Multipulse Phases in k-Mixtures of Bose–Einstein Condensates

For the system

$-\Delta U_i+ U_i=U_i^3-\beta U_i\sum_{j\neq i}U_j^2,\quad i=1,\dots,k,$

(with k ≧ 3), we prove the existence for β large of positive radial solutions on \({\mathbb R^N}\) . We show that as β →  + ∞, the profile of each component U _i separates, in many pulses, from the others. Moreover, we can prescribe the location of such pulses in terms of the oscillations of the changing-sign solutions of the scalar equation  ? ΔW  +  W  =  W³. Within an Hartree–Fock approximation, this provides a theoretical indication of phase separation into many nodal domains for the k-mixtures of Bose–Einstein condensates.

     

Radial Solutions of¶Superlinear Equations on ℝN¶Part II: The Forced Case

We study the effect of a forcing term in the context of the search of multiple nodal solutions u∈h ¹(? ^N ) to a class of elliptic equations of type¶?Δu(x)=f(|x|,u(x))+h(|x|), x∈? ^N ,¶where f(|x|≡0 and f is superlinear but subcritical at infinity.     

An age‐dependent population equation with delayed birth process

Within a semigroup framework, we discuss well posedness and qualitative behaviour of an age‐dependent population equation with delay in the birth process. Using positivity and Perron–Frobenius theory we obtain an explicit stability criterion. Copyright © 2004 John Wiley & Sons, Ltd.     

Hierarchical decomposition of domains with fractures

We consider the efficient and robust numerical solution of elliptic problems with jumping coefficients occurring on a network of thin fractures. We present an iterative solution concept based on a hierarchical separation of the fractures and the surrounding rock matrix. Upper estimates for the convergence rates are independent of the width of the fractures and of the jumps of the coefficients. Inexact solution of the local subproblems is also considered. The theoretical results are illustrated by numerical experiments.

     

New strategies for the synthesis of partially fluorinated acrylic polymers as possible materials for the protection of stone monuments

The conservation of the cultural heritage requires the development of new materials having specific characteristics that encompass particular attention to durability and efficacy. We approached this problem by synthesizing polyacrylic esters containing variable amounts of fluorine in the α-position of the main chain. These products were obtained from the copolymerisation of ammonium 2-fluoroacrylate and acrylic acid. The polyacrylic acids were esterified using different procedures. The polyester characteristics vary in relation to the polymerisation procedures and degree of esterification. The best esterification results, were obtained using a reaction catalyzed by BF₃ or TMSCl. These materials show good properties and are of potential interest for their use as protective agents for stone conservation.     

A test case for time-dependent density functional theory calculations of electronic circular dichroism: 2-chloro-4-methoxy-6- [(R)-1-phenylethylamino]-1,3,5- triazine

The three-dimensional structure of an optically active substituted s-triazine derivative, 2-chloro-4-methoxy-6-[(R)-1-phenylethylamino]-1,3,5-triazine, has been studied by conformational analysis using density functional theory (DFT) both in vacuo and in acetonitrile solution in the polarizable continuum model integral equation formalism framework. Time-dependent DFT methods have been used to investigate the molecular electronic CD and absorption UV spectra. Comparison with experimental results allowed the reliability of the theoretical predictions to be enhanced and suggested a possible interpretation of the measured data. Electronic Supplementary Material The online version of this article doi:contains supplementary material, which is available to authorized users.     

Quantum molecular dynamics study of water on TiO2(110) surface

The adsorption of water on perfect TiO(2)(110) surface is studied by quantum molecular dynamics simulation adopting a periodic model formed by five water molecules on a (5 x 1) surface unit cell of a five layer slab of TiO(2). The total simulation time is 3.2 ps. At about 1.3 ps, one water molecule dissociates with the help of other adsorbed waters and surface bridging oxygens. During the remaining 1.9 ps, the waters and OH groups vibrate, but no more dissociation or recombination is observed. By comparing recent experimental O1s photoemission (x-ray photoelectron spectroscopy) spectra of H(2)O/TiO(2)(110) to the computed spectrum of the adsorbate in the configurations supplied by the molecular dynamics simulation, the observed peaks can be attributed to different oxygen species. The proposed assignment of the main spectral features supports the occurrence of partial water dissociation (approximately 20%) also on a perfect TiO(2) surface.