Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

BTBPs versus BTPhens: some reasons for their differences in properties concerning the partitioning of minor actinides and the advantages of BTPhens

Two members of the tetradentate N-donor ligand families 6,6′-bis(1,2,4-triazin-3-yl)-2,2′-bipyridine (BTBP) and 2,9-bis(1,2,4-triazin-3-yl)-1,10-phenanthroline (BTPhen) currently being developed for separating actinides from lanthanides have been studied. It has been confirmed that CyMe4-BTPhen 2 has faster complexation kinetics than CyMe4-BTBP 1. The values for the HOMO−LUMO gap of 2 are comparable with those of CyMe4-BTBP 1 for which the HOMO−LUMO gap was previously calculated to be 2.13 eV. The displacement of BTBP from its bis-lanthanum(III) complex by BTPhen was observed by NMR, and constitutes the only direct evidence for the greater thermodynamic stability of the complexes of BTPhen. NMR competition experiments suggest the following order of bis-complex stability: 1:2 bis-BTPhen complex ≥ heteroleptic BTBP/BTPhen 1:2 bis-complex > 1:2 bis-BTBP complex. Kinetics studies on some bis-triazine N-donor ligands using the stopped-flow technique showed a clear relationship between the rates of metal ion complexation and the degree to which the ligand is preorganized for metal binding. The BTBPs must overcome a significant (ca. 12 kcal mol−1) energy barrier to rotation about the central biaryl C−C axis in order to achieve the cis−cis conformation that is required to form a complex, whereas the cis−cis conformation is fixed in the BTPhens. Complexation thermodynamics and kinetics studies in acetonitrile show subtle differences between the thermodynamic stabilities of the complexes formed, with similar stability constants being found for both ligands. The first crystal structure of a 1:1 complex of CyMe4-BTPhen 2 with Y(NO3)3 is also reported. The metal ion is 10- coordinate being bonded to the tetradentate ligand 2 and three bidentate nitrate ions. The tetradentate ligand is nearly planar with angles between consecutive rings of 16.4(2)°, 6.4(2)°, 9.7(2)°, respectively.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Jet characterization in the upper troposphere/lower stratosphere (UTLS): applications to climatology and transport studies

A method of classifying the upper tropospheric/lower stratospheric (UTLS) jets has been developed that allows satellite and aircraft trace gas data and meteorological fields to be efficiently mapped in a jet coordinate view. A detailed characterization of multiple tropopauses accompanies the jet characterization. Jet climatologies show the well-known high altitude subtropical and lower altitude polar jets in the upper troposphere, as well as a pattern of concentric polar and subtropical jets in the Southern Hemisphere, and shifts of the primary jet to high latitudes associated with blocking ridges in Northern Hemisphere winter. The jet-coordinate view segregates air masses differently than the commonly-used equivalent latitude (EqL) coordinate throughout the lowermost stratosphere and in the upper troposphere. Mapping O3 data from the Aura Microwave Limb Sounder (MLS) satellite and the Winter Storms aircraft datasets in jet coordinates thus emphasizes different aspects of the circulation compared to an EqL-coordinate framework: the jet coordinate reorders the data geometrically, thus highlighting the strong PV, tropopause height and trace gas gradients across the subtropical jet, whereas EqL is a dynamical coordinate that may blur these spatial relationships but provides information on irreversible transport. The jet coordinate view identifies the concentration of stratospheric ozone well below the tropopause in the region poleward of and below the jet core, as well as other transport features associated with the upper tropospheric jets. Using the jet information in EqL coordinates allows us to study trace gas distributions in regions of weak versus strong jets, and demonstrates weaker transport barriers in regions with less jet influence. MLS and Atmospheric Chemistry Experiment-Fourier Transform Spectrometer trace gas fields for spring 2008 in jet coordinates show very strong, closely correlated, PV, tropopause height and trace gas gradients across the jet, and evidence of intrusions of stratospheric air below the tropopause below and poleward of the subtropical jet; these features are consistent between instruments and among multiple trace gases. Our characterization of the jets is facilitating studies that will improve our understanding of upper tropospheric trace gas evolution.

