Numerical methods for the simulation of a coalescence-driven droplet size distribution

The droplet size distribution in a turbulent flow field is considered and modeled by means of a population balance system. This paper studies different numerical methods for the 4D population balance equation and their impact on an output of interest, the time-space-averaged droplet size distribution at the outlet, which is known from experiments. These methods include different interpolations of the experimental data at the inlet, various discretizations in time and space, and different schemes for computing the coalescence integrals. It will be shown that noticeable changes in the output of interest might occur. In addition, the computational efficiency of the studied methods is discussed.     

Parallel simulation of large scale multibody systems

Virtual prototyping plays an ever increasing role in the engineering disciplines. Nowadays, engineers can rely on powerful tools like object oriented modeling languages, e.g., Modelica. Models written in this language can be simulated by open source software as well as commercial tools. The advantage of this approach is that the engineers can concentrate themselves on modeling, whereas the numerical intricacies of the simulation are handled by the software. On the other hand the simulations are usually slower than implementations which are parallelized and optimized manually. This can lead to computation times which are infeasible in practice, e.g., when a real time simulation is necessary for a hardware-in-the-loop simulation. In this contribution we are concerned with speeding up such automated simulations by parallelization (on desktop hardware as well as HPC systems). We examine the parallelism across the system approaches. Additionally, the influence of the problem formulation on the simulation time is discussed. The implemented methods are demonstrated on engineering examples. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fixed index gratings in LiNbO(3):Fe upon long-term exposure to an intense laser beam

Permanently fixed noisily recorded refractive index gratings are discovered in single crystals of LiNbO(3):Fe upon long-term exposure to a single laser beam with high intensities of I=100 kW/m(2) and ambient temperature. The fixing process is explained by considering the effect of laser-induced heating of the sample and the well-known simultaneous thermal fixing procedure.     

Worldsheet instantons,torsion curves and non-perturbative superpotentials

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov–Witten invariants for a Calabi–Yau threefold with fundamental group π₁(X)=Z₃×Z₃${\pi }_1(X)={\mathbb{Z}}_3\times {\mathbb{Z}}_3$. We find that the curves fall into homology classes in H₂(X,Z)=Z³⊕(Z₃⊕Z₃)$H_2(X,\mathbb{Z})={\mathbb{Z}}^3\oplus ({\mathbb{Z}}_3\oplus {\mathbb{Z}}_3)$. The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. However, we succeed in computing the complete genus-0 prepotential. Expanding it as a power series, the number of instantons in any integral homology class can be read off. This is the first explicit calculation of the Gromov–Witten invariants of homology classes with torsion. We find that some curve classes contain only a single instanton. This ensures that the contribution to the superpotential from each such instanton cannot cancel.     

Third-order Nonlinear Optical Properties of Octa-substituted Metal-free Phthalocyanine Thin Films

Third-order nonlinear optical susceptibility, χ⁽³⁾ of symmetrically octa-substituted metal-free phthalocyanine thin films measured by the third-harmonic generation technique are reported. The metal-free phthalocyanine has been found to show a χ⁽³⁾ (−3ω; ω,ω, ω) value as large as 7.73×10⁻¹² esu at 1.80 μm. The figure of merit, χ⁽³⁾/α, was estimated to be 4.17×10¹⁷ esu cm at 1.05 μm and 6.97×10¹⁶ esu cm at 1.65 μm. Both linear and third-order optical properties of liquid-crystalline metal-free phthalocyanines are discussed