Broad boron sheets and boron nanotubes: An ab initio study of structural, electronic, and mechanical properties

Based on a numerical ab initio study, we discuss a structure model for a broad boron sheet, which is the analog of a single graphite sheet, and the precursor of boron nanotubes. The sheet has linear chains of sp hybridized sigma bonds lying only along its armchair direction, a high stiffness, and anisotropic bonds properties. The puckering of the sheet is explained as a mechanism to stabilize the sp sigma bonds. The anisotropic bond properties of the boron sheet lead to a two-dimensional reference lattice structure, which is rectangular rather than triangular. As a consequence the chiral angles of related boron nanotubes range from 0 to 90 degrees. Given the electronic properties of the boron sheets, we demonstrate that all of the related boron nanotubes are metallic, irrespective of their radius and chiral angle, and we also postulate the existence of helical currents in ideal chiral nanotubes. Furthermore, we show that the strain energy of boron nanotubes will depend on their radii, as well as on their chiral angles. This is a rather unique property among nanotubular systems, and it could be the basis of a different type of structure control within nanotechnology.Comment: 16 pages, 17 figures, 2 tables, Versions: v1=preview, v2=first final, v3=minor corrections, v4=document slightly reworke

The formation of paranodal spirals at the ends of CNS myelin sheaths requires the planar polarity protein Vangl2

During axonal ensheathment, noncompact myelin channels formed at lateral edges of the myelinating process become arranged into tight paranodal spirals that resemble loops when cut in cross section. These adhere to the axon, concentrating voltage-dependent sodium channels at nodes of Ranvier and patterning the surrounding axon into distinct molecular domains. The signals responsible for forming and maintaining the complex structure of paranodal myelin are poorly understood. Here, we test the hypothesis that the planar cell polarity determinant Vangl2 organizes paranodal myelin. We show that Vangl2 is concentrated at paranodes and that, following conditional knockout of Vangl2 in oligodendrocytes, the paranodal spiral loosens, accompanied by disruption to the microtubule cytoskeleton and mislocalization of autotypic adhesion molecules between loops within the spiral. Adhesion of the spiral to the axon is unaffected. This results in disruptions to axonal patterning at nodes of Ranvier, paranodal axon diameter and conduction velocity. When taken together with our previous work showing that loss of the apico-basal polarity protein Scribble has the opposite phenotype—loss of axonal adhesion but no effect on loop–loop autotypic adhesion—our results identify a novel mechanism by which polarity proteins control the shape of nodes of Ranvier and regulate conduction in the CNS

Cometary Escape in the Restricted Circular Planar Three Body Problem

The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. This principle is utilized along with Aubry-Mather theory to construct regions of instability for a certain three body problem, given by a Hamiltonian system of two degrees of freedom. In principle, these methods can be applied to construct instability regions for a variety of Hamiltonian systems with $2$ degrees of freedom. The Hamiltonian model considered in this thesis describes the dynamics of a Sun-Jupiter-Comet system and under some simplifying assumptions, the existence of instabilities for the orbit of the comet is shown. In particular it is shown that a comet which starts close to an orbit in the shape of an ellipse of eccentricity $e=0.66$ can increase in eccentricity to beyond $e=1$. Furthermore, there exist ejection orbits for the comet. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity. Several new theoretical tools are introduced in this thesis as well. The most notable is a checkable sufficient condition to verify that an exact area preserving map is an exact area preserving twist map in a certain coordinate system. This coordinate system is constructed by ``spreading the cumulative twist'' which arises from the long term dynamics of system. Many of the results of the thesis are `computer assisted' and utilize recent advances in rigorous numerical integration. It is through the application of these advances in computing that it has become possible to state deep results for realistic solar systems. This has been the dream of many since humans first observed the stars so long ago

Self-assembly of Nanoparticles on Fluid and Elastic Membranes

This dissertation presents studies on self-assembly of nanoparticles adsorbed onto fluid and elastic membranes. It focuses on particles that are at least one order of magnitude larger than the surface thickness, in which case all chemical details of the surface can be ignored in favor of a coarse-grained representation, and the collective behavior of many particles can be analyzed. We use Monte Carlo and molecular dynamics simulations to study the phase behavior of these systems, and its dependence on the mechanical and geometrical properties of the surface, the strength of the particle-surface interaction and the size and the concentration of the nanoparticles. We present scaling laws and accurate free-enegy calculations to understand the occurrence of the phases of interest, and discuss the implications of our results. Chapters 3 and 4 deal with fluid membranes. We show how fluid membranes can mediate linear aggregation of spherical nanoparticles binding to them for a wide range of biologically relevant bending rigidities. This result is in net contrast with the isotropic aggregation of nanoparticles on fluid interfaces or the expected clustering of isotropic insertions in biological membranes. We find that the key to understanding the stability of linear aggregates resides in the interplay between bending and binding energies of the nanoparticles. Furthermore, we demonstrate how linear aggregation can lead to membrane tubulation and determine how tube formation compares with the competing budding process. The development of tubular structures requires less adhesion energy than budding, pointing to a potentially unexplored route of viral infection and nanoparticle internalization in cells. In Chapters 5 - 8, we shift focus to elastic membranes and study self-assembly of nanoparticles mediated by elastic surfaces of different geometries, namely planar, cylindrical and spherical. Again, a variety of linear aggregates are obtained, but their spatial organization can be controlled by changing the stretching rigidity of the elastic membrane, the strength of the particle adhesion, the curvature of the surface, as well as by introducing surface defects. Furthermore, we show how a fully flexible filament binding to a cylindrical elastic membrane may acquire a macroscopic persistence length and a helical conformation. We find that the filaments helical pitch is completely determined by the mechanical properties of the surface, and can be easiliy tuned. Moreover, we study the collapse of unstretchable (thin) hollow nanotube due to the collective behavior of nanoparticles assembling on its surface, resulting in an ordered nanoparticle engulfment inside the collapsed structure. Our hope is that the results presented in this Dissertation will stimulate further experimental studies of the mechanical properties of fluid and cross-linked membranes, in particular the long range correlations arising due to the particle binding