Rotation Of Plane Research Articles

Identification of characteristics of foot position and angle during swing phase in fallers using principal component analysis.

Identifying the characteristics of fallers is important for preventing falls because such events may reduce quality of life. It has been reported that several variables related to foot positions and angles during gait (e.g., sagittal foot angle and minimum toe clearance) differ between fallers and non-fallers. However, examining such representative discrete variables may not be sufficient to detect crucial information, which may be contained in the large portions of unanalyzed data. Therefore, we aimed to identify the comprehensive characteristics of foot position and angle during the swing phase of gait in non-fallers and fallers using principal component analysis (PCA). Thirty non-fallers and 30 fallers were recruited for this study. We performed PCA to reduce the dimensions of foot positions and angles during the swing phase and obtained principal component scores (PCSs) for each principal component vector (PCV), which were then compared between groups. The results revealed that the PCS of PCV3 in fallers was significantly larger than that in non-fallers (p = 0.003, Cohen's d = 0.80). We reconstructed waveforms of foot positions and angles during the swing phase using PCV3 and our main findings can be summarized as follows. Compared to non-fallers, fallers have a 1) low average foot position in the z-axis (i.e., height) during the initial swing phase 2) small average foot angle in the x-axis (i.e., rotation in the sagittal plane), during the initial swing phase, and 3) large variability in foot position in the y-axis (i.e., anterior/posterior position) during the initial swing phase. We can conclude that these are characteristics of gait related to fallers. Therefore, our findings may be beneficial for evaluating fall risk during gait using a device such as a shoe- or insole-embedded inertial measurement unit.

Minimally Invasive Arthrodesis of the Equine Proximal Interphalangeal Joint: A Biomechanical Comparison of Three 5.5-mm Cortical Screws Inserted in Lag Fashion and Two 7.0-mm Headless Cannulated Dual-Pitch Compression Screws.

The aim of this study was to compare the biomechanical properties of two minimally invasive arthrodesis techniques of the equine proximal interphalangeal (PIP) joint (three transarticular 5.5-mm cortical screws [AO-3TLS] vs. two transarticular 7.0-mm headless cannulated multi-use compression screws [MUC-2TS]) in dynamic non-destructive testing and compression testing to failure. The experimental study included six pairs of cadaveric adult equine forelimbs; one limb from each horse was randomly assigned to one of the treatments, and the contralateral limb was submitted to the remaining treatment. The dynamic test was performed alternating non-destructive compression tests at a displacement rate of 5 mm/min up to 5,000 N and sinusoidal compressive cyclic tests at 6 Hz, using a 3,600-N amplitude for 8,550 cycles. Construct stiffness and maximum sagittal plane rotation about the PIP joint markers were determined during the dynamic test. After the dynamic test reached 136,800 cycles, the monotonic compressive test until failure was performed on each construct: load, displacement and sagittal plane rotation about the PIP joint marker at failure were analysed. The evaluated biomechanical properties showed no statistical difference between the AO-3TLS and MUC-2TS treatment groups in any of the ramps of the dynamic non-destructive test and in the compression loading until failure test. The MUC-2TS treatment produced biomechanical properties equivalent to the AO-3TLS treatment for PIP joint arthrodesis.

Mapping atomic trapping in an optical superlattice onto the libration of a planar rotor in electric fields

We show that two seemingly unrelated problems—the trapping of an atom in an optical superlattice (OSL) and the libration of a planar rigid rotor in combined electric and optical fields (PR) – have isomorphic Hamiltonians. Formed by the interference of optical lattices whose spatial periods differ by a factor of two, OSL gives rise to a periodic potential that acts on atomic translation via the AC Stark effect. The PR system, also known as the generalized planar pendulum, is realized by subjecting a planar rigid rotor to combined orienting and aligning interactions due to the coupling of the rotor’s permanent and induced electric dipole moments to the combined fields. The PR system belongs to the class of conditionally quasi-exactly solvable problems and exhibits intriguing spectral properties that have been established in our previous work Becker et al (2017 Eur. Phys. J. D 71 149). Herein, we make use of both the PR OSL mapping and the quasi-exact solvability of the PR system to treat ultracold atoms in an OSL as a semifinite-gap system. The band structure of this system follows from the eigenenergies and their genuine and avoided crossings obtained previously for the PR system as solutions of the Whittaker-Hill equation. These solutions characterize both the squeezing and the tunneling of atoms trapped in an OSL and pave the way to unraveling their dynamics in analytic form. Furthermore, the PR OSL mapping makes it possible to establish correspondence between concepts developed for the two eigenproblems individually, such as localization on the one hand and orientation/alignment on the other.

