←X ˜ A 1 1 ÃA21←X̃A11 2 1 0 4 3 0 201403 , 2 2 0 4 1 0 202401 , 2 2 0 4 3 0 202403 , 2 3 0 4 1 0 203401 , and 2 1 0 5 1 0 201501 bands of H 2 CO H2CO were studied. The total kinetic energy release spectra so derived can be used to determine partial rotational state population distributions of the HCO cofragment. HCO product state distributions have been derived following the population of various different N K a NKa levels in the A ˜ A 2 1 ÃA21 2 2 4 3 2243 and 2 3 4 1 2341 states. Two distinct spectral signatures are identified, suggesting competition between dissociation pathways involving the X ˜ A 1 1 X̃A11 and the a ˜ A 2 3 ãA23 potential energy surfaces. Most rovibrational states of H 2 CO(A ˜ A 2 1 ) H2CO(ÃA21) investigated in this work produceH+HCO(X ˜ A ′ 2 ) H+HCO(X̃A′2) photofragments with a broad kinetic energy distribution and significant population in high energy rotational states of HCO. Photodissociation via the A ˜ A 2 1 ÃA21 2 2 4 3 2243 1 1,1 11,1 (and 1 1,0 11,0 ) rovibronic states yields predominantly HCO fragments with low internal energy, a signature that these rovibronic levels are perturbed by the a ˜ A 2 3 ãA23 state. The results also suggest the need for further careful measurements of the H+HCO H+HCO quantum yield from H 2 CO H2CO photolysis at energies approaching, and above, the barrier to C–H bond fission on the a ˜ A 2 3 ãA23 potential energy surface.

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.

Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.

Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.