Preferred Angle Research Articles

Numerical simulation on fluid flow behavior during 3-dimensional dendrite growth with random preference angle

The flow behavior of three-dimensional (3D) dendrite growth with random preferred angle under natural convection was studied by using the Lattice Boltzmann-Cellular Automata (LB-CA) method with dynamic and static grids. In this model, the temperature field, flow field and solute field calculated by Lattice Boltzmann method (LBM) and dendrite growth calculated by CA method were carried out in static and dynamic grids respectively, and the coupling between LBM and CA was performed by interpolation of calculation parameters between dynamic and static grids. Results show that the asymmetry of solid phase distribution makes the streamline distribution more complex. At the initial stage of multiple dendrites growth, the fluid flow is relatively free. When dendrites grow close to each other, the fluid flow is blocked and can only flow along the gap between dendrites. During the wall equiaxed-columnar-central equiaxed crystals transformation (ECET) process, dense eddy current is formed at the wall equiaxed crystals at first. Then, when the wall equiaxed crystals gradually develop into columnar crystals, the eddy current moves with the solid-liquid interface. When the central equiaxed crystals are formed, the eddy current at the front of the columnar crystals gradually disappears. New eddies appear as the central equiaxed crystal grows.

The Torsion Library: Semiautomated Improvement of Torsion Rules with SMARTScompare.

The Torsion Library is a collection of torsion motifs associated with angle distributions, derived from crystallographic databases. It is used in strain assessment, conformer generation, and geometry optimization. A hierarchical structure of expert curated SMARTS defines the chemical environments of rotatable bonds and associates these with preferred angles. SMARTS can be very complex and full of implications, which make them difficult to maintain manually. Recent developments in automatically comparing SMARTS patterns can be applied to the Torsion Library to ensure its correctness. We specifically discuss the implementation and the limits of such a procedure in the context of torsion motifs and show several examples of how the Torsion Library benefits from this. All automated changes are validated manually and then shown to have an effect on the angle distributions by correcting matching behavior. The corrected Torsion Library itself is available including both PDB as well as CSD histograms in the Supporting Information and can be used to evaluate rotatable bonds at https://torsions.zbh.uni-hamburg.de.

Variability in surgical techniques for cochlear implantation: an international survey study

Objective This study aimed to gain insight into current practices regarding the surgical techniques used for positioning and fixation of internal components of the cochlear implant. Methods A questionnaire focused on surgical techniques used for cochlear implantation was distributed among 441 cochlear implant surgeons. Descriptive statistics were reported. Results The questionnaire was completed by 59 surgeons working in 13 different countries. The most preferred incision shapes were the S-shape (41%) and the C-shape (36%). The preferred implantation angle for the receiver/stimulator device was either 45° (64%) or 60° (30%), relative to the Frankfurter Horizontal Plane. Most respondents used a drilled bony well with (42%) or without a subperiosteal pocket (31%) to fixate the receiver/stimulator device. All respondents used the facial recess approach. Most used the round window insertion technique to enter the scala tympani (73%). Approximately half of the respondents preferred the lateral wall electrode array, whereas the other half preferred the perimodiolar electrode array. During their career, most (86%) changed their technique towards structure preservation and minimizing trauma. Conclusion This study indicates variability in the surgical techniques used to position and fixate the internal components of the cochlear implant. Additionally, surgical preference transits towards structure preservation and minimal invasiveness.

Microscopic Evolution of Pore Characteristics and Particle Orientation of Granite Residual Soil in One-Dimensional Compression

