Rotational Phase Research Articles

Shortening and asthenospheric flow drove Miocene vertical-axis rotations in the northern Tibetan Plateau: A palaeomagnetic study of the northeast Qaidam Basin of China

The timing and magnitude of upper crustal deformation in the northern Tibetan Plateau are important for testing models of plateau uplift and for understanding Cenozoic environmental variations and monsoon evolution in central and eastern Asia. Most published studies focus on the upward and outward growth of the northern Tibetan Plateau, whereas its tectonic, vertical-axis rotation history has received less attention. Here we evaluate paleomagnetic data from six stratigraphic sections in the northeastern Qaidam Basin of China, revealing a phase of clockwise rotation from ca. 20–11 Ma followed by counterclockwise rotation from ca. 11–5 Ma. We propose that differential crustal shortening and right-lateral shear drove early to middle Miocene clockwise rotation, whereas eastward flow of the Tibetan asthenosphere induced the post-middle Miocene counterclockwise rotation. These processes coincide with increased activity of first-order strike-slip faults in the northeastern plateau, emphasizing the important role of strike-slip faults in accommodating crustal deformation in northern Tibetan Plateau during the late Cenozoic.

ANALYSIS OF ASYMMETRIC PLASTIC BENDING DEFORMATION OF WELDED TUBE SHEETS AND DERIVATION OF A DAMAGE LAW FOR J SHAPE-C SHAPE -O SHAPE FORMING

The J shape-C shape -O shape (JCO) forming method of sheets for large-diameter longitudinally welded pipes has been widely used to manufacture oil and gas pipelines. The quality of welded pipes formed through the JCO process is directly affected by the accurate control of asymmetric bending springback and damage during the procedure. A finite element model (FEM) for JCO asymmetric bending was constructed to investigate the characteristics of asymmetric plastic bending deformation and the distribution laws of damage in JCO forming. This model was based on a nonlinear mixed hardening Lemaitre damage model coupled with the Quasi-Plastic-Elastic (QPE) model. Then, residual stress, forming shape, and damage degree of crimping, first bending, second bending, and third bending were analyzed. Moreover, the accuracy of the model was experimentally verified. Results demonstrate that, the asymmetric bending deformation process can be divided into five stages, including rigid body rotation phase, full elastic deformation phase, elastic–plastic uncladded deformation phase, elastic–plastic cladded phase, and springback phase. In the first bending, the stress centerline significantly misaligns with the mold centerline. Asymmetry is not evident in the second and third bending stages. Furthermore, the peak residual stress and peak damage can be effectively reduced by a larger punch radius, while the peak damage can be reduced by a larger die span. This study lays a foundation for optimizing the technical parameters of JCO forming. Keywords: JCO forming, asymmetric bending, finite element, QPE model, deformation characteristics

Self-shaping of triglyceride and alkane drops: Similarities and differences

Small emulsion drops typically exhibit spherical shape at positive interfacial tension due to the energy minimization principle. However, in a series of studies (Denkov et al., Nature, 2015, 528, 392–395; Cholakova et al., Nature Phys., 2021, 17, 1050–1055) we showed that alkane droplets stabilized by appropriate saturated long-chain surfactants may spontaneously change their shape upon cooling, morphing into various polyhedra; hexagonal, tetragonal and triangular platelets; rod-like particles and even synthetic swimmers. These deformations are governed by the formation of thin plastic rotator phases adjacent to the drop surface. Although alkanes have numerous industrial applications, they cannot be used in food and pharma related products, in which most often triglyceride molecules are employed. The possibility for self-shaping of triglyceride drops has been demonstrated, but the detailed understanding of the process is currently missing. In the present study, we performed model experiments aimed to reveal the conditions under which the triglyceride emulsion drops may change their shape upon cooling. We show that most of the various non-spherical shapes known for alkanes can be reproduced with triglyceride droplets providing that the surfactant adsorption layer freezes before the nucleation of the oily molecules inside the drops. By comparing the behavior of triglyceride and alkane droplets, we draw unified picture and provide guiding principles which can be used for selection of appropriate surfactants enabling the spontaneous shape deformations upon cooling of oily drops of different chemical compositions.

