Topological events on wave dislocation lines: birth and death of small loops, and reconnection

In three-dimensional space, a wave dislocation, that is, a quantized (optical) vortex or phase singularity, is a line zero of a complex scalar wavefunction. As a 'time' parameter varies, the topology of the vortex can change by encounter with a line of vanishing vorticity (curl of the current associated with the wavefunction). An isolated critical point of the field intensity, sliding along the zero-vorticity line like a bead on a wire, meets the vortex as it encounters the line, and so participates in the singular event. Local expansio n and gauge and coordinates transformations show that the vortex topology can change generically by the appearance or disappearance of a loop, or by the reconnection of branches of a pair of hyperbolas

Polarization singularities in the clear sky

Ideas from singularity theory provide a simple account of the pattern of polarization directions in daylight. The singularities (two near the Sun and two near the anti-Sun) are points in the sky where the polarization line pattern has index +1/2 and the intensity of polarization is zero. The singularities are caused by multiple scattering that splits into two each of the unstable index +1 singularities at the Sun and anti-Sun, which occur in the single-dipole scattering (Rayleigh) theory. The polarization lines are contours of an elliptic integral. For the intensity of polarization (unnormalized degree), it is necessary to incorporate the strong depolarizing effect of multiple scattering near the horizon. Singularity theory is compared with new digital images of sky polarization, and gives an excellent description of the pattern of polarization directions. For the intensity of polarization, the theory can reproduce not only the zeros but also subtle variations in the polarization maxima

Deformation of liquid drops containing ions in the presence of an electric field

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.The deformation and breakup of a conducting water drop immersed in hexadecane in the presence of an electric field is investigated using a numerical tool for a range of field strengths and ion concentrations. At low electric field strengths, the drop deformation is a linear function of the electric capillary number. For high electric field strengths, the dependence is no longer linear, and significant drop deformation occurs. The drop deformation increases with increasing ion concentration, due to a separation of ions within the drop, leading to a redistribution of charge at either end of the drop.dc201

Vortex lines of the electromagnetic field

Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded in the solutions of wave equations from Schroedinger wave mechanics to Maxwell theory. It is shown that time evolution of vortex lines has universal features; in Maxwell theory it is very similar to that in Schroedinger wave mechanics. Connection with some early work on geometrodynamics is established. Simple examples of solutions of Maxwell equations with embedded vortex lines are given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.

Universal spectral statistics of Andreev billiards: semiclassical approach

The classification of universality classes of random-matrix theory has recently been extended beyond the Wigner-Dyson ensembles. Several of the novel ensembles can be discussed naturally in the context of superconducting-normal hybrid systems. In this paper, we give a semiclassical interpretation of their spectral form factors for both quantum graphs and Andreev billiards.Comment: final improved version (to be published in Physical Review E), 6 pages, revtex

The JCMT Gould Belt survey: Dense core clusters in Orion B

The James Clerk Maxwell Telescope Gould Belt Legacy Survey obtained SCUBA-2 observations of dense cores within three sub-regions of OrionB: LDN1622, NGC2023/2024, and NGC2068/2071, all of which contain clusters of cores. We present an analysis of the clustering properties of these cores, including the two-point correlation function and Cartwright’s Q parameter. We identify individual clusters of dense cores across all three regions using a minimal spanning tree technique, and find that in each cluster, the most massive cores tend to be centrally located. We also apply the independent M–Σ technique and find a strong correlation between core mass and the local surface density of cores. These two lines of evidence jointly suggest that some amount of mass segregation in clusters has happened already at the dense core stage

Current correlations and quantum localization in 2D disordered systems with broken time-reversal invariance

We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic field. Our result is universal, i.e. it does not depend on the type (random potential or random magnetic field) or correlation length of disorder. This contradicts recent sigma-model calculations of Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well as for the renormalization of the conductivity. We show explicitly that the new term in the sigma-model derived by TS&E and claimed to lead to delocalization does not exist. The error in the derivation of TS&E is traced to an incorrect ultraviolet regularization procedure violating current conservation and gauge invariance.Comment: 8 pages, 3 figure

Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model

We propose a formula for the eigenvalue integral of the hermitian one matrix model with infinite well potential in terms of dressed twist fields of the su(2) level one WZW model. The expression holds for arbitrary matrix size n, and provides a suggestive interpretation for the monodromy properties of the matrix model correlators at finite n, as well as in the 1/n-expansion.Comment: 27 pages, 4 figures; v2: typos corrected, reference added, version to be published in JHE

A framework for assessing and implementing the co-benefits of nature-based solutions in urban areas

To address challenges associated with climate resilience, health and well-being in urban areas, current policy platforms are shifting their focus from ecosystem-based to nature-based solutions (NBS), broadly defined as solutions to societal challenges that are inspired and supported by nature. NBS result in the provision of co-benefits, such as the improvement of place attractiveness, of health and quality of life, and creation of green jobs. Few frameworks exist for acknowledging and assessing the value of such co-benefits of NBS and to guide cross-sectoral project and policy design and implementation. In this paper, we firstly developed a holistic framework for assessing co-benefits (and costs) of NBS across elements of socio-cultural and socio-economic systems, biodiversity, ecosystems and climate. The framework was guided by a review of over 1700 documents from science and practice within and across 10 societal challenges relevant to cities globally. We found that NBS can have environmental, social and economic co-benefits and/or costs both within and across these 10 societal challenges. On that base, we develop and propose a seven-stage process for situating co-benefit assessment within policy and project implementation. The seven stages include: 1) identify problem or opportunity; 2) select and assess NBS and related actions; 3) design NBS implementation processes; 4) implement NBS; 5) frequently engage stakeholders and communicate co-benefits; 6) transfer and upscale NBS; and 7) monitor and evaluate co-benefits across all stages. We conclude that the developed framework together with the seven-stage co-benefit assessment process represent a valuable tool for guiding thinking and identifying the multiple values of NBS implementation

Dynamics and Berry phase of two-species Bose-Einstein condensates

In terms of exact solutions of the time-dependent Schrodinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2)coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.Comment: 18 pages,5 figure