Symmetry Of Pattern Research Articles

Tailoring vapor film beneath a Leidenfrost drop

For a drop on a very hot solid surface, a vapor film will form beneath the drop, which has been discovered by Leidenfrost in 1756. The vapor escaping from the Leidenfrost film causes uncontrollable flows, and actuates the drop to move around. Recently, although numerous strategies have been used to regulate the Leidenfrost vapor, the understanding of surface chemistry for modulating the phase-change vapor dynamics remains incomplete. Here, we report how to rectify vapor by “cutting” the Leidenfrost film using chemically heterogeneous surfaces. We demonstrate that the segmented film cut by a Z-shaped pattern can spin a drop, since the superhydrophilic region directly contacts the drop and vaporizes the water, while a vapor film is formed on the superhydrophobic surrounding to jet vapor and reduce heat transfer. Furthermore, we reveal the general principle between the pattern symmetry design and the drop dynamics. This finding provides new insights into the Leidenfrost dynamics modulation, and opens a promising avenue for vapor-driven miniature devices.

Rise and fall of Mott insulating gaps in YNiO3 paramagnets as a reflection of symmetry breaking and remaking

The ${\mathrm{YNiO}}_{3}$ nickelate is a paradigm $d$-electron oxide that manifests the intriguing temperature-mediated sequence of three phases transitions from (i) magnetically ordered insulator to (ii) paramagnetic (PM) insulator and then to (iii) PM metal. Such phenomena raised the question of the nature of the association of magnetism and structural symmetry breaking with the appearance in (i) and (ii) and disappearance in (iii) of insulating band gaps. It is demonstrated here that first-principles mean-field--like density-functional theory (DFT), driven by molecular dynamics temperature evolution, can describe not only the origin of the magnetically long-range ordered insulating phase (i), but also the creation of an insulating paramagnet (ii) that lacks spin- long-range order, and of a metallic paramagnet (iii) as temperature rises. This approach provides the patterns of structural and magnetic symmetry breaking at different temperatures, in parallel with band gaps obtained when the evolving geometries are used as input to DFT electronic band-structure calculations. This disentangles the complex interplay among spin, charge, and orbital degrees of freedom. Analysis shows that the success in describing the rise and fall of the insulating band gaps along the phase transition sequence is enabled by allowing sufficient flexibility in describing diverse local structural and magnetic motifs as input to DFT. This entails the use of sufficiently large supercells that allow expressing structural disproportionation of octahedra, as well as a description of PM phases as a distribution of local magnetic moments (rather than using a single averaged moment). It appears that the historic dismissal of mean-field--like DFT as being unable to describe such Mott-like transitions was premature, as it was based on consideration of averaged crystallographic unit cells, a description that washes out local symmetry-breaking motifs. The magnetically ordered insulating ${\mathrm{YNiO}}_{3}$ phase (i) and the PM insulating phase (ii) result in DFT from allowing symmetry breaking, evident already by considering the athermal internal energy. In contrast, the PM metallic phase (iii) is formed thermally by smearing out thus weakening symmetry breaking. Analysis of snapshots of the different forms of structural vs magnetic symmetry breaking shows that only the loss of the polymorphous distribution of magnetic moments existing in (ii) causes the fall of the band gap, resulting in the metallic state in (iii). The interesting conclusion is that such a description of the rise [in phases (i) and (ii)] and fall [in phase (iii)] of the insulating gap does not rely on the traditional Mott-like strong correlation understanding, but on breaking and remaking of magnetic and structural symmetries reflected in energy lowering.