Investigation on the site of coronal deformities in Hallux valgus

Hallux valgus (HV) is a common foot deformity that is more prevalent in females, characterised by abnormal adduction of the first metatarsal (MT) and valgus deviation of the phalanx on the transverse plane. Increasing evidence indicates that HV is more than a 2D deformity but a 3D one with rotational malalignment. Pronation deformity is seen during clinical examination for HV patients, but the exact origin of this rotational deformity is still unknown. Some attribute it to first tarsometatarsal (TMT) joint rotation, while others attribute it to intra-metatarsal bony torsion. In addition, the correlation between the rotational and transverse plane deformity is inconclusive. Identifying the origin of the rotational deformity will help surgeons choose the optimal surgical procedure while also enhancing our understanding of the pathophysiology of HV. This study aims to (1) develop an objective method for measuring the first MT torsion and first TMT joint rotation; (2) investigate the exact location of the coronal deformity in HV; (3) investigate the relationship between the severity of deformity on the transverse and coronal planes as well as the correlation between deformity severity and foot function/symptoms in HV. Age-matched females with and without HV were recruited at the Foot and Ankle Clinic of the Department of Orthopaedics and Traumatology. Computed tomography was conducted for all subjects with additional weight-bearing dorsal-plantar X-ray examination for HV subjects. Demographic information of all subjects was recorded, with symptoms and functions related to HV evaluated. The intra-class correlation was used to explore the relationship between deformities on different planes and the deformity severity and functional outcomes, respectively. An Independent t-test was used to compare joint rotation and bone torsion degrees. TMT joint rotation is significantly correlated with foot function. HV patients had more TMT joint rotation but not MT torsion compared to normal controls. No relationship was found between the coronal rotation and the 1,2-intermetatarsal angle (IMA) or Hallux valgus angle (HVA) on the transverse plane. Our results indicate that coronal deformities in HV may originate from TMT joint rotation. In addition, the severity of the TMT joint coronal rotation correlates with worse foot function; thus, multi-plane assessment and examination will be necessary for more precise surgical correction.

Spatial data modeling by means of Gibbs–Markov random fields based on a generalized planar rotator model

We introduce a Gibbs–Markov random field for spatial data on Cartesian grids, which is based on the generalized planar rotator (GPR) model. The GPR model generalizes the recently proposed modified planar rotator (MPR) model by including in the Hamiltonian additional terms that better capture realistic features of spatial data, such as smoothness, non-Gaussianity, and geometric anisotropy. In particular, the GPR model can include an infinite number of higher-order harmonics with exponentially vanishing interaction strength, directional dependence of the bilinear interaction term between nearest neighbors, longer-distance neighbor interactions, and two types of an external bias field. Hence, in contrast with the single-parameter MPR, the GPR model features five additional parameters: the number n of higher-order terms and the decay-rate parameter α, the exchange anisotropy parameter Jnn, the further-neighbor interaction coupling Jfn, and the external field (bias) parameters K (or K′). We present numerical tests on various synthetic and real data which demonstrate the effects of the respective terms on the model’s prediction performance, and we discuss these results in connection with the data properties.

