Rotation Correction Research Articles

Multi-Color Code with High Data Capacity

Quick Response (QR) code is commonly utilized in this era to serve multiple purposes. In order to uplift the data size of QR code, higher versions of QR code are introduced for greater data size. Nonetheless, the current QR code has met the bottleneck of data size. The latest version of QR code (version 40) now can only encode up to 4 kilobytes of data. Besides, QR code version 40 is unable to be decoded easily due to the high layout density. Hence, this research’s objective is to develop a Multi-color Code which involves multiple colors to uplift the data size. Similar to the QR Code, the Multi-color Code (McC) also consists of the features of auto rotation and error correction. The outcome of the research is the developed McC can achieve up to 10Kb. Besides, McC is capable to encode image file for offline identification. The results shows that the auto rotation feature, Reed-Solomon error correction algorithm, developed Lanczos-8 interpolation method and adaptive piecewise transformed normalization contribute in yielding 100% decoding accuracy.

Clinical Outcomes and Rotational Correction of First Metatarso-Cuneiform Fusion With First Metatarsal to Second Cuneiform Fixation.

Background:The modified Lapidus procedure (first metatarso-cuneiform fusion) is a powerful technique for correcting triplanar deformity in hallux valgus. Although traditionally fixed with cross-screws (CS), growing awareness of intercuneiform stability and pronation deformity has led to fixation using a plate and first metatarsal–second cuneiform (1MT-2C) screw fixation (PS). We investigated Lapidus patient cohorts using CS vs PS fixation to understand patient-reported outcomes, angular and rotational correction, and complication rates.Methods:We retrospectively reviewed cases of modified Lapidus for hallux valgus by a single surgeon. Patients were divided into CS or PS groups according to fixation. All patients had preoperative Patient Reported Outcome Measurement Information System (PROMIS) scores and minimum 12 months of follow-up. PROMIS scores in 6 key domains were compared within and between groups. Radiographic assessment of hallux valgus angle and intermetatarsal angle were performed on pre- and postoperative XR. Pronation of the first ray was measured on pre- and postoperative weightbearing computed tomography.Results:We compared 42 patients with PS fixation to 43 with CS fixation. Both groups had significant improvement in hallux valgus angle and intermetatarsal angle (P < .001), with no difference between groups. PS patients experienced a greater correction of first metatarsal pronation, an average reduction of 11 degrees, compared to 8 degrees in the CS group (P < .039). Both cohorts experienced improvement in PROMIS physical function, pain interference, pain intensity, and global physical function. There were no differences in PROMIS score improvements between the cohorts. The CS group started weightbearing at 6 weeks vs 3.6 weeks for the PS group. Complication and revision rates were similar.Conclusion:A plate and 1MT-2C screw fixation provides safe, robust fixation of Lapidus procedure and prevents instability through the intercuneiform joint. We observed similar improvement in PROMIS compared with patients treated with cross-screws. Complications did not increase despite the PS group weightbearing much earlier. PS patients achieved greater first ray rotational correction.Level of Evidence:Level III, retrospective cohort study.

An In - vivo study to evaluate the force decay of three different orthodontic elastomeric ligatures.

