Symmetry Of Pattern Research Articles

Fractionalized time reversal, parity, and charge conjugation symmetry in a topological superconductor: A possible origin of three generations of neutrinos and mass mixing

The existence of three generations of neutrinos(charged leptons/quarks) and their mass mixing are deep mysteries of our universe. Recently, Majorana's spirit returns in modern condensed matter physics -- in the context of topological Majorana zero modes in certain classes of topological superconductors(TSCs). In this paper, we attempt to investigate the topological nature of the neutrino by assuming that a relativistic Majorana fermion can be divided into four topological Majorana zero modes at cutoff energy scale, e.g. planck scale. We begin with an exactly solvable $1$D lattice model which realizes a $T^2=-1$ time reversal symmetry protected TSC, and show that a pair of topological Majorana zero modes can realize a $T^4=-1$ time reversal symmetry.Moreover, we find that a pair of topological Majorana zero modes can also realize a $P^4=-1$ parity symmetry and even a nontrivial $\overline C^4=-1$ charge conjugation symmetry. Next, we argue that the origin of three generations of neutrinos(charged leptons and quarks) can be naturally explained as three distinguishable ways of forming a pair of complex fermions(with opposite spin polarizations) out of four topological Majorana zero modes, characterized by the $T^4=-1$, $(TP)^4=-1$ and $(T \overline C)^4=-1$ fractionalized symmetries that each complex fermion carries at cutoff energy scale. Finally, we use a semiclassical approach to compute the neutrino mass mixing matrix at leading order(LO), e.g., in the absence of $CP$ violation correction. We obtain $\theta_{12}=31.7^\circ, \theta_{23}=45^\circ$ and $\theta_{13}=0^\circ$(the golden ratio pattern), which is consistent with an $A_5$ flavor symmetry pattern. We further predict an exact mass ratio of the three mass eigenstates of neutrinos with $m_1/m_3=m_2/m_3=3/\sqrt{5}$ and an effective mass of neutrinoless double beta decay $m_{0\nu\beta\beta}=m_1/\sqrt{5}$.

Acoustic Waves for Active Reduction of Contact Time in Droplet Impact

Minimizing droplet impact contact time is critical for applications such as self-cleaning, antierosion or anti-icing. Recent studies have used the texturing of surfaces to split droplets during impact or inducing asymmetric spreading, but these require specifically designed substrates that cannot be easily reconfigured. A key challenge is to realize an effective reduction in contact time during droplet impingement on a smooth surface without texturing but with active and programmable control. Our experimental results show that surface acoustic waves (SAWs), generated at a location distant from a point of droplet impact, can be used to minimize contact time by as much as 35% without requiring a textured surface. Additionally, the ability to switch on and off the SAWs means that a reduction in droplet impact contact time on a surface can be controlled in a programmable manner. Moreover, our results show that, by applying acoustic waves, the impact regime of the droplet on the solid surface can be changed from deposition or partial rebound to complete rebound. To study the dynamics of droplet impact, we develop a numerical model for multiphase flow and simulate different droplet impingement scenarios. Numerical results reveal that the acoustic waves can be used to modify and control the internal velocity fields inside the droplet. By breaking the symmetry of the internal recirculation patterns inside the droplet, the kinetic energy recovered from interfacial energy during the retraction process is increased, and the droplet can be fully separated from the surface with a much shorter contact time. Our work opens up opportunities to use SAW devices to minimize the contact time, change the droplet impact regime, and program or control the droplet's rebounding on smooth or planar and curved surfaces, as well as rough or textured surfaces.

