Symmetry Of Pattern Research Articles

Particle size and convergent electron diffraction patterns of triangular prismatic gold nanoparticles

Convergent beam diffraction (CBED) patterns of nanoparticles are possible. CBED of triangular prismatic shaped Au nanoparticle with focus on diffraction pattern symmetry and forbidden reflections observed along [111] and [112] zone axes are reported in this work. It is well known that the CBED patterns of nanoparticles of 30 nm or less in size only show bright kinematical discs. The dynamic contrast with Kikuchi and sharp HOLZ lines within the bright discs, as observed in CBED of volumetric materials, is well observed in particles larger of 500 nm in size. In addition, it is shown that the 1/3[422] and 1/2[311] weak forbidden reflections observed in the [111] and [112] electron diffraction patterns of these particles do not modify the symmetry of the CBED patterns, but they disappear as the size of the particle increases. The symmetry of the CBED patterns are always observed in concordance with the space group Fm3m (No. 225) of the Au unit cell. The possible explanations for observing forbidden reflections are the incomplete ABC stacking due to surface termination and the stacking faults in the fcc structure.

Measurements of periodically perturbed dewetting force fields and their consequences on the symmetry of the resulting patterns

We studied the origin of breaking the symmetry for moving circular contact lines of dewetting polymer films suspended on a periodic array of pillars. There, dewetting force fields driving polymer flow were perturbed by elastic micro-pillars arranged in a regular square pattern. Elastic restoring forces of deformed pillars locally balance driving capillary forces and broke the circular symmetry of expanding dewetting holes. The observed envelope of the dewetting holes reflected the symmetry of the underlying pattern, even at sizes much larger than the characteristic period of the pillar array, demonstrating that periodic perturbations in a driving force field can establish a well-defined pattern of lower symmetry. For the presented system, we succeeded in squaring the circle.

Symmetry of diffraction patterns of two-dimensional crystal structures

Conventionally, theoretical considerations in electron microscopy employ the weak phase approximation (WPA), which is only valid for weak scattering atomic elements (C, B, N) but not for transition metal dichalcogenide (TMD) materials. This leads to many exciting phenomena being overlooked. The present theoretical study goes beyond the weak phase approximation and thus the obtained results can be applied for two-dimensional (2D) crystals made of weakly as well of strongly scattering atoms, including the TMD materials. We show that the symmetry of an electron diffraction pattern, characterized by the Friedel’s pairs, is governed by the symmetry of the exit wave distribution. For an infinite periodic crystal, the exit wave is an infinite and periodic 2D distribution which can be assigned an exit wave unit cell. The latter is determined by both the chemical composition of the crystallographic unit cell and the distance between the atomic layers. For 2D crystals of identical atoms, such as graphene, the exit wave unit cell is symmetrical and, thus, a symmetrical diffraction pattern is expected. For TMD materials, the exit wave unit cell is not symmetrical and a non-symmetrical diffraction pattern is expected for both monolayer and bilayer. Conventionally asymmetry in diffraction patterns has been explained by presence of dynamical (multiple) scattering effects. Our study shows that the asymmetry of a diffraction pattern can be explained solely by the asymmetry of the exit wave unit cell. The exit wave unit cell can be asymmetrical even in kinematic (single) scattering model. Therefore, conclusions about dynamical (multiple) scattering effects in 2D materials cannot be made based solely on asymmetry of a diffraction pattern. We also show that for hexagonally arranged atoms the second-order diffraction peaks show perfectly symmetrical intensities independently on the symmetry of the exit wave unit cell distribution.