Abstract: Background: In vitro studies conducted under simulated oral environment under estimated the force decay of elastomeric ligatures. There are only few invivo studies that are reported evaluating the force decay of elastomeric ligatures. Aim &amp; Objectives: The aim of this in-vivo study was to evaluate the force decay of three different clear elastomeric ligature modules stretched over the lower incisor brackets intra orally over three different time periods at 24 hrs, 7 days and 21 days by comparing it with the force levels evaluated at as received conditions . Materials and methods: Ten patients undergoing fixed orthodontic treatment with Roth Prescription, 0.022" slot preadjusted edgewise stainless steel brackets with aligning and levelling completed and 0.019" x 0.025" SS arch wire placed passively in the lower arch were included in the study. The three types of elastomeric ligature modules formed the three study groups [Group I: Molded“O” (Ormco, USA),Group II: Alastik (3M Unitek, USA)&amp;Group III: Uni-stick (American orthodontics, USA)] Each group was assigned with a specific lower incisor in each patient and the respective modules were used in the teeth during the study period. The force levels required to stretch the modules to a predetermined length of 4.1mm were evaluated at 4 different time intervals at 0 hour (as received), 24, 7 days, and 21 days after intra-oral use using a universal testing machine (Instron model 1112, Instron Corp.). The mean force values and standard deviations for all the groups at each time period. The mean percentage of force decay between time periods for each study group was calculated. One way ANOVA followed by Post hoc Tukey HSD was performed for within the group and between group comparisons. Paired T test was done for pairwise comparisons. (P value≤ 0.05) Results: The mean force level recorded were high at the base line level with as received modules before inserting into the patients mouth for all the three study groups. The mean force level was 766.50 ± 3.659 gms, 650.50±2.759 gms and 594 .10 ± 4.630 gms for group I, II &amp; III respectively in the as received condition. The percentage of force decay was 32.94 % at 24 hrs and 69.85% at 7 days and 79.31% at 21 days for Group I. A force decay of 31.36%, 70.76% and 79.83% from the base line value was noted in group II at the same time intervals. In Group III The force decay rate at 24 hrs, 7 days and 21 days were 33.29%, 66.10% and 77.12% respectively. One way ANOVA for within group and between group comparison showed a significant difference between the force levels recorded at different time intervals within and between all the three study groups. Post Hoc Tukey HSD revealed a significant difference between the three groups at all the time intervals tested except at 7 days and 21 days where the force levels exerted by the group II and Group III samples were not significantly different. Paired sample T test for pairwise comparison of force exerted between different time intervals in all the three groups revealed a significant difference. Conclusion: Group I clear modules exhibited significantly high mean force and less force decay compared to other groups at all four time intervals tested. The elastomeric modules exhibited significant force decay after 24 hours, 7days and 21 days of intra-oral use except at 7 days and 21 days where the force levels exerted by the group II and Group III samples were not significantly different. The forces at the end of three weeks of intra oral use appeared to be insufficient for effective torquing effect and severe rotational corrections in all the three study groups and hence changing modules sfter three weeks may be beneficial in those cases

Correction of full-field rigid body rotation and strain using a hybrid peridynamics and digital image correlation approach

Rigid body rotation is difficult to be removed independently while using digital image correlation (DIC) technique for monitoring the displacement and deformation of an object. Furthermore, strain measurement can also become inaccurate due to the presence of displacement caused by rigid body rotation. Common solutions to this problem, such as tracking a single-point's rotation, require additional reference information and only obtain one rigid body rotation angle of the object. In this study, a hybrid computational and experimental mechanics method based on peridynamics (PD) and DIC technique is proposed to measure the full-field rigid body rotation and strain. A DIC-based PD model can be established based on the full-field position data obtained by DIC. The calculation formulas for rigid body rotation and strain are derived in the framework of PD and the calculations of rotation and strain are mutually insensitive and independent. Therefore, without any additional reference information, the rigid body rotation and strain information can be obtained in the presence of simultaneous rigid body rotation and deformation. Different rigid body rotations in various regions of an object, whether large or small rotations, can be calculated by this method. Correspondingly, this method is effective for calculating the local rigid body rotations of objects undergoing local fracture. Numerical simulations and experimental tests were performed to verify the effectiveness of the proposed method. The calculation results show that the proposed method owns the ability to accurately calculate the rotation and strain in the above scenarios.

Correcting rotational error in rectal cancer radiation therapy: Can planning target volume margins be safely reduced?

The magnitude and impact of rotational error is unclear in rectal cancer radiation therapy. This study evaluates rotational errors in rectal cancer patients, and investigates the feasibility of planning target volume (PTV) margin reduction to decrease organs at risk (OAR) irradiation. In this study, 10 patients with rectal cancer were retrospectively selected. Rotational errors were assessed through image registration of daily cone beam computed tomography (CBCT) and planning CT scans. Two reference treatment plans (TPR ) with PTV margins of 5 mm and 10 mm were generated for each patient. Pre-determined rotational errors (±1°, ±3°, ±5°) were simulated to produce six manipulated treatment plans (TPM ) from each TPR . Differences in evaluated dose-volume metrics between TPR and TPM of each rotation were compared using Wilcoxon Signed-Rank Test. Clinical compliance was investigated for statistically significant dose-volume metrics. Mean rotational errors in pitch, roll and yaw were -0.72 ± 1.81°, -0.04 ± 1.36° and 0.38 ± 0.96° respectively. Pitch resulted in the largest potential circumferential displacement of clinical target volume (CTV) at 1.42 ± 1.06 mm. Pre-determined rotational errors resulted in statistically significant differences in CTV, small bowel, femoral heads and iliac crests (P < 0.05). Only small bowel and iliac crests failed clinical compliance, with majority in the PTV 10 mm margin group. Rotational errors affected clinical compliance for OAR dose but exerted minimal impact on CTV coverage even with reduced PTV margins. Both PTV margin reduction and rotational correction decreased irradiated volume of OAR. PTV margin reduction to 5 mm is feasible, and rotational corrections are recommended in rectal patients to further minimise OAR irradiation.

