A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

On the harmonic analysis of cup anemometer rotation speed: A principle to monitor performance and maintenance status of rotating meteorological sensors

The calibration results of one anemometer equipped with several rotors, varying their size, were analyzed. In each case, the 30-pulses pert turn output signal of the anemometer was studied using Fourier series decomposition and correlated with the anemometer factor (i.e., the anemometer transfer function). Also, a 3-cup analytical model was correlated to the data resulting from the wind tunnel measurements. Results indicate good correlation between the post-processed output signal and the working condition of the cup anemometer. This correlation was also reflected in the results from the proposed analytical model. With the present work the possibility of remotely checking cup anemometer status, indicating the presence of anomalies and, therefore, a decrease on the wind sensor reliability is revealed.

Availability and uptake of trace elements in a forage rotation under conservation and plough tillage

After 14 years under conventional plough tillage (CT) or conservation minimum tillage (MT), the soil available Al, Fe, Mn, Cu and Zn (0-5, 5-15 and 15-30 cm layers) and their plant uptake were evaluated during two years in a ryegrass-maize forage rotation in NW Spain (t emperate-humid region). The three-way ANOVA showed that trace element concentrations in soil were mainly influenced by sampling date, followed by soil depth and tillage system (35-73 %, 7-58 % and 3- 11 % of variance explained, respectively). Excepting for Fe (CT) and Al (CT and MT), the elemental concentrations decreased with depth, the stratification being stronger under MT. For soil available Al, Fe, Mn and Cu, the concentrations were higher in CT than in MT (5-15 and 15-30 cm layers) or were not affected by tillage system (0-5 cm). In contrast, the available Zn contents were higher in MT than CT at the soil surface and did not differ in deeper layers. The concentration of Al, Fe and Cu in crops were not influenced by tillage system, which explain 22 % of Mn variance in maize (CT > MT in the more humid year) and 18 % of Zn variance in ryegrass (MT > CT in both years). However, in the summer crop (maize) the concentrations of Fe, Mn and Zn tended to be higher in MT than in CT under drought conditions, while the opposite was true in the year without water limitation. Therefore, under the studied conditions of climate, soil, tillage and crop rotation, little influence of tillage system on crop nutritive value would be expected. To minimize the potential deficiency of Zn (maize) and Cu (maize and ryegrass) on crop yields the inclusion of these micro-nutrients in fertilization schedule is reco mmended, as well as liming to alleviate Al toxicity on maize crops.

Soil P and cation availability and crop uptake in a forage rotation under conventional and reduced tillage

Long-term conservation tillage can modify vertical distribution of nutrients in soil profiles and alter nutrient availability and yields of crops.

Model inter-comparison on crop rotation effects ? an intermediate report

Data of diverse crop rotations from five locations across Europe were distributed to modelers to investigate the capability of models to handle complex crop rotations and management interactions.

Comparative study of the effect of several trains on the ballast rotation

The ballast pick-up (or ballast train-induced-wind erosion (BTE)) phenomenon is a limiting factor for the maximum allowed operational train speed. The determination of the conditions for the initiation of the motion of the ballast stones due to the wind gust created by high-speed trains is critical to predict the start of ballast pick-up because, once the motion is initiated, a saltation-like chain reaction can take place. The aim of this paper is to present a model to evaluate the effect of a random aerodynamic impulse on stone motion initiation, and an experimental study performed to check the capability of the proposed model to classify trains by their effect on the ballast due to the flow generated by the trains. A measurement study has been performed at kp 69 + 500 on the Madrid – Barcelona High Speed Line. The obtained results show the feasibility of the proposed method, and contribute to a technique for BTE characterization, which can be relevant for the development of train interoperability standards

Subunit rotation in Escherichia coli FoF1–ATP synthase during oxidative phosphorylation

We report evidence for proton-driven subunit rotation in membrane-bound FoF1–ATP synthase during oxidative phosphorylation. A βD380C/γC87 crosslinked hybrid F1 having epitope-tagged βD380C subunits (βflag) exclusively in the two noncrosslinked positions was bound to Fo in F1-depleted membranes. After reduction of the β–γ crosslink, a brief exposure to conditions for ATP synthesis followed by reoxidation resulted in a significant amount of βflag appearing in the β–γ crosslinked product. Such a reorientation of γC87 relative to the three β subunits can only occur through subunit rotation. Rotation was inhibited when proton transport through Fo was blocked or when ADP and Pi were omitted. These results establish FoF1 as the second example in nature where proton transport is coupled to subunit rotation.

