Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium

We consider the Dirichlet boundary-value problem for the Helmholtz equation, Au + x2u = 0, with Imx > 0. in an hrbitrary bounded or unbounded open set C c W. Assuming continuity of the solution up to the boundary and a bound on growth a infinity, that lu(x)l < Cexp (Slxl), for some C > 0 and S~< Imx, we prove that the homogeneous problem has only the trivial salution. With this resnlt we prove uniqueness results for direct and inverse problems of scattering by a bounded or infinite obstacle.

Crooks' fluctuation theorem for a process on a two dimensional fluid field

We investigate the behavior of a two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the two-dimensional vorticity equation with spectral truncation on a rectangular domain. For a sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. We interpret this as doing work to the system. Evolving along a forward and its corresponding backward process, we find numerical evidence that the distributions of the work performed satisfy the Crooks relation. We confirm our results by proving the Crooks relation for this system rigorously.

On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

On the interpretation of Andrews’ theorem

Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Computer Theorem Proving and HoTT

Theorem-proving is a one-player game. The history of computer programs being the players goes back to 1956 and the ‘LT’ LOGIC THEORY MACHINE of Newell, Shaw and Simon. In game-playing terms, the ‘initial position’ is the core set of axioms chosen for the particular logic and the ‘moves’ are the rules of inference. Now, the Univalent Foundations Program at IAS Princeton and the resulting ‘HoTT’ book on Homotopy Type Theory have demonstrated the success of a new kind of experimental mathematics using computer theorem proving.

Direct evidence for attention-dependent influences of the frontal eye-fields on feature-responsive visual cortex

Voluntary selective attention can prioritize different features in a visual scene. The frontal eye-fields (FEF) are one potential source of such feature-specific top-down signals, but causal evidence for influences on visual cortex (as was shown for "spatial" attention) has remained elusive. Here, we show that transcranial magnetic stimulation (TMS) applied to right FEF increased the blood oxygen level-dependent (BOLD) signals in visual areas processing "target feature" but not in "distracter feature"-processing regions. TMS-induced BOLD signals increase in motion-responsive visual cortex (MT+) when motion was attended in a display with moving dots superimposed on face stimuli, but in face-responsive fusiform area (FFA) when faces were attended to. These TMS effects on BOLD signal in both regions were negatively related to performance (on the motion task), supporting the behavioral relevance of this pathway. Our findings provide new causal evidence for the human FEF in the control of nonspatial "feature"-based attention, mediated by dynamic influences on feature-specific visual cortex that vary with the currently attended property.

Direct experimental evidence that early-life farm environment influences regulation of immune responses

Background: In mammals, early-life environmental variations appear to affect microbial colonization and therefore competent immune development, and exposure to farm environments in infants has been inversely correlated with allergy development. Modelling these effects using manipulation of neonatal rodents is difficult due to their dependency on the mother, but the relatively independent piglet is increasingly identified as a valuable translational model for humans. This study was designed to correlate immune regulation in piglets with early-life environment. Methods: Piglets were nursed by their mother on a commercial farm, while isolatorreared siblings were formula fed. Fluorescence immunohistology was used to quantify T-reg and effector T-cell populations in the intestinal lamina propria and the systemic response to food proteins was quantified by capture ELISA. Results: There was more CD4+ and CD4+CD25+ effector T-cell staining in the intestinal mucosa of the isolator-reared piglets compared with their farm-reared counterparts. In contrast, these isolator-reared piglets had a significantly reduced CD4+CD25+Foxp3+ regulatory T-cell population compared to farm-reared littermates, resulting in a significantly higher T-reg-to-effector ratio in the farm animals. Consistent with these findings, isolator-reared piglets had an increased serum IgG anti-soya response to novel dietary soya protein relative to farm-reared piglets. Conclusion: Here, we provide the first direct evidence, derived from intervention, that components of the early-life environment present on farms profoundly affects both local development of regulatory components of the mucosal immune system and immune responses to food proteins at weaning. We propose that neonatal piglets provide a tractable model which allows maternal and treatment effects to be statistically separated.

The origins of domestic horses in north-west Europe: new direct dates on the horses of Newgrange, Ireland

This paper presents direct radiocarbon measurements on horse skeletal remains from the Beaker period settlement at the site of Newgrange in Ireland, finds which have previously been argued as the earliest domestic horses in Ireland. The new determinations date the horse remains to the Irish Iron Age and shed important new light on the introduction of domestic horses to Ireland and to north-west Europe more generally. Although the new dates undermine the idea for the introduction of horses as part of a ‘Beaker package’, the early use of horse is not well defined archaeologically or chronologically and the earliest use of domestic horses in Ireland and Britain is still uncertain. This paper also identifies evidence for heavy bitting damage on the Iron Age Newgrange horse teeth and presents some possible parallels between the evidence from Newgrange and that at Tara, which has been previously linked with kingship rituals

