A conformal mapping algorithm for the Bernoulli free boundary value problem

We propose a new numerical method for the solution of the Bernoulli free boundary value problem for harmonic functions in a doubly connected domain D in where an unknown free boundary Γ₀ is determined by prescribed Cauchy data on Γ₀ in addition to a Dirichlet condition on the known boundary Γ₁. Our main idea is to involve the conformal mapping method as proposed and analyzed by Akduman, Haddar, and Kress for the solution of a related inverse boundary value problem. For this, we interpret the free boundary Γ₀ as the unknown boundary in the inverse problem to construct Γ₀ from the Dirichlet condition on Γ₀ and Cauchy data on the known boundary Γ₁. Our method for the Bernoulli problem iterates on the missing normal derivative on Γ₁ by alternating between the application of the conformal mapping method for the inverse problem and solving a mixed Dirichlet–Neumann boundary value problem in D. We present the mathematical foundations of our algorithm and prove a convergence result. Some numerical examples will serve as proof of concept of our approach. Copyright © 2015 John Wiley & Sons, Ltd.     

A mechanism for the decomposition of dinitropropyl compounds

A decomposition mechanism is proposed for 2,2-dinitro-1-methoxypropane, a compound whose structure resembles the nitroplasticizer (NP) component of plastic-bonded explosive PBX 9501. A library of key reactions is presented and is based on the results of NP aging studies and existing decomposition mechanisms for similar nitro compounds. Density functional electronic structure calculations on these reactions were used to develop a decomposition mechanism at lower temperatures, which begins with HONO elimination and leads to intermediates that can produce CO, CO(2), NO, and N(2)O gases. These gases were observed in low temperature (48 to 64 degrees C) aging studies of NP. A high temperature mechanism involving NO(2) scission is compared to a thermal decomposition mechanism determined by simultaneous thermogravimetric modulated beam mass spectrometry. The calculated energy barriers for HONO elimination and NO(2) scission in the gas phase are reported and compared to experimental results.     

A New Algorithm in Electromagnetic Inverse Scattering Theory with an Application to Medical Imaging

We consider the electromagnetic inverse scattering problem of determining the index of refraction of an isotropic inhomogeneous medium from a knowledge of the total electric near field data. We consider both the case of scattering by an infinite inhomogeneous cylinder and a bounded inhomogeneous region in space. We conclude by giving an application of our method to the problem of imaging leukemia in the upper leg by means of microwaves. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.     

Sparse convolution quadrature for time domain boundary integral formulations of the wave equation

S. A. Sauter Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ^{Many important physical applications are governed by the waveequation. The formulation as time domain boundary integral equationsinvolves retarded potentials. For the numerical solution ofthis problem, we employ the convolution quadrature method forthe discretization in time and the Galerkin boundary elementmethod for the space discretization. We introduce a simple apriori cut-off strategy where small entries of the system matricesare replaced by zero. The threshold for the cut-off is determinedby an a priori analysis which will be developed in this paper.This analysis will also allow to estimate the effect of additionalperturbations such as panel clustering and numerical integrationon the overall discretization error. This method reduces thestorage complexity for time domain integral equations from O(M2N)to O(M2N logM), where N denotes the number of time steps andM is the dimension of the boundary element space.}     

Fries rearrangement of aryl formates: a mechanistic study by means of 1H, 2H, and 11B NMR spectroscopy and DFT calculations

1H, 2H, and 11B NMR spectroscopy has been used to study the mechanism of the Fries rearrangement of aryl formates promoted by boron trichloride by monitoring both the substrate and the Lewis acid. DFT calculations were employed to investigate the energetics of several reaction paths and to calculate NMR chemical shifts of key intermediates and products. After the formation of a 1:1 substrate-Lewis acid adduct, the rearrangement proceeds in two steps, beginning with the cleavage of the ester bond and the release of formyl chloride in situ, which, in turn, acts as a formylating agent, introducing an aldehydic functionality into the aromatic ring. The high regioselectivity (only the ortho product is obtained) is also accounted for by the proposed intermolecular, Lewis acid-assisted mechanism.     