This study investigates the microstructural changes of granite residual soil (GRS) upon compression, the aim being to understand further the deformation mechanism from a microscopic perspective and establish the relationship between the mechanical behavior and microstructural characteristics of GRS. By means of (i) experimental compression tests with different loadings and (ii) scanning electron microscopy (SEM), the structural evolution of GRS during compression tests is investigated systematically from both macroscopic and microscopic perspectives. Microstructural characteristics including particle morphology, pore size distribution, and particle preferred orientation are investigated specifically through SEM quantification methods. With an obvious turning point, thee–log σv′curve for natural GRS approaches the intrinsic compression line gradually when the vertical pressure exceeds the preconsolidation pressure, which indicates the significant influence of cementation bonding on the mechanical behavior of intact GRS. At the microscopic scale, the deformation of natural GRS is attributed to the compression and transformation of large pores, while the deformation of remolded GRS is also related to the transformation from mesopores to small pores. Upon compression loading, particles show higher preferred direction angle perpendicular to vertical loading, thereby facilitating the preferred orientation. With increasing vertical loading, the microfabric can no longer sustain the initial alignment pattern and tends to be rearranged and reoriented into a more stable and stronger structure. This study offers guidance for the deformation analysis of subgrade related to GRS.

Effects of welding angle on microstructure and mechanical properties of longitudinal weld in 6063 aluminum alloy extrusion profiles

In order to explore the effects of welding angle on microstructure and mechanical properties of longitudinal weld, a porthole die with different welding angles was designed and manufactured, by using which various extrusion experiments were carried out. The microstructure and mechanical properties of longitudinal weld were characterized, and the extrusion process was simulated. The results show that as welding angle increases, the longitudinal weld gradually transforms from a linear shape to a cross shape. A larger welding angle will not only reduce stress triaxiality and strain rate in the main welding zone, but also increase area of the dead metal zone, thus leading to poor welding quality. The crystal orientations of <100> and <111>//ED can be found in the welding zones of the profiles extruded by using the dies with different welding angles, and the texture components exhibit significant differences. There are a certain number of dislocations, a small amount of Mg2Si precipitates and insoluble iron-containing intermetallic compounds in the welding zones. By comprehensively considering the influence of welding angle on welding quality, extrusion load, effective stress and strain of the porthole die, the welding angle ranges under different welding quality requirements were determined. It is found that the welding quality is higher when the range of welding angle is 38–46°, the welding quality is lower when the range of welding angle is 54–68°. If taking in account both of welding quality and porthole die strength requirement, the preferred welding angle is recommended to be in the range of 46–54°.

Influence of feet’s position on maximum forward lean using a new estimate of functional balance

Purpose Functional stability is crucial to the daily activity of an independent person, functional balance testing is widely used in laboratories and has proven to be a reliable indicator of fall risk. So far, only few studies have paid attention to the impact of foot positioning on the results of functional balance measurements. Methods Thirty healthy adults took part in experiment. LOS test was performed for four stance position: preferred width, wide stance (feet parallel, 28 cm apart), narrow stance (feet together) and angle stance (heels together, toes pointing outside, 90O angle between them) with eyes opened and closed. Results The results of the study show significant differences between angle and narrow stance according to wide and preferred width stances – angle and narrow positions didn’t allow participants to lean as far as other positions. Vision had stabilizing influence on maximum forward lean in all tested positions. Conclusions Feet position influence maximum forward lean. The width of the stance is not critical for the functional balance. Lack of visual control deteriorates functional balance. Researchers should use parallel feet placement in research.

The effects of stature, age, gender, and posture preferences on preferred joint angles after real driving

Few studies have investigated preferred driving posture involving real-world driving. For this purpose, seven preferred joint angles of 127 participants were recorded three times from sagittal plane photographs after a short, standardized drive on public roads. Participants' individual driving posture preferences were determined using a word-based questionnaire. The inter- and intraindividual joint angle differences were calculated and some significant effects of stature, age, and gender on these joint angle differences were found. Additionally, significant correlations were found between posture preferences and joint angles, except for the lower extremities. The results show that the factors stature, age, gender, and posture preferences have influence on the preferred joint angles. However, other human-, vehicle-, and context-related factors also seem relevant and should be considered in future studies.The results provide important field-based knowledge for an application-oriented understanding of driving posture and for the human-centered design process of future vehicle interior research and development.