A general principle for spontaneous genetic symmetry breaking and pattern formation within cell populations

Elements within biological systems interact and frequently self-organize from initially disordered states into highly structured patterns. The local self-activation and lateral inhibition mechanism, derived from the coupling between two reacting and diffusing chemicals, has been believed to be one of the main causes for biological pattern formation.Graded positional information can be produced by the limited diffusion of one single signaling molecule through cell populations with no pre-patterns being required. We demonstrate, using multiscale computations, that spontaneous symmetry breaking can be driven within expanding and non-expanding cell populations, without local self-enhancement of activators and long-range inhibition. Instead, cells can self-organize into structured gene patterns via a combination of timing gene expression in cells and the graded positional information which has been coupled to the gene expression.We show that the genetic symmetry breaking in expanding E. coli populations occurs at a critical colony size, which is independent of the cell doubling time but scales with the diffusion speed of the signaling molecule. We also show the quasi-3D structure of gene patterns, and observe that the wave length of periodic genetic stripes is in proportion to the genetic oscillation cycle time and in inverse proportion to cell doubling time. Our results provide insights into relevant biological development processes.

Three-loop corrections to the muon and heavy quark decay rates

Recently, $O(\alpha^3)$ corrections to the muon decay rate and $O(\alpha_s^3)$ to heavy quark decays have been determined by Fael, Sch\"onwald, and Steinhauser. This is the first such perturbative improvement of these important quantities in more than two decades. We reveal and explain a symmetry pattern in these new corrections, and confirm the most technically difficult parts of their evaluation.

Bioengineering Self-Organizing Signaling Centers to Control Embryoid Body Pattern Elaboration.

Multicellular systems possess an intrinsic capacity to autonomously generate nonrandom state distributions or morphologies in a process termed self-organization. Facets of self-organization, such as pattern formation, pattern elaboration, and symmetry breaking, are frequently observed in developing embryos. Artificial stem cell-derived structures including embryoid bodies (EBs), gastruloids, and organoids also demonstrate self-organization, but with a limited capacity compared to their in vivo developmental counterparts. There is a pressing need for better tools to allow user-defined control over self-organization in these stem cell-derived structures. Here, we employ synthetic biology to establish an efficient platform for the generation of self-organizing coaggregates, in which HEK-293 cells overexpressing P-cadherin (Cdh3) spontaneously form cell clusters attached mostly to one or two locations on the exterior of EBs. These Cdh3-expressing HEK cells, when further engineered to produce functional mouse WNT3A, evoke polarized and gradual Wnt/β-catenin pathway activation in EBs during coaggregation cultures. The localized WNT3A provision induces nascent mesoderm specification within regions of the EB close to the Cdh3-Wnt3a-expressing HEK source, resulting in pattern elaboration and symmetry breaking within EBs. This synthetic biology-based approach puts us closer toward engineering synthetic organizers to improve the realism in stem cell-derived structures.

Interaction of surface pattern and contour shape in the tilt after effects evoked by symmetry

Integration of multiple properties of an object is a fundamental function of the visual cortex in object recognition. For instance, surface patterns and contour shapes are thought to be crucial characteristics that jointly contribute to recognition. However, the mechanisms of integration and corresponding cortical representations have not been fully clarified. We investigated the integration of surfaces and shapes by examining the tilt after effects (TAEs) evoked by the symmetry of patterns and contours. As symmetry in both pattern and contour evokes TAEs, we can directly measure the interaction between the two. The measured TAEs exhibited mutual transfer between the symmetry of the pattern (SP) and that of the contour shape (SS), i.e., adaptation by SP (SS) evoked TAEs when tested by SS (SP), suggesting the existence of an integrated representation. Next, we examined the interaction between SP and SS when both were simultaneously presented in adaptation. Congruent adaptors wherein their symmetry axes aligned evoked compressive interaction, whereas incongruent adaptors wherein the axes of SP and SS tilted to the opposite directions evoked subtractive interaction. These results suggest the existence of a cortical representation that integrates the properties of the surface and shape with suppressive interactions, which can provide crucial insights into the formation of object representation as well as the integration of visual information in the cortex.

