Lagrange solution for three wavelength solitary wave clusters in nematic liquid crystals

We investigate the interaction of three optical solitary waves propagating with angular momentum in bulk nematic liquid crystals. The resulting cluster of solitary waves, or nematicons, is shown to orbit about its common centre of “mass”. An elongated isosceles triangle configuration is derived, this solution being the equivalent of the Lagrange solution of Newtonian gravitation. This triangle solution is found to be stable owing to diffractive radiation. A modulation theory explains the existence of the triangle solution as due to the non-monotonicity of an effective potential for the interaction of the solitary waves. This modulation theory also gives good agreement with numerical solutions for the trajectories of the nematicons in the three colours. Finally, it is shown that a cut-off in the shed diffractive radiation prevents the break-up of the triangle due to radiative losses.     

General Synthesis and Physicochemical Characterisation of a Series of Peptide‐Mimic Lysine‐Based Amino‐Functionalised Lipids

A series of novel malonic acid diamides (second generation) with two long hydrophobic alkyl chains and an alkaline polar head group was synthesised and characterised as a new class of amino‐functionalised lipids. These peptide‐mimic lipids are suitable for polynucleotide transfer. The lipids bear a novel backbone consisting of a lysine unit and a malonic acid unit. Six different head‐group structures, which vary in size and number of amino groups that can be protonated, were attached to the backbone structure. Furthermore, different alkyl chains were used to build the lipophilic part (namely tetradecyl, hexadecyl, and oleyl). Phase transitions of the new compounds in aqueous dispersions at pH 10 were analysed and discussed in terms of head group and alkyl chain variations. The shape and size of the formed aggregates of selected lipid dispersions were investigated by dynamic light scattering and transmission electron microscopy.     

New Process Simulation Procedure for High-Rate Plasma Jet Machining

Surface figuring using chemically reactive plasma jet machining (PJM) is a promising non-conventional technology for deterministic ultra-precision machining of optical components. Based on chemical reactions between plasma generated radicals and the surface atoms this technology is capable to fabricate complex shaped free form surfaces. Since the material removal rate during PJM depends strongly on the surface temperature which itself is influenced by the jet heat flux to the surface, the arising nonlinear effects on the etch result have to be regarded. Conventionally applied dwell time calculation algorithms do not consider those effects leading to significant machining errors in some cases. In order to improve the machining procedure with respect to deterministic material removal yielding predictable results a process simulation model has been developed. This model considers spatio-temporal variations of surface temperature and temperature dependent material removal and is able to predict the final workpiece topography after machining.     

L2Roe: a low dissipation version of Roe's approximate Riemann solver for low Mach numbers

A modification of the Roe scheme called L²Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M_∞=0.001) to hypersonic (M_∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L²Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases. Copyright © 2015 John Wiley & Sons, Ltd.     

Polaronic origin of the isotope effect on the London penetration depth in high-temperature superconducting oxides

Direct measurements of the in-plane London penetration depth λ _L have recently been performed on high-temperature superconducting copper oxides by a new low-energy muon spin rotation technique. The results show that λ _L is isotope dependent, evidencing unconventional electron–phonon interactions as its source. The data are interpreted here in terms of polaronic effects on the single-particle energies, which leads to level shifts and exponential band narrowing. Good agreement with the experimental data is obtained.     

Double-knife EDGE problems with elastic/plastic type screens

A problem of diffraction of a wave by a pair of semi-infinite screens is considered. The screens are lined with two different wave bearing materials that can support surface waves. This type of problem arises in the propagation and, scattering of acoustic and electromagnetic waves by surface wave guides. To be specific, we shall couch our problem in terms of acoustics. These diffraction problems for two parallel wave bearing screens lead to boundary value problems which are governed by the Helmholtz equation, and some specific third kind boundary conditions. Such problems are shown to be well-posed for finite energy space solutions. Their representation is given by means of the canonical factorization of a non-rational matrix function.This work was supported by DFG grant KO 634/32-1