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Cyanobacteria are prokaryotes that can grow photoautotrophically using oxygenic photosynthesis. Some filamentous cyanobacteria in media with insufficient fixed nitrogen develop a regular pattern of heterocyst cells that fix nitrogen for the remaining vegetative cells. We have built an integrated computational model of fixed nitrogen transport and cell growth for filamentous cyanobacteria. With our model, two qualitatively different experimentally observed nitrogen distributions between a pair of heterocysts are reconciled. By adding dynamic heterocyst placement into our model, we can optimize heterocyst frequency with respect to growth. Further introduction of modest leakage leads to distinct growth rates between different heterocyst placement strategies. A local placement strategy yields maximal growth and steady state heterocyst spacings similar to those observed experimentally. Adding more realistic fixed nitrogen storage based heterocyst commitment together with lateral inhibition to the model allows us to address initial heterocyst commitment and qualitatively reproduces many aspects of heterocyst differentiation. We also investigate patterns of starving cells and correlations of fixed nitrogen in filaments without heterocysts. We find percolation transitions in both spatial one dimensional patterns and space-time two dimensional patterns.

Thesis (M.S.)--Villanova University, 2009. / Biology Dept. Includes bibliographical references.

sand hops and bounces -see the dunes grow, run, collide -form the field's pattern.Aeolian sand dune morphologies and sizes are strongly connected to the environmental context and physical processes active since dune formation. As such, the patterns and measurable features found within dunes and dune fields can be interpreted as records of environmental conditions. Using mathematical models of dune and dune field evolution, it should be possible to quantitatively predict dune field dynamics from current conditions or to determine past field conditions based on present-day observations.In this dissertation, we focus on the construction and quantitative analysis of a continuum dune evolution model. We then apply this model towards interpretation of the formative history of terrestrial and martian dunes and dune fields. Our first aim is to identify the controls for the characteristic lengthscales seen in patterned dune fields. Variations in sand flux, binary dune interactions, and topography are evaluated with respect to evolution of individual dunes. Through the use of both quantitative and qualitative multiscale models, these results are then extended to determine the role such processes may play in (de)stabilization of the dune field. We find that sand flux variations and topography generally destabilize dune fields, while dune collisions can yield more similarly-sized dunes. We construct and apply a phenomenological macroscale dune evolution model to then quantitatively demonstrate how dune collisions cause a dune field to evolve into a set of uniformly-sized dunes. Our second goal is to investigate the influence of reversing winds and polar processes in relation to dune slope and morphology. Using numerical experiments, we investigate possible causes of distinctive morphologies seen in Antarctic and martian polar dunes. Finally, we discuss possible model extensions and needed observations that will enable the inclusion of more realistic physical environments in the dune and dune field evolution models.By elucidating the qualitative and quantitative connections between environmental conditions, physical processes, and resultant dune and dune field morphologies, this research furthers our ability to interpret spacecraft images of dune fields, and to use present-day observations to improve our understanding of past terrestrial and martian environments.

This paper considers a free energy functional and corresponding free boundary problem for multilayered structures which arise from a mixture of a block copolymer and a weak solvent. The free boundary problem is formally derived from the limit of large solvent/polymer segregation and intermediate segregation between monomer species. A change of variables based on Legendre transforms of the effective bulk energy is used to explicitly construct a family of equilibrium solutions. The second variation of the effective free energy of these solutions is shown to be positive. This result is used to show more generally that equilibria are local minimizers of the free energy.

Thesis (Ph. D.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 101-109). Also available in print.

This dissertation is devoted to better understanding the role that fluids play in the selection of the shapes and functions of objects and creatures in nature. Toward that end, three specific examples are considered: stalactites, icicles, and species of colonial green algae known as Volvox. In the cases of stalactites and icicles, the object's growth is considered as a free-boundary problem. For stalactites, the coupling of thin-film fluid dynamics with calcium carbonate chemistry leads to a local, geometric growth law that is proportional to the thickness of the water layer covering the surface at any point. Application of this law to a uniformly translating shape allows a universal stalactite form to be derived; the comparison of this shape to images of actual stalactites supports the theory. In the case of icicles, the transport of the latent heat of fusion is coupled with the dynamics of both the thin-film of water encompassing the icicle and a thermally buoyant boundary layer in the immediately surrounding air. The uniformly translating shape solution is found to be parameter-free, and is, in fact, the same shape exhibited by stalactites. A comparison between this shape and icicle images validates the theory. The final example considers how advection of nutrients due to the stirring of water by the flagella of a Volvox colony leads to a metabolite uptake rate that is much greater than would occur by diffusion alone. Moreover, nutrient acquisition by pure diffusion would limit the size of Volvox species to a certain bottleneck radius at the point where diffusional uptake just meets metabolic demands, whereas advection increases the uptake in such a way as to avoid this problem entirely, thus enabling the evolution of the larger Volvox species.

Mes activités de recherche actuelles se situent dans le cadre de la morphogenèse optique et plus généralement de la dynamique non-linéaire. Les systèmes étudiés sont les milieux Kerr (cristaux liquides et fibres optiques) en cavité ou avec feedback optique. J'y étudie plus particulièrement les phénomènes d'instabilités temporelles et spatio-temporelles tels que : - la formation de structures transverses et les instabilités modulationnelles - les solitons dissipatifs et les structures localisées - les systèmes convectifs et leurs instabilités convectives et absolues - les effets du bruit sur ces instabilités, tels que les structures entretenues par le bruit.