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Certain types of long, axially compressed structures have the potential to buckle locally in one or more regions rather than uniformly along their length. Here, the potential for localized buckle patterns in an elastic layer embedded in a visco-elastic medium is investigated using a strut-on-foundation model. Applications of this model include the growth of geological folds and other time-dependent instability processes. The model consists of an elastic strut of uniform flexural stiffness supported by a Winkler-type foundation made up of discrete Maxwell elements. Mathematically, this model corresponds to a nonlinear partial differential equation which is fourth-order in space and first-order in time. The nature of the buckling process is characterized by an initial period of elastic deformation followed by an evolutionary phase in which both elasticity and viscosity have a role to play. Two different formulations are studied: the first combines linear strut theory with a nonlinear foundation and is valid for small, but finite, deflections; the other incorporates the exact expression for curvature of the strut resulting in geometrical nonlinearities and is capable of modelling large deflections. The evolution of non-periodic buckle patterns in each system is examined under the constraint of controlled end displacement. Two independent methods are used to approximate the solution of the governing equations. Modal solutions, based on the method of weighted residuals, complement accurate numerical solutions obtained with a boundary-value solver. In either case, the results suggest that for the perfect system, localized solutions follow naturally from the inclusion of nonlinear elasticity with softening characteristics. Emphasis throughout is on the qualitative features displayed by the phenomenon of localization rather than specific applications. Nevertheless, the ideas and results are a step towards accounting for the rich variety of deformed shapes exhibited by nature.

Errors in DNA replication can cause chromosome instability and gross chromosomal rearrangements (GCRs). For my thesis work I investigate how chromosome instability can originate in the telomere. Here I report how defects in Cdc13, a telomere specific protein, lead to chromosome instability and GCRs in Saccharomyces cerevisiae. Using a temperature sensitive mutant of Cdc13, I find that cdc13-induced instability can be induced in a single cell cycle and synergizes with replication stress (dNTP depletion via hydroxyurea). Additionally, I find that Cdc13 has to be functional during the cell’s S phase to suppress chromosome instability. Further genetic analysis suggests that that cdc13-induced chromosome instability depends on the generation of single stranded (ss)DNA, but not on the activity of canonical double strand break (DSB) repair pathways such as homologous recombination or non-homologous end joining. Finally, I demonstrate that telomeric unstable chromosomes can later progress and trigger rearrangements at centromeric loci. This system, using the conditional nature of the cdc13 mutation, promises a more complex analysis of the ontogeny of chromosome instability: in this case from errors semi-conservative DNA replication through the telomere to the formation and resolution of unstable chromosomes.

Inertial granular flows lie in a region of parameter space between quasi-static and collisional regimes. In each of these phases the mechanisms of energy dissipation are often taken to be the defining features. Frictional contacts between grains and the transmission of energy through co-operative force chains dominate slowly sheared flows. In the opposite extreme infrequent high-energy collisions are responsible for dissipation in so-called gaseous granular flows. Borrowing from each of these extremes, it is postulated that during liquid-like flow, grain energy is transferred through frequent frictional interactions as the particles rearrange. This thesis focuses on the μ(I)-rheology which generalises the simple Coulomb picture, where greater normal forces lead to greater tangential friction, by including dependence on the inertial number I, which reflects the frequency of grain rearrangements. The equations resulting from this rheology, assuming that the material is incompressible, are first examined with a maximal-order linear stability analysis. It is found that the equations are linearly well-posed when the inertial number is not too high or too low. For inertial numbers in which the equations are instead ill-posed numerical solutions are found to be grid-dependent with perturbations growing unboundedly as their wavelength is decreased. Interestingly, experimental results also diverge away from the original μ(I) curve in the ill-posed regions. A generalised well-posedness analysis is used alongside the experimental findings to suggest a new functional form for the curve. This is shown to regularise numerical computations for a selection of inclined plane flows. As the incompressibility assumption is known to break down more drastically in the high-I and low-I limits, compressible μ(I) equations are also considered. When the closure of these equations takes the form suggested by critical state soil mechanics, it is found that the resultant system is well-posed regardless of the details of the deformation. Well-posed equations can also be formed by depth-averaging the μ(I)-rheology. For three-dimensional chute flows experimental measurements are captured well by the depth-averaged model when the flows are shallow. Furthermore, numerical computations are much less expensive than those with the full μ(I) system.

We report upon an experimental study of internal gravity waves generated by the large-amplitude vertical oscillations of a circular cylinder in uniformly stratified fluid. Quantitative measurements are performed using a modified synthetic schlieren technique for strongly stratified solutions of NaCl or NaI. Oscillatory turbulent patches that develop around the cylinder are found to be the primary source of the observed quasi-monochromatic wave beams whose characteristics differ from theoretical predictions and experimental investigations of waves generated by small-amplitude cylinder oscillations. Over long times the waves break down into turbulence that is examined quantitatively through conductivity probe measurements and qualitatively through unprocessed synthetic schlieren images. Based on observations of the location of wave breakdown we determine that the likely mechanism for breakdown is through parametric subharmonic instability. This conclusion is supported by fully nonlinear numerical simulations of the evolution of a temporally monochromatic internal wave beam.