Cationic Ring-Opening Photopolymerization of Long-Chain Epoxides in the Rotator Phase: Confirmation, Mechanism, and Combination

Cationic Ring-Opening Photopolymerization of Long-Chain Epoxides in the Rotator Phase: Confirmation, Mechanism, and Combination

A Robust Switching Control Strategy for Three-Phase Voltage Source Converters with Uncertain Circuit Parameters

This study proposes a novel double closed-loop robust control strategy based on a power switching affine model of three-phase voltage source converters (VSCs). The aim is to overcome the challenges posed by inaccurate mathematical models, complex controller configurations, indirect switching control, and performance degradation under circuit parameters uncertainty or load variation in conventional methods. These conventional methods rely on linearization models, duty ratio regulation, and pulse width modulation (PWM) technologies. The contributions of work are the following: (1) A two-dimensional (2D) power switching affine model is constructed without any approximation or averaging. (2) The proposed approach achieves direct switching control of three-phase VSCs, eliminating the need for complex rotation coordinate transformation, PWM, and phase locking loop (PLL), which are utilized in traditional control methods. (3) The rigor of the system stability analysis is enhanced based on the 2D power switching model compared to the existing three-dimensional (3D) current switching model. (4) A simple control structure with only two control parameters is employed to address circuit parameter uncertainties. The effectiveness and superiority of the proposed method is validated through simulation and experimental comparison results.

Bound-Extended Mode Transition in Type-II Synthetic Photonic Weyl Heterostructures.

Photonic structures with Weyl points (WPs), including type I and type II, promise nontrivial surface modes and intriguing light manipulations for their three-dimensional topological bands. While previous studies mainly focus on exploring WPs in a uniform Weyl structure, here we establish Weyl heterostructures (i.e., a nonuniform Weyl lattice) with different rotational orientations in the synthetic dimension by nanostructured photonic waveguides. In this work, we unveil a transition between bound and extended modes on the interface of type-II Weyl heterostructures by tuning their rotational phases, despite the reversed topological order across the interface. This mode transition is also manifested from the total transmission to total reflection at the interface. All of these unconventional effects are attributed to the tilted dispersion of type-II Weyl band structure that can lead to mismatched bands and gaps across the interface. As a comparison, the type-I Weyl heterostructures lack the phase transition due to the untilted band structure. This work establishes a flexible scheme of artificial Weyl heterostructures that opens a new avenue toward high-dimensional topological effects and significantly enhances our capabilities in on-chip light manipulations.

Rotational phase transitions in antifluorite-type osmate and iridate compounds

We present temperature-dependent single-crystal diffraction results on seven antifluorite-type A2MeX6 compounds with Me = Os or Ir: K2OsCl6, A 2OsBr6 with A = K, Rb, Cs and NH4, and K2IrX 6 with X = Cl and Br. The structural transitions in this family arise from MeX 6 octahedron rotations that generate a rich variety of symmetries depending on the rotation axis and stacking schemes. In order to search for local distortions in the high-symmetry phase we perform refinements of anharmonic atomic displacement parameters with comprehensive data sets. Even at temperatures close to the onset of structural distortions, these refinements only yield a small improvement indicating only small anharmonic effects. The phase transitions in these antifluorites are essentially of displacive character. However, some harmonic displacement parameters are very large reflecting soft phonon modes with the softening covering large parts of the Brillouin zone. The occurrence of the rotational transitions in the antifluorite-type family can be remarkably well analyzed in terms of a tolerance factor of ionic radii.

An exact new solution of the Schrödinger equation with a zero potential energy analogous to Fick’s equation of diffusion

This paper presents a novel and exact solution of the Schrödinger equation with zero potential energy, based on the analogy with Fick’s equation of diffusion. The author derived the wavefunction of a particle in a vacuum as an error function of the rotational phase angle, which corresponds to the geometry of a flat space. This solution reduces to the sinusoidal form of the wavefunction commonly used in quantum mechanics. The author also explored the implications of this solution for the connection between quantum physics and gas mechanics, and the possibility of using error functions and general transforms to model past, present, and future events in physics. The author used computer simulations to compare the error function solution and the sinusoidal solution in terms of response time, accuracy, and fit to the geometry of a flat space. The results showed that the error function solution was superior to the sinusoidal solution in all aspects, and that it had a stronger link to the gas mechanics, useful to Quantum ASTROPHYSICS. The results also suggested that the error function solution could be used to model past, present, and future events in physics, using error functions and general transforms. This paper is a preliminary analysis of the deeper physics underlying the error function solution of the Schrödinger equation, based on the author’s previous publications on point physics generalizing to Hod-PDP mechanism, field tensor modeling, string-metrics, and information-time event matrix formulations. The paper recommends that future research should extend the error function solution to space time geometry higher dimensions, non-zero potentials, and more diverse experiments. The paper also recommends that future research should explore the applications of error functions and general transforms within physics and other mathematical physical general related fields of sciences.