A High Energy X-ray Diffraction Study of Amorphous Indomethacin

Amorphous pharmaceuticals often possess a wide range of molecular conformations and bonding arrangements. The x-ray pair distribution function (PDF) method is a powerful technique for the characterization of variations in both intra-molecular and inter-molecular packing arrangements. Here, the x-ray PDF of amorphous Indomethacin is shown to be particularly sensitive to the preferred orientations of the chlorobenzyl ring found in isomers in the crystalline state. In some cases, the chlorobenzyl ring has no preferred torsional angle in the amorphous form, while in others evidence of distinct isomer orientations are observed. Amorphous samples with no preferred torsion angles of the chlorobenzyl ring are found to favor enhanced inter-molecular hydrogen bonding, and this is reflected in the intensity of the first sharp diffraction peak. These significant variations in structure rule out amorphous Indomethacin as a possible standard for x-ray PDF measurements. At high humidity, time resolved PDF's for >40 h reveal water molecules forming hydrogen bonds with Indomethacin molecules. A simple linear hydrogen bond model indicates that water molecules in the wet amorphous form have similar hydrogen bond strengths to those found between Indomethacin dimers or chains in the dry amorphous form.

Robust gimbal reorientation singularity-avoidance steering strategy for regular pentagonal pyramid configuration with two control moment gyroscopes failed

The failure configuration which consists of four single-gimbal control moment gyroscopes (SGCMGs) of the widely-used regular pentagonal pyramid SGCMG system, i.e. failure 4-SGCMG configuration, is investigated in this paper. On account of the symmetry of regular pentagonal pyramid configuration, a conversion method which could transform any failure 4-SGCMG configuration to the chosen failure system is introduced. Then, the zero-momentum gimbal angle of the chosen failure system is derived and its distribution in gimbal angle space is analyzed. In order to avoid internal singularity, preferred initial gimbal angles are calculated basing on derivation of zero-momentum gimbal angles and the corresponding terminal singular surfaces are obtained through numerical simulations. Furthermore, a constraint about maneuver direction is introduced and a robust gimbal reorientation steering strategy is proposed. Finally, simulations on a non-chosen failure configuration with inertia matrix uncertainty demonstrate the effectiveness of the conversion method and robustness of the proposed steering law.

From Propaganda to Attraction: Reassessing the Role of the Public in the Newsreel Jornal Português (1938–1951)

The Jornal Português: Revista Mensal de Actualidades was a newsreel produced between 1938 and 1951 for the SPN/SNI, the main organ of propaganda of the Portuguese Estado Novo (1933–1974). It therefore offers a privileged view into the relationship between the cinematographic field and the dictatorship of António de Oliveira Salazar (1889–1970), in its first years. Propaganda has, unsurprisingly, been the preferred angle of analysis, encouraging most scholars to treat these films as a vehicle of ideological indoctrination. The article argues that this approach relies (often unwittingly) on an outmoded concept of ‘mass communication’ that downplays the cinematic specificities of these films in two ways: by foregrounding government-led ‘hard topics’ to the detriment of ‘soft topics’, and by reducing onscreen images of the public to instances of political manipulation. I suggest, as an alternative, that we understand these topics and images within a ‘cinema of attractions’ framework, which acknowledges the central role the audience plays in the cinematic apparatus. In the absence of empirical work on these films’ reception, this kind of theoretical intervention enables us to recover the figure of the public in newsreels, and gain a better grasp of the Jornal Português as a filmic, rather than a journalistic, genre.

Short-Wave Sensitive ("Blue") Cone Activation Is an Aggravating Factor for Visual Snow Symptoms.