Bogoliubov Fermi surfaces in spin- 12 systems: Model Hamiltonians and experimental consequences

Bogoliubov Fermi surfaces (BFSs) are topologically protected regions of zero energy excitations in a superconductor whose dimension equals that of the underlying normal state Fermi surface. Examples of Hamiltonians exhibiting this "ultranodal" phase are known to preserve charge-conjugation ($C$) and parity ($P$) but break time-reversal ($T$). In this work, we provide examples of model Hamiltonians that do not necessarily preserve this symmetry pattern but have well-defined sign-changing Pfaffians yielding BFSs. While their topological character has not been recognized previously, some of the models we present have been extensively studied in prior literature. We further examine thermodynamic and electronic properties arising from the ultranodal state. In particular, we study the effect of a weak Zeeman field close to the topological transition and propose distinguishing features of BFSs using residual specific heat and tunneling conductance. Our calculation of the superfluid density in a toy multi-band model indicates a window of interband pairing strength where BFSs are stable with a positive superfluid density. We also present additional signatures of BFSs in spin-polarized spectral weight and total magnetization measurements.

Root Canal Morphology of the Permanent Mandibular Incisors by Cone Beam Computed Tomography: A Systematic Review

Knowledge of dental anatomy through the assessment of the anatomic variations of each tooth’s root canal system is essential to undertake endodontic therapy. The aim of this systematic review was to analyze the different studies on the internal morphology of permanent mandibular incisors where Cone-Beam Computed Tomography (CBCT) X-ray imaging is used. Pubmed, CENTRAL, Wiley Library and Web of Science electronic databases were searched for scientific studies included until March 2020. The terms used in the search were: “permanent mandibular incisors”, “root canal morphology” and “cone-beam computed tomography”. The search was limited to studies whose aim was the analysis of the morphology of the root canal system evaluating the parameters of methodology, population, sample, number and configuration. A total of 19 studies met the inclusion criteria. There was a noticeable lack of unanimity in the setting adjustments of each of the CBCT devices used. The presence of two root canals varied from 0.4% to 45%. The most frequent configurations were Vertucci’s Types I, III, II, V, IV, VII and VI. Type VIII configuration was non-existent. CBCT revealed the existence of anatomical symmetry patterns, and there was no unanimity of criteria regarding the presence of a second root canal. Results concerning the presence of a second root canal in the mandibular incisors differ widely, with a possible influence of the geographic area where the study was conducted. The prevalence of a second canal is higher in mandibular lateral incisors than in mandibular central incisors. There was no direct relationship between voxel size (0.125–0.3 mm) and increased prevalence of a second canal.

Broken Symmetries, Random Morphogenesis, and Biometric Distance

This paper discusses the role of symmetry-breaking in biometric recognition. Using publicly available databases, we investigate three kinds of broken symmetries in iris patterns: binocular, monocular, and monozygotic. We report a small but statistically significant difference in similarities between the ipsilateral and the contralateral eyes of twins, and also between genetically identical and nonidentical eyes. Another new finding is a doubling in the variance of Hamming distance scores under a simple monocular mirror transformation, which is consistent with an assessment of entropy.

Plane and Frieze Symmetry Group Determination for Educational Purposes.

Three-dimensional symmetry plays a crucial role in crystallography education. The educational process can be facilitated by introducing the analysis of friezes and plane patterns such as parquets before presenting more sophisticated crystal structures. Analysis of the symmetry of parquets can serve as an opportunity to follow the full routine of finding symmetry group symbols through incorporation of a two-step procedure involving the determination of Bravais lattice type. The aim of this paper is to provide a simple description of the analysis of Bravais lattices and pattern symmetry that can be used by students as well as crystallography educators. The procedure is also summarized in the form of comprehensive tree charts. This form is easy to use and popular with students. It may also aid in the retention of certain facts concerning crystallographic methodology. Examples of patterns in frieze and parquet forms were taken from the interiors of Kórnik Castle (Poland), which exhibit Moorish-style ornamentation including dichroic patterns and constitute an important locus of cultural heritage capable of strengthening students’ motivation.

