Distributed branch points and the shape of elastic surfaces with constant negative curvature

We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic sheets, they carry a topological index which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating energy. We develop a discrete differential geometric (DDG) approach to study the deformations of hyperbolic objects with distributed branch points. We present evidence that the maximum curvature of surfaces with geodesic radius $R$ containing branch points grow sub-exponentially, $O(e^{c\sqrt{R}})$ in contrast to the exponential growth $O(e^{c' R})$ for surfaces without branch points. We argue that, to optimize norms of the curvature, i.e. the bending energy, distributed branch points are energetically preferred in sufficiently large pseudospherical surfaces. Further, they are distributed so that they lead to fractal-like recursive buckling patterns.Comment: 59 pages, 20 figures. Major revisions including new proofs with weakened hypotheses, expanded discussion and additional references. Some images are not at their original resolution to keep them at a reasonable size. Comments are very welcome and much appreciate

A survey of impulsive trajectories Final report

Literature survey of astrodynamics problems on intercept, transfer, and rendezvous trajectorie

Mathematical and computational modelling for the design of pipe bends and compliant systems

This thesis is divided into three parts. In part I some theoretical and numerical processes are considered which arise when modelling the flow of a fluid through a pipe bend or deflector nozzle. These numerical processes include a new form of numerical integration and a finite element formulation which, it is suggested, could readily be extended to handle further realistic problems based on the pseudo three dimensional model chosen here. An introduction to nonlinear dynamics is included in part II leading towards a classification of bifurcational events in the light of recent advances in dynamics research. Most of the dynamical systems considered are dissipative such that the dynamic behaviour of the system decays onto a final steady state motion which may be modelled by a low order system of equations. In this way any resulting instability will adequately be described, qualitatively at least, by the low order bifurcation classified in part II. In part III the application of the geometrical theory of dynamical systems is used to study the wave driven motions of specified compliant offshore facilities with real data provided from structures currently in use in the offshore industry. In particular predictions are sought of any incipient jumps to resonance of the systems which might lead to potentially dangerous loads in the mooring lines or excessive displacements. Throughout the dynamics work stable steady state paths are closely followed and monitored so that any resulting bifurcation, including the possibility of chaotic behaviour, can be analysed with a view to its subsequent prediction

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Modeling the interplay of mechanics and self-assembly in the actin cytoskeleton

Many cellular processes such as cell migration or division require a trade-off between structural integrity and dynamic reorganization of the load-bearing elements. The actin cytoskeleton has evolved to provide this function for animal cells, but a physical understanding of the interplay between its mechanics and self-assembly is missing. Here I model theoretically two paradigmatic situations of this kind. First, I consider the self-assembly of non-muscle myosin II minifilaments, with a special focus on the stochastic effects that arise due to the small system size of around 30 load bearing elements that turn-over simultaneously to producing contractile force. The self-assembly model follows a consensus architecture, thereby relating the geometrical neighborhood relations of the myosin II monomers with associated binding energies. I find that the turn-over of monomers depends on the mechanochemistry of the cross-bridge cycle by simulating the associated master equation explicitly and by a mean-field approach that maps the complex assembly structure to a simple monomer-addition scheme. Using a rheological framework, I characterize the distinct mechanical properties of non-muscle myosin II minifilaments that arise due to differences in the cross-bridge cycle of the different myosin II isoforms, that can co-assemble in one hetero-filament. Quantitative analysis of the frequency dependent response by a complex modulus, reveals a cross over from viscous to elastic behavior as the ratio of slow to fast isoforms working together is increased. Second I consider the dynamical stability of a peripheral stress fiber, that depends on the interplay of contraction by myosin II minifilaments, self-assembly of new actin filaments at both ends of the fiber and cortical tension. In collaboration with an experimental group, we could show how the myosin II isoform content is differentially reflected by the phenotype of peripheral stress fibers and show their position in a stability phase diagram of the stress fiber. These results demonstrate quantitatively how mechanics and self-assembly interact on different scales in the actin cytoskeleton

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

The Statistical Mechanics Approach to Protein Sequence Data: Beyond Contact Prediction

The recent application of models from inverse statistical mechanics to protein sequence data in has been a large success. In my thesis, I will build upon these models but also use them beyond their original aim of residue contact prediction. This includes the improvement of contact prediction itself by extending the models, the application of the methods in the wider scope of protein interaction networks and the prediction of further biological characteristics from the extracted information