A note on a Liouville type result of Gilbarg and Weinberger for the stationary Navier–Stokes equations in 2<Emphasis Type="Italic">D</Emphasis>

We show that a velocity field u satisfying the stationary Navier–Stokes equations on the entire plane must be constant under the growth condition lim sup |x|^−α |u(x)| < ∞ as |x| → ∞ for some α ∈ [0, 1/7).^† Bibliography: 10 titles.     

Functionalized N‐Aryl‐Substituted Cyclens by Nucleophilic Aromatic Substitution

The reaction of trifold protected cyclen with fluorinated dinitroarenes yields aryl‐substituted or aryl‐bridged cyclen derivatives in good yield. The two arene nitro groups, necessary for the nucleophilic aromatic substitution, are subsequently selectively reduced to amines and further functionalized by amide formation. As an example, a cyclen derivative bearing a heterocyclic oligoamide with potential DNA binding ability was prepared.     

Lattice dynamics of Eu<Subscript>1-x</Subscript>Y<Subscript>x</Subscript>MnO<Subscript>3</Subscript> (0 ≤ x ≤ 0.5)

A systematic and detailed study of Raman and infrared active lattice excitations in the orthorhombic multiferroic manganite Eu_1−xY_xMnO₃ (0 ≤ x ≤ 0.5) was carried out at room temperature. For the infrared active phonon modes the eigenfrequencies, damping constants and oscillator strengths were analyzed by Fourier-Transform Infrared Spectroscopy in the far infrared frequency range. For the Raman active phonons the same analysis for eigenfrequencies and damping constants was carried out using Raman spectroscopy in the range from 200 cm⁻¹ to 700 cm⁻¹. Y doping leads to mode-dependent phonon frequency shifts up to 8%. These are interpreted in terms of the interplay between the decrease of the reduced ion masses and the axis-dependent change of bond lengths. The latter leads to a bond softening along the a-axis and a strengthening along the c-axis, for which the highest phonon frequency increase is observed. The application of both Raman and Infrared Spectroscopy gives us sensitivity not only to symmetry properties via the selection rules but also to the involvement of different ion types within the unit cell. It is clearly shown that the disorder induced effects are of minor impact on the lattice properties and solely detected on the rare earth sites. The MnO₆ octahedra remain unaffected and show the same behavior as in the stochiometric RMnO₃ making Eu_1−xY_xMnO₃ an excellent model system for a quasi-continuous fine-tuning of the lattice parameters relevant for the appearance of multiferroicity.     

Lithography potentials of UV-nanoimprint

In the past decade nanoimprint has been developed to a serious alternative for next generation lithography (NGL). In this work, the most recent developments of UV-nanoimprint Lithography (UV-NIL) with special emphasis to the work accomplished at AMO and the IHT-RWTH Aachen are reviewed and functional applications demonstrated. Further the potentials of various UV-NIL concepts are evaluated and possible interests in certain application areas are discussed.     

The effect of a surface energy term on the distribution of phases in an elastic medium with a two‐well elastic potential

We consider the problem of minimizing among functions u:?^d?Ω→?^d, u_∣?Ω=0, and measurable subsets E of Ω. Here f_h⁺, f^? denote quadratic potentials defined on Ω¯×{symmetric d×d matrices}, h is the minimum energy of f_h⁺ and ε(u) is the symmetric gradient of the displacement field u. An equilibrium state û, Ê of J(u,E) is called one‐phase if E=?? or E=Ω, two‐phase otherwise. For two‐phase states, σ∣?E∩Ω∣ measures the effect of the separating surface, and we investigate the way in which the distribution of phases is affected by the choice of the parameters h??, σ>0. Additional results concern the smoothness of two‐phase equilibrium states and the behaviour of inf J(u,E) in the limit σ↓0. Moreover, we discuss the case of additional volume force potentials, and extend the previous results to non‐zero boundary values. Copyright © 2002 John Wiley & Sons, Ltd.     

The effect of a penalty term involving higher order derivatives on the distribution of phases in an elastic medium with a two‐well elastic potential

We consider the problem of minimizing 0<p<1, h∈?, σ>0, among functions u:?^d?Ω→?^d, u_∣?Ω=0, and measurable characteristic functions χ:Ω→?. Here ?⁺_h, ?^?, denote quadratic potentials defined on the space of all symmetric d×d matrices, h is the minimum energy of ?⁺_h and ε(u) denotes the symmetric gradient of the displacement field. An equilibrium state û, χ?, of I [·,·,h, σ] is termed one‐phase if χ?≡0 or χ?≡1, two‐phase otherwise. We investigate the way in which the distribution of phases is affected by the choice of the parameters h and σ. Copyright 2002 John Wiley & Sons, Ltd.     

Discharges in the JET tokamak where the safety factor profile is identified as the critical factor for triggering internal transport barriers

Joint European Torus discharges which demonstrate the critical role the safety factor profile, q, can play in the formation of internal transport barriers (ITB) are examined. In these discharges, the target parameters, including the E x B flows, were kept virtually the same, except for the q profile. In a discharge with a nonmonotonic q, an ITB was triggered whereas a discharge with monotone q made no such transition. Thus, there is strong evidence that the q profile was the critical factor for the triggering of an ITB. Possible interpretations of this finding are discussed.