Intrinsic chiral field as vector potential of the magnetic current in the zig-zag lattice of magnetic dipoles

Chiral magnetic insulators manifest novel phases of matter where the sense of rotation of the magnetization is associated with exotic transport phenomena. Effective control of such phases and their dynamical evolution points to the search and study of chiral fields like the Dzyaloshinskii–Moriya interaction. Here we combine experiments, numerics, and theory to study a zig-zag dipolar lattice as a model of an interface between magnetic in-plane layers with a perpendicular magnetization. The zig-zag lattice comprises two parallel sublattices of dipoles with perpendicular easy plane of rotation. The dipolar energy of the system is exactly separable into a sum of symmetric and antisymmetric long-range exchange interactions between dipoles, where the antisymmetric coupling generates a nonlocal Dzyaloshinskii–Moriya field which stabilizes winding textures with the form of chiral solitons. The Dzyaloshinskii–Moriya interaction acts as a vector potential or gauge field of the magnetic current and gives rise to emergent magnetic and electric fields that allow the manifestation of the magnetoelectric effect in the system.

Large magnetic anisotropy and magnetostriction in thin films of CoV2O4

Spinel Cobalt Vanadate CoV$_2$O$_4$ has been grown on (001) SrTiO$_3$ substrates. Using torque magnetometry experiments, we find that the previously observed temperature induced anisotropy change, where the easy axis changes from the out of plane [001] direction to a biaxial anisotropy with planar <100> easy axes, occurs in a gradual second-order structural phase transition. This work characterizes this transition and the magnetic anisotropies in the (001), (100), and (-110) rotation planes, and explores their field dependence up to 30~T. Below 80~K, hysteretic features appear around the hard axes, i.e., the out-of-plane direction in (-110) and (010) rotations and the planar <110> directions in (001) rotations. This is due to a Zeeman Energy that originates from the lag of the magnetization with respect to the applied magnetic field as the sample is rotated. The appearance of the hysteresis, which persist up to very high fields, shows that the anisotropy at low temperature is rather strong. Additionally, field dependent distortions to the symmetry of the torque response in increasing applied fields shows that magnetostriction plays a large role in determining the direction and magnitude of the anisotropy.

Coherent radiation from a chain of charged particles on a circular orbit around a dielectric ball

We investigate the spectral and angular distribution of the electromagnetic radiation from a chain of relativistic charged particles uniformly rotating along equatorial orbit around a dielectric ball. It is shown that, for weak absorption in the ball material and under relatively mild conditions on the distribution of the particles, the radiation intensity at specific rotation frequencies is essentially stronger than the corresponding radiation for a chain circulating in free space or in a homogeneous transparent medium with the same dielectric constant as that for the ball. We determine the values of parameters of the problem for which the charges in the chain emit coherently and the radiation intensity on a given harmonic increases in proportion to the square of the number of emitting charges. We also show that relative shifts in the particles locations up to 10% do not destroy the coherence properties of the radiation. It is demonstrated that the coherence effects may also dominate in the radiation intensity for chains with non-equidistant distributions of particles. The numerical results obtained for different dielectric balls have revealed the emitted radiation to be in the GHz/THz frequency ranges. The high-power radiation from the chain is confined near the rotation plane within the angular region determined by the Cherenkov angle for the velocity of the chain image on the ball surface. In the special case of an equidistant distribution of charged particles along the orbit the results of the present paper for angle integrated frequency distribution of the radiation are in agreement with those previously obtained by our group. We argue that similar coherence effects will be present in the radiation from a chain of bunches circulating around the ball.

Hybrid magnetization dynamics in Cu2OSeO3/NiFe heterostructures

We investigate the coupled magnetization dynamics in heterostructures of a single crystal of the chiral magnet Cu2OSeO3 (CSO) and a polycrystalline ferromagnet NiFe (Py) thin film using broadband ferromagnetic resonance (FMR) at cryogenic temperatures. We observe the excitation of a hybrid mode (HM) below the helimagnetic transition temperature of CSO. This HM is attributed to the spin dynamics at the CSO/Py interface. We study the HM by measuring its resonance frequencies for in plane rotations of the external magnetic field. We find that the HM exhibits dominantly fourfold anisotropy in contrast to the FMR of CSO and Py.