Absence of a barrier to backwards rotation of the bacterial flagellar motor demonstrated with optical tweezers

A cell of the bacterium Escherichia coli was tethered covalently to a glass coverslip by a single flagellum, and its rotation was stopped by using optical tweezers. The tweezers acted directly on the cell body or indirectly, via a trapped polystyrene bead. The torque generated by the flagellar motor was determined by measuring the displacement of the laser beam on a quadrant photodiode. The coverslip was mounted on a computer-controlled piezo-electric stage that moved the tether point in a circle around the center of the trap so that the speed of rotation of the motor could be varied. The motor generated ≈4500 pN nm of torque at all angles, regardless of whether it was stalled, allowed to rotate very slowly forwards, or driven very slowly backwards. This argues against models of motor function in which rotation is tightly coupled to proton transit and back-transport of protons is severely limited.

Inactivating one hippocampus impairs avoidance of a stable room-defined place during dissociation of arena cues from room cues by rotation of the arena

Unilateral intrahippocampal injections of tetrodotoxin were used to temporarily inactivate one hippocampus during specific phases of training in an active allothetic place avoidance task. The rat was required to use landmarks in the room to avoid a room-defined sector of a slowly rotating circular arena. The continuous rotation dissociated room cues from arena cues and moved the arena surface through a part of the room in which foot-shock was delivered. The rat had to move away from the shock zone to prevent being transported there by the rotation. Unilateral hippocampal inactivations profoundly impaired acquisition and retrieval of the allothetic place avoidance. Posttraining unilateral hippocampal inactivation also impaired performance in subsequent sessions. This allothetic place avoidance task seems more sensitive to hippocampal disruption than the standard water maze task because the same unilateral hippocampal inactivation does not impair performance of the variable-start, fixed hidden goal task after procedural training. The results suggest that the hippocampus not only encodes allothetic relationships amongst landmarks, it also organizes perceived allothetic stimuli into systems of mutually stable coordinates. The latter function apparently requires greater hippocampal integrity.

Energy-driven subunit rotation at the interface between subunit a and the c oligomer in the FO sector of Escherichia coli ATP synthase

Subunit rotation within the F1 catalytic sector of the ATP synthase has been well documented, identifying the synthase as the smallest known rotary motor. In the membrane-embedded FO sector, it is thought that proton transport occurs at a rotor/stator interface between the oligomeric ring of c subunits (rotor) and the single-copy a subunit (stator). Here we report evidence for an energy-dependent rotation at this interface. FOF1 was expressed with a pair of substituted cysteines positioned to allow an intersubunit disulfide crosslink between subunit a and a c subunit [aN214C/cM65C; Jiang, W. & Fillingame, R. H. (1998) Proc. Natl. Acad. Sci. USA 95, 6607–6612]. Membranes were treated with N,N′-dicyclohexyl-[14C]carbodiimide to radiolabel the D61 residue on less than 20% of the c subunits. After oxidation to form an a–c crosslink, the c subunit properly aligned to crosslink to subunit a was found to contain very little 14C label relative to other members of the c ring. However, exposure to MgATP before oxidation significantly increased the radiolabel in the a–c crosslink, indicating that a different c subunit was now aligned with subunit a. This increase was not induced by exposure to MgADP/Pi. Furthermore, preincubation with MgADP and azide to inhibit F1 or with high concentrations of N,N′-dicyclohexylcarbodiimide to label most c subunits prevented the ATP effect. These results provide evidence for an energy-dependent rotation of the c ring relative to subunit a.

Rotation of subunits during catalysis by Escherichia coli F1-ATPase.

During oxidative and photo-phosphorylation, F0F1-ATP synthases couple the movement of protons down an electrochemical gradient to the synthesis of ATP. One proposed mechanistic feature that has remained speculative is that this coupling process requires the rotation of subunits within F0F1. Guided by a recent, high-resolution structure for bovine F1 [Abrahams, J. P., Leslie, A. G., Lutter, R. & Walker, J. E. (1994) Nature (London) 370, 621-628], we have developed a critical test for rotation of the central gamma subunit relative to the three catalytic beta subunits in soluble F1 from Escherichia coli. In the bovine F1 structure, a specific point of contact between the gamma subunit and one of the three catalytic beta subunits includes positioning of the homolog of E. coli gamma-subunit C87 (gamma C87) close to the beta-subunit 380DELSEED386 sequence. A beta D380C mutation allowed us to induce formation of a specific disulfide bond between beta and gamma C87 in soluble E. coli F1. Formation of the crosslink inactivated beta D380C-F1, and reduction restored full activity. Using a dissociation/reassembly approach with crosslinked beta D380C-F1, we incorporated radiolabeled beta subunits into the two noncrosslinked beta-subunit positions of F1. After reduction of the initial nonradioactive beta-gamma crosslink, only exposure to conditions for catalytic turnover results in similar reactivities of unlabeled and radiolabeled beta subunits with gamma C87 upon reoxidation. The results demonstrate that gamma subunit rotates relative to the beta subunits during catalysis.