Effect of auditory neurosensorial stimulation in gait pattern after acute stroke

Introduction Auditory sensory stimulation is a therapy that influences cognitive, motor, emotional and behavioural functions and also patients’ quality of life. This approach is referred to be effective in optimising motor responses in neurological conditions [1]. When a stimulation occurs in the frontal lobe region of the brain it is possible to see through functional magnetic resonance imaging (fMRI) [2] that it trigger a response in motor regulation [3]. The purpose of this study is to investigate the effect of an auditory neurosensory stimulus (music) on gait pattern in post stroke individuals. Materials and methods A cross sectional study was performed. Five patients (66.6 ± 14.1 years) with ischaemic stroke diagnostic participated in the study. Patients were assessed during the stance phase of gait cycle through 5-meter walking test, before and after the auditory neurosensory stimulus (music). STOMP was used to evaluate musical preference; cell phone camera to record gait pattern, speed and tibial angle in a lateral view and these data were analysed by Kinovea. All subjects signed an informed consent. This study followed all the principles of Helsinki Declaration. Results Patients showed gait speed improvement (7.01 ± 0.94°) with auditory neurosensory stimulus (preference music). Data analysis in a lateral view of stroke limb by Kinovea showed better results in tibial angle in initial contact with stimulation (74.0 ± 8.0°) versus before stimulus (70.4 ± 11.0°). Also during mid-stance, results in toes/ground angle with stimulation (37.6 ± 16.1°) were higher than the results without stimulation (29.8 ± 14.9°) Discussion and conclusions Stroke gait pattern observed in these patients changed with auditory neurosensory stimulation (preference music) which suggests increase of the responsiveness of the paretic ankle flexion. Some previous studies have shown that auditory neurosensory stimulation in stroke patient is efficient in the symmetry of the gait pattern and is a therapeutic advantage for motor recovery of the gait pattern [5]. This result enhances the importance of auditory stimulation (preference music) in a rehabilitation gait program for stroke patients. Nevertheless, only 5 patients were included, which is a limitation, so further studies are needed to extend these results.

Improvement of output efficiency of p-face up photonic-crystal surface-emitting lasers.

We optimized the p-side emission device configuration of photonic-crystal surface-emitting laser (PCSEL) to facilitate the easier chip process and wafer level testing as well as the feasibility of lasing at shorter wavelength. Typically, in order to obtain uniformly distributed current for larger emission area of PCSELs, laser output is designed through the n-side window due to the low hole mobility and thin p-side cladding layer. However, the substrate as well as the epi-layers have to be isolated before the test of each single die on the wafer, which compromised the advantage of wafer-level test of surface emitters. On the other hand, for lasers with emission photon energy higher than the bandgap energy of GaAs substrate, the power will be entirely attenuated. In this study, the optimized p-side emission by applying the transparent conduction layer on top of the p side contact layer to enhance the current distribution and breaking the symmetry of conventional circle pattern in a unit cell to boost the output efficiency is investigated. Through this approach, a high efficiency p-side up PCSEL platform with lower fabrication cost is developed, which is also applicable for short wavelength PCSELs.

Exchangeability and Non-Conjugacy of Braid Representatives

We obtain some fairly general conditions on the linking numbers and geometric properties of a link, under which it has infinitely many conjugacy classes of [Formula: see text]-braid representatives if and only if it has one admitting an exchange move. We investigate a symmetry pattern of indices of conjugate iterated exchanged braids. We then develop a test based on the Burau matrix showing examples of knots admitting no minimal exchangeable braids, admitting non-minimal non-exchangeable braids, and admitting both minimal exchangeable and minimal non-exchangeable braids. This in particular proves that conjugacy, exchange moves and destabilization do not suffice to simplify braid representatives of a general link.