Phase behavior and mesophase structures of 1,3,5-benzene- and 1,3,5-cyclohexanetricarboxamides: towards an understanding of the losing order at the transition into the isotropic phase

One of the simplest and most-versatile motifs in supramolecular chemistry is based on 1,3,5-benzenetricarboxamides. Variation of the core structure and subtle changes in the structures of the lateral substituents govern the self-assembly and determine the phase behavior. Herein, we provide a comprehensive comparison between the phase behavior and mesophase structure of a series of 1,3,5-benzene- and 1,3,5-cyclohexanetricarboxamides that contain linear and branched alkyl substituents. Depending on the substituent, different crystalline, plastic crystalline, and liquid crystalline phases were formed. The relatively rare columnar nematic (N(C)) phase was only observed in cyclohexane-based trisamides that contained linear alkyl substituents. Of fundamental interest in liquid crystalline supramolecular systems is the transition from the mesomorphic state into the isotropic state and, in particular, the question of how the order decreases. Temperature-dependent IR spectroscopy and XRD measurements revealed that columnar H-bonded aggregates were still present in the isotropic phase. At the clearing transition, mainly the lateral order was lost, whilst shorter columnar aggregates still remained. A thorough understanding of the phase behavior and the mesophase structure is relevant for selecting processing conditions that use supramolecular structures in devices or as fibrillar nanomaterials.     

Phase Behavior and Mesophase Structures of 1,3,5‐Benzene‐ and 1,3,5‐Cyclohexanetricarboxamides: Towards an Understanding of the Losing Order at the Transition into the Isotropic Phase

One of the simplest and most‐versatile motifs in supramolecular chemistry is based on 1,3,5‐benzenetricarboxamides. Variation of the core structure and subtle changes in the structures of the lateral substituents govern the self‐assembly and determine the phase behavior. Herein, we provide a comprehensive comparison between the phase behavior and mesophase structure of a series of 1,3,5‐benzene‐ and 1,3,5‐cyclohexanetricarboxamides that contain linear and branched alkyl substituents. Depending on the substituent, different crystalline, plastic crystalline, and liquid crystalline phases were formed. The relatively rare columnar nematic (N_C) phase was only observed in cyclohexane‐based trisamides that contained linear alkyl substituents. Of fundamental interest in liquid crystalline supramolecular systems is the transition from the mesomorphic state into the isotropic state and, in particular, the question of how the order decreases. Temperature‐dependent IR spectroscopy and XRD measurements revealed that columnar H‐bonded aggregates were still present in the isotropic phase. At the clearing transition, mainly the lateral order was lost, whilst shorter columnar aggregates still remained. A thorough understanding of the phase behavior and the mesophase structure is relevant for selecting processing conditions that use supramolecular structures in devices or as fibrillar nanomaterials.     

Synthesis of electronically modified Ru-based neutral 16 VE allenylidene olefin metathesis precatalysts

Electronic modifications within Ru-based olefin metathesis precatalysts have provided a number of new complexes with significant differences in reactivity profiles. So far, this aspect has not been studied for neutral 16 VE allenylidenes. The first synthesis of electronically altered complexes of this type is reported. Following the classical dehydration approach (vide infra) modified propargyl alcohols were transformed to the targeted allenylidene systems in the presence of PCy?. The catalytic performance was investigated in RCM reaction (ring closing metathesis) of benchmark substrates such as diallyltosylamide and diethyl diallylmalonate.     

Efficient strategies for transporting mobile forces

During a military operation, it may be necessary to move military units quickly and efficiently from one zone at the theatre of operations to another one. This need is prevalent in particular at the earlier stages of an operation when combat units are accumulating at the theatre of operations. Such mobility missions are carried out by specially designed semi-trailers, called transporters, that carry the armoured fighting vehicles (AFVs) of the military unit. In many cases the number of available transporters is smaller than the number of AFVs that are to be carried, thus several tours of the transporters may be needed to transport the entire unit to its destination. In this paper we examine three generic transportation strategies that may apply to such mobility missions: fixed unloading point, variable unloading point and a flexible strategy in which both loading and unloading points may vary from one tour to another. The efficiency of each specific transportation plan, within a given generic strategy, is evaluated with respect to the criterion of minimum accumulation time.