The evolution of plasma parameters on a coronal source surface at 2.3 Rs during solar minimum

We analyze data from the Solar and Heliospheric Observatory to produce global maps of coronal outflow velocities and densities in the regions where the solar wind is undergoing acceleration. The maps use UV and white light coronal data obtained from the Ultraviolet Coronagraph Spectrometer and the Large Angle Spectroscopic Coronagraph, respectively, and a Doppler dimming analysis to determine the mean outflow velocities. The outflow velocities are defined on a sphere at 2.3 Rs from Sun-center and are organized by Carrington Rotations during the solar minimum period at the start of solar cycle 23. We use the outflow velocity and density maps to show that while the solar minimum corona is relatively stable during its early stages, the shrinkage of the north polar hole in the later stages leads to changes in both the global areal expansion of the coronal hole and the derived internal flux tube expansion factors of the solar wind. The polar hole areal expansion factor and the flux tube expansion factors (between the coronal base and 2.3 Rs) start out as super-radial but then they become more nearly radial as the corona progresses away from solar minimum. The results also support the idea that the largest flux tube expansion factors are located near the coronal hole/streamer interface, at least during the deepest part of the solar minimum period.Comment: 12 Figures, Accepted for publication in Ap

The dispersive self-dual Einstein equations and the Toda lattice

The Boyer-Finley equation, or $SU(\infty)$-Toda equation is both a reduction of the self-dual Einstein equations and the dispersionlesslimit of the $2d$-Toda lattice equation. This suggests that there should be a dispersive version of the self-dual Einstein equation which both contains the Toda lattice equation and whose dispersionless limit is the familiar self-dual Einstein equation. Such a system is studied in this paper. The results are achieved by using a deformation, based on an associative $\star$-product, of the algebra $sdiff(\Sigma^2)$ used in the study of the undeformed, or dispersionless, equations.Comment: 11 pages, LaTeX. To appear: J. Phys.

Non-linear optical imaging – Introduction and pharmaceutical applications

Nonlinear optical imaging is an emerging technology with much potential in pharmaceutical analysis. The technique encompasses a range of optical phenomena, including coherent anti-Stokes Raman scattering (CARS), second harmonic generation (SHG), and twophoton excited fluorescence (TPEF). The combined potential of these phenomena for pharmaceutical imaging includes chemical and solidstate specificity, high optical spatial and temporal resolution, nondestructive and non-contact analysis, no requirement for labels, and the compatibility with imaging in aqueous and biological environments. In this article, the theory and practical aspects of nonlinear imaging are briefly introduced and pharmaceutical and biopharmaceutical applications are considered. These include material and dosage form characterization, drug release, and drug and nanoparticle distribution in tissues and within live cells. The advantages and disadvantages of the technique in the context of these analyses are also discussed

A regional and international framework for evaluating seagrass management and conservation

Seagrass meadows provide a range of key ecosystem services that are of high economic and societal value; seagrass meadows enhance biodiversity, provide food security through fisheries support, and are increasingly recognised for the role they play in mitigating climate change by the process of carbon sequestration. Whilst there is an increasing understanding of the global significance of seagrass habitats, the extent of these habitats is declining globally. The requirement to implement effective seagrass conservation and management strategies is thus becoming increasingly important. If the ambitions of the United Nations 2030 Agenda for Sustainable Development and the Sustainable Development Goals are to be achieved, then nations need ambitious and applicable marine conservation plans. This includes management and protection to vulnerable ecosystems such as seagrass meadows. This study aims to evaluate a range of seagrass management and conservation approaches identified in different geographic regions, using a critique framework developed from the United Nations Environment Programme 2020 report on seagrass “Out Of The Blue: The Value Of Seagrasses To The Environment And To People’. Using the framework, seagrass management in Scotland is used as a case study and compared nationally to the rest of the UK (England, Wales and Northern Ireland) and internationally, to Europe (Wadden Sea), Australia (Great Barrier Reef Marine Park) and West Africa (Senegal). The results identify potential areas of development in Scotland to enhance its seagrass conservation effort, including increased research in seagrass science, widespread mapping of seagrass, long-term monitoring programmes, improved marine protected areas, inclusion of seagrass protective measures into environmental laws and policies and the implementation of appropriate habitat restoration schemes. The results also identify the need for open data if effective knowledge sharing is to take place, and to ensure that ocean science can fully support countries to achieve the 2030 Agenda for Sustainable Development

Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of solutions of the WDVV equations

The superpotential in the Landau-Ginzburg construction of solutions to the Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations is modified to include logarithmic terms. This results in deformations - quadratic in the deformation parameters- of the normal prepotential solutions of the WDVV equations. Such solutions satisfy various pseudo-quasi-homogeneity conditions, on assigning a notional weight to the deformation parameters. These solutions originate in the so-called `water-bag' reductions of the dispersionless KP hierarchy. This construction includes, as a special case, deformations which are polynomial in the flat coordinates, resulting in a new class of polynomial solutions of the WDVV equations

Mean and extreme precipitation over European river basins better simulated in a 25km AGCM

Limited spatial resolution is one of the factors that may hamper applications of global climate models (GCMs), in particular over Europe with its complex coastline and orography. In this study, the representation of European mean and extreme precipitation is evaluated in simulations with an atmospheric GCM (AGCM) at different resolutions between about 135 and 25km grid spacing in the mid-latitudes. The continent-wide root-mean-square error in mean precipitation in the 25km model is about 25% smaller than in the 135km model in winter. Clear improvements are also seen in autumn and spring, whereas the model's sensitivity to resolution is very small in summer. Extreme precipitation is evaluated by estimating generalised extreme value distributions (GEVs) of daily precipitation aggregated over river basins whose surface area is greater than 50000km2. GEV location and scale parameters are measures of the typical magnitude and of the interannual variability of extremes, respectively. Median model biases in both these parameters are around 10% in summer and around 20% in the other seasons. For some river basins, however, these biases can be much larger and take values between 50% and 100%. Extreme precipitation is better simulated in the 25km model, especially during autumn when the median GEV parameter biases are more than halved, and in the North European Plains, from the Loire in the west to the Vistula in the east. A sensitivity experiment is conducted showing that these resolution sensitivities in both mean and extreme precipitation are in many areas primarily due to the increase in resolution of the model orography. The findings of this study illustrate the improved capability of a global high-resolution model in simulating European mean and extreme precipitation

Hypercomplex Integrable Systems

In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds. A number of different field equations for such hypercomplex manifolds are derived, one of which is in Cauchy-Kovaleskaya form which enables a formal general solution to be given. Various other properties of the field equations and their solutions are studied, such as their symmetry properties and the associated hierarchy of conservation laws.Comment: Latex file, 19 page

Gate Coupling to Nanoscale Electronics

The realization of single-molecule electronic devices, in which a nanometer-scale molecule is connected to macroscopic leads, requires the reproducible production of highly ordered nanoscale gaps in which a molecule of interest is electrostatically coupled to nearby gate electrodes. Understanding how the molecule-gate coupling depends on key parameters is crucial for the development of high-performance devices. Here we directly address this, presenting two- and three-dimensional finite-element electrostatic simulations of the electrode geometries formed using emerging fabrication techniques. We quantify the gate coupling intrinsic to these devices, exploring the roles of parameters believed to be relevant to such devices. These include the thickness and nature of the dielectric used, and the gate screening due to different device geometries. On the single-molecule (~1nm) scale, we find that device geometry plays a greater role in the gate coupling than the dielectric constant or the thickness of the insulator. Compared to the typical uniform nanogap electrode geometry envisioned, we find that non-uniform tapered electrodes yield a significant three orders of magnitude improvement in gate coupling. We also find that in the tapered geometry the polarizability of a molecular channel works to enhance the gate coupling

The Moyal bracket and the dispersionless limit of the KP hierarchy

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. This Lax equation is closer to that used in the study of the dispersionless KP hierarchy, and is obtained by replacing the Poisson bracket with the Moyal bracket. The dispersionless limit, underwhich the Moyal bracket collapses to the Poisson bracket, is particularly simple.Comment: 9 pages, LaTe

On the B\"acklund Transformation for the Moyal Korteweg-de Vries Hierarchy

We study the B\"acklund symmetry for the Moyal Korteweg-de Vries (KdV) hierarchy based on the Kuperschmidt-Wilson Theorem associated with second Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes the result of Adler for the ordinary KdV.Comment: 9 pages, Revte