Multiwavelength Pulsations and Surface Temperature Distribution in the Middle-aged Pulsar B1055–52

We present a detailed study of the X-ray emission from PSR B1055–52 using XMM-Newton observations from 2019 and 2000. The phase-integrated X-ray emission from this pulsar is poorly described by existing models of neutron star atmospheres. Instead, we confirm that, similar to other middle-aged pulsars, the best-fitting spectral model consists of two blackbody components, with substantially different temperatures and emitting areas, and a nonthermal component characterized by a power law. Our phase-resolved X-ray spectral analysis using this three-component model reveals variations in the thermal emission parameters with the pulsar’s rotational phase. These variations suggest a nonuniform temperature distribution across the neutron star’s surface, including the cold thermal component and probable hot spot(s). Such a temperature distribution can be caused by external and internal heating processes, likely a combination thereof. We observe very high pulse fractions, 60%–80% in the 0.7–1.5 keV range, dominated by the hot blackbody component. This could be related to temperature nonuniformity and potential beaming effects in an atmosphere. We find indication of a second hot spot that appears at lower energies (0.15–0.3 keV) than the first hot spot (0.5–1.5 keV) in the X-ray light curves and is offset by about half a rotation period. This finding aligns with the nearly orthogonal rotator geometry suggested by radio observations of this interpulse pulsar. If the hot spots are associated with polar caps, a possible explanation for their temperature asymmetry could be an offset magnetic dipole and/or an additional toroidal magnetic field component in the neutron star crust.

Observation of Doppler shift modulated by the internal kink mode using conventional reflectometry in the EAST tokamak

In this paper we present a new experimental observation using a conventional reflectometry technique, poloidal correlation reflectometry (PCR), in the Experimental Advanced Superconducting Tokamak (EAST). The turbulence spectrum detected by the PCR system exhibits an asymmetry and induced Doppler shift during the internal kink mode (IKM) rotation phase. This Doppler shift is the target measurement of Doppler reflectometry, but captured by conventional reflectometry. Results show that the Doppler shift is modulated by the periodic changes in the effective angle between the probing wave and cutoff layer normal, but not by plasma turbulence. The fishbone mode and saturated long-lived mode are typical IKMs, and this modulation phenomenon is observed in both cases. Moreover, the value of the Doppler shift is positively correlated with the amplitude of the IKM, even when the latter is small. However, the positive and negative frequency components of the Doppler shift can be asymmetric, which is related to the plasma configuration. A simulated analysis is performed by ray tracing to verify these observations. These results establish a clear link between and IKM rotation, and are helpful for studying the characteristics of IKM and related physical phenomena.

Production of twisted particles in magnetic fields

The use of a (quasi)uniform magnetic field opens new possibilities for the production of twisted particles having orbital angular momenta. We ascertain these possibilities. Quantum states suitable for the creation of charged particles in a uniform magnetic field are determined. The particle penetration from a solenoid to vacuum or another solenoid is analyzed in detail. It is shown that a previously proposed approach can be utilized for the successful production of twisted positrons and positroniums. We also find a new effect of increasing the uncertainty of the phase of the particle rotation with the distance passed by the particle in the solenoid. This effect, based on the fundamentals of quantum mechanics, leads to exciting new possibilities for the production of twisted particles in real solenoids without additional particle sources therein.