Highly resolved observations of trace gases in the lowermost stratosphere and upper troposphere from the SPURT project: an overview

During SPURT (Spurenstofftransport in der Tropopausenregion, trace gas transport in the tropopause region) we performed measurements of a wide range of trace gases with different lifetimes and sink/source characteristics in the northern hemispheric upper troposphere (UT) and lowermost stratosphere (LMS). A large number of in-situ instruments were deployed on board a Learjet 35A, flying at altitudes up to 13.7 km, at times reaching to nearly 380 K potential temperature. Eight measurement campaigns (consisting of a total of 36 flights), distributed over all seasons and typically covering latitudes between 35° N and 75° N in the European longitude sector (10° W–20° E), were performed. Here we present an overview of the project, describing the instrumentation, the encountered meteorological situations during the campaigns and the data set available from SPURT. Measurements were obtained for N2O, CH4, CO, CO2, CFC12, H2, SF6, NO, NOy, O3 and H2O. We illustrate the strength of this new data set by showing mean distributions of the mixing ratios of selected trace gases, using a potential temperature-equivalent latitude coordinate system. The observations reveal that the LMS is most stratospheric in character during spring, with the highest mixing ratios of O3 and NOy and the lowest mixing ratios of N2O and SF6. The lowest mixing ratios of NOy and O3 are observed during autumn, together with the highest mixing ratios of N2O and SF6 indicating a strong tropospheric influence. For H2O, however, the maximum concentrations in the LMS are found during summer, suggesting unique (temperature- and convection-controlled) conditions for this molecule during transport across the tropopause. The SPURT data set is presently the most accurate and complete data set for many trace species in the LMS, and its main value is the simultaneous measurement of a suite of trace gases having different lifetimes and physical-chemical histories. It is thus very well suited for studies of atmospheric transport, for model validation, and for investigations of seasonal changes in the UT/LMS, as demonstrated in accompanying and elsewhere published studies.

Safe construction through design: perspectives from the site team

How does the work of designers impact on the safety of operatives at the construction site? Safety research and policy emphasize the importance of designing for safe construction, yet the interface between design and construction is poorly understood: accidents have multiple causes making it hard to establish causal links between design choices and safety outcomes. An in-depth case study of a major station project examines how professionals on the construction site perceive and manage the safety challenges of a building design. Analyses reveal understandings that, on the project studied, design has an impact on safety because of: (1) the timing of design work, where the volume of late design changes increased the difficulty of planning safe procedures, e.g. for working at height, lifting heavy items, refurbishing and demolishing old buildings; and (2) inputs from design stakeholders with insufficient practical knowledge of construction and operation required unplanned work-arounds, e.g. to coordinate different sub-systems, provide maintenance access, and manage loads during construction. These findings suggest that safety suffers where projects are under-designed, and that alongside regulation, there is a need for robust management attention to the contractual structures, incentives, processes and tools that enable clients and designers to understand material practices of construction and operation.

Genetic responses to phosphorus deficiency

Background: Phosphorus (P) is an essential macronutrient for plants. Plants take up P as phosphate (Pi) from the soil solution. Since little Pi is available in most soils, P fertilizers are applied to crops. However, the use of P fertilizers is unsustainable and may cause pollution. Consequently, there is a need to develop more P-use-efficient (PUE) crops and precise methods to monitor crop P-status. Scope: Manipulating the expression of genes to improve the PUE of crops could reduce their P fertilizer requirement. This has stimulated research towards the identification of genes and signalling cascades involved in plant responses to P deficiency. Genes that respond to P deficiency can be grouped into 'early' genes that respond rapidly and often non-specifically to P deficiency, or 'late' genes that impact on the morphology, physiology or metabolism of plants upon Prolonged P deficiency. Summary: The use of micro-array technology has allowed researchers to catalogue the genetic responses of plants to P deficiency. Genes whose expression is altered by P deficiency include various transcription factors, which are thought to coordinate plant responses to P deficiency, and other genes involved in P acquisition and tissue P economy. Several common cis-regulatory elements have been identified in the promoters of these genes, suggesting that their expression might be coordinated. It is suggested that knowledge of the genes whose expression changes in response to P deficiency might allow the development of crops with improved PUE, and could be used in diagnostic techniques to monitor P deficiency in crops either directly using 'smart' indicator plants or indirectly through transcript profiling. The development of crops with improved PUE and the adoption of diagnostic technology could reduce production costs, minimize the use of a non-renewable resource, reduce pollution and enhance biodiversity.

