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.

Two- and three-dimensional shape fabric analysis by the intercept method in grey levels

The count intercept is a robust method for the numerical analysis of fabrics Launeau and Robin (1996). It counts the number of intersections between a set of parallel scan lines and a mineral phase, which must be identified on a digital image. However, the method is only sensitive to boundaries and therefore supposes the user has some knowledge about their significance. The aim of this paper is to show that a proper grey level detection of boundaries along scan lines is sufficient to calculate the two-dimensional anisotropy of grain or crystal distributions without any particular image processing. Populations of grains and crystals usually display elliptical anisotropies in rocks. When confirmed by the intercept analysis, a combination of a minimum of 3 mean length intercept roses, taken on 3 more or less perpendicular sections, allows the calculation of 3-dimensional ellipsoids and the determination of their standard deviation with direction and intensity in 3 dimensions as well. The feasibility of this quick method is attested by numerous examples on theoretical objects deformed by active and passive deformation, on BSE images of synthetic magma flow, on drawing or direct analysis of thin section pictures of sandstones and on digital images of granites directly taken and measured in the field. (C) 2010 Elsevier B.V. All rights reserved.

Square wave adsorptive cathodic stripping voltarnmetry automated by sequential injection analysis - Potentialities and limitations exemplified by the determination of methyl parathion in water samples

This paper describes the development and evaluation of a sequential injection method to automate the determination of methyl parathion by square wave adsorptive cathodic stripping voltammetry exploiting the concept of monosegmented flow analysis to perform in-line sample conditioning and standard addition. Accumulation and stripping steps are made in the sample medium conditioned with 40 mmol L-1 Britton-Robinson buffer (pH 10) in 0.25 mol L-1 NaNO3. The homogenized mixture is injected at a flow rate of 10 mu Ls(-1) toward the flow cell, which is adapted to the capillary of a hanging drop mercury electrode. After a suitable deposition time, the flow is stopped and the potential is scanned from -0.3 to -1.0 V versus Ag/AgCl at frequency of 250 Hz and pulse height of 25 mV The linear dynamic range is observed for methyl parathion concentrations between 0.010 and 0.50 mgL(-1), with detection and quantification limits of 2 and 7 mu gL(-1), respectively. The sampling throughput is 25 h(-1) if the in line standard addition and sample conditioning protocols are followed, but this frequency can be increased up to 61 h(-1) if the sample is conditioned off-line and quantified using an external calibration curve. The method was applied for determination of methyl parathion in spiked water samples and the accuracy was evaluated either by comparison to high performance liquid chromatography with UV detection, or by the recovery percentages. Although no evidences of statistically significant differences were observed between the expected and obtained concentrations, because of the susceptibility of the method to interference by other pesticides (e.g., parathion, dichlorvos) and natural organic matter (e.g., fulvic and humic acids), isolation of the analyte may be required when more complex sample matrices are encountered. (C) 2007 Elsevier B.V. All rights reserved.

A New Indirect Electroanalytical Method to Monitor the Contamination of Natural Waters with 4-Nitrophenol Using Multiwall Carbon Nanotubes

The electrochemical detection of the hazardous pollutant 4-nitrophenol (4-NP) at low potentials, in order to avoid matrix interferences, is an important research challenge. This study describes the development, electrochemical characterization and utilization of a multiwall carbon nanotube (MWCNT) film electrode for the quantitative determination of 4-NP in natural water. Electrochemical impedence spectroscopy measurements showed that the modified surface exhibits a decrease of ca. 13 times in the charge transfer resistance when compared with a bare glassy carbon (GC) surface. Voltammetric experiments showed the possibility to oxidize a hydroxylamine layer (produced by the electrochemical reduction of 4-NP on the GC/MWNCT surface) in a potential region which is approximately 700 mV less positive than that needed to oxidize 4-NP, thus minimizing the interference of matrix components. The limit of detection for 4-NP obtained using square-wave voltammetry (0.12 mu mol L(-1)) was lower than the value advised by EPA. A natural water sample from a dam located in Sao Carlos (Brazil) was spiked with 4-NP and analyzed by the standard addition method using thee GC/MWCNT electrode, without any further purification step. the recovery procedure yielded a value of 96.5% for such sample, thus confirming the suitability of the developed method to determine 4-NP in natural water samples. The electrochemical determination was compared with that obtained by HPLC with UV-vis detection.