Computational comparison of anterior lumbar interbody fusion and oblique lumbar interbody fusion with various supplementary fixation systems: a finite element analysis

Background and objectiveAnterior lumbar interbody fusion (ALIF) and oblique lumbar interbody fusion (OLIF) have shown a great surgical potential, while it has always been controversial which surgical approach and which type of fixation system should be selected. This study investigated the biomechanical response of ALIF and OLIF with various supplementary fixation systems using the finite element method.Materials and methodsLumbar L4–L5 ALIF and OLIF models stabilized by different supplementary fixation systems (stand-alone cage, integrated stand-alone cage, anterior plate, and bilateral pedicle screw) were developed to assess the segmental range of motion (ROM), endplate stress (EPS), and screw-bone interface stress (SBIS).Experimental resultsALIF showed lower ROM and EPS than OLIF in all motion planes and less SBIS in the most of motion planes compared with OLIF when the anterior plate or pedicle screw was used. ALIF induced higher ROM, while lower EPS and SBIS than OLIF in the majority of motion planes when integrated stand-alone cage was utilized. Using a stand-alone cage in ALIF and OLIF led to cage migration. Integrated stand-alone cage prevented the cage migration, whereas caused significantly larger ROM, EPS, and SBIS than other fixation systems except for the rotation plane. In the most of motion planes, the pedicle screw had the lowest ROM, EPS, and SBIS. The anterior plate induced a slightly larger ROM, EPS, and SBIS than the pedicle screw, while the differences were not significant.ConclusionALIF exhibited a better performance in postoperative segmental stability, endplate stress, and screw-bone interface stress than OLIF when the anterior plate or the pedicle screw was used. The pedicle screw could provide the greatest postoperative segmental stability, less cage subsidence incidence, and lower risk of fixation system loosening in ALIF and OLIF. The anterior plate could also contribute to the stability required and fewer complications, while not as effectively as the pedicle screw. Extreme caution should be regarded when the stand-alone cage is used due to the risk of cage migration. The integrated stand-alone cage may be an alternative method; however, further optimization is needed to reduce complications and improve postoperative segmental stability.

Numerical simulation of deformations of a specimen of a composite helicopter blade as part of a resonant vibration set-up

To determine the fatigue life of the tail rotor blade of a helicopter made of polymer composite materials (CM), a method of fatigue testing of the specimens of the blade with accompanied numerical modeling of the deformed state has been developed. The tests are carried out on a resonant vibration set-up, with simultaneous reproduction of a forcing harmonic transverse force and a constant longitudinal tensile force. The tests are carried out by a vibration loading mode equivalent in fatigue damage, which includes one level of variable load in the thrust plane and in the plane of rotation. The equivalent mode is formed based on the variable loading spectrum of the blade, which is obtained from the results of flight measurements of the loads on the tail rotor, as well as the repeatability of the expected operating conditions of the helicopter. The tests are accompanied by computational and experimental studies, which include finite element calculation of the stress state and modal analysis of the standard blade and the test specimen, as well as the strain measuring of the structure. According to the results of the research, the vibration loading modes are corrected.

STUDY OF THE MOVEMENT OF A MATERIAL PARTICLE ON A FLAT DISK ROTATING AROUND A PERPENDICULAR AXIS INCLINED TO THE HORIZON

The movement of material particles along rotational planes is complex, since it should be considered as the result of the movement of the plane itself and the particle along this plane. The task becomes more difficult if the moving plane is inclined at a certain angle to the horizon. Its solution makes it possible to find out the regularities of the movement of a particle along an inclined plane, which rotates around an axis perpendicular to it. The purpose of the study is to establish the patterns of movement of material particles on a flat disc with and without blades, which rotates around a perpendicular axis inclined to the horizon. If a round disk rotating around an axis perpendicular to it is located horizontally, then the kinematic parameters of the particle's motion on it do not depend on the point of impact of the particle on the disk. If the disk is tilted at a certain angle β to the horizon, it is obvious that the absolute trajectories of the particle's movement and other parameters of the movement will not be the same and will depend on the sector of the disk from which the particle starts its movement. The relative and absolute motion of a particle on an inclined disk with and without rectilinear blades is considered. A system of differential equations of particle motion has been compiled using the accompanying trihedron of the transfer trajectory, which is a circle, and Frenet's formulas. Numerical integration of the system was carried out. The obtained results were visualized. It was established that when particles hit an inclined disk that rotates around its own axis, the absolute trajectories of motion differ significantly from the trajectories of motion along a horizontal disk, and the difference in trajectories increases with an increase in the angle of inclination β. If rectilinear vanes are installed on the disc in the radial direction, the difference between the particle motion parameters will increase insignificantly as the angle β increases. When increasing the angular speed of rotation of the disk at a given angle, the shape of the absolute trajectories of particle motion practically does not change, but they are different depending on the point of impact on the disk. There is a certain area of impact and a certain sector of trajectories, after passing which the particle flies up after leaving the disc. Among this set, it is possible to analytically find the point of impact and the corresponding trajectory, which provide the maximum angle of elevation of the particle (equal to the angle β).