The 22-Year Hale Cycle in cosmic ray flux: evidence for direct heliospheric modulation

The ability to predict times of greater galactic cosmic ray (GCR) fluxes is important for reducing the hazards caused by these particles to satellite communications, aviation, or astronauts. The 11-year solar-cycle variation in cosmic rays is highly correlated with the strength of the heliospheric magnetic field. Differences in GCR flux during alternate solar cycles yield a 22-year cycle, known as the Hale Cycle, which is thought to be due to different particle drift patterns when the northern solar pole has predominantly positive (denoted as qA>0 cycle) or negative (qA<0) polarities. This results in the onset of the peak cosmic-ray flux at Earth occurring earlier during qA>0 cycles than for qA<0 cycles, which in turn causes the peak to be more dome-shaped for qA>0 and more sharply peaked for qA<0. In this study, we demonstrate that properties of the large-scale heliospheric magnetic field are different during the declining phase of the qA<0 and qA>0 solar cycles, when the difference in GCR flux is most apparent. This suggests that particle drifts may not be the sole mechanism responsible for the Hale Cycle in GCR flux at Earth. However, we also demonstrate that these polarity-dependent heliospheric differences are evident during the space-age but are much less clear in earlier data: using geomagnetic reconstructions, we show that for the period of 1905 - 1965, alternate polarities do not give as significant a difference during the declining phase of the solar cycle. Thus we suggest that the 22-year cycle in cosmic-ray flux is at least partly the result of direct modulation by the heliospheric magnetic field and that this effect may be primarily limited to the grand solar maximum of the space-age.

An “A-train” strategy for quantifying direct climate forcing by anthropogenic aerosols

This document outlines a practical strategy for achieving an observationally based quantification of direct climate forcing by anthropogenic aerosols. The strategy involves a four-step program for shifting the current assumption-laden estimates to an increasingly empirical basis using satellite observations coordinated with suborbital remote and in situ measurements and with chemical transport models. Conceptually, the problem is framed as a need for complete global mapping of four parameters: clear-sky aerosol optical depth δ, radiative efficiency per unit optical depth E, fine-mode fraction of optical depth ff, and the anthropogenic fraction of the fine mode faf. The first three parameters can be retrieved from satellites, but correlative, suborbital measurements are required for quantifying the aerosol properties that control E, for validating the retrieval of ff, and for partitioning fine-mode δ between natural and anthropogenic components. The satellite focus is on the “A-Train,” a constellation of six spacecraft that will fly in formation from about 2005 to 2008. Key satellite instruments for this report are the Moderate Resolution Imaging Spectroradiometer (MODIS) and Clouds and the Earth's Radiant Energy System (CERES) radiometers on Aqua, the Ozone Monitoring Instrument (OMI) radiometer on Aura, the Polarization and Directionality of Earth's Reflectances (POLDER) polarimeter on the Polarization and Anistropy of Reflectances for Atmospheric Sciences Coupled with Observations from a Lidar (PARASOL), and the Cloud and Aerosol Lider with Orthogonal Polarization (CALIOP) lidar on the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO). This strategy is offered as an initial framework—subject to improvement over time—for scientists around the world to participate in the A-Train opportunity. It is a specific implementation of the Progressive Aerosol Retrieval and Assimilation Global Observing Network (PARAGON) program, presented earlier in this journal, which identified the integration of diverse data as the central challenge to progress in quantifying global-scale aerosol effects. By designing a strategy around this need for integration, we develop recommendations for both satellite data interpretation and correlative suborbital activities that represent, in many respects, departures from current practice

Estimating the direct aerosol radiative perturbation: impact of ocean surface representation and aerosol non-sphericity

Atmospheric aerosols are now actively studied, in particular because of their radiative and climate impacts. Estimations of the direct aerosol radiative perturbation, caused by extinction of incident solar radiation, usually rely on radiative transfer codes and involve simplifying hypotheses. This paper addresses two approximations which are widely used for the sake of simplicity and limiting the computational cost of the calculations. Firstly, it is shown that using a Lambertian albedo instead of the more rigorous bidirectional reflectance distribution function (BRDF) to model the ocean surface radiative properties leads to large relative errors in the instantaneous aerosol radiative perturbation. When averaging over the day, these errors cancel out to acceptable levels of less than 3% (except in the northern hemisphere winter). The other scope of this study is to address aerosol non-sphericity effects. Comparing an experimental phase function with an equivalent Mie-calculated phase function, we found acceptable relative errors if the aerosol radiative perturbation calculated for a given optical thickness is daily averaged. However, retrieval of the optical thickness of non-spherical aerosols assuming spherical particles can lead to significant errors. This is due to significant differences between the spherical and non-spherical phase functions. Discrepancies in aerosol radiative perturbation between the spherical and non-spherical cases are sometimes reduced and sometimes enhanced if the aerosol optical thickness for the spherical case is adjusted to fit the simulated radiance of the non-spherical case.