A transfer map for singular fibrations

Using a new group of singular chains on polyhedra, a transfer map is defined on the chain level for fibrations with singularities. These include usual transfer on homology as well as Oliver transfer and other cases.     

Combinatorial criteria for uniqueness of Gibbs measures

We generalize previously known conditions for uniqueness of the Gibbs measure in statistical physics models by presenting conditions of any finite size for models on any underlying graph. We give two dual conditions, one requiring that the total influence on a site is small, and the other that the total influence of a site is small. Our proofs are combinatorial in nature and use tools from the analysis of discrete Markov chains, in particular the path coupling method. The implications of our conditions for the mixing time of natural Markov chains associated with the models are discussed as well. We also present some examples of models for which the conditions hold. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005     

Layer-by-Layer electrostatic self-assembly of polyelectrolyte nanoshells on individual carbon nanotube templates

Carbon nanotubes have been featured prominently in the nanotechnology research for some time, yet robust strategies for noncovalent chemical modification of the nanotube surface are still missing. Such strategies are essential for the creation of functional device architectures. Here, we present a new general procedure for carbon nanotube modification based on polyelectrolyte layer-by-layer assembly. We have built multilayer structures around individual carbon nanotube bridges by first modifying the nanotube surface with a pyrene derivative followed by layer-by-layer deposition of polyelectrolyte macroions on the nanotube. Transmission electron microscopy and scanning confocal fluorescence microscopy images confirm the formation of nanometer-thick amorphous polymer nanoshells around the nanotubes. These multilayer polyelectrolyte shells on individual carbon nanotubes introduce nearly unlimited opportunities for the incorporation of various functionalities into nanotube devices, which, in turn, opens up the possibility of building more complex multicomponent structures.     

Fine Tuning of Chlorophyll Spectra by Protein‐Induced Ring Deformation

The ability to tune the light‐absorption properties of chlorophylls by their protein environment is the key to the robustness and high efficiency of photosynthetic light‐harvesting proteins. Unfortunately, the intricacy of the natural complexes makes it very difficult to identify and isolate specific protein–pigment interactions that underlie the spectral‐tuning mechanisms. Herein we identify and demonstrate the tuning mechanism of chlorophyll spectra in type II water‐soluble chlorophyll binding proteins from Brassicaceae (WSCPs). By comparing the molecular structures of two natural WSCPs we correlate a shift in the chlorophyll red absorption band with deformation of its tetrapyrrole macrocycle that is induced by changing the position of a nearby tryptophan residue. We show by a set of reciprocal point mutations that this change accounts for up to 2/3 of the observed spectral shift between the two natural variants.     

Entropic barriers in nanoscale adhesion studied by variable temperature chemical force microscopy

Intermolecular interactions drive the vast majority of condensed phase phenomena from molecular recognition to protein folding to particle adhesion. Complex energy barriers encountered in these interactions include contributions from van der Waals forces, hydrogen bonding, and solvent medium. With the spectacular exception of hydrophobic interactions, contributions from the medium are usually considered secondary. We report a variable temperature force microscopy study of the interactions between several hydrogen bonds in different solvents that challenges this point of view. Surprisingly, we observed an increase in the strength of the interaction between carboxylic acid groups in ethanol as the temperature increased. Moreover, when we switched to a nonpolar solvent we observed the opposite behavior: The binding force decreased as the temperature increased. Kinetic model of bond dissociation provided quantitative interpretation of our measurements. We attributed the observed phenomena to a large entropic contribution from the ordered solvent layers that are forming on the probe and sample surfaces upon detachment. The observed reversal in the force vs temperature trend is a manifestation of a transition between thermodynamic and kinetic regimes of unbinding predicted by the model. Our results indicate that entropic barriers dominated by the interactions of solvent molecules with the surface exist in a much wider variety of systems than previously thought.     

Use of metallic and dielectric films for hollow fibers

The problem of transmission of CO₂ laser radiation through hollow fibers and waveguides was studied theoretically and confirmed experimentally. The transmission of the laser radiation through metal and metal-dielectric tubes was measured and compared with the theoretical data based on a ray model solution. This makes possible the investigation of the transmission of the CO₂ radiation through waveguides when the internal wall is covered with a metal or a metal- dielectric film. It was shown theoretically and proved experimentally that the transmission of the CO₂ radiation is possible even through bent waveguides.     

Lower bounds on the number of crossing-free subgraphs of KN

We improve previous lower bounds on the number of simple polygonizations, and other kinds of crossing-free subgraphs, of a set of N points in the plane by analyzing a suitable configuration. We also prove that the number of crossing-free perfect matchings and spanning trees is minimum when the points are in convex position.