Secular change in the spin states of asteroids due to radiation and gravitation torques

Context. The rotation state of small asteroids is affected in the long term by perturbing torques of gravitational and radiative origin (the YORP effect). The former can be detected by a change in the spin-axis orientation in the inertial space; the latter manifests itself by a quadratic increase in the rotation phase. Aims. Direct observational evidence of the YORP effect is the primary goal of our work. This includes both the YORP detection for new objects and an improvement in the accuracy of previously known detections. Methods. We carried out photometric observations of five near-Earth asteroids: (1862) Apollo, (2100) Ra-Shalom, (85989) 1999 JD6, (138852) 2000 WN10, and (161989) Cacus. Then we applied the light-curve inversion method to all available data to determine the spin state and a convex shape model for each of the five studied asteroids. The YORP effect was modeled as a linear change of the rotation frequency υ ≡ dω/dt. In the case of (2100) Ra-Shalom, the analysis required that the spin-axis precession due to the solar gravitational torque also be included. Results. We obtained two new detections of the YORP effect: (i) υ = (2.9 ± 2.0) × 10−9 rad d−2 for (2100) Ra-Shalom, and (ii) υ = (5.5 ± 0.7) × 10−8 rad d−2 for (138852) 2000 WN10. The analysis of Ra-Shalom also reveals a precession of the spin axis with a precession constant α ~ 3000″ yr−1. This is the first such detection from Earth-bound photometric data. For the other two asteroids, we improved the accuracy of the previously reported YORP detection: (i) υ = (4.94 ± 0.09) × 10−8 rad d−2 for (1862) Apollo, and (ii) υ = (1.86 ± 0.09) × 10−8 rad d−2 for (161989) Cacus. With this value, Apollo has the most precisely determined YORP effect so far. Despite the recent report of a detected YORP effect for (85989) 1999 JD6, we show that the model without YORP cannot be rejected statistically. Therefore, the detection of the YORP effect for this asteroid requires future observations. In several of our targets, the currently available observations do not provide enough constraints on the shape model (even at large scales) to compute the theoretical YORP effect with sufficient precision. Nevertheless, the interpretation of the detected signal as the YORP effect is fairly plausible. The spin-axis precession constant of Ra-Shalom determined from observations matches the theoretically expected value. Conclusions. The total number of asteroids with a YORP detection has increased to 12. In all cases, the rotation frequency increases in time. The analysis of a rich photometric data set of irregularly shaped asteroids may require inclusion of spin-axis precession in future studies.

From convective stellar dynamo simulations to Zeeman-Doppler images

Context. Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic field of late-type stars from high-resolution spectropolarimetric observations. The results are usually described in terms of characteristics of the field topology, such as poloidality versus toroidality and axisymmetry versus non-axisymmetry, in addition to the field strength. Aims. In this study, we want to test how well these characteristics are preserved when applying the ZDI method to simulated data. We are particularly interested in how accurately the field topology is preserved and to what extent stellar parameters, such as projected rotation velocity and rotation axis inclination, influence the reconstruction. Methods. For these tests, we used published magnetic field vector data from direct numerical magnetohydrodynamic simulations taken near the surface of the simulation domain. These simulations have variable rotation rates and therefore represent different levels of activity of an otherwise Sun-like setup with a convective envelope of solar thickness. Our ZDI reconstruction is based on spherical harmonics expansion. By comparing the original values to those of the reconstructed images, we study the ability to reconstruct the surface magnetic field in terms of various characteristics of the field. Results. In general, the ZDI method works as expected. The main large-scale features are reasonably well recovered, but the strength of the recovered magnetic field is just a fraction of the original input. The quality of the reconstruction shows clear correlations with the data quality. Furthermore, there are some spurious dependencies between stellar parameters and the characteristics of the field. Conclusions. Our study uncovers some limits of ZDI. Firstly, the recovered field strength will generally be lower than the ‘real’ value, as smaller structures with opposite polarities will be blurred in the inversion. This is also seen in the relative distribution of magnetic energy in terms of the angular degree ℓ. Secondly, the axisymmetry is overestimated. The poloidality versus toroidality is better recovered. The reconstruction works better for a stronger field and faster rotation velocity. Still, the ZDI method works surprisingly well even for a weaker field and slow rotation provided the data have a high signal-to-noise ratio and good rotation phase coverage.

