Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

Ultralow-frequency modulation of whistler-mode wave growth

Measurements from ground-based magnetometers and riometers at auroral latitudes have demonstrated that energetic (~30-300keV) electron precipitation can be modulated in the presence of magnetic field oscillations at ultra-low frequencies. It has previously been proposed that an ultra-low frequency (ULF) wave would modulate field and plasma properties near the equatorial plane, thus modifying the growth rates of whistler-mode waves. In turn, the resulting whistler-mode waves would mediate the pitch-angle scattering of electrons resulting in ionospheric precipitation. In this paper, we investigate this hypothesis by quantifying the changes to the linear growth rate expected due to a slow change in the local magnetic field strength for parameters typical of the equatorial region around 6.6RE radial distance. To constrain our study, we determine the largest possible ULF wave amplitudes from measurements of the magnetic field at geosynchronous orbit. Using nearly ten years of observations from two satellites, we demonstrate that the variation in magnetic field strength due to oscillations at 2mHz does not exceed ±10% of the background field. Modifications to the plasma density and temperature anisotropy are estimated using idealised models. For low temperature anisotropy, there is little change in the whistler-mode growth rates even for the largest ULF wave amplitude. Only for large temperature anisotropies can whistler-mode growth rates be modulated sufficiently to account for the changes in electron precipitation measured by riometers at auroral latitudes.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Wave activity in the tropical tropopause layer in seven reanalysis and four chemistry climate model data sets

Sub-seasonal variability including equatorial waves significantly influence the dehydration and transport processes in the tropical tropopause layer (TTL). This study investigates the wave activity in the TTL in 7 reanalysis data sets (RAs; NCEP1, NCEP2, ERA40, ERA-Interim, JRA25, MERRA, and CFSR) and 4 chemistry climate models (CCMs; CCSRNIES, CMAM, MRI, and WACCM) using the zonal wave number-frequency spectral analysis method with equatorially symmetric-antisymmetric decomposition. Analyses are made for temperature and horizontal winds at 100 hPa in the RAs and CCMs and for outgoing longwave radiation (OLR), which is a proxy for convective activity that generates tropopause-level disturbances, in satellite data and the CCMs. Particular focus is placed on equatorial Kelvin waves, mixed Rossby-gravity (MRG) waves, and the Madden-Julian Oscillation (MJO). The wave activity is defined as the variance, i.e., the power spectral density integrated in a particular zonal wave number-frequency region. It is found that the TTL wave activities show significant difference among the RAs, ranging from ∼0.7 (for NCEP1 and NCEP2) to ∼1.4 (for ERA-Interim, MERRA, and CFSR) with respect to the averages from the RAs. The TTL activities in the CCMs lie generally within the range of those in the RAs, with a few exceptions. However, the spectral features in OLR for all the CCMs are very different from those in the observations, and the OLR wave activities are too low for CCSRNIES, CMAM, and MRI. It is concluded that the broad range of wave activity found in the different RAs decreases our confidence in their validity and in particular their value for validation of CCM performance in the TTL, thereby limiting our quantitative understanding of the dehydration and transport processes in the TTL.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

Simple method for sub-diffraction resolution imaging of cellular structures on standard confocal microscopes by three-photon absorption of quantum dots

This study describes a simple technique that improves a recently developed 3D sub-diffraction imaging method based on three-photon absorption of commercially available quantum dots. The method combines imaging of biological samples via tri-exciton generation in quantum dots with deconvolution and spectral multiplexing, resulting in a novel approach for multi-color imaging of even thick biological samples at a 1.4 to 1.9-fold better spatial resolution. This approach is realized on a conventional confocal microscope equipped with standard continuous-wave lasers. We demonstrate the potential of multi-color tri-exciton imaging of quantum dots combined with deconvolution on viral vesicles in lentivirally transduced cells as well as intermediate filaments in three-dimensional clusters of mouse-derived neural stem cells (neurospheres) and dense microtubuli arrays in myotubes formed by stacks of differentiated C2C12 myoblasts.

Easterly wave disturbances over Northeast Brazil: an observational analysis

This paper aims to identify the circulation associated with Easterly Wave Disturbances (EWDs) that propagate toward the Eastern Northeast Brazil (ENEB) and their impact on the rainfall over ENEB during 2006 and 2007 rainy seasons (April–July). The EWDs identification and trajectory are analyzed using an automatic tracking technique (TracKH). The EWDs circulation patterns and their main features were obtained using the composite technique. To evaluate the TracKH efficiency, a validation was done by comparing the EWDs number tracked against observed cases obtained from an observational analysis. The mean characteristics of EWDs are 5.5-day period, propagation speed of ~9.5 m·s−1, and a 4500 km wavelength. A synoptic analysis shows that between days −2 d and 0 d, the low level winds presented cyclonic relative vorticity and convergence anomalies both in 2006 and 2007. The EWDs signals are strongest at low levels. The EWDs propagation is associated with relative humidity and precipitation positive anomalies and OLR and omega negative anomalies. The EWDs tracks are seen over all ENEB and their lysis occurs between the ENEB and marginally inside the continent. The tracking captured 71% of EWDs in all periods, indicating that an objective analysis is a promising method for EWDs detection.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Geometric polarimetry − part I: spinors and wave states

A new formal approach for representation of polarization states of coherent and partially coherent electromagnetic plane waves is presented. Its basis is a purely geometric construction for the normalised complex-analytic coherent wave as a generating line in the sphere of wave directions, and whose Stokes vector is determined by the intersection with the conjugate generating line. The Poincare sphere is now located in physical space, simply a coordination of the wave sphere, its axis aligned with the wave vector. Algebraically, the generators representing coherent states are represented by spinors, and this is made consistent with the spinor-tensor representation of electromagnetic theory by means of an explicit reference spinor we call the phase flag. As a faithful unified geometric representation, the new model provides improved formal tools for resolving many of the geometric difficulties and ambiguities that arise in the traditional formalism.

