Precise Coupling Terms in Adiabatic Quantum Evolution

It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems with real-symmetric Hamiltonian we construct such a superadiabatic representation and explicitly determine the asymptotic behavior of the exponentially small coupling term. First order perturbation theory in the superadiabatic representation then allows us to describe the time-development of exponentially small adiabatic transitions. The latter result rigorously confirms the predictions of Sir Michael Berry for our family of Hamiltonians and slightly generalizes a recent mathematical result of George Hagedorn and Alain Joye.submitted 29/06/04, accepted 14/08/04     

cos πρ theorems for δ-subharmonic functions

For ϕ a δ-subharmonic function, sharp results are obtained that connectA(r, ϕ), B(r, ϕ) andT(r, ϕ), whereA(r, ϕ)=inf_|z|=r ϕ(z),B(r, ϕ)=sup_|z|=r ϕ(z), andT(r, ϕ) is the Nevanlinna characteristics.     

2‐Amino‐4‐chloro‐6‐[N‐methyl‐N‐(4‐methylphenyl)amino]pyrimidine: formation versus fragmentation of hydrogen‐bonded chains of edge‐fused R22(8) rings in 4,6‐disubstituted 2‐aminopyrimidines

Molecules of the title compound, C₁₂H₁₃ClN₄, are linked by two independent N—H...N hydrogen bonds into a chain of edge‐fused R₂²(8) rings. The significance of this study lies in its attempt to rationalize the patterns of supramolecular aggregation in the title compound and in a range of analogous 4,6‐disubstituted 2‐aminopyrimidines.     

Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder

This paper presents a numerical study of a two‐dimensional time‐dependent flow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time. In addition, the accuracy of these values obtained with different time stepping schemes and different finite element methods is studied. Copyright © 2004 John Wiley & Sons, Ltd.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Proteins Entrapped in Silica Monoliths Prepared from Glyceroxysilanes

The preparation of discrete polyol based silane precursors derived from glycerol by a simple one-pot process is described. These polyol-based silanes could be hydrolyzed under mild pH conditions and upon gelation resulted in the formation of optically clear, monolithic, mesoporous silica. The hydrolysis and condensation reactions lead to cure rates that are very sensitive to ionic strength, but are almost unaffected by pH in contrast to those of alkoxysilanes derived from primary alcohols such as Si(OEt)₄. Residual glycerol in the silica monolith could be removed by washing, or could be left in the silica to reduce the magnitude of shrinkage during long term storage. The biocompatible glyceroxysilane precursors lead to materials that were able to retain the activity of entrapped enzymes over repeated cycles of use for periods of up to several months.     

Synthesis of Organic-Inorganic Hybrid Particles by Sol-Gel Chemistry

The synthesis of ORganically MOdified SILica (ORMOSIL) particles has been carried out using both the hydrolytic and non-hydrolytic sol-gel routes. The hybrid (nano)composites are organically modified with an alkyl or aryl group covalently bonded to silicon. Hybrids have been synthesised in an aqueous sol-gel process by a modified Stöber route, producing spherical nanoparticles with diameters in the range 50–300 nm. The size of the particles can be controlled by control of certain reaction parameters. Smaller ormosil nanoparticles can be synthesised by a base-catalysed emulsion polymerisation route, by varying the type and concentration of surfactant and precursor feed rate. In this case, particles in the size range 3.5–10 nm can be obtained. Hybrids have been synthesised from hyperbranched polyesters by encapsulation in a silica matrix using the hydrolytic sol-gel route. Optimisation of the reaction conditions allows the hybrids to be produced as isolated sub-micron spherical particles. Ormosil particles have also been synthesised using the non-hydrolytic sol-gel route, which may lead to products of different morphologies because of the different polarity of the reaction medium. Different reaction conditions were studied in order to optimise the size and shape of the particles, including choice of solvent, use of surfactants and addition of polystyrene. Dimethylsulfoxide acts as a novel oxygen donor for the catalyst-free formation of colourless silsesquioxanes.     

Large melting point depression of 2–3‐nm length‐scale nanocrystals formed by the self‐assembly of an associative polymer: Telechelic,pyrene‐labeled poly(dimethylsiloxane)

Large melting point depressions for organic nanocrystals, in comparison with those of the bulk, were observed in an associative polymer: telechelic, pyrene‐labeled poly(dimethylsiloxane) (Py‐PDMS‐Py). Nanocrystals formed within nanoaggregates of pyrenyl units that were immiscible in poly(dimethylsiloxane). For 5 and 7 kg/mol Py‐PDMS‐Py, physical gels resulted, with melting points exceeding 40 °C and with small‐angle X‐ray scattering peaks indicating that the crystals were nanoconfined, were 2–3 nm long, and contained roughly 18–30 pyrenyl dye end units. In contrast, 30 kg/mol Py‐PDMS‐PY was not a gel and exhibited no scattering peak at room temperature; however, after 12 h of annealing at ?5 °C, multiple melting peaks were present at 5–30 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3470–3475, 2004     

The interfacial conformation of polypropylene glycols and foam behaviour

The foam behaviour of low molecular weight polypropylene glycols (PPG) was investigated as a function of concentration and molecular weight (190–2000 g mol⁻¹). For each polypropylene glycol, foam stability increases with concentration and passes through a maximum, beyond which foamability is suppressed as the solubility limit of the glycol is exceeded and droplets of glycol form. Light-scattering data as well as static and dynamic surface tension results provide the key information leading to these interpretations. A maximum in foamability was observed for the PPG molecules with increasing molecular weight (caused by a change in molecular conformation at the interface). This suppresses the Marangoni effect and leads to a decrease in foam stability.