An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDE

We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a \emph{convection dominated} Dirichlet boundary control problem. Dirichlet boundary control problems and convection dominated problems are each very challenging numerically due to solutions with low regularity and sharp layers, respectively. Although there are some numerical analysis works in the literature on \emph{diffusion dominated} convection diffusion Dirichlet boundary control problems, we are not aware of any existing numerical analysis works for convection dominated boundary control problems. Moreover, the existing numerical analysis techniques for convection dominated PDEs are not directly applicable for the Dirichlet boundary control problem because of the low regularity solutions. In this work, we obtain an optimal a priori error estimate for the control under some conditions on the domain and the desired state. We also present some numerical experiments to illustrate the performance of the HDG method for convection dominated Dirichlet boundary control problems

Guidelines for delineation of lymphatic clinical target volumes for high conformal radiotherapy: head and neck region

The success of radiotherapy depends on the accurate delineation of the clinical target volume. The delineation of the lymph node regions has most impact, especially for tumors in the head and neck region. The purpose of this article was the development an atlas for the delineation of the clinical target volume for patients, who should receive radiotherapy for a tumor of the head and neck region. Literature was reviewed for localisations of the adjacent lymph node regions and their lymph drain in dependence of the tumor entity. On this basis the lymph node regions were contoured on transversal CT slices. The probability for involvement was reviewed and a recommendation for the delineation of the CTV was generated

Multiblock copolymer synthesis via controlled radical polymerization in aqueous dispersions. Part 1: Synthesis of S-tert-alkyl-N,N-alkoxycarbonylalkyldithiorcarbamates

In a novel two- or three-step synthetic route, S-(1,4-phenylenebis(propane-2,2-diyl)) bis(N-methyldithiocarbamate) is reacted at low temperature with various alkyl chloroformates to form various S-tert-alkyl-N,N-alkoxycarbonylmethyl-dithiocarbamate RAFT agents. Also an alternative and novel synthetic route towards S-(1,4-phenylenebis(propane-2,2-diyl)) bis(N-methyldithiocarbamate), is proposed

High-pressure living free-radical polymerization of styrene in the presence of RAFT

Reversible addition-fragmentation chain transfer (RAFT) polymerization of styrene was studied at high pressure, employing two dithioester RAFT agents with an isopropylcyano (5) and a cumyl (6) leaving group, respectively. The high-pressure reaction resulted in low polydispersity polymer. It was found that controlled polymerizations can be performed at increased pressures with a high degree of monomer conversion, which signifies that high-pressure polymerizations can be utilized for the production of higher molecular weight polystyrene of controlled microstructure. Retardation of styrene polymerization was also observed at high pressure in the presence of RAFT agents (5) and (6). It is postulated that the retarding potential of these two RAFT agents is associated with an intermediate radical termination mechanism. High-pressure free-radical polymerizations open the way to producing living polymers with high rates, and thus lower impurities such as 'dead' polymer that are formed through bimolecular termination reactions

Multiblock copolymers synthesized in aqueous dispersions using multifunctional RAFT agents

Triblock copolymers were synthesized in aqueous dispersions in two polymerization steps using a low molar mass difunctional dithiocarbamate-based RAFT agent, and in merely one polymerization step using a macromolecular difunctional dithiocarbamate-based RAFT agent. Segmented block copolymers containing several alternating blocks of different polarities were synthesized in miniemulsion in merely two polymerization steps by applying multifunctional, dithiocarbamate-based RAFT agents. All polymerizations showed a linear increase of with monomer conversion. Evidence that this novel synthetic concept resulted in the formation of (multi)block copolymers was obtained by combining normal gel permeation chromatography with gradient polymer elution chromatography

Multiblock copolymers synthesized by miniemulsion polymerization using multifunctional RAFT agents

Communication to the Editor - No Abstrac