Crystal preferred orientations, deformation mechanisms and seismic properties of high pressure metamorphic rocks from the Central Qiangtang metamorphic belt, Tibetan Plateau

Crystal preferred orientation (CPO) of high pressure metamorphic rocks is an important contributor to seismic anisotropy in the subduction interface and continental crust. However, the mechanisms of deformation and CPO development, as well as the effect of CPO patterns on the seismic anisotropies remain not fully solved. By analyzing the microstructures, CPOs and seismic properties of the high pressure rocks from the Central Qiangtang metamorphic belt in the northern Tibetan Plateau, we found that the mineral CPOs (e.g., omphacite and amphibole) are developed dominantly by non-dislocation based deformation mechanisms in the eclogites and amphibolites, while quartz and phengite CPOs are primarily formed by dislocation creep in the garnet-quartz-mica schists. The variations of CPO patterns are mainly controlled by the strain geometry and/or strain magnitude, which also regulate the first-order symmetry patterns of seismic anisotropies among samples. Besides, amphibole enrichment can remarkably increase the anisotropies and decrease the velocities of seismic waves in the eclogite‒amphibolite suite. A combination of seismic parameters such as Vp, Vs, Vp/Vs ratio, intensities and symmetries of P-wave anisotropy (AVp) and shear wave splitting (AVs), and P- or S-wave reflection coefficients can be used to discriminate eclogites, amphibolites and their garnet-quartz-mica schists country rocks at depth when high resolution seismic methods can be applied. Notably, amphibolite and garnet-quartz-mica schists showing moderate-to-large AVp and max. AVs can make considerable contributions to field-observed crustal anisotropy near the strike-slip continental shear zones or mantle wedge anisotropy in the subduction zones.

The Implication of Financial Derivable from Abroad on West African Monetary Zone’s ECO Currency

This study aims to determine the extent to which the West African Monetary Zone (WAMZ) can fulfill the Expost conditions for achieving convergence. This study, therefore, evaluates the pattern of shock symmetry and convergence in connection to WAMZ’s Pillar III policy strategy. Time series data sourced from the World Bank for the period covering 1970 to 2017 were utilized for this study. Two basic econometric tools such as Impulse Response Function (IRF) and the ADF convergence test were employed to determine whether WAMZ can achieve selected Macroeconomic Convergence Criteria (MCC) in the long-run. From the study, we found that WAMZ is not a full potential candidate for ECO Economic and Monetary Union (EMU) due to the inability of the available results to show overall shock asymmetry in the entire models studied. Also, the study found that WAMZ could attain convergence in its inflation targets, but could not attain convergence in its GDP targets. Thus the results imply that in the long-run, WAMZ does not practically possess the attribute to achieve its MCC. Hence, it is imperative that for the adoption of the ECO currency, WAMZ should design and implement a short-run adjustment method to manage country-wise shocks and implement structural buffers to guard the WAMZ economies against structural shocks. Hence, we recommend that ECO currency be a reserve currency managed by the West African Currency Board (WACB) while the EMU member maintains its domestic currency. WAMZ is basically a quasi EMU.

Modeling the formation of non-diffraction parabolic beams

In this article we perform a numerical study of the generalization of parabolic non-diffraction beams of two orders formed from an analytically given distribution of the ring spatial spectrum. The formation and propagation of non-diffraction parabolic beams are simulated using the Fourier transform and the Fresnel transform. The influence of the radius and width of the circular spatial spectrum on the non-diffraction properties of the beams, as well as the nature of the symmetry of the transverse beam patterns depending on the orders of the beam are researched.

Continuous Symmetry Measure vs Voronoi Entropy of Droplet Clusters

Symmetry and orderliness of two-dimensional (2D) levitating microdroplet clusters are quantified with the Voronoi entropy (VE) and the continuous symmetry measure (CSM). The time evolution of both VE and CSM is investigated. To compare the correlation between the two measures of orderliness, the Pearson correlation coefficient (PCC) was calculated. The maximum correlation between the VE and CSM was found for clusters containing the number of droplets enabling the formation of hexagons, i.e., droplet clusters possessing 6-fold symmetry. In other cases, the maxima and minima of the VE and CSM are not always well correlated; moreover, in certain cases, maxima of the CSM may correspond to the minima of the VE. Symmetry and orderliness of 2D patterns could not be quantified with a single mathematical measure.