Background and Purpose: Visual Snow (VS) is a disorder characterised by the subjective perception of black-and-white visual static. The aetiology of this condition is not known. In our previous work we suggested that there is a link between short-wave (S or “blue” cone) signals and severity of visual snow symptoms. Therefore we aimed to further characterise this potential link.Methods: Patients (n = 22) with classic VS based on the diagnostic criteria and healthy controls (n = 12), underwent Intuitive Colorimetry (IC) testing (Cerium Visual Technologies). Twelve hue directions (expressed as angle in CIE 1976 LUV space relative to D65) were rated on a five-point scale from preferred (relieving, positive score) to non-preferred (exacerbating, negative score), and overall preferred and non-preferred angles were chosen.Results: A non-preferred violet region near the tritanopic confusion line / S-cone axis (267 deg.) was strongly associated with exacerbation of VS symptoms (range 250–310 deg, mean 276 ± 16, n = 20, Rayleigh p < 0.001). Two subjects with non-preferred region > 90 deg from mean were considered as outliers. Median rank at hue angle 270 deg was significantly lower than at angle 90 (−1.5 vs. 0.0, p < 0.001, Wilcoxon non-parametric rank-sum test). Patients showed preference for one of two spectral regions which relieved VS symptoms: orange-yellow (range 50–110 deg., mean 79 ± 24, n = 14) and turquoise-blue (range (210–250 deg., mean 234 ± 27, n = 8).Conclusion: Our results show that visual snow symptoms are exacerbated by colour modulation that selectively increased levels of S-cone excitation. Because S-cone signals travel on primordial brain pathways that regulate cortical rhythms (koniocellular pathways) we hypothesis that these pathways contribute to the pathogenesis of this disorder.

Numerical Simulation of the Effect of Wall-Equiaxed Crystal Density on the Number of Columnar Crystals and the Thickness of an Equiaxed Crystal Layer for Al-4.7%Cu Alloy Ingot Based on 3D LBM-CA Method

In this paper, the lattice Boltzmann–cellular automata (LBM-CA) model with dynamic and static grids was used to study the growth of three-dimensional (3D) multidendrites under directional solidification with random preferred angles. In the static grid, the temperature field, flow field, and solute field during solidification were calculated by the LBM method, and in the dynamic grid, each dendrite evolution was calculated based on the CA method at its preferential crystallographic orientation. The coupling of LBM and CA was made by interpolation of the correlation quantities between the two sets of grids. The effects of wall-equiaxed crystal density on the number of columnar crystals and the thickness of the equiaxed crystal layer were studied by this model. The results showed that the density of the wall-equiaxed crystal has little effect on the number of columnar crystals and the thickness of the equiaxed crystal layer. When other conditions were the same, the lower the undercooling, the fewer the columnar crystals, and the thicker the equiaxed layer. In addition, the smaller the heat transfer coefficient, the lower the number of columnar grains, and the smaller the thickness of equiaxed grains.

Phase Resetting in the Anterior Cingulate Cortex Subserves Childhood Attention and Is Impaired by Epilepsy.

The neural mechanisms that underlie selective attention in children are poorly understood. By administering a set-shifting task to children with intracranial electrodes stereotactically implanted within anterior cingulate cortex (ACC) for epilepsy monitoring, we demonstrate that selective attention in a set-shifting task is dependent upon theta-band phase resetting immediately following stimulus onset and that the preferred theta phase angle is predictive of reaction time during attentional shift. We also observe selective enhancement of oscillatory coupling between the ACC and the dorsal attention network and decoupling with the default mode network during task performance. When transient focal epileptic activity occurs around the time of stimulus onset, phase resetting is impaired, connectivity changes with attentional and default mode networks are abolished, and reaction times are prolonged. The results of the present work highlight the fundamental mechanistic role of oscillatory phase in ACC in supporting attentional circuitry and present novel opportunities to remediate attention deficits in children with epilepsy.

Influence of Substitutional Groups on the Ordering and Crystallization of Amphiphilic Silsesquioxanes at the Air-Water Interface.