Deep learning of interfacial curvature: A symmetry-preserving approach for the volume of fluid method

Estimation of interface curvature in surface-tension dominated flows is a remaining challenge in Volume of Fluid (VOF) methods. Data-driven methods are recently emerging as a promising alternative in this domain. They outperform conventional methods on coarser grids but diverge with grid refinement. Furthermore, unlike conventional methods, data-driven methods are sensitive to coordinate system and sign conventions, thus often fail to capture basic symmetry patterns in interfaces. The present work proposes a new data-driven strategy which conserves the symmetries in a cost-effective way and delivers consistent results over a wide range of grids. The method is based on artificial neural networks with deep multilayer perceptron (MLP) architecture which read volume fraction fields on regular grids. The anti-symmetries are preserved with no additional cost by employing a neural network model with input normalization, odd-symmetric activation functions and bias-free neurons. The symmetries are further conserved by height-function inspired rotations and averaging over several different orientations. The new symmetry-preserving MLP model is implemented into a flow solver (OpenFOAM) and tested against conventional schemes in the literature. It shows superior performance compared to its standard counterpart and has similar accuracy and convergence properties with the state-of-the-art conventional method despite using smaller stencil.

Categorizing Drunkard's Path type quilting patterns

The Drunkard's Path quilt block is a basic square quilt block consisting of a quarter circle in one corner on a square of some contrasting fabric. In this paper, we use symmetry to organize a library of quilting patterns using the Drunkard's Path quilt block. The organizational strategy begins by arranging the basic quilt blocks into squares that we call arrangements. We categorize these arrangements by symmetry type. We also act upon the arrangements by rotations, reflections, and colour exchanges, using the results to produce squares that we call tiles. These tiles are subsequently considered as tiles for quilt tops, thereby giving fodder for analysis of the underlying wallpaper symmetry groups and sometimes even two-colour symmetry patterns. Over 90 of the tiles are shown representing just a small number of the possible quilt patterns.

Numerical and experimental investigation of the in-phase and out-phase plasma actuation effects on the wake flow for Re = 1000

The aim is to characterize the role of symmetry pattern on the flow control induced by dielectric barrier discharge plasma actuators. Two DBD actuators are employed for in-phase excitation with duty cycle 50% leading to symmetric wake pattern and out-phase excitation for two pulsing frequencies St=0.2 and St=1 at Re=1000 which forms quasi-symmetric and asymmetric flow structures respectively. The modes deduced from POD and DMD methods represent the competition between symmetric (S) and asymmetric mode (K) in all cases. The harmonic in-phase plasma actuation with 50% duty cycle is the most effective flow control method with lowest power consumption. The harmonic out-phase excitation is not much effective; however adjustment of the actuator position can form the symmetric pattern with minimum power consumption. The superharmonic out-phase plasma actuation reduces the wake region however is not effective in lift reduction significantly and consumes high amount of energy. This indicates that phase difference and plasma location influence on the size and symmetry of the vortical structure. Then, based on the symmetry properties of the designed wake pattern created by frequency and phase difference of the plasma actuator, the effective active flow control can be performed. The numerical results are validated with experiments.

Numerical investigation on intensified mixing performance with modified dual impeller

Process intensification is important for achieving efficient fluid mixing. In this study, the process intensification mechanism of mixing was investigated based on the evolution of sub-steady flow pattern. The results showed that the modified dual impeller (Mod-DI) could eliminate the isolation zone and symmetry of the flow pattern, which always appears in the traditional dual impeller (Trad-DI) system. Furthermore, the mixing time (tm) and dynamic equilibrium time (tde) of the Mod-DI system were significantly shorter than those of the Trad-DI system, which could be attributed to the enhancement of fluid flow fluctuations caused by the loss of stability of sub-steady flow field. In the presence of baffles, tm and tde could be further reduced. The shortening of time was at the expense of increasing power consumption. Overall, the intensification mechanism of the Mod-DI is mainly since the formation of sub-steady flow field, which enhances the instability of the fluid flow.

