Influence of dynamic interfacial properties on droplet breakup in simple shear flow

The breakup of drops in an inhomogeneous flow is the key to emulsification. Frequently, the local flow experienced by the drops is a (quasi-) simple shear flow. The breakup of drops in a steady, simple shear flow in the absence of emulsifiers has been studied extensively. In the presence of emulsifiers, the drop interface may acquire viscoelastic properties, which are important in the prevention of coalescence, but their influence on drop breakup has not been established solidly. This article reports on a phenomenol. approach, which links the drop breakup dynamics to the interfacial viscoelasticity, identifying the latter with the elasticity modulus of a deforming planar interface. Over a viscosity ratio range of three decades, the results have been found to agree with the model, which uses only independently known quantities derived from equil. interfacial tension properties. [on SciFinder (R)

Strehl ratio and optimum focus of high-numerical-aperture beams

We analytically calculate the focus setting for a beam with a high numerical aperture (NA) that optimizes its Strehl ratio in the case of small aberrations up to the ’just’ diffraction-limited value (Strehl ratio ≥0.80). The optimum focus setting deviates from the one that follows from a minimization of the wavefront aberration with the aid of the Zernike aberration coefficients. This deviation stems largely from the fact that the common quadratic approximation of the focus term becomes inadequate in the high-NA case. Fundamental high-NA amplitude nonuniformity in the exit pupil of an optical system in the case of a linearly polarized incident beam also nfluences the optimum focus setting. Results for spherical aberration and astigmatism are presented for an NA-value of 0.95

High-NA aberration retrieval with the extended Nijboer-Zernike vector diffraction theory - Erratum

In the paper ”High-NA aberration retrieval with the Extended Nijboer-Zernike vector diffraction theory” by S. van Haver, J.J.M. Braat, P. Dirksen and A.J.E.M. Janssen, published in J. Europ. Opt. Soc. Rap. Public. 1, 06004 (2006), some regrettable notation errors are present in Eq.(10), page 06004-3. In this Erratum, the correct expression is given

Spectral properties of a generalized chGUE

We consider a generalized chiral Gaussian Unitary Ensemble (chGUE) based on a weak confining potential. We study the spectral correlations close to the origin in the thermodynamic limit. We show that for eigenvalues separated up to the mean level spacing the spectral correlations coincide with those of chGUE. Beyond this point, the spectrum is described by an oscillating number variance centered around a constant value. We argue that the origin of such a rigid spectrum is due to the breakdown of the translational invariance of the spectral kernel in the bulk of the spectrum. Finally, we compare our results with the ones obtained from a critical chGUE recently reported in the literature. We conclude that our generalized chGUE does not belong to the same class of universality as the above mentioned model.Comment: 12 pages, 3 figure

Shifting states, shifting services: Linking regime shifts to changes in ecosystem services of shallow lakes

Shallow lakes can shift between stable states as a result of anthropogenic or natural drivers. Four common stable states differ in dominant groups of primary producers: submerged, floating, or emergent macrophytes or phytoplankton. Shifts in primary producer dominance affect key supporting, provisioning, regulating, and cultural ecosystem services supplied by lakes. However, links between states and services are often neglected or unknown in lake management, resulting in conflicts and additional costs. Here, we identify major shallow lake ecosystem services and their links to Sustainable Development Goals (SDGs), compare service provisioning among the four ecosystem states and discuss potential trade-offs. We identified 39 ecosystem services potentially provided by shallow lakes. Submerged macrophytes facilitate most of the supporting (86%) and cultural (63%) services, emergent macrophytes facilitate most regulating services (60%), and both emergent and floating macrophytes facilitate most provisioning services (63%). Phytoplankton dominance supports fewer ecosystem services, and contributes most to provisioning services (42%). The shallow lake ecosystem services we identified could be linked to 10 different SDGs, notably zero hunger (SDG 2), clean water and sanitation (SDG 6), sustainable cities and communities (SDG 11), and climate action (SDG13). We highlighted several trade-offs (1) among ecosystem services, (2) within ecosystem services, and (3) between ecosystem services across ecosystems. These trade-offs can have significant ecological and economic consequences that may be prevented by early identification in water quality management. In conclusion, common stable states in shallow lakes provide a different and diverse set of ecosystem services with numerous links to the majority of SDGs. Conserving and restoring ecosystem states should account for potential trade-offs between ecosystem services and preserving the natural value of shallow lakes

Chiral Random Matrix Model for Critical Statistics

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a non-interacting Fermi-gas we show that for energy differences less than a critical energy $E_c$ the spectral correlations are given by chiral Random Matrix Theory whereas for energy differences larger than $E_c$ the number variance shows a linear dependence on the energy difference with a slope that depends on the parameters of the model. If the parameters are scaled such that the slope remains fixed in the thermodynamic limit, this model provides a description of QCD Dirac spectra in the universality class of critical statistics. In this way a good description of QCD Dirac spectra for gauge field configurations given by a liquid of instantons is obtained.Comment: 21 pages, 3 figures, Latex; added two references and minor correction