New Perspective on the Optical Theorem of Classical Electrodynamics

A general proof of the optical theorem (also known as the optical cross-section theorem) is presented that reveals the intimate connection between the forward scattering amplitude and the absorption-plus-scattering of the incident wave within the scatterer. The oscillating electric charges and currents as well as the electric and magnetic dipoles of the scatterer, driven by an incident plane-wave, extract energy from the incident beam at a certain rate. The same oscillators radiate electro-magnetic energy into the far field, thus giving rise to well-defined scattering amplitudes along various directions. The essence of the proof presented here is that the extinction cross-section of an object can be related to its forward scattering amplitude using the induced oscillations within the object but without an actual knowledge of the mathematical form assumed by these oscillations.Comment: 7 pages, 1 figure, 12 reference

Fashion micro-enterprises in London, Berlin, Milan

This report provides an account of a series of interviews, observational visits and hosted events with 8-10 fashion designers in three cities: London, Berlin and Milan, carried out from 2012-2016. In some cases we interviewed the same designers two or three times over a period of nearly three years. The research project also entailed documented conversations and meetings with a range of fashion experts, consultants, legal advisors and policy makers in each city. Often these took place within the context of organised events undertaken as part of the research process. The aim was to investigate the kind of start-ups or micro-enterprises which have come into being in the last decade. We were interested in whether these were the outcome of pro-active urban creative economy policies or if they were self-organised initiatives, a reaction to the crisis of the euro-zone of 2008 and the consequent recession. Was it the case that long-term austerity policies and exceptionally high rates of youth and graduate unemployment across Europe had spawned these kinds of seemingly independent economic activities? We were also minded to consider the role of intellectual property (IP) and copyright in fashion as part of the wider UK government agenda for growth and wealth creation within the creative economy as a whole

The distribution of polycomb-group proteins during cell division and development in Drosophila embryos: Impact on models for silencing

The subcellular three-dimensional distribution of three polycomb-group (PcG) proteins—polycomb, polyhomeotic and posterior sex combs—in fixed whole-mount Drosophila embryos was analyzed by multicolor confocal fluorescence microscopy. All three proteins are localized in complex patterns of 100 or more loci throughout most of the interphase nuclear volume. The rather narrow distribution of the protein intensities in the vast majority of loci argues against a PcG-mediated sequestration of repressed target genes by aggregation into subnuclear domains. In contrast to the case for PEV repression (Csink, A.K., and S. Henikoff. 1996. Nature. 381:529–531), there is a lack of correlation between the occurrence of PcG proteins and high concentrations of DNA, demonstrating that the silenced genes are not targeted to heterochromatic regions within the nucleus. There is a clear distinction between sites of transcription in the nucleus and sites of PcG binding, supporting the assumption that most PcG binding loci are sites of repressive complexes. Although the PcG proteins maintain tissue-specific repression for up to 14 cell generations, the proteins studied here visibly dissociate from the chromatin during mitosis, and disperse into the cytoplasm in a differential manner. Quantitation of the fluorescence intensities in the whole mount embryos demonstrate that the dissociated proteins are present in the cytoplasm. We determined that <2% of PH remains attached to late metaphase and anaphase chromosomes. Each of the three proteins that were studied has a different rate and extent of dissociation at prophase and reassociation at telophase. These observations have important implications for models of the mechanism and maintenance of PcG- mediated gene repression

DAnkrd49 and Bdbt act via casein kinase Iε to regulate planar polarity in Drosophila

The core planar polarity proteins are essential mediators of tissue morphogenesis, controlling both the polarised production of cellular structures and polarised tissue movements. During development the core proteins promote planar polarisation by becoming asymmetrically localised to opposite cell edges within epithelial tissues, forming intercellular protein complexes that coordinate polarity between adjacent cells. Here we describe a novel protein complex that regulates the asymmetric localisation of the core proteins in the Drosophila pupal wing. DAnkrd49 (an ankyrin repeat protein) and Bride of Doubletime (Bdbt, a non-canonical FK506 binding protein family member) physically interact, and regulate each other's levels in vivo. Loss of either protein results in a reduction in core protein asymmetry and disruption of the placement of trichomes at the distal edge of pupal wing cells. Post-translational modifications are thought to be important for the regulation of core protein behaviour and their sorting to opposite cell edges. Consistent with this, we find that loss of DAnkrd49 or Bdbt leads to reduced phosphorylation of the core protein Dishevelled and to decreased Dishevelled levels both at cell junctions and in the cytoplasm. Bdbt has previously been shown to regulate activity of the kinase Discs Overgrown (Dco, also known as Doubletime or Casein Kinase Iε), and Dco itself has been implicated in regulating planar polarity by phosphorylating Dsh as well as the core protein Strabismus. We demonstrate that DAnkrd49 and Bdbt act as dominant suppressors of Dco activity. These findings support a model whereby Bdbt and DAnkrd49 act together to modulate the activity of Dco during planar polarity establishment

Gaussian random waves in elastic media

Similar to the Berry conjecture of quantum chaos we consider elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors. Based on that we derive the correlation functions for amplitudes and intensities of elastic displacements. Comparison to numerics in a quarter Bunimovich stadium demonstrates excellent agreement.Comment: 4 pages, 4 figure

Manipulating mud: (re-)constructing cosmogonical landscapes in the Nile Valley, Thebes, Egypt

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Growth in densely populated Asia: implications for primary product exporters

Economic growth and integration in Asia is rapidly increasing the global economic importance of the region. To the extent that this growth continues and is strongest in natural resource-poor Asian economies, it will add to global demand for imports of primary products, to the benefit of (especially nearby) resource-abundant countries. How will global production, consumption and trade patterns change by 2030 in the course of such economic developments and structural changes? We address this question using the GTAP model and Version 8.1 of the 2007 GTAP database, together with supplementary data from a range of sources, to support projections of the global economy from 2007 to 2030 under various scenarios. Factor endowments and real gross domestic product are assumed to grow at exogenous rates, and trade-related policies are kept unchanged to generate a core baseline, which is compared with an alternative slower growth scenario. We also consider the impact of several policy changes aimed at increasing China's agricultural self-sufficiency relative to the 2030 baseline. Policy implications for countries of the Asia-Pacific region are drawn out in the final section

Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model

We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the space coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.Comment: 4 pages, REVTe

Accelerator measurements of magnetically-induced radio emission from particle cascades with applications to cosmic-ray air showers

For fifty years, cosmic-ray air showers have been detected by their radio emission. We present the first laboratory measurements that validate electrodynamics simulations used in air shower modeling. An experiment at SLAC provides a beam test of radio-frequency (RF) radiation from charged particle cascades in the presence of a magnetic field, a model system of a cosmic-ray air shower. This experiment provides a suite of controlled laboratory measurements to compare to particle-level simulations of RF emission, which are relied upon in ultra-high-energy cosmic-ray air shower detection. We compare simulations to data for intensity, linearity with magnetic field, angular distribution, polarization, and spectral content. In particular, we confirm modern predictions that the magnetically induced emission in a dielectric forms a cone that peaks at the Cherenkov angle and show that the simulations reproduce the data within systematic uncertainties.Comment: 5 pages, 7 figure