We report on the surface ordering and crystallization sequences in differently organic-substituted amphiphilic polyhedral silsesquioxane (POSS) variants induced by regulated compression at the air-water interface. Such molecular systems floating at the interface serve as a model system to study dynamic crystallization mediated by weak interactions. In situ grazing incidence X-ray scattering (GIXS) measurements, performed at a synchrotron X-ray source using a liquid surface diffractometer and corroborated with Brewster angle microscopy, revealed transformations for the different POSS variants (viz. trisilanol isobutyl POSS (TBPOSS), trisilanol cyclohexyl POSS (TCHPOSS), disilanol octaisobutly POSS (DOBPOSS), and trisilanol isooctyl POSS (TOPOSS)) from a weakly correlated monolayer structure to appreciably different structural and crystalline phases in various packing schemes. GIXS measurements revealed a stable nature of the crystallization of DOBPOSS, varying degrees of metastable crystallization for TCHPOSS and TBPOSS, and complete absence of crystalline phase in TOPOSS molecules. Incidentally, for all POSS variants showing crystalline phases, the motifs always assembled in a triclinic lattice with P1̅ symmetry. For the metastable crystals, preferential surface ordering of the crystallites promotes selective crystalline planes to exhibit preferred tilt angles with respect to the interface. The structural transformations of the differently substituted POSS molecules and their variations therein are attributed to the changing balance of the hydrophobic vs hydrophilic interaction in the layers, which is determined by the anisotropic shape and distribution of substitutional groups over the nanosized core cage of the monomer, steric interaction between nearest dimeric neighbors, as well as the in-plane and out-of-plane assembly of the overlayers.

Individualized left anterior oblique projection based on pigtail catheter visualization facilitates leadless pacemaker implantation.

BackgroundPacemaker positioning on the right ventricular (RV) septum during implantation is conventionally conducted utilizing two fixed fluoroscopy angles, a 45° left anterior oblique (LAO) and 35° right anterior oblique projection. However, placement location can be suboptimal, especially for leadless pacemakers (LPMs).ObjectiveTo evaluate the safety and ease of LPM implantation using individualized LAO projection.MethodsConsecutive patients undergoing LPM implantation were prospectively included. The angle of the RV septum was recorded for each patient by studying the angle at which an RV pigtail catheter (RV‐PC) could be seen edge on. This was then used as the preferred LAO projection angle for that patient. We evaluated the success rate and safety of this method. We also compared the RV septum angle as measured by this method versus that measured by chest CT.ResultsOf the 31 patients (mean age 80.6 ± 7.0 years, 15 females), LPM implantation was successful in 30. The pacemaker was implanted on the RV septum in 29 and on the free wall in one. LPM implantation was abandoned for anatomical reasons in one. Complications were limited to a groin arteriovenous fistula and one deep vein thrombosis. The angle of RV septum as measured by pigtail catheter and chest CT was not significantly different (CT: 54.8 ± 6.0°, RV pigtail catheter: 52.9 ± 6.1°, P = .07).ConclusionsUsing an RV‐PC to determine the preferred angle of LAO projection facilitates differentiation between the RV septum and free wall, which in turn facilitates optimal LPM placement.

100 Effects of space and exercise on the rolling behaviour in stabled horses

Scientific studies on the mechanism of rolling behavior are limited. Therefore, the objective of this current study was to investigate the factors that influence the rolling behavior in stabled horses. This study hypothesized that if rolling is an intrinsically motivated behavior, the horses may frequently demonstrate the behavior if given enough space and this will be heightened after hard exercise. The frequency and angles of rolling behavior were video recorded using all occurrence sampling in the confined and open spaces (stable box vs riding arena) as well as after exercise (no exercise vs post-light vs post-hard exercises). Nine healthy geldings aged from 11 to 20 years old were used for this study. Four of the horses were Thoroughbred, 3 were Arabian, one American Quarter horse, and one Holsteiner with body weights ranging between 450 and 650 kg and withers ranging from 150cm to 165cm tall. To measure the effects of space, horses were observed individually in their stable box and riding arena for an hour between 08:00 to 11:00 over 6 consecutive days. Whereas for the effects of exercise, horses were shifted from the stable box into the riding arena without prior exercise (no exercise). For post-light and post-hard exercises, horses were released into the riding arena after 45 min of exercise. The light exercise consisted of riding activity divided into 40% walk, 50% trot, and 10% canter. On the other hand, the horses were ridden at 20% walk, 50% trot, and 30% canter for hard exercise. All tacks were removed before observations. Data was analyzed by using SPSS for Window, Version 26.0. Wilcoxon signed-rank test was used to determine the differences in the frequency and angles of rolling behavior between stable box and riding arena. Whereas, the effects of exercise were analyzed with Friedman test, P < 0.05. The horses rolled significantly more in the riding arena (25.1%) than stable box (6.15%). The rolling frequency was also significantly higher after post-hard exercise (41%) compared with post-light (37%) and no exercise (21%). Three types of rolling angles that of 0–45°, 45–90°, and 90–180° were observed. 45–90° was the most preferred angle in both stable box and arena whereas 90–180° was not seen in the stable box and was less frequently observed in the arena. These findings indicated that the standard size of the stable box, 12 × 12 ft, allows sufficient room for the horses to roll safely at a maximum of 45–90° and they should be allowed to roll after a hard exercise.