Repressor element 1 silencing transcription factor couples loss of pluripotency with neural induction and neural differentiation

Neural differentiation of embryonic stem cells (ESCs) requires coordinated repression of the pluripotency regulatory program and reciprocal activation of the neurogenic regulatory program. Upon neural induction, ESCs rapidly repress expression of pluripotency genes followed by staged activation of neural progenitor and differentiated neuronal and glial genes. The transcriptional factors that underlie maintenance of pluripotency are partially characterized whereas those underlying neural induction are much less explored, and the factors that coordinate these two developmental programs are completely unknown. One transcription factor, REST (repressor element 1 silencing transcription factor), has been linked with terminal differentiation of neural progenitors and more recently, and controversially, with control of pluripotency. Here, we show that in the absence of REST, coordination of pluripotency and neural induction is lost and there is a resultant delay in repression of pluripotency genes and a precocious activation of both neural progenitor and differentiated neuronal and glial genes. Furthermore, we show that REST is not required for production of radial glia-like progenitors but is required for their subsequent maintenance and differentiation into neurons, oligodendrocytes, and astrocytes. We propose that REST acts as a regulatory hub that coordinates timely repression of pluripotency with neural induction and neural differentiation.

An assessment of observed vertical flux divergence in long-term eddy-covariance measurements over two Midwestern forest ecosystems

Vertical divergence of CO2 fluxes is observed over two Midwestern AmeriFlux forest sites. The differences in ensemble averaged hourly CO2 fluxes measured at two heights above canopy are relatively small (0.2–0.5 μmol m−2 s−1), but they are the major contributors to differences (76–256 g C m−2 or 41.8–50.6%) in estimated annual net ecosystem exchange (NEE) in 2001. A friction velocity criterion is used in these estimates but mean flow advection is not accounted for. This study examines the effects of coordinate rotation, averaging time period, sampling frequency and co-spectral correction on CO2 fluxes measured at a single height, and on vertical flux differences measured between two heights. Both the offset in measured vertical velocity and the downflow/upflow caused by supporting tower structures in upwind directions lead to systematic over- or under-estimates of fluxes measured at a single height. An offset of 1 cm s−1 and an upflow/downflow of 1° lead to 1% and 5.6% differences in momentum fluxes and nighttime sensible heat and CO2 fluxes, respectively, but only 0.5% and 2.8% differences in daytime sensible heat and CO2 fluxes. The sign and magnitude of both offset and upflow/downflow angle vary between sonic anemometers at two measurement heights. This introduces a systematic and large bias in vertical flux differences if these effects are not corrected in the coordinate rotation. A 1 h averaging time period is shown to be appropriate for the two sites. In the daytime, the absolute magnitudes of co-spectra decrease with height in the natural frequencies of 0.02–0.1 Hz but increase in the lower frequencies (<0.01 Hz). Thus, air motions in these two frequency ranges counteract each other in determining vertical flux differences, whose magnitude and sign vary with averaging time period. At night, co-spectral densities of CO2 are more positive at the higher levels of both sites in the frequency range of 0.03–0.4 Hz and this vertical increase is also shown at most frequencies lower than 0.03 Hz. Differences in co-spectral corrections at the two heights lead to a positive shift in vertical CO2 flux differences throughout the day at both sites. At night, the vertical CO2 flux differences between two measurement heights are 20–30% and 40–60% of co-spectral corrected CO2 fluxes measured at the lower levels of the two sites, respectively. Vertical differences of CO2 flux are relatively small in the daytime. Vertical differences in estimated mean vertical advection of CO2 between the two measurement heights generally do not improve the closure of the 1D (vertical) CO2 budget in the air layer between the two measurement heights. This may imply the significance of horizontal advection. However, a reliable assessment of mean advection contributions in annual NEE estimate at these two AmeriFlux sites is currently an unsolved problem.

Fast identification algorithms for Gaussian process model

A class identification algorithms is introduced for Gaussian process(GP)models.The fundamental approach is to propose a new kernel function which leads to a covariance matrix with low rank,a property that is consequently exploited for computational efficiency for both model parameter estimation and model predictions.The objective of either maximizing the marginal likelihood or the Kullback–Leibler (K–L) divergence between the estimated output probability density function(pdf)and the true pdf has been used as respective cost functions.For each cost function,an efficient coordinate descent algorithm is proposed to estimate the kernel parameters using a one dimensional derivative free search, and noise variance using a fast gradient descent algorithm. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

Spectroelectrochemical study of complexes [Mo(CO)2(h3-allyl)(adiimine)(NCS)] (a-diimine ¼ bis(2,6-dimethylphenyl)- acenaphthenequinonediimine and 2,20-bipyridine) exhibiting different molecular structure and redox reactivity

