Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Relevance of sampling schemes in light of Ruelle's linear response theory

We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We �rst show that by using a general functional decomposition for space-time dependent forcings, we can de�ne elementary susceptibilities that allow to construct the response of the system to general perturbations. Starting from the de�nition of SRB measure, we then study the consequence of taking di�erent sampling schemes for analysing the response of the system. We show that only a speci�c choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows to obtain the formula �rst presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be �ne-tuned to make the de�nition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analyzing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick.

Paul the Silentiary’s description of Hagia Sophia in the light of new archaeological evidence

A discussion of the implications of of recent archaeological work at Hagia Sophia in Istanbul for understanding Paul the Silentiary's sixth-century Ekphrasis of the Byzantine church.

Physicality, difference, and the challenge of representation: Werner Herzog in the Light of the new waves

This chapter looks into the gap between presentational realism and the representation of physical experience in Werner Herzog's work so as to retrieve the indexical trace – or the absolute materiality of death. To that end, it draws links between Herzog and other directors akin to realism in its various forms, including surrealism. In particular, it focuses on François Truffaut and Glauber Rocha, representing respectively the Nouvelle Vague and the Cinema Novo, whose works had a decisive weight on Herzog’s aesthetic choices to the point of originating distinct phases of his outputs. The analyses, though restricted to a small number of films, intends to re-evaluate Herzog’s position within, and contribution to, film history.

Electron trapping in shear Alfvén waves that power the aurora

Results from 1D Vlasov drift-kinetic plasma simulations reveal how and where auroral electrons are accelerated along Earth’s geomagnetic field. In the warm plasma sheet, electrons become trapped in shear Alfven waves, preventing immediate wave damping. As waves move to regions with larger vTe=vA, their parallel electric field decreases, and the trapped electrons escape their influence. The resulting electron distribution functions compare favorably with in situ observations, demonstrating for the first time a self-consistent link between Alfven waves and electrons that form aurora.

Using coordinated observations in polarized white light and Faraday rotation to probe the spatial position and magnetic field of an interplanetary sheath

Coronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons and therefore depend on both viewing geometry and electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component B ∥ and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modeling of an Earth-directed shock and synthesize the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance I decreases with heliocentric distance r roughly according to the expression Ir –3. The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site r sheath and the mass of plasma at that position M sheath can be inferred from the polarization of the shock-associated enhancement in WL radiance. From the FR measurements, the local B ∥sheath at r sheath can then be estimated. Simultaneous observations in polarized WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties.

Reduced-order modeling of light transport in tissue for real-time monitoring of brain hemodynamics using diffuse optical tomography

This paper proposes a new reconstruction method for diffuse optical tomography using reduced-order models of light transport in tissue. The models, which directly map optical tissue parameters to optical flux measurements at the detector locations, are derived based on data generated by numerical simulation of a reference model. The reconstruction algorithm based on the reduced-order models is a few orders of magnitude faster than the one based on a finite element approximation on a fine mesh incorporating a priori anatomical information acquired by magnetic resonance imaging. We demonstrate the accuracy and speed of the approach using a phantom experiment and through numerical simulation of brain activation in a rat's head. The applicability of the approach for real-time monitoring of brain hemodynamics is demonstrated through a hypercapnic experiment. We show that our results agree with the expected physiological changes and with results of a similar experimental study. However, by using our approach, a three-dimensional tomographic reconstruction can be performed in ∼3  s per time point instead of the 1 to 2 h it takes when using the conventional finite element modeling approach

Leaf trapping and retention of particles by holm oak and other common tree species in Mediterranean urban environments

Holm oak (Quercus ilex), a widespread urban street tree in the Mediterranean region, is widely used as biomonitor of persistent atmospheric pollutants, especially particulate-bound metals. By using lab- and field-based experimental approaches, we compared the leaf-level capacity for particles’ capture and retention between Q. ilex and other common Mediterranean urban trees: Quercus cerris, Platanus × hispanica, Tilia cordata and Olea europaea. All applied methods were effective in quantifying particulate capture and retention, although not univocal in ranking species performances. Distinctive morphological features of leaves led to differences in species’ ability to trap and retain particles of different size classes and to accumulate metals after exposure to traffic in an urban street. Overall, P. × hispanica and T. cordata showed the largest capture potential per unit leaf area for most model particles (Na+ and powder particles), and street-level Cu and Pb, while Q. ilex acted intermediately. After wash-off experiments, P. × hispanica leaves had the greatest retention capacity among the tested species and O. europaea the lowest. We concluded that the Platanus planting could be considered in Mediterranean urban environments due to its efficiency in accumulating and retaining airborne particulates; however, with atmospheric pollution being typically higher in winter, the evergreen Q. ilex represents a better year-round choice to mitigate the impact of airborne particulate pollutants.

Direct observation by time-resolved infrared spectroscopy of the bright and the dark excited states of the [Ru(phen)2(dppz)]2+ light-switch compound in solution and when bound to DNA

The [Ru(phen)2(dppz)]2+ complex (1) is non-emissive in water but is highly luminescent in organic solvents or when bound to DNA, making it a useful probe for DNA binding. To date, a complete mechanistic explanation for this “light-switch” effect is still lacking. With this in mind we have undertaken an ultrafast time resolved infrared (TRIR) study of 1 and directly observe marker bands between 1280–1450 cm-1, which characterise both the emissive “bright” and the non-emissive “dark” excited states of the complex, in CD3CN and D2O respectively. These characteristic spectral features are present in the [Ru(dppz)3]2+ solvent light-switch complex but absent in [Ru(phen)3]2+, which is luminescent in both solvents. DFT calculations show that the vibrational modes responsible for these characteristic bands are predominantly localised on the dppz ligand. Moreover, they reveal that certain vibrational modes of the “dark” excited state couple with vibrational modes of two coordinating water molecules, and through these to the bulk solvent, thus providing a new insight into the mechanism of the light-switch effect. We also demonstrate that the marker bands for the “bright” state are observed for both L- and D enantiomers of 1 when bound to DNA and that photo-excitation of the complex induces perturbation of the guanine and cytosine carbonyl bands. This perturbation is shown to be stronger for the L enantiomer, demonstrating the different binding site properties of the two enantiomers and the ability of this technique to determine the identity and nature of the binding site of such intercalators.