A Flexible Inference Machine for Global Alignment of Wall Openings

Openings such as windows and doors are essential components of architectural wall surfaces. It is still a challenge to reconstruct them robustly from unstructured 3D point clouds because of occlusions, noises and non-uniformly distributed points. Current research primarily focuses on meliorating the robustness of detection and pays little attention to the geometric correctness. To improve the reconstruction quality, assumptions on the opening layout are usually applied as rules to support the reconstruction algorithm. The commonly used assumptions, such as the strict grid and symmetry pattern, however, are not suitable in many cases. In this paper, we propose a novel approach, named an inference machine, to identify and use flexible rules in wall opening modelling. Our method first detects and models openings through a data-driven method and then refines the opening boundaries by global and flexible rules. The key is to identify the global flexible rules from the detected openings, composed by various combinations of alignments. As our method is oblivious of the type of architectural layout, it can be applied to both interior wall surfaces and exterior building facades. We demonstrate the flexibility of our approach in both outdoor and indoor scenes with a variety of opening layouts. The qualitative and quantitative evaluation results indicate the potential of the approach to be a general method in opening detection and modelling. However, this data-driven method suffers from the existence of occlusions and non-planar wall surfaces.

Atomic resolution energy-loss magnetic chiral dichroism measurements enabled by patterned apertures

We give an experimental demonstration of two types of recently proposed ventilator apertures which can be used to acquire electron magnetic circular dichroic (EMCD) signals in zone axis orientation with high spatial resolution. To simplify the experimental procedures, we propose a third type of aperture and experimentally demonstrate the use of this modified ventilator aperture for the case of multiple symmetries in the diffraction patterns. To show the feasibility of the atomic resolution EMCD, EMCD signals are acquired for a range of beam convergence angles. High quality EMCD signals with convergence angles corresponding to atomic resolution electron probes are obtained.

Coevolutionary patterns caused by prey selection

Many theoretical models have been formulated to better understand the coevolutionary patterns that emerge from antagonistic interactions. These models usually assume that the attacks by the exploiters are random, so the effect of victim selection by exploiters on coevolutionary patterns remains unexplored. Here we analytically studied the payoff for predators and prey under coevolution assuming that every individual predator can attack only a small number of prey any given time, considering two scenarios: (i) predation occurs at random; (ii) predators select prey according to phenotype matching. We also develop an individual based model to verify the robustness of our analytical prediction. We show that both scenarios result in well known similar coevolutionary patterns if population sizes are sufficiently high: symmetrical coevolutionary branching and symmetrical coevolutionary cycling (Red Queen dynamics). However, for small population sizes, prey selection can cause unexpected coevolutionary patterns. One is the breaking of symmetry of the coevolutionary pattern, where the phenotypes evolve towards one of two evolutionarily stable patterns. As population size increases, the phenotypes oscillate between these two values in a novel form of Red Queen dynamics, the episodic reversal between the two stable patterns. Thus, prey selection causes prey phenotypes to evolve towards more extreme values, which reduces the fitness of both predators and prey, increasing the likelihood of extinction.

Phononic and photonic properties of shape-engineered silicon nanoscale pillar arrays

We report the results of Brillouin–Mandelstam spectroscopy and Mueller matrix spectroscopic ellipsometry of the nanoscale ‘pillar with the hat’ periodic silicon structures, revealing intriguing phononic and photonic—phoxonic—properties. It has been theoretically shown that periodic structures with properly tuned dimensions can act simultaneously as phononic and photonic crystals, strongly affecting the light-matter interactions. Acoustic phonon states can be tuned by external boundaries, either as a result of phonon confinement effects in individual nanostructures, or as a result of artificially induced external periodicity, as in the phononic crystals. The shape of the nanoscale pillar array was engineered to ensure the interplay of both effects. The Brillouin–Mandelstam spectroscopy data indicated strong flattening of the acoustic phonon dispersion in the frequency range from 2 GHz to 20 GHz and the phonon wave vector extending to the higher-order Brillouin zones. The specifics of the phonon dispersion dependence on the pillar arrays’ orientation suggest the presence of both periodic modulation and spatial localization effects for the acoustic phonons. The ellipsometry data reveal a distinct scatter pattern of four-fold symmetry due to nanoscale periodicity of the pillar arrays. Our results confirm the dual functionality of the nanostructured shape-engineered structure and indicate a possible new direction for fine-tuning the light–matter interaction in the next generation of photonic, optoelectronic, and phononic devices.