Computational and Experimental Approaches to Controlling Bacterial Microcompartment Assembly.

Bacterial microcompartments compartmentalize the enzymes that aid chemical and energy production in many bacterial species. They are postulated to help bacteria survive in hostile environments. Metabolic engineers are interested in repurposing these organelles for non-native functions. Here, we use computational, theoretical, and experimental approaches to determine mechanisms that effectively control microcompartment self-assembly. We find, via multiscale modeling and mutagenesis studies, the interactions responsible for the binding of hexamer-forming proteins in a model system, the propanediol utilization bacterial microcompartments from Salmonella enterica serovar Typhimurium LT2. We determine how the changes in the microcompartment hexamer protein preferred angles and interaction strengths can modify the assembled morphologies. We demonstrate that such altered strengths and angles are achieved via amino acid mutations. A thermodynamic model provides guidelines to design microcompartments of various morphologies. These findings yield insight in controlled protein assembly and provide principles for assembling microcompartments for biochemical or energy applications as nanoreactors.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle that leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuthally dependent, introduce a Gaussian function to describe the fractures’ azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over the azimuth. We investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the [Formula: see text] plane than in the [Formula: see text] plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can degenerate into the VFTI medium.

Selection rules of twistronic angles in two-dimensional material flakes via dislocation theory

Interlayer rotation angle couples strongly to the electronic states of twisted van der Waals layers. However, not every angle is energetically favorable. Recent experiments on rotation-tunable electronics reveal the existence of a discrete set of angles at which the rotation-tunable electronics assume the most stable configurations. Nevertheless, a quantitative map for locating these intrinsically preferred twist angles in twisted bilayer system has not been available, posing challenges for the on-demand design of twisted electronics that are intrinsically stable at desired twist angles. Here we reveal a simple mapping between intrinsically preferred twist angles and geometry of the twisted bilayer system, in the form of geometric scaling laws for a wide range of intrinsically preferred twist angles as a function of only geometric parameters of the rotating flake on a supporting layer. We reveal these scaling laws for triangular and hexagonal flakes since they frequently appear in chemical vapor deposition growth. We also present a general method for handling arbitrary flake geometry. Such dimensionless scaling laws possess universality for all kinds of two-dimensional material bilayer systems, providing abundant opportunities for the on-demand design of intrinsic "twistronics". For example, the set of increasing magic-sizes that intrinsically prefers zero-approaching sequence of multiple magic-angles in bilayer graphene system can be revealed.

Deep neural network application: Higgs boson CP state mixing angle in H→ττ decay and at the LHC

The consecutive steps of cascade decay initiated by H to tau tau can be useful for the measurement of Higgs couplings and in particular of the Higgs boson parity. In the previous papers we have found, that multi-dimensional signatures of the tau^pm to pi^pm pi^0 nu and tau^pm to 3pi^pm nu decays can be used to distinguish between scalar and pseudoscalar Higgs state. The Machine Learning techniques (ML) of binary classification, offered break-through opportunities to manage such complex multidimensional signatures. The classification between two possible CP states: scalar and pseudoscalar, is now extended to the measurement of the hypothetical mixing angle of Higgs boson parity states. The functional dependence of H to tau tau matrix element on the mixing angle is predicted by theory. The potential to determine preferred mixing angle of the Higgs boson events sample including $\tau$-decays is studied using Deep Neural Network. The problem is adressed as classification or regression with the aim to determine the per-event: a) probability distribution (spin weight) of the mixing angle; b) parameters of the functional form of the spin weight; c) the most preferred mixing angle. Performance of methods are evaluated and compared. Numerical results are collected.