Cone-beam computed tomography study of mandibular morphology and tooth compensation in asymmetrical patients

This study evaluated mandibular morphology and transverse dental compensation between symmetrical and asymmetrical subjects, allocated according to sagittal skeletal patterns. In addition, the hypothesis that mandibular morphology and dental compensations differed between symmetrical/asymmetrical groups and also among the different types of sagittal skeletal patterns was tested. Cone-beam computed tomography images of 96 patients were included in this study and were divided into 2 groups according to the degree of menton deviation: a symmetrical group with deviation up to 2.0 mm (n= 48; mean age, 15 ± 6 years), and an asymmetrical group with deviation from 3.5 mm (n= 48; mean age, 16 ± 8 years). The 2 groups were divided in accordance with the ANB angle: Class I, II, and III. Skeletal and dental measurements were performed. Intergroup and intragroup analyses were carried out, using a 2-way analysis of variance to assess the interaction of factors: symmetry and sagittal skeletal pattern; and the Student t test for differences between deviated (Dv) and nondeviated (NDv) sides. Symmetrical/asymmetrical groups and Class I, II, and III groups were similar in relation to demographic aspects (P= 0.412 and P= 0.357 for sex and age, respectively). Asymmetrical patients had higher values for body length and mandibular ramus and condyle height on the NDv side (P= 0.011, P= 0.024, and P= 0.001, respectively). When comparing the different skeletal patterns, patients with a Class III relationship demonstrated higher values for mandibular ramus height. Intergroup analysis showed no differences in dental parameters. In the comparison between the sides, the asymmetrical group showed a significant difference in canine inclination (P= 0.008), mandibular ramus height (P= 0.004), condyle height (P= 0.010) and gonion to midsagittal plane distance (P= 0.018). Asymmetrical subjects showed higher values for canine inclination and mandibular body, ramus and condylar height on the NDv side. The hypothesis was partially confirmed that mandibular morphology and dental compensations are different between symmetrical/asymmetrical groups and among different sagittal skeletal patterns.

Dimensional Reduction of Cobordism and K-theory

It has been proposed that cobordism and K-theory groups, which can be mathematically related in certain cases, are physically associated to generalised higher-form symmetries. As a consequence, they should be broken or gauged in any consistent theory of quantum gravity, in accordance with swampland conjectures. We provide further support to this idea by showing that cobordism and K-theory groups of a general manifold X reproduce the pattern of symmetries expected from the dimensional reduction of the theory on X, as well as their breaking and gauging. To this end, we employ the Atiyah-Hirzebruch spectral sequence to compute such groups for common choices of X in string compactifications.

Spin canting and lattice symmetry in La2CuO4

While the dominant magnetic interaction in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ is superexchange between nearest-neighbor Cu moments, the pinning of the spin direction depends on weak anisotropic effects associated with spin-orbit coupling. The symmetry of the octahedral tilt pattern allows an out-of-plane canting of the Cu spins, which is compensated by an opposite canting in nearest-neighbor layers. A strong magnetic field applied perpendicular to the planes can alter the spin canting pattern to induce a weak ferromagnetic phase. In light of recent evidence that the lattice symmetry is lower than originally assumed, we take another look at the nature of the field-induced spin-rotation transition. Comparing low-temperature neutron diffraction intensities for several magnetic Bragg peaks measured in fields of 0 and 14 T, we find that a better fit is provided by a model in which spins rotate within both neighboring planes but by different amounts, resulting in a noncollinear configuration. This model allows a more consistent relationship between lattice symmetry and spin orientation at all Cu sites.

Mysterious Triality and Rational Homotopy Theory

Mysterious Duality has been discovered by Iqbal, Neitzke, and Vafa (Adv Theor Math Phys 5:769–808, 2002) as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series $$E_k$$ . It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics that gives rise to the same $$E_k$$ symmetry pattern. We present a sequence of topological spaces, starting with the four-sphere $$S^4$$ , and then forming its iterated cyclic loop spaces $$\mathscr {L}_c^k S^4$$ , within which we discover the $$E_k$$ symmetry pattern via rational homotopy theory. For this sequence of spaces, the correspondence between its $$E_k$$ symmetry pattern and that of toroidal compactifications of M-theory is no longer a mystery, as each space $$\mathscr {L}_c^k S^4$$ is naturally related to the compactification of M-theory on the k-torus via identification of the equations of motion of $$(11-k)$$ -dimensional supergravity as the defining equations of the Sullivan minimal model of $$\mathscr {L}_c^k S^4$$ . This gives an explicit duality between algebraic topology and physics. Thereby, we extend Iqbal-Neitzke-Vafa’s Mysterious Duality between algebraic geometry and physics into a triality, also involving algebraic topology. Via this triality, duality between physics and mathematics is demystified, and the mystery is transferred to the mathematical realm as duality between algebraic geometry and algebraic topology. Now the question is: Is there an explicit relation between the del Pezzo surfaces $$\mathbb {B}_k$$ and iterated cyclic loop spaces of $$S^4$$ which would explain the common $$E_k$$ symmetry pattern?