Tenfold topology of crystals: Unified classification of crystalline topological insulators and superconductors

The celebrated tenfold way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of nonspatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a complete classification of weakly interacting electrons' noncrystalline topological phases for all symmetry classes. Over recent years, a plethora of topological phenomena with diverse surface states has been discovered in crystalline materials. In this paper, we obtain an exhaustive classification of topologically distinct ground states as well as topological phases with anomalous surface states of crystalline topological insulators and superconductors for key space-groups, layer-groups, and rod-groups. This is done in a unified manner for the full tenfold way of Altland-Zirnbauer nonspatial symmetry classes. We establish a comprehensive paradigm that harnesses the modern mathematical framework of equivariant spectra; it allows us to obtain results applicable to generic topological classification problems. In particular, this paradigm provides efficient computational tools that enable an inherently unified treatment of the full tenfold way.Received 23 September 2020Revised 10 December 2020Accepted 11 December 2020DOI:https://doi.org/10.1103/PhysRevResearch.3.013052Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEdge statesSurface statesSymmetry protected topological statesTopological insulatorsTopological materialsTopological superconductorsPhysical SystemsCrystalline systemsTechniquesAbstract algebraDiscrete symmetries in condensed matterGroup theoryTopologyCondensed Matter, Materials & Applied PhysicsInterdisciplinary PhysicsGeneral Physics

Multiple domain structure and symmetry types in narrow temperature and magnetic field ranges in layered Cr2Ge2Te6 crystal measured by magnetic force microscope

Intrinsic magnetism has recently been confirmed to survive in bilayer Cr2Ge2Te6. In this work, multiple domain structure and symmetry types and their transformations are firstly discovered in bulk layered Cr2Ge2Te6 crystal using a homebuilt magnetic force microscope (MFM). These transitions occur within a surprisingly narrow temperature range of 2 K and magnetic field range of 0.07 T, which colorful phenomenon hasn't been discovered in other materials but Cr2Ge2Te6. The MFM images show a series of basic domain patterns. Some of them also hasn't been found before, such as self-fitting disks and fine ladder structure within Y-connected walls. The symmetry of these magnetic domain patterns is discussed. The results not only are important in developing new magnetic domain theories but also may show some potential applications in storage depending on the future investigations.

The Fractal Geometry of the Nymphalid Groundplan: Self-Similar Configuration of Color Pattern Symmetry Systems in Butterfly Wings.

Simple SummaryHighly diverse color patterns of butterfly wings can be explained as modifications of an archetypical color pattern of nymphalid butterflies called the nymphalid groundplan. The nymphalid groundplan contains three major symmetry systems and a discal symmetry system, but their relationships have been elusive. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species color-pattern comparisons of the hindwings in nymphalid butterflies. It was shown that all symmetry systems can be expressed as various structures, suggesting the equivalence (homology) of these systems in developmental potential. In some cases, the discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, indicating a unified supersymmetry system covering the entire wing. These results suggest that butterfly color patterns are hierarchically constructed; one system is nested within another system, which is a self-similar relationship that achieves the fractal geometry. This self-similarity is likely mediated by the serial induction of organizers during development, and a possible mechanism is proposed for symmetry breaking of the system morphology, which contributes to the diversity of butterfly wing color patterns.The nymphalid groundplan is an archetypical color pattern of nymphalid butterflies involving three major symmetry systems and a discal symmetry system, which share the basic morphogenesis unit. Here, the morphological and spatial relationships among these symmetry systems were studied based on cross-species comparisons of nymphalid hindwings. Based on findings in Neope and Symbrenthia, all three major symmetry systems can be expressed as bands, spots, or eyespot-like structures, suggesting equivalence (homology) of these systems in developmental potential. The discal symmetry system can also be expressed as various structures. The discal symmetry system is circularly surrounded by the central symmetry system, which may then be surrounded by the border and basal symmetry systems, based mainly on findings in Agrias, indicating a unified supersymmetry system covering the entire wing. The border symmetry system can occupy the central part of the wing when the central symmetry system is compromised, as seen in Callicore. These results suggest that butterfly color patterns are hierarchically constructed in a self-similar fashion, as the fractal geometry of the nymphalid groundplan. This self-similarity is likely mediated by the serial induction of organizers, and symmetry breaking of the system morphology may be generated by the collision of opposing signals during development.