Surface Heterogeneity, Physical, and Shape Model of Near-Earth Asteroid (52768) 1998 OR2

On 2020 April 29, the near-Earth object (52768) 1998 OR2 experienced a close approach to Earth at a distance of 16.4 lunar distances (LD). 1998 OR2 is a potentially hazardous asteroid of absolute magnitude H = 16.04 that can currently come as close to Earth as 3.4 LD. We report here observations of this object in polarimetry, photometry, and radar. Our observations show that the physical characteristics of 1998 OR2 are similar to those of both M- and S-type asteroids. Arecibo’s radar observations provide a high radar albedo of σˆOC= 0.29 ± 0.08, suggesting that metals are present in 1998 OR2 near-surface. We find a circular polarization ratio of μ c = 0.291 ± 0.012, and the delay-Doppler images show that the surface of 1998 OR2 is a top-shape asteroid with large-scale structures such as large craters and concavities. The polarimetric observations display a consistent variation of the polarimetric response as a function of the rotational phase, suggesting that the surface of 1998 OR2 is heterogeneous. Color observations suggest an X-complex taxonomy in the Bus–DeMeo classification. Combining optical polarization, radar, and two epochs from the NEOWISE satellite observations, we derived an equivalent diameter of D = 1.80 ± 0.1 km and a visual albedo p v = 0.21 ± 0.02. Photometric and radar data provide a sidereal rotation period of P = 4.10872 ± 0.00001 hr, a pole orientation of (332.°3 ± 5°, 20.°7 ± 5°), and a shape model with dimensions of (2.08−0.10+0.10,1.93−0.10+0.10,1.60−0.05+0.05) km.

A MeerKAT view of the double pulsar eclipses

The double pulsar system, PSR J0737−3039A/B, consists of two neutron stars bound together in a highly relativistic orbit that is viewed nearly edge-on from the Earth. This alignment results in brief radio eclipses of the fast-rotating pulsar A when it passes behind the toroidal magnetosphere of the slow-rotating pulsar B. The morphology of these eclipses is strongly dependent on the geometric orientation and rotation phase of pulsar B, and their time evolution can be used to constrain the geodetic precession rate of the pulsar. We demonstrate a Bayesian inference framework for modelling high-sensitivity eclipse light curves obtained with MeerKAT between 2019 and 2023. Using a hierarchical inference approach, we obtained a precession rate of ΩSOB = 5.16°−0.34°+0.32° yr−1 (68% confidence intervals) for pulsar B, consistent with predictions from general relativity to a relative uncertainty of 6.5%. This updated measurement provides a 6.1% test of relativistic spin-orbit coupling in the strong-field regime. We show that a simultaneous fit to all of our observed eclipses can in principle return a ∼1.5% test of spin-orbit coupling. However, systematic effects introduced by the current geometric orientation of pulsar B along with inconsistencies between the observed and predicted eclipse light curves result in difficult to quantify uncertainties when using this approach. Assuming the validity of general relativity, we definitively show that the spin axis of pulsar B is misaligned from the total angular momentum vector by 40.6° ±0.1° and that the orbit of the system is inclined by approximately 90.5° from the direction of our line of sight. Our measured geometry for pulsar B suggests the largely empty emission cone contains an elongated horseshoe-shaped beam centred on the magnetic axis, and that it may not be re-detected as a radio pulsar until early 2035.

Is the Far-ultraviolet Flux of 21 Com Anticorrelated to its Optical Brightness?

The comparison of 20 ultraviolet spectra of 21 Com taken over continuous 24 hr to the optical counts collected by the Fine Error Sensor on board IUE reveals that large variations observed shortwards of 1700 Å occur in anti-phase with the optical brightness for part of the observations but not all. In this data, the FUV flux at 1540 Å reaches a minimum at rotational phase 0.32 and increases afterwards while the FES counts continue to increase after this phase. The Fe ii resonance line at 1608.45 Å is Doppler shifted by 0.13 Å at phase 0.00 and −0.13 Å at phase of FUV flux minimum.

Individual subpulses of PSR B1916+14 and their polarization properties

ABSTRACT The individual subpulses of pulsars are regarded as their basic emission components, providing invaluable information for our understanding of the radio emission process in the pulsar magnetosphere. Nevertheless, subpulses are overlapped with each other along the rotation phase for most pulsars, making it difficult to study the statistical properties of subpulses. Among the pulsars observed by the Five-hundred-meter Aperture Spherical radio Telescope (FAST), PSR B1916+14 has a large number of isolated well-resolved subpulses in the high-time-resolution observations, having a typical width of 0.15 ms and a high linear polarization. We find that the number distribution of subpulses contributes dominantly to the mean profile. According to the emission geometry, these emission units come from a region roughly 155 km above the polar cap in the pulsar magnetosphere, and the length-scale of the basic emission units is approximately 120 m. The deviations of the polarization position angles for these single subpulses from the standard S-shaped curve are closely related to their fractional linear and circular polarization, and the large deviations tend to come from drifting subpulses.