Design research with the use of visual and symmetry analysis in indigenous woven textiles.

Since ca the 1990s, there have been developments in the weaving process for making tin chok fabrics in the Long district, Phrae province, northern Thailand, with the aim of reducing the production time and increasing the production capacity with respect to poverty alleviation and cultural revitalization. In this article, the symmetry patterns in tin chok fabrics in a collection of 17 vintage (traditional) skirts held in the Komol Antique Textile Museum, in the Long district, are examined to determine how to distinguish tin chok fabrics woven by the integrated method from those woven by the traditional method. The research includes visual and symmetry analysis, literature review, fieldwork, and the creation of a pattern booklet. This research reveals that the hem, which is one of the four parts (supplementary part one, the main part, supplementary part two and the hem) of the detachable tin chok, is key to distinguishing the fabrics made by the two methods. The four parts of tin chok made by the integrated method will always have a common vertical axis of symmetry, whereas the vertical axes of symmetry of the hem of a fabric made by the traditional method may not be aligned with the motifs in the other three parts. The frieze groups of the individual parts of the 17 vintage (traditional) skirts are decoded and possible corresponding patterns for weaving by the integrated method are generated.

Membrane protein structural symmetry and assembly patterns.

The evolution of membrane proteins depends on the physicochemical constraints imposed by the lipid bilayer, and by extension, their folding mechanisms. Repetition of well-folded motifs following these rules is frequently observed within protein sequences and has allowed efficient creation of larger macromolecules capable of more complex functions. Such repeated elements within individual protein chains can result in structural symmetry, as does association of subunits into higher-order assemblies. Nevertheless, much remains to be learned about interplay between folding, assembly, symmetry, and evolution. Structural data obtained by crystallography or electron cryo-microscopy provides an evolutionary snapshot with which to examine these questions in greater detail. At the time of writing, almost 8000 membrane protein structures have been collated into our structure and symmetry database, EncoMPASS. We present a systematic analysis of these data and discuss the implications for folding, function, and evolution.

Patterns of gauge symmetry in the background field method

The correlation functions of Yang–Mills theories formulated in the background field method satisfy linear Slavnov–Taylor identities, which are naive generalizations of simple tree level relations, with no deformations originating from the ghost-sector of the theory. In recent years, a stronger version of these identities has been found to hold at the level of the background gluon self-energy, whose transversality is enforced separately for each special block of diagrams contributing to the gluon Schwinger–Dyson equation. In the present work we demonstrate by means of explicit calculations that the same distinct realization of the Slavnov–Taylor identity persists in the case of the background three-gluon vertex. The analysis is carried out at the level of the exact Schwinger–Dyson equation for this vertex, with no truncations or simplifying assumptions. The demonstration entails the contraction of individual vertex diagrams by the relevant momentum, which activates Slavnov–Taylor identities of vertices and multi-particle kernels nested inside these graphs; the final result emerges by virtue of a multitude of extensive cancellations, without the need of performing explicit integrations. In addition, we point out that background Ward identities amount to replacing derivatives of propagators by zero-momentum background-gluon insertions, in exact analogy to standard properties of Abelian gauge theories. Finally, certain potential applications of these results are briefly discussed.

