Graphs with Branchwidth at Most Three

In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph as a minor. A set of four graphs is shown to be the obstruction set for the class of graphs with branchwidth at most three. Moreover, we give a safe and complete set of reduction rules for the graphs with branchwidth at most three. Using this set, a linear time algorithm is given that verifies if a given graph has branchwidth at most three, and, if so, outputs a minimum width branch decomposition.     

A simple and effective method for phosphoryl transfer using TiCl(4) catalysis

[reaction: see text] A number of Lewis acids have been evaluated as catalysts for the phosphoryl transfer, the most efficient being TiCl(4). Application of this methodology to the phosphorylation of a number of representative target alcohols is presented     

Nonlocal dynamics of spontaneous imbibition fronts

We have studied spontaneous imbibition fronts generated by capillary rise between two roughened glass plates, the separation d of which varied between 10 and 50 microm. Perfect agreement with Washburn's law was obtained. We have determined the roughness exponent chi of the fronts, and found chi=0.81+/-0.01 for small length scales. Above a certain crossover length xi, it reached chi=0.58+/-0.04, as predicted by the quenched noise Kardar-Parisi-Zhang equation. The crossover length is found to scale with the plate separation as sqrt[d], as predicted by recent models which properly include nonlocal dynamics effects on the front. We believe this to be the first clear identification of crossover from nonlocal to local dynamics.     

Collision-induced absorption in non-polar molecular liquids: Tetrahedral molecules

The far infrared absorption spectra of liquid CH₄, CF₄ and CCl₄ were measured in the range between 15 and 200 cm^?1 The octupole induced dicole moment correlation functions of these liquids and of liquid CBr₄, which was recalculated from literature data, were compared to the corresponding theoretical correlation functions obtained by molecular dynamics simulation and by analytical theory. At short times(0.05 ps in CH₄ and 0.2 ps in CCl₄) the experimental correlation function follows the model reorientational correlation functions. At longer times this is no more the case and the dynamics coherence observed is qualitatively interpreted in terms of a structural correlation in the liquids.     

Irreversibility and polymer adsorption

Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the resultant nonequilibrium layers. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) approximately f(-4/5), in rather close agreement with strong physisorption experiments [H. M. Schneider, Langmuir 12, 994 (1996)]].     

The ultrasensitivity of living polymers

Synthetic and biological living polymers are self-assembling chains whose chain length distributions (CLDs) are dynamic. We show these dynamics are ultrasensitive: Even a small perturbation (e.g., temperature jump) nonlinearly distorts the CLD, eliminating or massively augmenting short chains. The origin is fast relaxation of mass variables (mean chain length, monomer concentration) which perturbs CLD shape variables before these can relax via slow chain growth rate fluctuations. Viscosity relaxation predictions agree with experiments on the best-studied synthetic system, alpha-methylstyrene.     

Performance of Thyme Oil@Na-Montmorillonite and Thyme Oil@Organo-Modified Montmorillonite Nanostructures on the Development of Melt-Extruded Poly-L-lactic Acid Antioxidant Active Packaging Films

Today, the use of natural biodegradable materials in the production processes is more and more adopted by industry to achieve cyclic economy targets and to improve environmental and human health indexes. Active packaging is the latest trend for food preservation. In this work, nanostructures were prepared by incorporation of thyme oil with natural natrium-montmorillonite and organo-montmorillonite with two different techniques, direct impregnation and the green evaporation–adsorption process. Such nanostructures were mixed with poly-L-lactic-acid for the first time via an extrusion molding process to develop a new packaging film. Comparisons of morphological, mechanical, and other basic properties for food packaging were carried out via XRD, FTIR, TG, SEM/EDS, oxygen and water vapor permeation, and antimicrobial and antioxidant activity for the first time. Results showed that poly-L-lactic-acid could be modified with clays and essential oils to produce improved active packaging films. The final product exhibits food odor prevention characteristics and shelf-life extension capabilities, and it could be used for active packaging. The films based on OrgMt clay seems to be more promising, while the thyme oil addition improves their behavior as active packaging. The PLLA/3%TO@OrgMt and PLLA/5%TO@OrgMt films were qualified between the tested samples as the most promising materials for this purpose.