A treatment of shocks in one-dimensional thermomechanical media

Received March 03, 1999     

On the Material Symmetry of Elastic Rods

This paper presents a treatment of material symmetry for hyperelastic rods. The rod theory of interest is based on a Cosserat (or directed) curve with two director fields, and was developed in a series of works by Green, Naghdi and several of their co-workers. The treatment is based on Murdoch and Cohen's work on material symmetry of Cosserat surfaces. Two material symmetry groups are discussed: one pertains to the strain-energy function, while the other pertains to the response functions. The paper closes by showing how the treatment relates to the form-invariant approach used in Green and Naghdi's papers and a treatment proposed recently by Cohen. This revised version was published online in July 2006 with corrections to the Cover Date.     

Characterization of rubber particles and rubber chain elongation in <Emphasis Type="Italic">Taraxacum koksaghyz</Emphasis>

Background  

Natural rubber is a biopolymer with exceptional qualities that cannot be completely replaced using synthetic alternatives. Although several key enzymes in the rubber biosynthetic pathway have been isolated, mainly from plants such as Hevea brasiliensis, Ficus spec. and the desert shrub Parthenium argentatum, there have been no in planta functional studies, e.g. by RNA interference, due to the absence of efficient and reproducible protocols for genetic engineering. In contrast, the Russian dandelion Taraxacum koksaghyz, which has long been considered as a potential alternative source of low-cost natural rubber, has a rapid life cycle and can be genetically transformed using a simple and reliable procedure. However, there is very little molecular data available for either the rubber polymer itself or its biosynthesis in T. koksaghyz.     

Advances in the preparation of porous polymer monoliths in capillaries and microfluidic chips with focus on morphological aspects

Porous polymer monoliths have emerged as unique materials for many applications, including liquid-chromatographic analyses at an unrivaled speed, solid-phase extraction, and enzyme immobilization in capillary and microfluidic chip format. This article reviews the state of the art in the preparation of monoliths in narrow-bore capillaries and microfluidic chips and their miniaturization under conditions of spatial confinement. New developments in their preparation mainly using free radical polymerization techniques with a focus on morphological aspects in view of homogeneous porous materials are described. The suitability of monoliths for analysis of both large and small molecules is also discussed.     

Pd-Catalyzed Difluoromethylations of Aryl Boronic Acids,Halides, and Pseudohalides with ICF2H Generated ex Situ

An expedient ex-situ generation of difluoroiodomethane (DFIM) and its immediate use in a Pd-catalyzed difluoromethylation of aryl boronic acids and ester derivatives in a two-chamber reactor is reported. Heating a solution of bromodifluoroacetic acid with sodium iodide in sulfolane proved to be effective for the generation of near stoichiometric amounts of DFIM for the ensuing catalytic coupling step. A two-step difluoromethylation of aryl (pseudo)halides with tetrahydroxydiboron as a low-cost reducing agent, both promoted by Pd catalysis, proved effective to install this fluorine-containing C₁ group onto several pharmaceutically relevant molecules. Finally, the method proved adaptable to deuterium incorporation by simply adding D₂O to the DFIM-generating chamber.     

Polyphosphazene Based Star‐Branched and Dendritic Molecular Brushes

A new synthetic procedure is described for the preparation of poly(organo)phosphazenes with star‐branched and star dendritic molecular brush type structures, thus describing the first time it has been possible to prepare controlled, highly branched architectures for this type of polymer. Furthermore, as a result of the extremely high‐arm density generated by the phosphazene repeat unit, the second‐generation structures represent quite unique architectures for any type of polymer. Using two relativity straight forward iterative syntheses it is possible to prepare globular highly branched polymers with up to 30 000 functional end groups, while keeping relatively narrow polydispersities (1.2–1.6). Phosphine mediated polymerization of chlorophosphoranimine is first used to prepare three‐arm star polymers. Subsequent substitution with diphenylphosphine moieties gives poly(organo)phosphazenes to function as multifunctional macroinitiators for the growth of a second generation of polyphosphazene arms. Macrosubstitution with Jeffamine oligomers gives a series of large, water soluble branched macromolecules with high‐arm density and hydrodynamic diameters between 10 and 70 nm.

     

The evolution of subcritical Achlioptas processes

In Achlioptas processes, starting from an empty graph, in each step two potential edges are chosen uniformly at random, and using some rule one of them is selected and added to the evolving graph. AlthouSgh the evolution of such ‘local’ modifications of the Erd?s–Rényi random graph process has received considerable attention during the last decade, so far only rather simple rules are well understood. Indeed, the main focus has been on ‘bounded‐size’ rules, where all component sizes larger than some constant B are treated the same way, and for more complex rules very few rigorous results are known. In this paper we study Achlioptas processes given by (unbounded) size rules such as the sum and product rules. Using a variant of the neighbourhood exploration process and branching process arguments, we show that certain key statistics are tightly concentrated at least until the susceptibility (the expected size of the component containing a randomly chosen vertex) diverges. Our convergence result is most likely best possible for certain generalized Achlioptas processes: in the later evolution the number of vertices in small components may not be concentrated. Furthermore, we believe that for a large class of rules the critical time where the susceptibility ‘blows up’ coincides with the percolation threshold. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 174–203, 2015     

The Janson inequalities for general up‐sets

Janson and Janson, ?uczak and Ruciński proved several inequalities for the lower tail of the distribution of the number of events that hold, when all the events are up‐sets (increasing events) of a special form—each event is the intersection of some subset of a single set of independent events (i.e., a principal up‐set). We show that these inequalities in fact hold for arbitrary up‐sets, by modifying existing proofs to use only positive correlation, avoiding the need to assume positive correlation conditioned on one of the events. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 391–395, 2015     

A general hilbert space approach to wavelets and its application in geopotential determination

A general approach to wavelets is presented within a framework of a separable functional Hilbert space H. Basic tool is the construction of H-product kernels by use of Fourier analysis with respect to an orthonormal basis in H. Scaling functions and wavelet are defined in terms of H-product kernels. Wavelts are shown to be ‘building blocks’ that decorrelate the data. A pyramid scheme provides fast computation. Finally, the determination of the earth's gravitational potential from single and multipole expressions is organzied as an example of wavelet approximation in Hilbert space structure.