Vortex-induced vibration of a flexible splitter plate attached to a square cylinder in laminar flow

Vortex-induced vibration (VIV) of a flexible splitter plate attached to a square cylinder in laminar flow is investigated using fluid–structure interaction (FSI) simulation. The Reynolds number based on the edge length of the square cylinder (L) is fixed at Re= 100, while the structural parameters of the plate are set as ρp (density ratio) = 84.75, H/L (non-dimensional thickness) = 0.06, E (non-dimensional elastic modulus) = 5×103∼5×106 and l/L (non-dimensional length) = 0.5, 1 and 2, respectively. It is found that the bending rigidity and plate length have significant influences on the dynamic response of the plate, fluid loads on the cylinder–plate body and the vortex pattern in the flow field. At l/L= 0.5, the natural frequency of the plate does not intersect with the vortex shedding frequency in the parameter range considered; VIV of the flexible plate is negligible, and the fluid loads and flow pattern are similar to those in the case of a rigid plate. At l/L= 1, lock-in occurs when the first natural frequency approaches the vortex shedding frequency. In the lock-in regime, the vibrating frequency of the plate shifts to be commensurate with the first natural frequency, and the first-mode bending motion of large amplitude is observed, resulting in higher vortex shedding frequency and narrower vortex street in the wake. At l/L= 2, besides the first-natural-frequency lock-in, the off-centerline phenomenon and second-natural-frequency lock-in are also observed at low elastic modulus. In the off-centerline regime, the mean deflection of the splitter plate shifts to one side and a second-mode-like bending motion appears, which breaks the symmetry of the flow pattern and generates a non-zero mean lift. In the second-natural-frequency lock-in region, the plate vibration and fluid loads are also amplified. The model proposed could be taken as a benchmark for VIV of the flexible plate in laminar flow, and the results obtained are insightful to the design of FSI-based piezoelectric energy harvesters using flexible plates.

Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments.

The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated tip-splitting of evolving fingers. When anisotropy is present in the interfacial dynamics, the growth morphology changes to dendritic growth characterized by regular structures. We introduce anisotropy by engraving a six-fold symmetric lattice of channels on a Hele-Shaw cell. We show that the morphology transition in miscible fluids depends not only on the previously reported degree of anisotropy set by the lattice topography, but also on the viscosity ratio between the two fluids, ηin/ηout. Remarkably, ηin/ηout and the degree of anisotropy also govern the global features of the dendritic patterns, inducing a systematic change from six-fold towards twelve-fold symmetric dendrites. Varying either control parameter provides a new method to tune the symmetry of complex patterns, which may also have relevance for analogous phenomena of gradient-driven interfacial dynamics, such as directional solidification or electrodeposition.

Eikonal Amplitudes and Nonglobal Logarithms from the BMS Equation

The Banfi-Marchesini-Smye (BMS) equation accounts for non-global logarithms to all orders in perturbation theory in the large-Nc approximation. We show that the squared amplitudes for the emission of soft energy-ordered gluons are correctly embedded in this equation, and explicitly verify that they coincide with those derived in our previous work in the large-Nc limit up to sixth order in the strong coupling. We perform analytical calculations for the non-global logarithms up to fourth order for the specific hemisphere mass distribution in e+ e- collisions, thus confirming our previous semi-numerical results. We show that the solution to the BMS equation may be cast into a product of an infinite number of exponentials each of which resums a class of Feynman diagrams that manifest a symmetry pattern, and explicitly carry out the computation of the first of these exponentials.