Study of limits to the rotation function in the SA-RC turbulence model

The Rotation and Curvature (RC) correction is an important turbulence model modification approach, and the Spalart-Allmaras model with the RC correction (SA-RC) has been extensively studied and used. As a multiplier of the modelling equation’s production term, the rotation function fr1 should have a cautiously designed value range, but its limit varies in different models and flow solvers. Therefore, the need of restriction is discussed theoretically, and the common range of fr1 is explored in Burgers vortexes. Afterwards, the SA-RC model with different limits is tested numerically. Negative fr1 always appears in the SA-RC model, and the difference between simulation results brought by the limits is not negligible. A lower limit of 0 enhances turbulence production, and therefore the vortex structures are dissipated faster and shrink in size, while an upper limit plays an opposite role. Considering that the lower limit of 0 usually promotes the simulation accuracy and fixes the numerical defect, whereas the upper limit worsens the predictive performance in most cases, it is recommended to limit fr1 non-negative while utilizing the SA-RC model. In addition, the RC-corrected model has a better prediction of the attached flow near curved walls, while the SA-Helicity model largely improves the simulation accuracy of three-dimensional large-scale vortices. The model combining both corrections has the potential to become more adaptive and more accurate.

Effect of rotation and FLR corrections with radiative heat-loss functions on transverse thermal instability of astrophysical porous plasma in interstellar medium (ISM)

The effect of rotation, finite ion Larmor radius (FLR) corrections and porosity on the thermal instability of infinite homogeneous plasma has been explored taking the effects of radiative heat-loss function and thermal conductivity. The general dispersion relation is derived by means of the normal mode analysis scheme with the help of appropriate linearized perturbation equations of the problem. This dispersion relations is further reduces for rotation axis parallel and perpendicular to the magnetic field for transverse wave propagation. It is found that the presence of rotation, FLR corrections and porosity amend the fundamental thermal criterion of instability. Numerical computations have been executed. Our result demonstrates that the rotation, porosity and FLR corrections affect the dens molecular clouds configuration and star formation.

Improved Prediction of Aerodynamic Loss Propagation as Entropy Rise in Wind Turbines Using Multifidelity Analysis

Several physics-based enhancements are embedded in a low-fidelity general unducted rotor design analysis tool developed, py_BEM, including the local Reynolds number effect, rotational corrections to airfoil polar, stall delay model, high induction factor correction, polar at large angle of attack, exergetic efficiency calculation and momentum-based loss. A wind turbine rotor is analyzed in high fidelity designed from py_BEM using a 3D blade generator. It is a design derived from the NREL Phase VI rotor. Three design variations are analyzed using steady 3D CFD solutions to demonstrate the effect of geometry on aerodynamics. S809 and NACA 2420 airfoil properties are used for calculating the aerodynamic loading. Momentum, vorticity and energy transport are explained in depth and connected to entropy production as a measure of performance loss. KE dissipation downstream of the rotor is shown to be a significant contributor of entropy rise. Wake analysis demonstrates mixing with the free stream flow, which begins after 3 diameters downstream of the rotor and extends to about 25 diameters until the decay is very small. Vorticity dynamics is investigated using a boundary vorticity flux technique to demonstrate the relationship between streamwise vorticity and lift generated in boundary layers. Drag components are accounted as well. It is demonstrated using rothalpy that shaft power is not only torque multiplied by rotational velocity but a viscous power loss term must also be included. A multifidelity analysis of wind turbine aerodynamics is demonstrated by capturing flow physics at several levels.

Accuracy of Acetabular Cup Placement During Total Hip Arthroplasty in Supine Position Using a Pelvic Rotation Correction Device.

