Existence theorem for solitary waves on lattices

In this article we give an existence theorem for localized travelling wave solutions on one-dimensional lattices with Hamiltonian $$H = \sum\limits_{n \in \mathbb{Z}} {\left( {\tfrac{1}{2}p_n^2 + V(q_{n + 1} - q_n )} \right)} ,$$ whereV(·) is the potential energy due to nearest-neighbour interactions. Until now, apart from rare integrable lattices like the Toda latticeV(φ)=ab ^?1(e ^?bφ+bφ?1), the only evidence for existence of such solutions has been numerical. Our result in particular recovers existence of solitary waves in the Toda lattice, establishes for the first time existence of solitary waves in the (nonintegrable) cubic and quartic latticesV(φ)= 1/2φ ² + 1/3aφ ³,V(φ) = 1/2φ ² + 1/4bφ ⁴, thereby confirming the numerical findings in [1] and shedding new light on the recurrence phenomena in these systems observed first by Fermi, Pasta and Ulam [2], and shows that contrary to widespread belief, the presence of exact solitary waves is not a peculiarity of integrable systems, but “generic” in this class of nonlinear lattices. The approach presented here is new and quite general, and should also be applicable to other forms of lattice equations: the travelling waves are sought as minimisers of a naturally associated variational problem (obtained via Hamilton's principle), and existence of minimisers is then established using modern methods in the calculus of variations (the concentration-compactness principle of P.-L. Lions [3]).     

Dearomatising rearrangements of lithiated thiophenecarboxamides

Thiophene-3-carboxamides bearing allyl or benzyl substituents at nitrogen undergo dearomatising cyclisation on treatment with LDA. Rearrangements transform the dearomatised products into pyrrolinones, azepinones or partially saturated azepinothiophenes.     

Sulfoxides as ‘traceless’ resolving agents for the synthesis of atropisomers by dynamic or classical resolution

Reacting (−)-menthyl sulfinate with an atropisomeric but racemic aryllithium gives two atropdiastereoisomeric sulfoxides. Separation (by chromatography or crystallisation) and sulfoxide-lithium exchange of each diastereoisomer regenerates the aryllithium in enantiomerically pure form which can be quenched with a range of electrophiles with retention of stereochemical integrity. Overall the reaction sequence is a resolution but without the need for an acidic or basic substituent—a ‘traceless’ method. In certain instances, for example when the nucleophile is an ortholithiated peri-substituted 1-naphthamide, the diastereoisomeric sulfoxides may be interconverted thermally. This allows a dynamic resolution, under thermodynamic control, and hence in principle can give yields of the final products of greater than 50%. The utility of the method is demonstrated by the synthesis of a known atropisomeric phosphine ligand.     

Synthesis, crystal structure, and nonlinear optical behavior of beta-unsubstituted meso-meso E-vinylene-linked porphyrin dimers

[structure: see text] A vinylene-linked porphyrin dimer, with no substituents at the beta-positions, has been synthesized by CuI/CsF promoted Stille coupling. In the crystal structure of this dimer, the C(2)H(2) bridge is twisted by 45 degrees relative to the plane of the porphyrins. The absorption, emission spectra, and electrochemistry reveal substantial porphyrin-porphyrin pi-conjugation. The triplet excited-state absorption spectrum of this dimer makes it suitable for reverse saturable absorption at 710-900 nm.     

Binding Aedes aegypti densonucleosis virus to ion exchange membranes

Experimental and numerical results for binding Aedes aegypti densonucleosis virus (AeDNV) using anion and cation exchange membranes are presented. AeDNV particles are adsorbed by anion and cation exchange membranes providing the virus particles and membranes are oppositely charged. Q membranes which are strongly basic anion exchangers were the most effective. Dynamic and static capacities for Q membranes were found to be similar. A numerical model is proposed which assumes a log normal pore size distribution. By estimating the required parameters from static binding experiments, the model may be used to calculate the breakthrough curve for virus adsorption.     

Methyl, hydrochalcogenido, and phenylchalcogenolate complexes of zinc in a sulfur rich coordination environment: syntheses and structural characterization of the tris(2-mercapto-1-tert-butylimidazolyl)hydroboratozinc complexes [TmBut]ZnMe, [TmBut]ZnEH (E = S, Se) and [TmBut]ZnEPh (E = O, S, Se, Te)

A series of hydrochalcogenido and phenylchalcogenolate complexes of zinc supported by tris(2-mercapto-1-tert-butylimidazolyl)hydroborato ligation, [Tm(Bu(t))]ZnEH (E = S, Se) and [Tm(Bu(t))]ZnEPh (E = O, S, Se, Te) have been synthesized from [Tm(Bu(t))]ZnMe; structural characterization by X-ray diffraction indicates that the variation in Zn-E bonding as a function of the chalcogen is significantly different from that in other series of metal-chalcogenolate compounds.     

Lattice models of peptide aggregation: evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.     

First total synthesis of the 7,3'-linked naphthylisoquinoline alkaloid ancistrocladidine

[structure: see text] The first total synthesis of the rare 7,3'-linked naphthylisoquinoline alkaloid, ancistrocladidine, has been completed. The key feature of the synthesis is the formation of the extremely hindered biaryl linkage by Pinhey-Barton ortho-arylation of a naphthol with an aryllead triacetate. The biaryl aldehyde formed is elaborated in 10 steps to form a 1:1 mixture of ancistrocladidine and its atropisomer. Recrystallization of the mixture afforded ancistrocladidine, which was identical in all respects to the reported data.