SURFACE ALFVEN WAVE DAMPING IN A THREE-DIMENSIONAL SIMULATION OF THE SOLAR WIND

Here we investigate the contribution of surface Alfven wave damping to the heating of the solar wind in minima conditions. These waves are present in the regions of strong inhomogeneities in density or magnetic field (e.g., the border between open and closed magnetic field lines). Using a three-dimensional (3D) magnetohydrodynamics (MHD) model, we calculate the surface Alfven wave damping contribution between 1 and 4 R(circle dot) (solar radii), the region of interest for both acceleration and coronal heating. We consider waves with frequencies lower than those that are damped in the chromosphere and on the order of those dominating the heliosphere: 3 x 10(-6) to 10(-1) Hz. In the region between open and closed field lines, within a few R(circle dot) of the surface, no other major source of damping has been suggested for the low frequency waves we consider here. This work is the first to study surface Alfven waves in a 3D environment without assuming a priori a geometry of field lines or magnetic and density profiles. We demonstrate that projection effects from the plane of the sky to 3D are significant in the calculation of field line expansion. We determine that waves with frequencies >2.8 x 10(-4) Hz are damped between 1 and 4 R(circle dot). In quiet-Sun regions, surface Alfven waves are damped at further distances compared to active regions, thus carrying additional wave energy into the corona. We compare the surface Alfven wave contribution to the heating by a variable polytropic index and find it as an order of magnitude larger than needed for quiet-Sun regions. For active regions, the contribution to the heating is 20%. As it has been argued that a variable gamma acts as turbulence, our results indicate that surface Alfven wave damping is comparable to turbulence in the lower corona. This damping mechanism should be included self-consistently as an energy driver for the wind in global MHD models.

Coda wave attenuation in the Parecis Basin, Amazon Craton, Brazil: sensitivity to basement depth

Small local earthquakes from two aftershock sequences in Porto dos GaA(0)chos, Amazon craton-Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q (c)) of coda waves modeled usingwhere Q (0) is the coda quality factor at frequency of 1 Hz and eta is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239-252, 2008), based in the temporal attenuation coefficient, chi(f) instead of Q(f), given by the equation for the calculation of the geometrical attenuation (gamma) and effective attenuation Q (c) values have been computed at central frequencies (and band) of 1.5 (1-2), 3.0 (2-4), 6.0 (4-8), 9.0 (6-12), 12 (8-16), and 18 (12-24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin for the surrounding shield and for the whole region of Porto dos GaA(0)chos Using the independent frequency model, we found: for the cratonic zone, gamma = 0.014 s (-aEuro parts per thousand 1), nu a parts per thousand 1.12; for the basin zone with sediments of similar to 500 m, gamma = 0.031 s (-aEuro parts per thousand 1), nu a parts per thousand 1.27; and for the Parecis basin with sediments of similar to 1,000 m, gamma = 0.047 s (-aEuro parts per thousand 1), nu a parts per thousand 1.42. Analysis of the attenuation factor (Q (c)) for different values of the geometrical spreading parameter (nu) indicated that an increase of nu generally causes an increase in Q (c), both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, (in the deepest part of the basin), than in the basement, (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.

An automatic correction method for the heel effect in digitized mammography images

The most significant radiation field nonuniformity is the well-known Heel effect. This nonuniform beam effect has a negative influence on the results of computer-aided diagnosis of mammograms, which is frequently used for early cancer detection. This paper presents a method to correct all pixels in the mammography image according to the excess or lack on radiation to which these have been submitted as a result of the this effect. The current simulation method calculates the intensities at all points of the image plane. In the simulated image, the percentage of radiation received by all the points takes the center of the field as reference. In the digitized mammography, the percentages of the optical density of all the pixels of the analyzed image are also calculated. The Heel effect causes a Gaussian distribution around the anode-cathode axis and a logarithmic distribution parallel to this axis. Those characteristic distributions are used to determine the center of the radiation field as well as the cathode-anode axis, allowing for the automatic determination of the correlation between these two sets of data. The measurements obtained with our proposed method differs on average by 2.49 mm in the direction perpendicular to the anode-cathode axis and 2.02 mm parallel to the anode-cathode axis of commercial equipment. The method eliminates around 94% of the Heel effect in the radiological image and the objects will reflect their x-ray absorption. To evaluate this method, experimental data was taken from known objects, but could also be done with clinical and digital images.

Er : YAB nanoparticles and vitreous thin films by the polymeric precursor method

The synthesis of Y(0.9)Er(0.1)Al(3)(BO(3))(4) crystalline powders and vitreous thin films were studied. Precursor solutions were obtained using a modified polymeric precursor method using D-sorbitol as complexant agent. The chemical reactions were described. Y(0.)9Er(0.1)Al(3)(BO(3))(4) composition presents good thermal stability with regard to crystallization. The Y(0.9)Er(0.1)Al(3)(BO(3))(4) crystallized phase can be obtained at 1,150 degrees C, in agreement with other authors. Crack- and porosity-free films were obtained with very small grain size and low RMS roughness. The films thickness revealed to be linearly dependent on precursor solution viscosity, being the value of 25 mPa s useful to prepare high-quality amorphous multi-layers (up to similar to 800 nm) at 740 degrees C during 2 h onto silica substrates by spin coating with a gyrset technology.