BackgroundAccurate cup placement during total hip arthroplasty (THA) is difficult because the intraoperative pelvic position changes even in supine patient position. We developed a device known as HipPointer; it corrects pelvic rotation and creates a functional pelvic plane as a reference. The aim of this study was to determine the device placement accuracy and investigate causes of error.Material and methodsHipPointer was used for cup placement in 353 hips of 308 patients who underwent direct-anterior-approach THA in supine position. The mean age at surgery and body mass index were 63.9 (17-90) years and 24.9 (16.6-42.0) kg/m2, respectively. The mean observation period was 40.5 (12-73) months. To investigate the accuracy of HipPointer, preoperative planning and postoperative cup placement angles relative to the functional pelvic plane were evaluated using a three-dimensional analysis software, and absolute errors were determined.ResultsThe means ± standard deviations of radiographic inclination (RI) and radiographic anteversion (RA) were 40.2 ± 3.0° and 15.8 ± 3.6°, respectively. The absolute errors of RI and RA were 2.2 ± 2.0° and 2.7 ± 2.3°, respectively. The ratio of the cup placement angle for which both RI and RA are ≤10° in the target zone was 99% (350/353 hips), and the ratio of the absolute errors for which both RI and RA are ≤5° was 80.4% (284/353 hips).ConclusionsHipPointer is simple in structure, easy to use, and useful for direct-anterior-approach THA in supine position. It provides good cup placement accuracy.

Computer Image Content Retrieval considering K-Means Clustering Algorithm

The traditional computer image content retrieval technology can only meet the specific requirements of customers; because of its general features, it cannot comply with the requirements of various environments, purposes, and time simultaneously. This study presents a computer image content retrieval method for a K-means clustering algorithm (KCA). The information collected by computer is preprocessed by K-means clustering algorithm, and the unacquired computer image is labeled based on the optimal learning order according to the KCA. The K-means clustering algorithm classifies the color, pattern, shape, and content of computer images and takes advantage of the invariance advantages of image content retrieval such as scale, rotation, illumination, and blur correction to effectively solve the recurring problems of computer images during retrieval and increase its accuracy. The results of the experiment indicate that the proposed K-means clustering algorithm can enhance the efficiency and performance effectively during image retrieval by computer as compared to the traditional content search algorithm and also help to quickly converge to the query content; it also shows that KCA has good robustness.

Calculation of set-up margin in frameless stereotactic radiotherapy accounting for translational and rotational patient positing error.

Rotation corrected set-up margins in stereotactic radiotherapy (SRT). This study aimed to calculate the rotational positional error corrected set-up margin in frameless SRT. 6D setup errors for the steriotactic radiotherapy patients were converted to 3D translational only error mathematically. Setup margins were calculated with and without considering the rotational error and compared. A total of 79 patients of SRT each received >1 fraction (3-6 fractions) incorporated in this study. Two cone-beam computed tomography (CBCT) scans were acquired for each session of treatment, before and after the robotic couch-aided patient position correction using a CBCT. The postpositional correction set-up margin was calculated using the van Herk formula. Further, a planning target volume_R (PTV_R) (with rotational correction) and PTV_NR (without rotational correction) were calculated by applying the rotation corrected and uncorrected set-up margins on the gross tumor volumes (GTVs). Statistical Analysis Used: General. A total of 380 sessions of pre- (190) and post (190) table positional correction CBCT was analyzed. Posttable position correction mean positional error for lateral, longitudinal, and vertical translational and rotational shifts was (x)-0.01 ± 0.05 cm, (y)-0.02 ± 0.05 cm, (z) 0.00 ± 0.05 cm, and (θ) 0.04° ± 0.3°, (Φ) 0.1° ± 0.4°, (Ψ) 0.0° ± 0.4°, respectively. The GTV volumes show a range of 0.13 cc-39.56 cc, with a mean volume of 6.35 ± 8.65 cc. Rotational correction incorporated postpositional correction set-up margin the in lateral (x), longitudinal (y) and vertical (z) directions were 0.05 cm, 0.12 cm, and 0.1 cm, respectively. PTV_R ranges from 0.27 cc to 44.7 cc, with a mean volume of 7.7 ± 9.8 cc. PTV_NR ranges from 0.32 cc to 46.0 cc, with a mean volume of 8.1 ± 10.1 cc. The postcorrection linear set-up margin matches well with the conventional set-up margin of 1 mm. Beyond a GTV radius of 2 cm, the difference between PTV_NR and PTV_R is ≤2.5%, hence not significant.

Improvement of Adolescent Idiopathic Scoliosis Primary Correction by Brace Design Optimization.