Spider lures exploit insect preferences for floral colour and symmetry

Sensory systems can capture only a fraction of available information, which creates opportunities for deceptive signalling. The sensory traps and sensory bias models have proven valuable for explaining how visual systems and environments shape the design of sexual signals, but their application to deceptive signals is largely limited to the context of pollination. Here we use the ‘jewelled’ orb-web spider Gasteracantha fornicata to experimentally test two longstanding hypotheses for the function of deceptive visual lures. Namely, that they: (1) exploit generalised preferences for conspicuous colouration (sensory bias), or (2) co-opt the otherwise-adaptive foraging response of prey toward flowers (sensory traps). In a field-based study we manipulated the conspicuous dorsal signals of female spiders along two axes—colour pattern and symmetry—to generate a gradient of floral resemblance and monitored the per-individual consequences for prey interception. As predicted by the sensory traps model, the most attractive phenotypes were those with flower-like radial symmetry and solid colour patterns, and their attractiveness equaled that of natural spiders. Taken with recent work demonstrating a close resemblance between G. fornicata and sympatric floral ‘models’, and pollinating insects as primary prey items, our results suggest that the deceptive colour-based lures of spiders function as inter-kingdom sensory traps via floral mimicry, and support the broader extension of sensory-based models to deceptive signalling contexts.

E/H-평면의 방사 패턴 대칭성이 개선된 이중슬롯 비발디 안테나의 설계

E/H-평면의 방사 패턴 대칭성이 개선된 이중슬롯 비발디 안테나의 설계

Patterns of Symmetry Expression in Angiosperms: Developmental and Evolutionary Lability

Variation in flower symmetry is a remarkable aspect of flowering plant diversity. Multiple evolutionary transitions from an ancestral form of radial symmetry to bilateral symmetry and reversals from bilateral to radial symmetry have occurred during angiosperm evolution. The high incident of symmetry transitions poses the question concerning the homology of underlying developmental processes. I conducted a comprehensive study of developmental expression of symmetry across angiosperms covering 72 families and 39 orders. A wide range of timing for the expression of symmetry was found from organ initiation, to enlargement, to late differentiation of organs. In many studied genera, the symmetry pattern was transient during development. Mapping the floral symmetry patterns on the phylogenetic tree indicated the scattered distribution of patterns across angiosperms. The expression of symmetry was also versatile within families. The developmental constraints exerted by the inflorescence, bracts, neighbor flowers or neighbor organs within a flower could provide a possible explanation for the observed variation of symmetry expression.

Classification and Treatment of Glabella-Radix Deficiency in Primary Augmentation Rhinoplasty.

BackgroundA systematic approach to treating glabella-radix deficiency is lacking, and the management of brow-tip aesthetic lines remains technically challenging.ObjectivesThe authors describe implantation of a customized Gore-Tex prosthesis combined with primary augmentation rhinoplasty to address the glabella-radix deficiency.MethodsFifty Asian patients with glabella-radix deficiency who received implantation and primary augmentation rhinoplasty were retrospectively evaluated in an 8-year period. Patients were assigned to categories based on brow-tip contour lines and symmetry patterns, and implant dimensions were ascertained from the contour type and from simulated postoperative results.ResultsEleven men and 39 women were included in the study; the mean patient age was 27.22 years, and mean follow-up was 22.8 months. Seven of the patients were assigned to the type I/Ia category, 24 to type II/IIa, and 19 to type III/IIIa. Forty-five patients were considered to have satisfactory surgical results, with curved, symmetric, and normally spaced brow-tip lines on front view and a smooth frontonasal transition on profile view. Complications occurred in 5 patients and included infection (1 patient), inadequate augmentation (2), and palpable margin folding of the Gore-Tex device (2).ConclusionsDeformities of brow-tip contour lines coincide with glabella-radix deficiencies in terms of severity. Knowledge of the patterns of brow-tip lines, combined with postoperative image simulation, can help the surgeon design an appropriate glabella-radix prosthesis. When placed in conjunction with other augmentation rhinoplasty procedures, the glabella-radix implant yields sufficient, predictable nasal projection and a harmonious facial aesthetic.Level of Evidence: 4

Kinematic Gait Analysis After Primary Total Hip Replacement: A Systematic Review: Gait After Total Hip Replacement: A Systematic Review.