The redox properties and reactivity of [Mo(CO)2(η3-allyl)(α-diimine)(NCS)] (α-diimine = bis(2,6-dimethylphenyl)-acenaphthenequinonediimine (2,6-xylyl-BIAN) and 2,2′-bipyridine (bpy)) were studied using cyclic voltammetry and IR/UV–Vis spectroelectrochemistry. [Mo(CO)2(η3-allyl)(2,6-xylyl-BIAN)(NCS)] was shown by X-ray crystallography to have an asymmetric (B-type) conformation. The extended aromatic system of the strong π-acceptor 2,6-xylyl-BIAN ligand stabilises the primary 1e−-reduced radical anion, [Mo(CO)2(η3-allyl)(2,6-xylyl-BIAN•−)(NCS)]−, that can be reduced further to give the solvento anion [Mo(CO)2(η3-allyl)(2,6-xylyl-BIAN)(THF)]−. The initial reduction of [Mo(CO)2(η3-allyl)(bpy)(NCS)] in THF at ambient temperature results in the formation of [Mo(CO)2(η3-allyl)(bpy)]2 by reaction of the remaining parent complex with [Mo(CO)2(η3-allyl)(bpy)]− produced by dissociation of NCS− from [Mo(CO)2(η3-allyl)(bpy•−)(NCS)]−. Further reduction of the dimer [Mo(CO)2(η3-allyl)(bpy)]2 restores [Mo(CO)2(η3-allyl)(bpy)]−. In PrCN at 183 K, [Mo(CO)2(η3-allyl)(2,6-xylyl-BIAN•−)(NCS)]− converts slowly to 2e−-reduced [Mo(CO)2(η3-allyl)(2,6-xylyl-BIAN)(PrCN)]− and free NCS−. At room temperature, the reduction path in PrCN involves mainly the dimer [Mo(CO)2(η3-allyl)(bpy)]2; however, the detailed course of the reduction within the spectroelectrochemical cell is complicated and involves a mixture of several unassigned products. Finally, it has been shown that the five-coordinate anion [Mo(CO)2(η3-allyl)(bpy)]− promotes in THF reduction of CO2 to CO and formate via the formation of the intermediate [Mo(CO)2(η3-allyl)(bpy)(O2CH)] and its subsequent reduction.

Visual sensor fusion for active security in robotic industrial environments

This work presents a method of information fusion involving data captured by both a standard CCD camera and a ToF camera to be used in the detection of the proximity between a manipulator robot and a human. Both cameras are assumed to be located above the work area of an industrial robot. The fusion of colour images and time of light information makes it possible to know the 3D localization of objects with respect to a world coordinate system. At the same time this allows to know their colour information. Considering that ToF information given by the range camera contains innacuracies including distance error, border error, and pixel saturation, some corrections over the ToF information are proposed and developed to improve the results. The proposed fusion method uses the calibration parameters of both cameras to reproject 3D ToF points, expressed in a common coordinate system for both cameras and a robot arm, in 2D colour images. In addition to this, using the 3D information, the motion detection in a robot industrial environment is achieved, and the fusion of information is applied to the foreground objects previously detected. This combination of information results in a matrix that links colour and 3D information, giving the possibility of characterising the object by its colour in addition to its 3D localization. Further development of these methods will make it possible to identify objects and their position in the real world, and to use this information to prevent possible collisions between the robot and such objects.

Representing 3D shape and location

The 3D shape of an object and its 3D location have traditionally thought of as very separate entities, although both can be described within a single 3D coordinate frame. Here, 3D shape and location are considered as two aspects of a view-based approach to representing depth, avoiding the use of 3D coordinate frames.

Visual sensor fusion for active security in robotic industrial environments

This work presents a method of information fusion involving data captured by both a standard charge-coupled device (CCD) camera and a time-of-flight (ToF) camera to be used in the detection of the proximity between a manipulator robot and a human. Both cameras are assumed to be located above the work area of an industrial robot. The fusion of colour images and time-of-flight information makes it possible to know the 3D localization of objects with respect to a world coordinate system. At the same time, this allows to know their colour information. Considering that ToF information given by the range camera contains innacuracies including distance error, border error, and pixel saturation, some corrections over the ToF information are proposed and developed to improve the results. The proposed fusion method uses the calibration parameters of both cameras to reproject 3D ToF points, expressed in a common coordinate system for both cameras and a robot arm, in 2D colour images. In addition to this, using the 3D information, the motion detection in a robot industrial environment is achieved, and the fusion of information is applied to the foreground objects previously detected. This combination of information results in a matrix that links colour and 3D information, giving the possibility of characterising the object by its colour in addition to its 3D localisation. Further development of these methods will make it possible to identify objects and their position in the real world and to use this information to prevent possible collisions between the robot and such objects.