Symmetries of Scan Patterns of Laser Scanners with Rotational Risley Prisms

Laser scanners with rotational Risley prisms produce scan patterns that can be classified as a type of rhodonea curve, because of their symmetry. The present study builds upon the novel, graphical method that we have developed to simulate and analyze such patterns using a commercially available mechanical design program, CATIA V5R20 (Dassault Systems, Paris, France). This graphical method has both the advantage of simplicity (regarding analytical methods) and of generating exact scan patterns (in contrast to approximate methods). The aim of this work is to utilize this method to study symmetry properties of scan patterns produced by a pair of rotational Risley prisms. A multi-parameter analysis is performed, considering the characteristic parameters of the approached scanner: refractive indexes and angles of the prisms, as well as their rotational velocities. Furthermore, Marshall’s parameters are considered: ratios of the rotational velocities and of the prism angles. Because the symmetries are identical for scan patterns generated by all the four possible configurations of a pair of prisms (and only their dimensions are different), the shape of these patterns is studied only for one of these configurations. Therefore, without losing generality, the symmetries of the patterns produced by such scanners are determined, as well as some of their characteristic dimensions. Rules-of-thumb were obtained to be able to generate patterns that are appropriate for a specific application. Moreover, we demonstrated that the existing symmetries simplify the process of obtaining the scan patterns by identifying repetitive parts (defined as structures of symmetry) of a pattern.

Macroscopic Spiral Patterns of Cholesteric Cellulose Nanocrystals Induced by Chiral Doping and Vortex Flowing.

Negatively surface-charged sulfate cellulose nanocrystals (CNCs) are always slowly self-assembled into left-handed cholesteric mesophases. In this work, macroscopic spiral patterns induced by counterclockwise vortex flowing or chiral doping were investigated. Results show that iridescent patterns of the arithmetic spiral, rose spiral, or latitude ripples were generated under the vortex rotation, indicating a severe microphase separation of CNCs. Moreover, the spiral pattern and rotational symmetry were highly correlated to the twisting and flowability of CNCs as well as chiral dopants. Alternatively, the cholesteric pitch and maximum reflective wavelength (λmax) of CNCs were strongly increased by sinistral dopants other than the dextral ones, indicating an enhanced torsion of left-handed CNC mesophases by the dextral dopants. In addition, macroscopic spiral patterns distinctly existed in dextrally doped CNCs owing to a synergistic chiral enhancement. Therefore, the mechanochiral or chemical chiral transition from microscopic twisting to macroscopic spiral provides a potential inspiration for chiral self-organization of biological macromolecules.

Numerical Study of New Small-twist Tape Insert on Heat Transfer and Pressure Drop for Laminar Flow Inside Circular Pipe

In this study, thermal performance of the laminar flow inside pipe with proposed small twisted tape insert is studied numerically by using computational fluid dynamic software. The proposed insert consists of three- and five-small twisted tapes insert that are arranged in radially symmetry pattern. These group of inserts are then arranged along the pipe with gap spacing to generate continuous flow disturbance. The inserts are proposed to be modelled as zero-thickness layer to reduce the computational cost. The proposed zero-thickness model is validated by compare the with the results of 1mm-model and reference experimental results. The zero-thickness model is then implemented on the proposed insert design for numerical study. Compare with plain twisted tape insert, Nusselt number of the new design is increases by the range of approximately 0.07-42.7% for three-small tapes design, and 4.7-48.0% for five-small tapes design. Performance evaluation criteria (PEC) of present design ranging from 2.2-3.7 for three-small tapes design, and 2.65-3.65 for five-small tapes design. The proposed insert is found to have more advantage over plain twisted tape at lower Reynolds number, reflected by more significant increase in PEC at lower Reynolds number. From the result of friction factor and PEC, the optimum gap distance of insert group is found to be .

Molecular mechanisms of vascular tissue patterning in Arabidopsis thaliana L. roots.