Total hip replacement (THR) is a surgical procedure indicated for patients affected by severe hip osteoarthritis. Although this technique has proved to be effective in relieving pain and restoring function, gait limitations may persist following this procedure. The objective of this systematic review was to evaluate gait kinematics after THR and compare the results with those of the pre-operative state and with healthy control individuals. PubMed/MEDLINE, Embase, Web of Science, CENTRAL and Scopus databases were searched until December 2019. Methodological quality and internal validity score of each study were assessed using the PEDro and the Newcastle-Ottawa scales. In all, ten studies met our inclusion criteria. Following THR, statistically significant improvements were seen in dynamic hip and knee range of motion of both the affected and the contralateral limb, single-limb support time symmetry, step length, stride length, walking speed and gait pattern. However, deficits were observed in all the previous parameters, as well as in hip adduction angle in comparison with healthy subjects. In conclusion, gait patterns improve after THR in comparison with the pre-operative state, although there are deficits relative to healthy individuals.

The Role of Feed Perturbation in the Design of Microstrip-fed Cylindrical Dielectric Resonator Antennas

In this paper, the role of feed perturbation in the design of a cylindrical dielectric resonator antenna (DRA) for maximum modal purity is investigated both numerically and experimentally. Modal purity is indicated by the purity of the far-field radiation which can be quantified by the radiation pattern symmetry and the cross-polarized radiation. To demonstrate the feed perturbation effect, a microstrip line proximity coupled to a cylindrical dielectric resonator exciting its lowest order broadside radiating mode is used. It is identified that the feed perturbation introduces higher order fields of TM01δ and HEM21δ types of the DRA to disturb the modal purity of the desired mode. Results suggest that optimum DRA design should consider the feed perturbation effects also in addition to the common performance parameters such as impedance matching, bandwidth and gain.

Simple Method for Aesthetic Symmetrical Post Burn Reconstruction of the Temporal and Sideburn Subunits

Post burn scaring and reconstruction of the scalp iscommon condition, which is challenging to plastic surgeons.Which might lead to social deprivation and severe psychologicaltrauma, and patients always try to hide these areas withscarf, hats, wigs, etc…. Although these attempts are commonand useful for the vertex and occipital region, temporo-parietal,temporal, and sideburn are difficult to be camouflaged.Different ways of reconstruction were used including:Serial scar excision, follicular hair transplant, tissue expansion,regional or remote tissue transfer with local or free flaps havebeen described.Although tissue expansion is the best and most popularmethod for scalp reconstruction, the results might be unexpectedand displeasing. Searching on English speaking literature,in all previous studies, success was attributed to theexpansion process in relation to the size, location of thealopecia and donor area ignoring the importance of achievingthe exact or near normal pattern of hair line and symmetry ofthe temporal, temporo-partial and side burn regions. This isdue to the absence of a simple method to guide surgeons whileplanning and reconstructing this critical zone. In this study,I am presenting a simple method utilizing the tissue expansionfor reconstruction of sideburn, temporal, and temporo-partialalopecia to achieve satisfactory, symmetry and near normalreconstruction.This is a retrospective analysis of prospectively maintainedrecords of 29 patients, was conducted from February 2016 toMay 2018 in the Department of Plastic Surgery, Ain ShamsUniversity, Cairo, Egypt. Twenty nine patients with scalp burn alopecia of age 6 to 35 years were included in this study.All patients were examined and assessment was done byobjective and subjective analysis.The results shows that by using this simple method toreconstruct temporal and lateral side burn area, it is provenfrom the objective and subjective evaluation the aestheticoutcome was satisfactory, symmetrical and standardized.

