A parallel version of the preconditioned conjugate gradient method for boundary element equations

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.     

Infinite-dimensional symplectic capacities and a squeezing theorem for Hamiltonian PDE's

We study partial differential equations of hamiltonian form and treat them as infinite-dimensional hamiltonian systems in a functional phase-space ofx-dependent functions. In this phase space we construct an invariant symplectic capacity and prove a version of Gromov's (non)squeezing theorem. We give an interpretation of the theorem in terms of the energy transition to high frequencies problem.     

The formation of biaxial nematic phases in binary mixtures of thermotropic liquid-crystals composed of uniaxial molecules

ABSTRACT

Monte Carlo simulations in the isothermal-isobaric ensemble are used to investigate the formation of an ordered, biaxial nematic phase in a binary mixture of thermotropic liquid crystals. The orientational dependence of the interaction between molecules of each pure component is the same as in the well-known Maier-Saupe model; each pure component of the mixture is therefore capable of forming a uniaxial nematic phase. For the interaction between molecules of different components, we use the same Maier-Saupe model but change the sign of the coupling constant. As a consequence a T-shaped arrangement of these molecules is energetically favoured. The formation of the biaxial phase occurs in two steps. At higher temperatures T, one of the components forms a uniaxial nematic phase whereas the other is in a quasi two-dimensional restricted isotropic liquid state. We develop a simple theoretical model to understand the high degree of (ostensible) nematic order in the latter. At lower T, the second component becomes nematic and then the entire mixture of the two compounds has biaxial symmetry. The biaxial nematic phase does not demix into domains rich in molecules of one or the other species.     

Fano blockade by a bose-einstein condensate in an optical lattice

We study the transport of atoms across a localized Bose-Einstein condensate in a one-dimensional optical lattice. For atoms scattering off the condensate, we predict total reflection as well as full transmission for certain parameter values on the basis of an exactly solvable model. The findings of analytical and numerical calculations are interpreted by a tunable Fano-like resonance and may lead to interesting applications for blocking and filtering atom beams.     

Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time, resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincare-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give a qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.     

Hidden chemistry of substituted aniline radical cations in water: a mechanistic study

Absolute rate constants for hydroxyl radical, azide radical, and hydrated electron reactions with a sulfa drug 4,4'‐diamino diphenyl sulfone (dapsone) in water have been evaluated using electron pulse radiolysis technique. Absolute rate constants for hydroxyl radical and azide radical were determined as (8.4 ± 0.3) × 10⁹ and (5.6 ± 0.5) × 10⁹ M^?1 s^?1, respectively. The reduction of dapsone with the hydrated electron occurred with rate constant of (9.2 ± 0.1) × 10⁹ M^?1 s^?1. Hydroxyl radical reactions result in the synchronous formation of adduct as well as anilino radical. The interesting observation is that the yield of the anilino radical increases with increase in pH. Contrary to this, the yield of the adduct decreases with pH. We propose that hydroxyl radical adds predominantly to the aniline. In contrast, the reaction of azide radical with the dapsone suggests that the reaction occurs at the –NH₂ moiety of the aniline ring. The free radical electron transfer from dapsone to parent radical cation of non‐polar solvent also results in the formation of anilino radical only suggesting that the radical cation of dapsone has a short lifetime. The reaction of hydrated electrons with the dapsone suggests that the reaction occurs at different reaction site. The experimental results supported by theoretical calculations of this study provide fundamental mechanistic parameters that probably decide the fate of the radical cation of aniline derivatives. Copyright © 2014 John Wiley & Sons, Ltd.     

Die Nusseltsche Zahl für laminare Strömung im zylindrischen Rohr mit konstanter Wandtemperatur

Summary The Nusselt modulus for laminar flow through a pipe with constant temperature of the walls has been determined as a function of the Peclet modulus. This function is represented by a diagram.     

Synthesis and characterization of (octaaryltetraazaporphyrinato)indium(III) complexes for optical limiting

The preparation of (octaaryltetraazaporphyrinato)indium(III) chlorides [aryl = phenyl (5a), p-tert-butylphenyl (6a), p-(trifluoromethyl)phenyl (7a), m-(trifluoromethyl)phenyl (8a)] and their reactions with aryl Grignard reagents XMgBr to give 5b-8b [X = p-(trifluoromethyl)phenyl] and 5c (R = 3,5-difluorophenyl) are described. The characterization of all compounds by UV-vis, FT-IR, and (1)H and (13)C NMR spectroscopy was performed. The hypsochromic shift of all bands in the absorption spectra of complexes 5a-8a is observed in the sequence 6a < 5a < 7a approximately 8a. This is associated with the increasing electron-withdrawing character of the aryl substituents in the periphery of the tetraazaporphyrin macrocycle. Compounds 8a,b are very good soluble in organic solvents with 8a exhibiting the higher photochemical stability among the various synthesized species. The optical limiting (OL) properties of the complexes have been studied and correlated with the structure of the (tetraazaporphyrinato)indium(III) complexes and the electronic nature of the different substituents. In particular, the OL effect at 532 nm increases on going from the series of compounds 5 to the series 8.