Comparing the Efficacy of Long Spinal Board, Sked Stretcher, and Vacuum Mattress in Cervical Spine Immobilization; a Method-Oriented Experimental Study.

Inadequate spinal motion restriction in patients suffering from spinal injuries could lead to further neurological damage, ultimately worsening their prognosis. This study aimed to investigate the efficacy of long spinal boards (LSB), ske stretcher, and vacuum mattress for cervical spine immobilization during transportation of patients by measuring the angular motion of the cervical spine following lifting, transferring, and tilting. We conducted an experimental study using a box of three randomizations and crossover designs without a washout period effect for the long spinal board, sked stretcher, and vacuum mattress. We concealed the randomization with sequentially numbered, opaque, sealed envelopes (SNOSE). Kinematic data were collected using eight optoelectronic cameras at 200 Hz (BTS Bioengineering, Milan, Italy) in triangular planes (lateral bending, flexion-extension, and axial rotation) while performing all three motions (static lift-hold, transfer, and 90° tilt). 12 cases (7 males and 5 females) with the mean age of 20 ± 3.03 (range: 18-28) years were studied. The three highest angular motions were observed in the axial rotation plane during patient's tilting under immobilization on all devices (Vacuum mattress having the highest value of 99.01±8.93, followed by the LSB at 89.89±34.35 and the sked stretcher at 86.30±7.73 degrees). During patient lifting, a higher angular motion was observed with vacuum mattress immobilization in flexion extension (Coefficient = 4.45; 95%CI: 0.46 - 8.45; p =0.029) and axial rotation (Coefficient = 3.70; 95%CI: 0.58 - 6.81; p =0.020) planes. During patient transfer, a higher angular motion was observed with sked stretcher in the flexion-extension plane (Coefficient = 2.98; 95%CI: 0.11 - 5.84; p = 0.042). During patient tilting to 90 degrees, a higher angular motion was observed with vacuum mattress immobilization in lateral bending (Coefficient = -4.08; 95%CI: -7.68 - -0.48; p = 0.026) for the vacuum mattress. Based on the finding of the present study, patients on the vacuum mattress experience significantly higher angular motion in flexion extension and axial rotation during lifting, as well as lateral bending during 90-degree tilting. In addition, patients on the sked stretcher showed significantly higher angular motion in flexion-extension during the transferring. However, the predictive margins for immobilization across all devices did not demonstrate clinically significant differences among the three immobilization devices.

3D CT scan—A valuable adjunct to radiography

Abstract Background: Deformity correction is based on Full-length True Antero-Posterior and Lateral radiographs. However, a 3D computed tomography (CT) Scan provides a more intricate and detailed understanding of the deformities, so as to plan for the correction with utmost precision. Objective: To prove that 3D computed tomography (CT) Scan provides a more intricate and detailed understanding of the deformities. Materials and Methods: A series of 107 cases, studied from 2017, for a period of 5 years, at our institute was done by means of 3D CT scan. Evaluation was done by measuring angles and lines for further deformity correction, especially in the complex rotational deformities; and osteotomies were performed with Ilizarov fixation. 3D printing was done in selected cases. The patient was made to walk in the immediate postoperative period. The Hexapods were tuned as per the calculations made on the SUV software, for gradual correction. Results: The greatest advantage of using 3D CT is a visualization of the minute details. This may alter the number of osteotomies needed. Eventually, this aids in better correction, when compared with a normal X-ray scannogram. Precision of up to 0.001° was achieved with the DICOM images obtained upon doing the 3D CT, in our study. Conclusion: The information on the deformity in sagittal, frontal, and rotational planes is obtained by doing a 3D CT scan, which allows for further precise planning of the correction. And, as a matter of fact, many Orthopedic Surgeons do not attempt deformity correction as they do not have access to proper full-length X-ray scannograms. Our method gives a precise, cheap, and easily available full-length picture of the deformity, with many more advantages.