(1) Background: Primary in-brace correction has been shown to be related to conservative adolescent idiopathic scoliosis (AIS) treatment outcome. The purpose of the study was to evaluate TLSO brace design changes over eight years regarding primary Cobb correction and de-rotation of the (major) curve. (2) Methods: This retrospective analysis included AIS patients treated with a full-time TLSO-brace in a single Orthopedic University hospital in 2012–2014 and 2017–2019. Brace design changes resulted from an evolutionary process, from a 3-point bending to a 3D TLSO. The brace parameters (presence of an anterior shoulder pad, posterior high-thoracic pad, thoracic space, and angle of the lumbar and thoracic pressure points) were analyzed regarding the primary (major) Cobb angle and apex rotation correction with a multivariate analysis. (3) Results: A total of 74 (63 female) patients were included in the study. The Cobb angle primary correction was significantly improved over the timeframe. The primary correction was significantly influenced by all design parameters and partially by its interactions with (curve specific) different effects on the Cobb correction and apex de-rotation. (4) Conclusions: Knowledge about the effects of brace design parameters on the curve’s angle and rotation correction enables improvements in individualized brace design and the brace optimization process.

Calibration of an Extended Eddy Viscosity Turbulence Model Using Bayesian Update

The present work aims at improving the performance of the eddy viscosity-based Menter - Shear Stress Transport turbulence model for complex aircraft flows by adding physical extensions to the length-scale equation along with calibration aided by uncertainty quantification methods. Three different extensions based on rotation and curvature correction, wake flow correction, and irrotational strain correction are added to the original model, resulting in a parametric model, which is then calibrated using Bayesian updates. A series of test cases is employed to assess the model performance, whereby delta wings with deflected flaps and vortical flows are the predominant target application.

Beyond-mean-field dynamical correlations for nuclear mass table in deformed relativistic Hartree-Bogoliubov theory in continuum * *Supported by the National Natural Science Foundation of China (11875225, 12005175, 11935003, 11875075, 11975031, 12070131001, 11790325), the Fundamental Research Funds for the Central Universities, the National Key R&D Program of China (2017YFE0116700, 2018YFA0404400), the State Key Laboratory of Nuclear Physics and Technology, Peking University (NPT2020ZZ01)

We extend the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) to go beyond-mean-field framework by performing a two-dimensional collective Hamiltonian. The influences of dynamical correlations on the ground-state properties are examined in different mass regions, picking Se, Nd, and Th isotopic chains as representatives. It is found that the dynamical correlation energies (DCEs) and the rotational correction energies in the cranking approximation have an almost equivalent effect on the description of binding energies for most deformed nuclei, and the DCEs can provide a significant improvement for the (near) spherical nuclei close to the neutron shells and thus reduce the rms deviations of by 17%. Furthermore, it is found that the DCEs are quite sensitive to the pairing correlations; taking Nd as an example, a 10% enhancement of pairing strength can raise the DCE by 37%.

Evaluation of Tooth Movement Accuracy with Aligners: A Prospective Study.

Background. Clear aligners treatment (CAT) is a common solution in orthodontics to treat both simple and complex malocclusions. This study aimed to evaluate the predictability of CAT, comparing the virtually planned and the achieved tooth movement at the end of stage 15, which is often the time of first refinement. Methods. Seventeen patients (mean age: 28.3 years) were enrolled in the study. Torque, tip and rotation were analyzed in 238 maxillary teeth on digital models at Pre-treatment (T0), at the end of stage 15 (T15) and at virtually planned stage 15 (T15i). Prescription, Achieved movement and performance values were calculated to compare the virtually planned and the clinical tooth position. Data were analyzed by means of Student’s t test with a level of significance set at p < 0.05. Results. The largest iper-performance was the torque correction of the second molars (+2.3° ± 3.1°), the greatest under-performance was the tip correction of the first molars (−2.3° ± 3.3°), while rotation corrections of all the teeth showed more accurate performance. No significant differences were found between mean Prescription and mean Achieved movement for all the assessed movements (p < 0.05). Conclusions. An accurate evaluation of CAT after the 15th aligner is fundamental in order to individuate the movements that are not matching the digital set-up.

Aircraft Propeller Design through Constrained Aero-Structural Particle Swarm Optimization

An aero-structural algorithm to reduce the energy consumption of a propeller-driven aircraft is developed through a propeller design method coupled with a Particle Swarm Optimization (PSO). A wide range of propeller parameters is considered in the optimization, including the geometry of the airfoil at each propeller section. The propeller performance prediction tool employs a convergence improved Blade Element Momentum Theory fed by airfoil aerodynamic characteristics obtained from XFOIL and a validated OpenFOAM. A stall angle correction is estimated from experimental NACA 4-digits data and employed where convergence issues emerge. The aerodynamic data are corrected to account for compressibility, three-dimensional, viscous, and Reynolds number effects. The coefficients for the rotational corrections are proposed from experimental data fitting. A structural model based on Euler-Bernoulli beam theory is employed and validated against Finite Element Analysis, while the impact of centrifugal forces is discussed. A case of study is carried out where the chord and pitch distributions are compared to minimal losses distribution from vortex theory. Wind tunnel tests were performed with printed propellers to conclude the feasibility of the entire routine and the differences between XFOIL and CFD optimal propellers. Finally, the optimal CFD propeller is compared against a commercial propeller with the same diameter, pitch, and operational conditions, showing higher thrust and efficiency.