Chatter prediction for parallel mirror milling of thin-walled parts by dual-robot collaborative machining system

Thin-walled parts with double-sided features are widely used in the aerospace industry, but the machining of such parts still faces great challenges due to their weak rigid structure and the positioning errors caused by turning/re-clamping of the workpiece. For this purpose, a novel machining approach for parallel mirror robotic milling of thin-walled parts is proposed. Different from conventional single-sided milling, it can simultaneously machine both sides of the workpiece while avoiding the above problems and improving machining efficiency. However, the introduction of multiple cutting excitations makes the vibration behavior of the workpiece more complicated, thus making it difficult for the dynamic modeling of the dual-robot machining system. This paper aims to uncover the dynamic mechanism of chatter phenomenon in parallel mirror robotic milling process in consideration of the interaction of tool-workpiece-tool system. A dual-robot collaborative machining system is first developed for the milling of thin-walled workpiece, and the method of synchronous motion planning for dual robots is described. The slave robot synchronously follows the master robot and the two milling cutters mounted on tool flange of the robot are kept in mirror position. Over a tooth passing period, the engagement state of the cutters and the workpiece is analyzed considering the effect of rotation phase lag (RPL) between the twin cutters. After that, the vibration state and the corresponding instantaneous displacement of the workpiece can be expressed explicitly, then the dynamic resultant cutting force acting on the workpiece is calculated according to the mechanistic force model. Comprehensively considering the dynamic interaction of the tool-workpiece-tool system, multi-mode and position-dependent modal characteristics of thin-walled part, a time-varying delay differential equation is constructed and solved to explore the dynamical behavior of parallel mirror milling process. The predicted stability lobe diagram is validated by a series of parallel mirror milling tests on thin-walled PMMA plates. Comparisons of numerical and experimental results show that the dynamic model successfully predicts the chatter stability for the parallel mirror milling of thin-walled parts.

Dual-mode spatial index modulation for MIMO-OWC.

In this Letter, we propose and demonstrate a dual-mode spatial index modulation (DM-SIM) scheme for spectral efficiency enhancement of band-limited multiple-input multiple-output optical wireless communication (MIMO-OWC) systems. By performing dual-mode index modulation in the spatial domain, DM-SIM can transmit both spatial and constellation symbols. Since constellation design plays a vital role in the proposed DM-SIM scheme, we further propose three dual-mode constellation design approaches including phase rotation, amplitude scaling and joint phase rotation and amplitude scaling. Moreover, we also designed a differential log-likelihood ratio (LLR) detector for the proposed DM-SIM scheme. Experimental results show that the joint phase rotation and amplitude scaling approach can achieve a remarkable 3.2 dB signal-to-noise ratio (SNR) gain compared with the phase rotation approach in a 2×2 MIMO-OWC system applying DM-SIM.

The effect of proposed changes for the rotation and throwing phases on some kinematics and performance variables for U20 weightlifters

Weightlifters from the youth division of five clubs in the Najaf Governorate. The researcher divided the research sample into two groups (experimental and control), and the proposed changes in technical performance were applied to the members of the experimental group while traditional technical performance was applied to the members of the control group.The educational program, which consists of three educational units for each week for a period of four weeks, was put into practice after the pre-tests, which included the option of (shooting from full performance), and the results showed that there were significant differences between the two groups and in favor of the experimental group in the post-test of throwing from the full movement, which came in line with the researchers' hypothesis .In order to give the shooter the most explosive power possible and to achieve the best mechanical position by managing the pause period between the rotation and propulsion phases, he attributed the reason to the significance and impact of the proposed changes on the throwing distance for this competition.The traditional technical performance, which is in the form of bending at the start of rotation, rotation, then extension, and pushing, results in difficulty controlling the stopping period between the two phases (rotation and pushing), as well as less explosive power. This is achieved by using the instantaneous rapid bending and stretching method and without a long pause. In contrast to the suggested modification, the researcher suggested performing research on examples of discus effectiveness.