IMPACTOS DA CORRIDA NAS ARTICULAÇÕES

ABSTRACT Introduction Running is a competitive sports activity based on speed. Its training methods aim to improve performance and physique but may lead to sports joint injuries. It is important to clarify the relationship between training methods and sports rehabilitation, including the influence of training methods on the quality of life, such as joint health. Objective Explore the relationship between the influence of running training methods on joints and their sports rehabilitation. Methods 44 running athletes were randomly divided into two groups. The joint and rehabilitation indices of the hip, knee, and ankle joints were recorded and statistically analyzed. Results The range of flexion and extension in the sagittal plane, the range of internal and external rotation in the horizontal plane, and the running performance of the knee joints of the athletes who received the variable speed running training were improved, indicating that the running training mode improves the joint performance and sports rehabilitation level of the athletes. Conclusion The appropriate running training method has a beneficial effect on the state of the joints in its athletes, including in the rehabilitation process. This effect is reflected in the physical parameters and the athlete’s competitive ability. Level of evidence II; Therapeutic studies - investigation of treatment outcomes.

Axial Rotation of the Talus in Progressive Collapsing Foot Deformity: A Weightbearing Computed Tomography Analysis

Category: Hindfoot; Midfoot/Forefoot Introduction/ Purpose: Progressive collapsing foot deformity (PCFD) is recognized as a three-dimensional deformity centered around the talus. Although sagittal plane talar sagging or coronal plane valgus talar tilt have been well described, axial plane alignment referencing the talus, calcaneus and second metatarsal to the ankle has not been studied in PCFD patients. The purpose of this study was to examine the axial plane alignment of PCFD versus controls using weightbearing computed tomography (WBCT) and to determine if talar rotation in the axial plane is associated with increased abduction deformity. We hypothesized that the talus would exhibit greater internal rotation in PCFD patients than in control patients, and that this rotation would increase with worsening abduction deformity. Methods: Multiplanar reconstructed (MPR) WBCT scans of 79 patients with PCFD were analyzed. Patients were divided into two groups according to their preoperative talonavicular coverage angle (TNC): moderate abduction (TNC 20-40, n=57) and severe abduction (TNC &gt;40, n=22). 39 WBCT scans from healthy patients without PCFD or hindfoot deformity were included as controls. Using the MPR WBCT images, the axis of talus (TM [transmalleolar]-Tal), calcaneus (TM-Calc), and 2nd metatarsal (TM-2MT) were measured in reference to the transmalleolar axis (Figure 1). Smaller angles represented internal rotation relative to the TM axis. The difference between TM-Tal and TM-Calc was calculated to assess talocalcaneal subluxation. The prevalence of medial tibiotalar joint space narrowing, which was assessed with medial to dorsal tibiotalar joint space ratio (M/D ratio &lt; 0.5 was defined as ‘narrowing’), and medial ankle spurs were also evaluated. Results: TM-Tal was significantly smaller in PCFD patients compared to controls (Figure 2). This difference was accentuated in PCFD with severe abduction, who saw significantly smaller TM-Tal than the moderate abduction group. TM-Calc did not differ between groups, indicating similar axial calcaneal orientation. The TM-2MT revealed a significant difference between groups, reflecting foot abduction in PCFD. Diff Tal-Calc values were greater in PCFD patients, indicating that PCFD patients have more talocalcaneal subluxation in the axial plane. The severe abduction group had a higher Diff Tal-Calc value than the moderate abduction group. PCFD patients had a significantly higher prevalence of medial ankle joint space narrowing and medial spur formation than controls; however, there were no significant differences between the severe and moderate abduction groups. Conclusion: This study found that internal rotation of the talus is a key component of PCFD and is accentuated in more severe abduction deformities. These findings suggest that talar malrotation in the axial plane should be considered an underlying feature of abduction deformity and that this deformity should be corrected at the time of reconstructive surgery, especially in cases of severe abduction deformity. In addition, these findings support the observations of medial joint narrowing and medial spur formation in PCFD patients. Further research is warranted to identify optimal strategies for correction of talar rotation and how to reproducibly assess this intraoperatively.