Magnetic activity and differential rotation in the young Sun-like stars KIC 7985370 and KIC 7765135

Aims. We present a detailed study of the two Sun-like stars KIC 7985370 and KIC 7765135, to determine their activity level, spot distribution, and differential rotation. Both stars were previously discovered by us to be young stars and were observed by the NASA Kepler mission. Methods. The fundamental stellar parameters (vsini, spectral type, T_eff, log g, and [Fe/H]) were derived from optical spectroscopy by comparison with both standard-star and synthetic spectra. The spectra of the targets allowed us to study the chromospheric activity based on the emission in the core of hydrogen Hα and Ca ii infrared triplet (IRT) lines, which was revealed by the subtraction of inactive templates. The high-precision Kepler photometric data spanning over 229 days were then fitted with a robust spot model. Model selection and parameter estimation were performed in a Bayesian manner, using a Markov chain Monte Carlo method. Results. We find that both stars are Sun-like (of G1.5 V spectral type) and have an age of about 100–200 Myr, based on their lithium content and kinematics. Their youth is confirmed by their high level of chromospheric activity, which is comparable to that displayed by the early G-type stars in the Pleiades cluster. The Balmer decrement and flux ratio of their Ca ii-IRT lines suggest that the formation of the core of these lines occurs mainly in optically thick regions that are analogous to solar plages. The spot model applied to the Kepler photometry requires at least seven persistent spots in the case of KIC 7985370 and nine spots in the case of KIC 7765135 to provide a satisfactory fit to the data. The assumption of the longevity of the star spots, whose area is allowed to evolve with time, is at the heart of our spot-modelling approach. On both stars, the surface differential rotation is Sun-like, with the high-latitude spots rotating slower than the low-latitude ones. We found, for both stars, a rather high value of the equator-to-pole differential rotation (dΩ ≈ 0.18 rad d^-1), which disagrees with the predictions of some mean-field models of differential rotation for rapidly rotating stars. Our results agree instead with previous works on solar-type stars and other models that predict a higher latitudinal shear, increasing with equatorial angular velocity, that can vary during the magnetic cycle.

Chromospheric activity and rotation of FGK stars in the solar vicinity. An estimation of the radial velocity jitter

Context. Chromospheric activity produces both photometric and spectroscopic variations that can be mistaken as planets. Large spots crossing the stellar disc can produce planet-like periodic variations in the light curve of a star. These spots clearly affect the spectral line profiles, and their perturbations alter the line centroids creating a radial velocity jitter that might “contaminate” the variations induced by a planet. Precise chromospheric activity measurements are needed to estimate the activity-induced noise that should be expected for a given star. Aims. We obtain precise chromospheric activity measurements and projected rotational velocities for nearby (d ≤ 25 pc) cool (spectral types F to K) stars, to estimate their expected activity-related jitter. As a complementary objective, we attempt to obtain relationships between fluxes in different activity indicator lines, that permit a transformation of traditional activity indicators, i.e., Ca II H & K lines, to others that hold noteworthy advantages. Methods. We used high resolution (~50 000) echelle optical spectra. Standard data reduction was performed using the IRAF ECHELLE package. To determine the chromospheric emission of the stars in the sample, we used the spectral subtraction technique. We measured the equivalent widths of the chromospheric emission lines in the subtracted spectrum and transformed them into fluxes by applying empirical equivalent width and flux relationships. Rotational velocities were determined using the cross-correlation technique. To infer activity-related radial velocity (RV) jitter, we used empirical relationships between this jitter and the R’_HK index. Results. We measured chromospheric activity, as given by different indicators throughout the optical spectra, and projected rotational velocities for 371 nearby cool stars. We have built empirical relationships among the most important chromospheric emission lines. Finally, we used the measured chromospheric activity to estimate the expected RV jitter for the active stars in the sample.

Cyclobutadiene automerization and rotation of ethylene: Energetics of the barriers by using Spin-polarized wave functions

Spin-projected spin polarized Møller–Plesset and spin polarized coupled clusters calculations have been made to estimate the cyclobutadiene automerization, the ethylene torsion barriers in their ground state, and the gap between the singlet and triplet states of ethylene. The results have been obtained optimizing the geometries at MP4 and/or CCSD levels, by an extensive Gaussian basis set. A comparative analysis with more complex calculations, up to MP5 and CCSDTQP, together with others from the literature, have also been made, showing the efficacy of using spin-polarized wave functions as a reference wave function for Møller–Plesset and coupled clusters calculations, in such problems.