A vascular system in plants is a product of aromorphosis that enabled them to colonize land because it delivers water, mineral and organic compounds to plant organs and provides effective communications between organs and mechanical support. Vascular system development is a common object of fundamental research in plant development biology. In the model plant Arabidopsis thaliana, early stages of vascular tissue formation in the root are a bright example of the self-organization of a bisymmetric (having two planes of symmetry) pattern of hormone distribution, which determines vascular cell fates. In the root, vascular tissue development comprises four stages: (1) specification of progenitor cells for the provascular meristem in early embryonic stages, (2) the growth and patterning of the embryo provascular meristem, (3) postembryonic maintenance of the cell identity in the vascular tissue initials within the root apical meristem, and (4) differentiation of their descendants. Although the anatomical details of A. thaliana root vasculature development have long been known and described in detail, our knowledge of the underlying molecular and genetic mechanisms remains limited. In recent years, several important advances have been made, shedding light on the regulation of the earliest events in provascular cells specification. In this review, we summarize the latest data on the molecular and genetic mechanisms of vascular tissue patterning in A. thaliana root. The first part of the review describes the root vasculature ontogeny, and the second reconstructs the sequence of regulatory events that underlie this histogenesis and determine the development of the progenitors of the vascular initials in the embryo and organization of vascular initials in the seedling root.

MODeLING.Vis: A Graphical User Interface Toolbox Developed for Machine Learning and Pattern Recognition of Biomolecular Data

Many scientific publications that affect machine learning have set the basis for pattern recognition and symmetry. In this paper, we revisit the concept of “Mind-life continuity” published by the authors, testing the symmetry between cognitive and electrophoretic strata. We opted for machine learning to analyze and understand the total protein profile of neurotypical subjects acquired by capillary electrophoresis. Capillary electrophoresis permits a cost-wise solution but lacks modern proteomic techniques’ discriminative and quantification power. To compensate for this problem, we developed tools for better data visualization and exploration in this work. These tools permitted us to examine better the total protein profile of 92 young adults, from 19 to 25 years old, healthy university students at the University of Lisbon, with no serious, uncontrolled, or chronic diseases affecting the nervous system. As a result, we created a graphical user interface toolbox named MODeLING.Vis, which showed specific expected protein profiles present in saliva in our neurotypical sample. The developed toolbox permitted data exploration and hypothesis testing of the biomolecular data. In conclusion, this analysis offered the data mining of the acquired neuroproteomics data in the molecular weight range from 9.1 to 30 kDa. This molecular weight range, obtained by pattern recognition of our dataset, is characteristic of the small neuroimmune molecules and neuropeptides. Consequently, MODeLING.Vis offers a machine-learning solution for probing into the neurocognitive response.

Locality and Antilocality: The Logic of Conflicting Requirements

This article discusses what happens when locality requirements—which favor short dependencies—come into conflict with antilocality requirements—which rule out dependencies that are too short. It is argued that in such circumstances, certain locality requirements may be minimally violated so that the antilocality requirement is satisfied. A theory along these lines is shown to derive a pervasive pattern of noniterative symmetry in A-movement—found in Haya and Luganda (Bantu), Tongan (Austronesian), and Japanese—in which the highest two arguments in a domain may undergo A-movement, but A-movement of lower arguments is systematically banned. The article concludes with some discussion of how interactions of this sort might be modeled in the grammar.

Splitting-merging transitions in tensor-vectors systems in exact large- N limits

Matrix models have phase transitions in which distributions of variables change topologically like the Gross-Witten-Wadia transition. In a recent study, similar splitting-merging behavior of distributions of dynamical variables was observed in a tensor-vectors system by numerical simulations. In this paper, we study the system exactly in some large-$N$ limits, in which the distributions are discrete sets of configurations rather than continuous. We find cascades of first-order phase transitions for fixed tensors, and first- and second-order phase transitions for random tensors, being characterized by breaking patterns of replica symmetries. The system is of interest across three different subjects at least: The splitting dynamics plays essential roles in emergence of classical spacetimes in a tensor model of quantum gravity; The splitting dynamics automatically detects the rank of a tensor in the tensor rank decomposition in data analysis; The system provides a variant of the spherical $p$-spin model for spin glasses with a new non-trivial parameter. We discuss some implications of the results from these perspectives. The results are compared with some numerical simulations to check the large-$N$ convergence and the assumptions made in the analysis.