A Relationship between Anterior Talar Migration in the Sinus Tarsi on Weightbearing Computed Tomography and Failure of the Talocalcaneal Interosseous Ligament in Progressive Collapsing Foot Deformity

Category: Hindfoot; Midfoot/Forefoot Introduction/ Purpose: Progressive collapsing foot deformity (PCFD) is a complex condition thought to be incited by ligament failure. The spring ligament has been extensively studied, and its reconstruction as part of the PCFD correction is becoming more popular. Failure of the interosseous ligament may also be a key contributor, although its role is less described. Since the advent of weightbearing computed tomography (WBCT), the sinus tarsi talocalcaneal relationship has been shown to correlate with the foot deformity as well as the ligament status surrounding the talus. This study aimed to identify when the interosseous and spring ligaments begin to fail in PCFD. Both WBCT and high-quality magnetic resonance imaging (MRI) were used to identify sinus tarsi morphologies involved in failure of the interosseous and spring ligaments. Methods: This study included 82 PCFD patients (mean age: 51.8 years) who underwent preoperative WBCT and MRI. Sinus tarsi morphology on WBCT was categorized into two major categories based on the anterior migration of the talus over the calcaneus on sagittal images: No-migration (Type 1) and Migration (Type 2). Then, a subgroup was established based on the presence of bony impingement: a: no-impingement; b: impingement (Figure 1). Two radiologists evaluated the status of the ligaments around the talus, including the spring and interosseous ligaments, as normal, insufficiency, or tear. On WBCT images, axial plane talocalcaneal subluxation was determined by comparing the talar and calcaneal axes to the transmalleolar axis. The status of the ligaments, degree of talocalcaneal subluxation and calcaneofibular impingement on WBCT, and four plain radiographic parameters of each type were compared. A weighted kappa test was used to determine the interrater reliability of the classification system among six observers. Results: Major categorization revealed distinct differences between the two types, with the migration type (n=38) demonstrating a larger prevalence of torn spring (superomedial: 47.4% and inferomedial: 42.1%) and interosseous (47.4%) ligaments, a greater degree of internal rotation of the talus and talocalcaneal subluxation, and a greater deformity on plain radiographs than the no- migration type (n=44, Table 1). Out of 21 patients with torn interosseous ligament, only 6 (28.6%) exhibited bony calcaneofibular impingement, and these were all Type 2b patients. Except for differences in Meary's angle and Talonavicular coverage angle between Type1a and Type1b, subtypes based on impingement did not exhibit significant differences on MRI, WBCT, or plain radiographic findings. Interrater reliability testing showed substantial agreement between observers, with a kappa of 0.792 (95% confidence interval: 0.713-0.877). Conclusion: While failure of the interosseous ligament is known to occur at the latest stage of PCFD when there is bone on bone calcaneofibular impingement, our study reveals that failure commences during the transition from moderate to severe deformities. This correlates with the anterior migration of the talar process relative to the angle of Gissane in the sagittal plane as well as talar internal rotation in the axial plane. These findings imply that like spring ligament reconstruction, interosseous ligament reconstruction may serve a role in correcting PCFD in somewhat earlier as well as more advanced stages.