Initial In-Brace Correction: Can the Evaluation of Cobb Angle Be the Only Parameter Predictive of the Outcome of Brace Treatment in Patients with Adolescent Idiopathic Scoliosis?

Background: Patients with a better initial in-brace correction could show a higher probability of a successful outcome. However, no one has investigated whether parameters can affect the outcomes. The aim of this retrospective study was to evaluate if the initial correction rate (ICR) could be predictive of the bracing outcome and to determine the role of some mechanical and biological parameters in ICR. Methods: The study population comprised 449 patients who met the inclusion criteria. Curve correction > 10° Cobb defines brace treatment success. Success and failure groups were compared in terms of the Risser sign, initial Cobb angle, initial Perdriolle value and ICR. Results: ICR significantly correlates with initial Perdriolle. The success group had a significantly lower value of Pedriolle and initial Cobb angles, Risser sign and ICR than the failure group. The ICR and lower Risser were significantly associated with the brace treatment outcome. This seems particularly suitable for positivity prediction (Predicting value VP+: 87%). Conclusions: This study confirms that immediate in-brace correction can foretell the brace treatment outcome. Patients with a low Risser sign and a high rate of in-brace correction showed a bracing success of 87%. A correlation between rotation and in-brace correction confirms that rotation is among the parameters that influence the deformed spine reaction to corrective actions the most.

A Modified RANS Model for Drag Prediction of Practical Configuration with Riblets and Experimental Validation

To reduce the computational cost, the k-ω SST turbulence model with Rotation and Curvature correction (SST-RC) is modified to predict the drag of practical aerodynamic configurations mounted with drag-reducing riblets. In the modified model, wall ω is reconstructed based on the existing experimental results and becomes a function of riblet geometry, angle of attack, position at the surface, and parameters of computational grids. The modified SST-RC model is validated by existing experimental and numerical examinations. Subsequently, a maximum error of 3.00% is achieved. Furthermore, experimental and numerical studies on a wing–body configuration are conducted in this work. The maximum error between the drag-reducing ratios obtained by numerical simulations and those of experiments is 3.21%. Analysis of numerical results demonstrates a maximum of 5.36% decline in skin friction coefficient for the model with riblets; moreover, the distribution of the pressure coefficient is also changed.

Utilizing correlation functions to develop a multistate model of P. denitrificans F1-ATPase and enhance single-molecule imaging resolution

F1-ATPase enzyme is a biological motor which hydrolyzes ATP. The enzyme has been observed via single-molecule imaging experiments wherein the enzyme is allowed to rotate freely while being recorded using a gold nanoparticle. During hydrolysis, the enzyme causes Brownian noise when rotating to new chemical states because of a size difference between the 4 nm enzyme and 40 nm probe. The unconvoluted rotary movement has been revealed using techniques including rotational correction, correlation functions, and comparison of average rotational jumps which contribute to developing a multistate model.

Interaction between a non-concentric rigid sphere immersed in a micropolar fluid and a spherical envelope with slip regime

A semi-analytical investigation of a quiescent micropolar fluid between a rigid sphere and a non-concentric spherical envelope with a slip regime is obtained. Two different cases have been considered one is the hydrodynamic drag strength and the translational wall correction factor (TWCF) exerted by the fluid on the inner sphere are proportional to the translational velocities and the second is the hydrodynamic torque and the rotational wall correction factor (RWCF) are applied to the inner sphere which is proportional to the angular velocities. The numerical solution is composed of the superposition of the fundamental solutions in the two spherical coordinate systems setups on the poles of the rigid sphere and the spherical envelope by using a collocation scheme. The boundary conditions, slip, and spin-slip are presented on the sphere’s surfaces. The results were achieved numerically with excellent convergence for the parameters, size ratio, separation distance, micropolarity parameter, slip, slip-spin parameters. Limiting cases are agreeable with the obtainable results in the literature.