Non-Markovian thermalisation of a two-level atom

We consider thermalisation and spontaneous decay of a two-level atom beyond the Markovian approximation. While the standard elimination of the continuum of radiation modes results in exponential decay represented by a Lindblad equation of motion, we use a simple toy model that takes into account the finite relaxation rate of the environment and present an exact non-Markovian master equation of the Nakajima-Zwanzig form. Because the exact derivation of non-Markovian equations has proved very difficult for all more realistic (and hence much more complicated) models, we analyze the master equation obtained and also discuss difficulties that are likely to arise with non-Markovian evolution operators.     

A fast direct solver for elliptic problems with a divergence constraint

A fast direct solution method for a discretized vector‐valued elliptic partial differential equation with a divergence constraint is considered. Such problems are typical in many disciplines such as fluid dynamics, elasticity and electromagnetics. The method requires the problem to be posed in a rectangle and boundary conditions to be either periodic boundary conditions or the so‐called slip boundary conditions in one co‐ordinate direction. The arising saddle‐point matrix has a separable form when bilinear finite elements are used in the discretization. Based on a result for so‐called p‐circulant matrices, the saddle‐point matrix can be transformed into a block‐diagonal form by fast Fourier transformations. Thus, the fast direct solver has the same structure as methods for scalar‐valued problems which are based on Fourier analysis and, therefore, it has the same computational cost ??(N log N). Numerical experiments demonstrate the good efficiency and accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Toward the enantioselective total synthesis of lyngbyatoxin A: on the stereocontrolled introduction of the quaternary stereogenic centre

This paper deals with an approach to the enantioselective total synthesis of Lyngbyatoxin A, with focus on the stereocontrolled introduction of the quaternary stereogenic centre. The key step in the synthesis involves an enantiospecific Lewis-acid mediated rearrangement of chiral vinyl epoxides carrying a 7-substituted indole moiety.     

Nanoporous Network Channels from Self‐Assembled Triblock Copolymer Supramolecules

Supramolecular complexes of a poly(tert‐butoxystyrene)‐block‐polystyrene‐block‐poly(4‐vinylpyridine) triblock copolymers and less than stoichiometric amounts of pentadecylphenol (PDP) are shown to self‐assemble into a core–shell gyroid morphology with the core channels formed by the hydrogen‐bonded P4VP(PDP)complexes. After structure formation, PDP was removed using a simple washing procedure, resulting in well‐ordered nanoporous films that were used as templates for nickel plating.

     

Thermoluminescence study of persistent luminescence materials: Eu2+- and R3+-doped calcium aluminates, CaAl2O4:Eu2+,R3+

Thermoluminescence properties of the Eu2+-, R3+-doped calcium aluminate materials, CaAl2O4:Eu2+,R3+, were studied above room temperature. The trap depths were estimated with the aid of the preheating and initial rise methods. The seemingly simple glow curve of CaAl2O4:Eu2+ peaking at ca. 80 degrees C was found to correspond to several traps. The Nd3+ and Tm3+ ions, which enhance most the intensity of the high-temperature TL peaks, form the most suitable traps for intense and long-lasting persistent luminescence, too. The location of the 4f and 5d ground levels of the R3+ and R2+ ions were deduced in relation to the band structure of CaAl2O4. No clear correlation was found between the trap depths and the R3+ or R2+ level locations. The traps may thus involve more complex mechanisms than the simple charge transfer to (or from) the R3+ ions. A new persistent luminescence mechanism presented is based on the photoionization of the electrons from Eu2+ to the conduction band followed by the electron trapping to an oxygen vacancy, which is aggregated with a calcium vacancy and a R3+ ion. The migration of the electron from one trap to another and also to the aggregated R3+ ion forming R2+ (or R3+-e-) is then occurring. The reverse process of a release of the electron from traps to Eu2+ will produce the persistent luminescence. The ability of the R3+ ions to trap electrons is probably based on the different reduction potentials and size of the R3+ ions. Hole trapping to a calcium vacancy and/or the R3+ ion may also occur. The mechanism presented can also explain why Na+, Sm3+, and Yb3+ suppress the persistent luminescence.     

Inverse problems with partial data for a Dirac system: A Carleman estimate approach

We prove that the material parameters in a Dirac system with magnetic and electric potentials are uniquely determined by measurements made on a possibly small subset of the boundary. The proof is based on a combination of Carleman estimates for first and second order systems, and involves a reduction of the boundary measurements to the second order case. For this reduction a certain amount of decoupling is required. To effectively make use of the decoupling, the Carleman estimates are established for coefficients which may become singular in the asymptotic limit.     

Tautomeric populations of the charged species of 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) studied with computer simulations and cluster expansions

Correct net charge and protonation pattern in the polyamine backbone is one of the major factors that define the interactions of this class of compounds. 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) is a isosteric charge deficient analogue of naturally occurring spermine (Spm) with different biological features. The tautomeric populations of each SpmTrien charge state were estimated with computer simulations, molecular dynamics (MD) and quantum mechanical calculations, and cluster expansions separately. In the computer simulations, tautomeric populations of each charge state were obtained by constrained least‐squares fitting the theoretically calculated (GIAO B3LYP/6‐311 + G**) ¹⁵ N NMR chemical shieldings of SpmTrien tautomers to the experimentally measured chemical shifts. Theoretical chemical shieldings were calculated for water complexes of SpmTrien obtained from MD simulations in explicit water. Both methods gave highly similar realistic results. SpmTrien has many major populations of tautomers at biologically relevant charge states of three (+3) and four (+4) thus enabling a large variety of structures for specific ionic interactions. Copyright © 2013 John Wiley & Sons, Ltd.     

Glass‐embedded silver nanoparticle patterns by masked ion‐exchange process for surface‐enhanced Raman scattering

Glass‐embedded silver nanoparticle patterns were fabricated by masked silver–sodium ion‐exchange process followed by etching to reveal the particles for surface‐enhanced Raman scattering (SERS). The intensity of the enhanced Raman signal is comparable to that of the fluorescence, and the detection limit of 1 nM for Rhodamine 6G has been achieved. Raman images at different etching depths and corresponding morphological images are compared to find optimal SERS signal. Our results demonstrate that silver nanoparticle patterns embedded in glass can be used as SERS‐active substrates. Nanoparticles can be formed in a glass of high optical quality and have potential to be integrated with optical waveguides for a sensor chip. Copyright © 2010 John Wiley & Sons, Ltd.