Does kinematic gait quality improve with functional gait recovery? A longitudinal pilot study on early post-stroke individuals

Typical clinical gait outcomes mostly focus on function; only sparse information exists on gait quality, i.e. symmetry or more natural gait patterns. It remains unclear whether functional gait recovery improves with gait quality, or whether these are two independent processes. The objective of this observational pilot study is to examine whether the gait quality improves with gait function (i.e. speed) over the course of early recovery. Full lower body gait kinematics were measured longitudinally in a clinical environment using wearable inertial measurement units. We recorded six individuals with subacute stroke (<1 month) for a total of 56 physical therapy sessions over the initial recovery stage of 12 weeks. We examined relations between gait symmetry in spatiotemporal, limb and joint kinematic parameters compared to gait function. We observed that overall gait symmetry improved with walking speed, but limb and joint kinematic parameters remained asymmetric at the maximum level of recovery (both p < 0.01). We also found that limb kinematic parameters (R2 = 41.9%) of the impaired side was preferentially associated with functional gait recovery over joint kinematics (R2 = 33.1%). These data suggest that our pilot cohort did not achieve “true” gait recovery despite achieving typical measures of recovery in gait speed and spatiotemporal symmetry. These initial results illustrate the multifaceted nature of recovery and justify further research on monitoring gait quality with a larger clinical study, providing insight for more effective training regimens.

Role of Video Laryngostroboscopy in Benign Disease of Larynx.

Benign disease of larynx frequently present with voice disorder. Observing the larynx with high resolution stroboscope and its mucosal wave pattern with greater precision aids in the better understanding of normal/abnormal anatomy and function, which forms the basis of designing treatment strategies.Videolaryngostroboscopy now a days is considered routinely used method of vocal fold examination and evaluation of patients with voice disorders. This valuable imaging tool can also be used to assess the outcomes of therapy of laryngeal diseases or functional result of phonosurgical procedures. Present study, videostroboscopic assessment of 81 cases of different benign vocal cord pathologies was done. Stroboscopic parameters like glottic closure, amplitude, vocal fold edge, symmetry, periodicity and mucosal wave pattern were studied and statistically significant relationship with different vocal pathologies were obtained.

Flow instability of cylinder embedded within two-parallel moving walls of cuboidal cavity at different radii sizes

A computational analysis has been performed to study the flow instability of two-parallel wall motions in a Cuboidal enclosure incorporated by a cylinder under different radii sizes. A numerical methodology based on the Finite Volume Method (FVM) and a full Multigrid acceleration is utilized in this paper. Left and right parallel walls of the cavity are maintained driven and all the other walls completing the domain are motionless. Different radii sizes ([Formula: see text], 0.1, 0.125, 0.15 and 0.175) are employed encompassing descriptive Reynolds numbers that range three orders of magnitude 100, 400 and 800 for the steady state. The obtained results show positions [Formula: see text] and [Formula: see text] of the inner cylinder promote cell distortion. Also, when the radius equates to [Formula: see text], it may lead to the birth of tertiary cells at [Formula: see text] which are more developed for [Formula: see text]. Thereafter, analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a Hopf bifurcation. A nonuniform variation with the radius size of the inner cylinder is observed. Otherwise said, elongating the radius of the cylinder leads to decrease in the critical Reynolds number. Hence, the acceleration of the unsteadiness is realized. On the other hand, by further increasing Reynolds number more than the critical value from 1200 to 2100, we note that the kinetic energy is monotonously increasing with Reynolds number and a stronger motion in the velocity near the rear wall of the enclosure is observed. Furthermore, the symmetry of flow patterns observed in the steady state has been lost. Therefore, a systematic description of various effects illuminating the optimum geometrical parameters to achieve effective flow behavior in those systems has been successfully established through this paper.