Lagrangian and Eulerian models for simulating turbulent dispersion and coalescence of droplets within a spray

Lagrangian and Eulerian modelling approaches are compared for simulating turbulent dispersion and coalescence of droplets within a spray. Both models predict similar droplet dispersion rates and shifts in droplet size distribution due to coalescence within the spray, over a wide range of droplet and gas flows, and for sprays with different droplet-size distributions at the nozzle exit. The computer time required for simulating coalescence within a steady axisymmetric spray is of a similar order of magnitude regardless of which formulation, Eulerian or Lagrangian, is adopted. However, the Lagrangian formulation is more practical in terms of the range of applicability and ease of implementation.     

Symmetries of BLT-Sets

We do the tentative beginnings of a study of BLT-sets of generalised quadrangles via their symmetries. In particular, the study of whorls about a line leads us to hyperbolic reflections preserving a BLT-set of Q(4, q).     

Higher order radiative corrections to the QED Compton events at HERA

We estimate the higher order QED corrections to the QED Compton events at HERA employing the leading logarithmic approximation to all orders in α. The Compton events are events of the typee+p→e′+γ+ Hadrons, wheree′ and γ have nearly balancedp _T .     

The photon two-point function in unitary approximation

The photon two-point function is calculated using the exponential representation for the time-evolution operator taking into account terms up to second order ine in the exponent. The limiting case of vanishing electron mass is examined and it is shown that mass singularities cancel by means of unitarity. Near mass shell the causal Green function exhibits in the limit of vanishing electron mass the expected cut behaviour, off mass shell we recover the result of the usual perturbation theory.     

Adaptive application of operators in standard representation

Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could be shown under the assumption that the entries in properly compressed standard representations are known or computable in average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption is justified in the context of elliptic boundary value problems. Dedicated to Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55. This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1.     

Evaluation of piezoelectric PVDF polymers for use in space environments. III. Comparison of the effects of vacuum UV and gamma radiation

Films of piezoelectric PVDF and P(VDF‐TrFE) were exposed to vacuum UV (115–300 nm VUV) and γ‐radiation to investigate how these two forms of radiation affect the chemical, morphological, and piezoelectric properties of the polymers. The extent of crosslinking was almost identical in both polymers after γ‐irradiation, but surprisingly, was significantly higher for the TrFE copolymer after VUV‐irradiation. Changes in the melting behavior were also more significant in the TrFE copolymer after VUV‐irradiation due to both surface and bulk crosslinking, compared with only surface crosslinking for the PVDF films. The piezoelectric properties (measured using d₃₃ piezoelectric coefficients and D‐E hysteresis loops) were unchanged in the PVDF homopolymer, while the TrFE copolymer exhibited more narrow D‐E loops after exposure to either γ‐ or VUV‐radiation. The more severe damage to the TrFE copolymer in comparison with the PVDF homopolymer after VUV‐irradiation is explained by different energy deposition characteristics. The short wavelength, highly energetic photons are undoubtedly absorbed in the surface layers of both polymers, and we propose that while the longer wavelength components of the VUV‐radiation are absorbed by the bulk of the TrFE copolymer causing crosslinking, they are transmitted harmlessly in the PVDF homopolymer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3253–3264, 2006