On the Foucault pendulum

The Foucault pendulum is a physical apparatus that shows the Earth’s rotation through the variation of the plane of oscillation over time. The main physical agent responsible for this phenomenon is the non-inertial Coriolis force, which couples the coordinates in the equation of motion. Although the Foucault pendulum is more than 170 years old, its theoretical description still lacks completeness, as there is no exact vector solution to the problem or even a decoupled equation of motion. Furthermore, the main prediction about the Foucault pendulum, the dependence of the pendulum’s plane of oscillation rotation on the latitude, needs to be revised as such dependence is more complex than is shown in the literature, once it depends essentially on the initial conditions. Here all these points raised are successfully answered.

CHANCES OF WRONG INFORMATION RECEPTION DURING ELECTROMAGNETIC INFLUENCE UPON OPTICAL CABLE

Long-distance communication lines are optical fiber lines in most cases now. This moment PM QPSK system (polarization-division multiplex with quadrature phase shift keying) appear. Polarization-division multiplex uses a fact that the optical signal can propagate as two orthogonal polarized modes that allows to use the modes independently and makes it possible to double carrier capacity (together with already other used multiplex system). Two orthogonal waves using in the same fiber can cause problems during lightning discharges close by cable line. Under influence of external cross electrical field (or longitudinal magnetic) the polarizations plane of lights wave can turns on angle, which depends on field value, light path length upon field action and fiber sensitivity. During the influence of external electromagnetic field issue a part of one polarization signal can pass to other orthogonal plane and it will perceive wrongly. The Wavelength Division Multiplexing (WDM) systems development with increasing number of carriers brought to transmission in the same transparency window some tens or hundreds waves. They are shifted relative to each other for some parts of nanometers during the lightning stroke. Therefore the polarization plane rotation will be different for each wave (other conditions being equal): the short waves rotated greater than the long waves. On input of optical amplifier there will be packet of waves with different polarizations, and it can produce problems to filters, optical insulators and amplifiers, to Raman amplifiers specially, which are sensitive to polarization. It is known that short and long waves are moving with different velocity as refraction index depends upon wave length. Usually the rotation angle quantity is small if resistivity of earth near cable is not heavy and if equipment does not contain sensitive to PMD (Polarization Modes Dispersion). This phenomenon passes usually unnoticed. But sometimes with strong thunderstorm and lightning stroke at a short distance the polarization plane rotation can exceed 45º or even 90º. Hereby, it is possible the complex electrical and magnetic fields influence during thunderstorm on orthogonal polarization using, that can lead to additional component appearance in orthogonal axes and to signal reception error. Error level for year is estimated.

Attempt to correlate dislocations network and distribution to macroscale plane rotations in &lt;001&gt; cast-mono ingots

This work aims to contribute to the understanding of the mechanisms behind electrically active crystalline defect formation in cast-mono (cm) ingots grown along the <001> axis. Both the spatial distributions of background dislocations in the cellular dislocation array and the driving force for dislocation multiplication in the sub-grains are not perfectly understood. Macroscale length crystal rotations are here characterized by the (θ/2θ) X-ray diffraction (XRD) method at different ingot heights and along two perpendicular sample axes. XRD measurements show the presence of crystal rotations in the large single grain domain. Two orthogonal misorientations components are found to evolve linearly along each sample axis forming plane orientation gradients up to (0.05 ± 0.02) degree/cm extending over 12 cm inside the cast-mono grain. (001) crystal structure deformation are also analysed by rocking curve imaging (RCI) using synchrotron radiation on wafers of a neighboring brick. First, results confirm the presence of the plane orientation gradient measured by XRD and its order of magnitude. Second, RCI results demonstrate that the plane orientation gradient is associated to the cellular dislocation network. Therefore, these results strongly suggest that background dislocations network of a cellular form can create an organized orientation gradient at large distance within the ingot. The involvement of the characterized orientation gradients in the formation and extension of electrically active SGBs in cast-mono ingots is discussed. • Crystal structure deformation measurements of cm-Si ingots. • Evidence of the presence of {001} planes orientation gradients. • Plane orientation gradients almost constant along the sample axes. • Orientation gradients increase with the ingot height. • Orientation gradients associated to the cellular network of dislocations.